U.S. patent application number 17/387810 was filed with the patent office on 2022-01-20 for method and apparatus to attain and maintain target arterial blood gas concentrations using ramp sequences.
The applicant listed for this patent is THORNHILL SCIENTIFIC INC.. Invention is credited to Anne BATTISTI-CHARBONNEY, James DUFFIN, Joseph FISHER, Shoji ITO, Cathie KESSLER, Michael KLEIN, Daniel Michael MANDELL, David MIKULIS, Marat SLESSAREV, Olivia SOBCZYK.
Application Number | 20220016368 17/387810 |
Document ID | / |
Family ID | 1000005872091 |
Filed Date | 2022-01-20 |
United States Patent
Application |
20220016368 |
Kind Code |
A1 |
KLEIN; Michael ; et
al. |
January 20, 2022 |
METHOD AND APPARATUS TO ATTAIN AND MAINTAIN TARGET ARTERIAL BLOOD
GAS CONCENTRATIONS USING RAMP SEQUENCES
Abstract
An apparatus and method for controlling the end tidal partial
pressure of a gas X in a subject's lung, and to the use of such an
apparatus and method for research, diagnostic and therapeutic
purposes, wherein the method consists of: -obtaining input of a
series of logistically attainable PetX values for a series of
respective breaths: -determining an amount of gas X required to be
inspired by the subject in an inspired gas to target the PetX for
each of said respective breaths; and controlling a gas delivery
device to deliver the amount of gas in a volume of gas delivered to
the subject in each of said respective breaths to target the
respective PetX for that breath.
Inventors: |
KLEIN; Michael; (Toronto,
CA) ; FISHER; Joseph; (Thornhill, CA) ;
DUFFIN; James; (Toronto, CA) ; SLESSAREV; Marat;
(Toronto, CA) ; KESSLER; Cathie; (Toronto, CA)
; ITO; Shoji; (Nagoya, JP) ; SOBCZYK; Olivia;
(Etobicoke, CA) ; BATTISTI-CHARBONNEY; Anne;
(Trois-Rivieres, CA) ; MANDELL; Daniel Michael;
(Toronto, CA) ; MIKULIS; David; (Oakville,
CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
THORNHILL SCIENTIFIC INC. |
North York |
|
CA |
|
|
Family ID: |
1000005872091 |
Appl. No.: |
17/387810 |
Filed: |
July 28, 2021 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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15904235 |
Feb 23, 2018 |
11077266 |
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17387810 |
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14398034 |
Oct 30, 2014 |
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PCT/CA2013/000427 |
Apr 30, 2013 |
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15904235 |
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61640570 |
Apr 30, 2012 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
A61M 2202/0208 20130101;
A61M 16/12 20130101; A61M 16/0045 20130101; A61M 16/0066 20130101;
A61M 16/1005 20140204; A61M 2016/1025 20130101; A61M 16/122
20140204; A61M 2202/0225 20130101; A61M 2230/202 20130101; A61B
5/091 20130101; A61M 2230/205 20130101; A61M 2230/04 20130101; A61M
2016/103 20130101; A61M 2205/52 20130101; A61M 2230/208 20130101;
A61B 5/082 20130101; A61M 2016/0036 20130101; A61M 2205/3303
20130101; A61M 2230/435 20130101; A61M 16/026 20170801; A61M
2205/502 20130101; A61M 2016/0027 20130101; A61M 2230/432
20130101 |
International
Class: |
A61M 16/00 20060101
A61M016/00; A61M 16/12 20060101 A61M016/12; A61M 16/10 20060101
A61M016/10 |
Claims
1. to 79. (canceled)
80. An apparatus for controlling an amount of at least one gas X in
a subject's lung to attain a targeted end tidal partial pressure of
the at least one gas X (PetX.sup.T), the apparatus comprising: (1)
a gas delivery device; (2) a control system for controlling the gas
delivery device, wherein the control system is adapted to target a
PETX.sup.T value with a respective breath [i], the PETX.sup.T value
comprising either a PETX.sup.T increment or a PETX.sup.Tdecrement,
the control system configured to: a. Obtain input of a logistically
attainable PETX.sup.T value for the respective breath [i]; b.
Perform a prospective computation of an amount of gas X required to
be inspired by the subject in an inspired gas to target the
PETX.sup.T for the respective breath [i] the performing comprising:
i. Computing a tidal model of the subject's lung including input of
the concentration of gas X in the mixed venous blood entering the
subject's pulmonary circulation for gas exchange in the respective
breath [i] (C.sub.MVX[i]); and ii. Outputting one or more values
required to control the amount of gas X in a volume of gas
delivered to the subject, based on the tidal model of the subject's
lung; and c. Control the amount of gas X in a volume of gas
delivered to the subject in the respective breath [i] (F.sub.IX) to
target the respective PETX.sup.T for the breath [i].
81. The apparatus of claim 1, wherein computing a tidal model of
the subject's lung further includes predicting the C.sub.MVX[i] by
compartmental modelling of gas dynamics.
82. The apparatus of claim 1, wherein computing a tidal model of
the subject's lung further includes estimating or measuring the
value of at least one parameter selected from a group consisting
of: functional residual capacity of the subject's lung, anatomic
dead space of the subject's lung, metabolic production of gas X in
the respective breath [i], metabolic consumption of gas X in the
respective breath [i], and tidal volume of the respective breath
[i].
83. The apparatus of claim 3, the control system further configured
to tune the estimated value of the functional residual capacity
over a series of tuning breaths.
84. The apparatus of claim 4 wherein tuning the estimated value of
the functional residual capacity comprises: changing the targeted
end tidal partial pressure of gas X between a tuning breath [i+x]
and a previous tuning breath [i+x-1]; comparing the magnitude of
the difference between the targeted end tidal partial pressure of
gas X for said tuning breaths [i+x] and [i+x-1] with the magnitude
of the difference between the measured end tidal partial pressure
of gas X for the same tuning breaths to quantify any discrepancy in
relative magnitude; and adjusting the estimated value of the
functional residual capacity in proportion to the discrepancy to
reduce the discrepancy in any subsequent prospective computing of
F.sub./X
85. The apparatus of claim 4 wherein tuning the estimated value of
the functional residual capacity comprises: obtaining input of a
measured baseline steady state value of P.sub.ETX[i] for computing
F.sub.IX at the start of a sequence; selecting a target end tidal
partial pressure of gas X (P.sub.ETX[i].sup.T) for at least one
tuning breath [i+x] wherein P.sub.ETX[i+x].sup.T differs from
P.sub.ETX[i+x-1].sup.T; comparing the magnitude of the difference
between the targeted end tidal partial pressure of gas X for said
tuning breaths [i+x] and [i+x-1] with the magnitude of the
difference between the measured end tidal partial pressure of gas X
for the same tuning breaths to quantify any discrepancy in relative
magnitude; and adjusting the estimated value of the functional
residual capacity in proportion to any discrepancy in magnitude to
reduce the discrepancy in a subsequent prospective computation of
F.sub./X including in any subsequent corresponding tuning breaths
[i+x-1] and [i+x] forming part of an iteration of the sequence.
86. The apparatus of claim 3, the control system further configured
to tune the estimated value of metabolic consumption of gas X over
a series of tuning breaths.
87. The apparatus of claim 7, wherein tuning the estimated value of
the metabolic production or consumption of gas X comprises
targeting a sequence of end tidal partial pressure of gas X, the
targeting comprising: comparing a targeted end tidal partial
pressure of gas X (P.sub.ETX [i+x].sup.T) for the at least one
tuning breath [i+x] with a corresponding measured end tidal partial
pressure of gas X for the corresponding breath [i+x] to quantify
any discrepancy; and adjusting the estimated value of the total
metabolic production or consumption of gas X in proportion to any
discrepancy to reduce the discrepancy in any subsequent prospective
computation of F.sub.IX
88. The apparatus of claim 7, wherein tuning the estimated value of
the metabolic production or consumption of gas X comprises
targeting a sequence of end tidal partial pressure of gas at least
once by: obtaining input of a measured baseline steady state value
for P.sub.ETX [i].sup.T for computing F.sub.IX at the start of a
sequence; targeting a selected target end tidal partial pressure of
gas X (P.sub.ETX [i+x].sup.T) for each of a series of tuning
breaths [i+1 . . . i+n], wherein P.sub.ETX [i].sup.T differs from
the baseline steady state value for P.sub.ETX[i]; comparing the
targeted end tidal partial pressure of gas X (P.sub.ETX[i+x].sup.T
for at least one tuning breath [i+x] in which the targeted end
tidal gas concentration of gas X has been achieved without drift in
a plurality of prior breaths [1+-1, 1+x-2 . . . ] with a
corresponding measured end tidal partial pressure of gas X for a
corresponding breath [i+x] to quantify any discrepancy and
adjusting the estimated value of the total metabolic production or
consumption of gas X in proportion to the discrepancy to reduce the
discrepancy to reduce the discrepancy in a subsequent prospective
computation of F.sub./X including in any subsequent corresponding
tuning breath [i+x] forming part of an iteration of the
sequence.
89. A computer program product for use in conjunction with a gas
delivery device to control an amount of at least one gas X in a
subject's lung to attain a target end tidal partial pressure of the
at least one gas X (P.sub.ETX.sup.T), the computer program
comprising program code for: a. obtaining input of a logistically
attainable end tidal partial pressure of gas X (P.sub.ETX.sup.T)
for a respective breath [i]; and b. performing a prospective
computation to obtain input of an amount of gas X required to be
inspired by the subject in an inspired gas to target the
P.sub.ETX.sup.Tfor the respective breath [i] (F.sub./X), the
performing comprising: i. computing a tidal model of the subject's
lung including input of the concentration of gas X in the mixed
venous blood entering the subject's pulmonary circulation for gas
exchange in the respective breath [i] (C.sub.MVX[i]); and ii.
outputting one or more values required to control F.sub.IX, based
on tidal model of the subject's lung.
90. A method for controlling an amount of at least one gas X in a
subject's lung to attain a targeted end tidal partial pressure of
at least one gas X (P.sub.ETX.sup.T), the method comprising: a.
obtaining input of a logistically attainable P.sub.ETX.sup.Tvalue
for a respective breath [i] comprising either a P.sub.ETX.sup.T
increment or a P.sub.ETX.sup.Tdecrement; and b. performing a
prospective computation of an amount of gas X required to be
inspired by the subject in an inspired gas to target the respective
P.sub.ETX.sup.Tfor the respective breath [i] (F.sub./X), the
performing comprising: i. computing a tidal model of the subject's
lung including input of the concentration of gas X in the mixed
venous blood entering the subject's pulmonary circulation for gas
exchange in the respective breath [i] (C.sub.MVX[i]); and ii. ii.
outputting one or more values required to control the amount of gas
X in a volume of gas delivered to the subject, based on the tidal
model of the subject's lung.
91. The method of claim 11, wherein computing a tidal model of the
subject's lung further includes predicting the C.sub.MVX[i] by
compartmental modelling of gas dynamics.
92. The method of claim 11, wherein computing a tidal model of the
subject's lung further includes estimating or measuring the value
of at least one parameter selected from a group consisting of:
functional residual capacity of the subject's lung, anatomic dead
space of the subject's lung, metabolic production of gas X in the
respective breath [i], metabolic consumption of gas X in the
respective breath [i], and tidal volume of the respective breath
[i].
93. The method of claim 13, the method further comprising tuning
the estimated value functional residual capacity over a series of
tuning breaths.
94. The method of claim 14 wherein tuning the estimation of the
functional residual capacity comprises: changing the targeted end
tidal partial pressure of gas X between a tuning breath [i+x] and a
previous tuning breath [i+x-1]; comparing the magnitude of the
difference between the targeted end tidal partial pressure of gas X
for said tuning breaths [i+x] and [i+x-1] with the magnitude of the
difference between the measured end tidal partial pressure of gas X
for the same tuning breaths to quantify any discrepancy in relative
magnitude; and adjusting the estimated value of the functional
residual capacity in proportion to the discrepancy to reduce the
discrepancy in any subsequent prospective computing of F.sub./X
95. The method of claim 14 wherein tuning the estimation of the
functional residual capacity comprises: obtaining input of a
measured baseline steady state value of P.sub.ETX[i] for computing
F.sub.IX at the start of a sequence; selecting a target end tidal
partial pressure of gas X (P.sub.ETX[i].sup.T) for at least one
tuning breath [i+x} wherein P.sub.ETX[i+x].sup.T differs from
P.sub.ETX[i+x-1]T; comparing the magnitude of the difference
between the targeted end tidal partial pressure of gas X for said
tuning breaths [i+x] and [i+x-1] with the magnitude of the
difference between the measured end tidal partial pressure of gas X
for the same tuning breaths to quantify any discrepancy in relative
magnitude; and adjusting the estimated value of the functional
residual capacity in proportion to any discrepancy in magnitude to
reduce the discrepancy in a subsequent prospective computation of
F.sub./X including in any subsequent corresponding tuning breaths
[i+x-1] and [i+x] forming part of an iteration of the sequence.
96. The method of claim 13, the method further comprising tuning
the estimated value of the metabolic production or consumption of
gas X over a series of tuning breaths.
97. The method of claim 17, wherein tuning the estimated value of
the metabolic production or consumption of gas X comprises
targeting a sequence of end tidal partial pressure of gas X, the
targeting comprising: comparing a targeted end tidal partial
pressure of gas X (P.sub.ETX [i+x].sup.T) for the at least one
tuning breath [i+x] with a corresponding measured end tidal partial
pressure of gas X for the corresponding breath [i+x] to quantify
any discrepancy; and adjusting the estimated value of the total
metabolic production or consumption of gas X in proportion to any
discrepancy to reduce the discrepancy in any subsequent prospective
computation of F.sub.IX.
98. The method of claim 17, wherein tuning the estimated value of
the metabolic production or consumption of gas X comprises
targeting a sequence of end tidal partial pressure of gas at least
once by: obtaining input of a measured baseline steady state value
for P.sub.ETX [i].sup.T for computing F.sub.IX at the start of a
sequence; targeting a selected target end tidal partial pressure of
gas X (P.sub.ETX [i+x].sup.T) for each of a series of tuning
breaths [i+1 . . . i+n], wherein P.sub.ETX [i] .sup.T differs from
the baseline steady state value for P.sub.ETX[i]; comparing the
targeted end tidal partial pressure of gas X (P.sub.ETX[i+x].sup.T
for at least one tuning breath [i+x] in which the targeted end
tidal gas concentration of gas X has been achieved without drift in
a plurality of prior breaths [1+x-1, 1+x-2 . . . ] with a
corresponding measured end tidal partial pressure of gas X for a
corresponding breath [i+x] to quantify any discrepancy and
adjusting the estimated value of the metabolic production or
consumption of gas X in proportion to the discrepancy to reduce the
discrepancy to reduce the discrepancy in a subsequent prospective
computation of F.sub./X including in any subsequent corresponding
tuning breath [i+x] forming part of an iteration of the
sequence.
99. The method of claim 13, wherein the gas X is selected from a
group consisting of carbon dioxide and oxygen.
Description
FIELD OF THE INVENTION
[0001] The present invention relates to an apparatus and method for
controlling end tidal gas partial pressures in spontaneously
breathing or ventilated subjects and to the use of such an
apparatus and method for research, diagnostic and therapeutic
purposes.
BACKGROUND OF THE INVENTION
[0002] Techniques for controlling end-tidal partial pressures of
carbon dioxide, oxygen and other gases are gaining increasing
importance for a variety of research, diagnostic and medicinal
purposes. Methods for controlling end tidal pressures of gases have
gained particular importance as a means for manipulating arterial
levels of carbon dioxide (and also oxygen), for example to provide
a controlled vasoactive stimulus to enable the measurement of
cerebrovascular reactivity (CVR) e.g. by MRI.
[0003] Conventional methods of manipulating arterial carbon dioxide
levels such as breath holding, hyperventilation and inhalation of
fixed concentration of carbon dioxide balanced with medical air or
oxygen are deficient in their ability to rapidly and accurately
attain targeted arterial carbon dioxide partial pressures for the
purposes of routinely measuring vascular reactivity in a rapid arid
reliable mariner.
[0004] The end-tidal partial pressures of gases are determined by
the gases inspired into the lungs, the mixed venous partial
pressures of gases in the pulmonary circulation, and the exchange
of gases between the alveolar space and the blood in transit
through the pulmonary capillaries. Changes in the end-tidal partial
pressures of gases are reflected in the pulmonary end-capillary
partial pressures of gases, which in turn flow into the arterial
circulation. The gases in the mixed-venous blood are determined by
the arterial inflow of gases to the tissues and the exchange of
gases between the tissue stores and the blood, while the blood is
in transit through the tissue capillary beds.
[0005] Robust control of the end-tidal partial pressures of gases
therefore requires precise determination of the gas storage,
transport, and exchange dynamics at the lungs and throughout the
body. Previous attempts at controlling the end-tidal partial
pressures of gases have failed to account for these complex
dynamics, and have therefore produced mediocre results.
[0006] In the simplest approaches, manipulation of the end-tidal
partial pressures of gases has been attempted with fixed changes to
the composition of the inspired gas. However, without any
additional intervention, the end-tidal partial pressures of gases
vary slowly and irregularly as exchange occurs at the lungs and
tissues. Furthermore, the ventilatory response to perturbations in
the end-tidal partial pressures of gases is generally unpredictable
and potentially unstable. Often, the ventilatory response acts to
restore the condition of the blood to homeostatic norms. Therefore,
any changes in the end-tidal partial pressures of gases are
immediately challenged by a disruptive response in the alveolar
ventilation. Consequently, fixed changes in the inspired gas
composition provoke only slow, irregular, and transient changes in
blood gas partial pressures.
[0007] In more complex approaches, manipulation of the end-tidal
partial pressures of gases has been attempted with negative
feedback control. These approaches continuously vary the
composition of the inspired gas so as to minimize error between
measured and desired end-tidal partial pressures of gases.
Technically, such a system suffers from the same limitations as all
negative feedback control systems--an inherent trade-off between
response time and stability.
[0008] Consequently, there is a need to overcome previous
limitations in end-tidal gas control, allowing for more precise and
rapid execution of end tidal gas targeting sequences in a wide
range of subjects and environments.
SUMMARY OF INVENTION
[0009] According to one aspect the invention is directed to a
method of controlling an amount of at least one gas X in a
subject's lung to attain at least one targeted end tidal partial
pressure of the at least one gas X, comprising the steps of: [0010]
a. Obtaining input of a logistically attainable end tidal partial
pressure of gas X (PetX[i].sup.T) for one or more respective
breaths [i]; [0011] b. Obtaining input of a prospective computation
of an amount of gas X required to be inspired by the subject in an
inspired gas to target the PetX[i].sup.T for a respective breath
[i] using inputs required to compute a mass balance equation,
wherein one or more values required to control the amount of gas X
in a volume of gas delivered to the subject is output from the mass
balance equation; and optionally [0012] c. Controlling the amount
gas X in a volume of gas delivered to the subject in a respective
breath m to target the respective PetX[i].sup.T based on the
prospective computation.
[0013] For present purposes a mass balance equation is understood
to be a mathematical relationship that applies the law of
conservation of mass (i.e. the amount of at least one gas X) to the
analysis of movement of at least one gas X, in and out of the lung,
for the purpose of prospectively targeting an end tidal partial
pressure of gas X. Optionally, where an end tidal partial pressure
of gas X is sought to be changed from a baseline steady state value
or controlled for a sequence of respective breaths [i] the mass
balance equation will account for the transfer of a mass of gas X
between a subject's lung and pulmonary circulation (i.e. the mixed
venous blood entering the pulmonary capillaries (C.sub.MVX[i])); so
that this key source of flux affecting the end tidal partial
pressure of gas X in the breath(s) of interest, is accounted
for.
[0014] Preferably the mass balance equation is computed based on a
tidal model of the lung as described hereafter.
[0015] In one embodiment of the method, a concentration of gas X
(F.sub.IX), for example in a first inspired gas (the first inspired
gas also referred to, in one embodiment of the invention, as a
controlled gas mixture) is computed to target or attain
PetX[i].sup.T in a respective breath [i].
[0016] Optionally, the mass balance equation is solved for
F.sub.IX.
[0017] It will be appreciated that F.sub.IX may be output from the
mass balance equation by testing iterations of its value without
directly solving for F.sub.IX.
[0018] Optionally, the volume of gas delivered to the subject is a
fixed tidal volume controlled by a ventilator
[0019] Optionally, the volume of gas delivered to the subject in a
respective breath [i] comprises a first inspired gas of known
volume and a second inspired neutral gas.
[0020] In accordance with a tidal model of the lung, in one
embodiment of the invention, the mass balance equation is computed
in terms of discrete respective breaths [i] including one or more
discrete volumes corresponding to a subject's FRC, anatomic dead
space, a volume of gas transferred between the subject's lung and
pulmonary circulation in the respective breath [i] and an
individual tidal volume of the respective breath [i].
[0021] According to another aspect, the invention is directed to a
method of controlling an amount of at least one gas X in a
subject's lung to attain a targeted end tidal partial pressure of
the at least one gas X, comprising the steps of: [0022] a.
Obtaining input of a concentration of gas X in the mixed venous
blood entering the subject's pulmonary circulation for gas exchange
in one or more respective breaths [i] (C.sub.MX[i]); [0023] b.
Obtaining input of a logistically attainable end tidal partial
pressure of gas X (PetX[i].sup.T) for a respective breath [i];
[0024] c. Obtaining input of a prospective computation of an amount
of gas X required to be inspired by the subject in an inspired gas
to target the PetX[i].sup.T for a respective breath [i] using
inputs required to compute a mass balance equation including
C.sub.MVX[i], wherein one or more values required to control the
amount of gas X in a volume of gas delivered to the subject is
output from the mass balance equation: and optionally [0025] d.
Controlling the amount gas X in a volume of gas delivered to the
subject in a respective breath [i] to target the respective
PetX[i].sup.T based on the prospective computation.
[0026] In one embodiment of the method, a concentration of gas X
(F.sub.IX) is computed to target or attain PetX[i].sup.T in a
respective breath [i].
[0027] Optionally, the mass balance equation is solved for
F.sub.IX.
[0028] According to one embodiment of the method, the mass balance
equation is computed based on a tidal model of the lung.
[0029] In accordance with a tidal model of the lung, in one
embodiment of the invention, the mass balance equation is computed
in terms of discrete respective breaths [i] including one or more
discrete volumes corresponding to a subject's FRC, anatomic dead
space, a volume of gas transferred between the subject's lung and
pulmonary circulation in the respective breath [i] and an
individual tidal volume of the respective breath [i].
[0030] According to another embodiment of the method, the method
comprises the step of tuning one or more inputs required for
computation of F.sub.IX, for example, with respect to any terms
and/or by any methods described in this application.
[0031] According to another embodiment of the method, the volume of
inspired gas entering the subject's alveoli is controlled by fixing
a tidal volume of an inspired gas containing gas X using a
ventilator and subtracting a volume of gas corresponding to an
estimated or measured value for the subject's anatomic dead space
volume.
[0032] According to another embodiment of the method, the gas
inspired by the subject is inspired via a sequential gas delivery
circuit (as defined below). Optionally, the rate of flow of gas
into the sequential gas delivery circuit is used to compute the
volume of inspired gas entering the subject's alveoli in a
respective breath [i].
[0033] According to one aspect of the method, the gas inspired by
the subject in each respective breath [i] comprises a first
inspired gas and a second inspired optionally neutral gas, wherein
the first inspired gas is delivered in the first part of a
respective breath [i] followed by a second inspired neutral gas for
the remainder of the respective breath [i], the volume of the first
inspired gas selected so that intake of the second inspired neutral
gas at least fills the entirety of the anatomic dead space.
F.sub.IX is computed prospectively from a mass balance equation
expressed in terms which correspond to all or an
application-specific subset of the terms in equation 1 and the
first inspired gas has a concentration of gas X which corresponds
to F.sub.IX for the respective breath [i]
[0034] A "tidal model of the lung" means any model of the movement
of gases into and out of the lung that acknowledges that
inspiration of gas into, and the expiration of gas from the lung,
occurs in distinct phases, each inspiration-expiration cycle
comprising a discrete breath, and that gases are inspired in to,
and expired from, the lungs via the same conduit.
[0035] In terms of computing a mass balance equation and capturing
relevant aspects of movement of gases Into and out of the lung, a
tidal model of lung is preferably understood to yield a value of
F.sub.IX on a breath by breath basis from a mass balance equation.
The mass balance equation is computed in terms of discrete
respective breaths [i] including one or more discrete volumes
corresponding to a subject's FRC, anatomic dead space, a volume of
gas transferred between the subject's lung and pulmonary
circulation in the respective breath [i] and an individual tidal
volume of the respective breath [i]. Optionally, the mass balance
equation is solved for F.sub.IX.
[0036] Preferably for optimal accuracy in a universal set of
circumstances, all these discrete volumes are accounted for in the
mass balance equation. However, it is possible for tho invention to
be exploited sub-optimally or for individual circumstances in which
the relative sizes of certain of these respective volumes (e.g.
anatomic dead space, volume of gas X transferred between the
pulmonary circulation and lung and even tidal volume (shallow
breaths) may be relatively small (compared to other volumes)
depending on the circumstances and hence failing to account for all
of these volumes may affect achievement of a target end tidal
partial pressure to an acceptable extent particularly where less
accuracy is demanded.
[0037] In one embodiment of the invention, the mass balance
equation (optionally written in terms of one or more concentration
of gas X in one or more discrete volumes of gas) : [0038] a.
Preferably accounts for the total amount of gas X in the lung
following inhalation of the inspired gas in a respective breath [i]
(M.sub.LX[i]) including transfer of gas X between the lung and the
pulmonary circulation; [0039] b. Assumes distribution of
M.sub.LX[i] into compartments including the subject's FRC
(M.sub.LX[i].sub.FRC), a fixed or spontaneously inspired tidal
volume (M.sub.LX[i].sub.VT) and preferably the subject's anatomic
dead space volume (M.sub.LX[i].sub.VD); [0040] c. Assumes uniform
distribution of the M.sub.LX[i].sub.FRC a and M.sub.LX[i].sub.VT in
the cumulative volume FRC+V.sub.T; [0041] d. Preferably includes a
term that accounts for re-inspiration in a respective breath [i] of
an amount of gas X left in the dead space volume after exhalation
in a previous breath [i-1].
[0042] As detailed below, according to one embodiment, in which the
invention is implemented via sequential gas delivery, the
individual respective tidal volume for a breath [i] may consist of
a first inspired gas having a concentration of gas X corresponding
to F.sub.IX and second inspired neutral gas. The volume of the
first inspired gas may be fixed, for example by controlling the
rate of flow of first inspired gas into a sequential gas delivery
circuit.
[0043] In one embodiment of the invention the mass balance equation
comprises terms corresponding to all or an application-specific
subset of the terms in equations 1 or 2 forth below as described
hereafter. An "application-specific subset" means a subset tailored
to either a minimum, intermediate or logistically optimal standard
of accuracy having regard to the medical or diagnostic application
of the invention in question or the sequence of PetX[i].sup.T
values targeted. Optional terms and mandatory inclusions in the
subset may be considered application-specific as a function of the
sequence of PetX[i].sup.T values targeted in terms of the absolute
size of the target value and/or the relative size of the target
value going from one breath to the next as discussed below, For
example, in most cases, the O.sub.2 or CO.sub.2 re-inspired from
the anatomical dead space (V.sub.D) is small compared to the
O.sub.2 or CO.sub.2 in the other volumes that contribute to the
end-tidal partial pressures. For example, where the volume of
O.sub.2 or CO.sub.2 in the first inspired gas is very large, in
trying to induce a large increase in the target end-tidal partial
pressures, the O.sub.2 or CO.sub.2 transferred into the lung from
the circulation may be comparatively small and neglected.
Neglecting any terms of the mass balance equations will decrease
computational complexity at the expense of the accuracy of the
induced end-tidal partial pressures of gases.
[0044] The demands of a diagnostic application may be ascertained
empirically or from the literature. For example, a measure of short
response times of brain blood vessels to hypercapnic stimulus can
be determined to require a square wave change in the stimulus such
as a change of 10 mmHg P.sub.ETCO.sub.2 from one breath to the
next. Another example is when measuring response of BOLD signal
with MRI to changes in partial pressure of CO.sub.2 in the blood,
the changes needed may be determined to be abrupt as the BOLD
signal has considerable random drift over time.
[0045] Optionally, one or more inputs for computation of
PetX[i].sup.T are "tuned" as defined below to adjust, as necessary
or desirable, estimated or measured values for FRC and/or total
metabolic production/consumption of gas X so as to reduce the
discrepancy between targeted and measured end tidal partial
pressures of gas X i.e. an actual value, optionally measured at the
mouth. Tuning can be done when a measured baseline steady state
value of PetX[i] is defined for a series of test breaths.
[0046] According to another aspect, the present invention is
directed to an apparatus for controlling an amount of at least one
gas X in a subject's lung to attain a targeted end tidal partial
pressure of the at least one gas X, comprising: [0047] (1) a gas
delivery device: [0048] (2) a control system for controlling the
gas delivery device including means for: [0049] a. Obtaining input
of a concentration of gas X in the mixed venous blood entering the
subject's pulmonary circulation for gas exchange in one or more
respective breaths [i] (C.sub.MVX[i]); [0050] b. Obtaining input of
a logistically attainable end tidal partial pressure of gas X
(PetX[i].sup.T) for a respective breath [i]; [0051] c. Obtaining
input of a prospective computation of an amount of gas X required
to be inspired by the subject in an inspired gas to target the
PetX[i].sup.T for a respective breath using inputs required to
compute a mass balance equation including C.sub.MVX[l], wherein one
or more values required to control the amount of gas X in a volume
of gas delivered to the subject is output from the mass balance
equation; and [0052] d. Controlling the amount of gas X in a volume
of gas delivered to the subject in a respective breath [i] to
target the respective PetX[i].sup.T based on the prospective
computation.
[0053] In one embodiment of the method, a concentration of gas X
(F.sub.IX) is computed to target or attain PetX[i].sup.T in a
respective breath [i].
[0054] Optionally, the mass balance equation is solved for
F.sub.IX.
[0055] It will be appreciated the control system may implement one
or more embodiments of the method described herein.
[0056] In one embodiment of the apparatus the gas delivery device
is a sequential gas delivery device.
[0057] In one embodiment of the apparatus, the control system is
implemented by a computer.
[0058] In one embodiment of the apparatus, the computer provides
output signals to one or more rapid flow controllers.
[0059] In one embodiment of the apparatus, the apparatus is
connected to a sequential gas delivery circuit.
[0060] In one embodiment of the apparatus, the computer receives
input from a gas analyzer and an input device adapted for providing
input of one or more logistically attainable target end tidal
partial pressure of gas X (PetX[i].sup.T) for a series of
respective breaths [i].
[0061] In one embodiment of the apparatus, the control system, in
each respective breath [i], controls the delivery of at least a
first inspired gas and wherein delivery of the first inspired gas
is coordinated with delivery a second inspired neutral gas, wherein
a selected volume of the first inspired gas is delivered in the
first part of a respective breath [i] followed by the second
inspired neutral gas for the remainder of the respective breath
[i], wherein volume of the first inspired gas is fixed or selected
for one or more sequential breaths by way of user input so that
intake of the second inspired neutral gas at least fill the
entirety of the anatomic dead space.
[0062] In one embodiment of the apparatus, the apparatus is
connected to a sequential gas delivery circuit.
[0063] In one embodiment of the apparatus, the gas delivery device
is a gas blender.
[0064] In one embodiment of the apparatus, the control system
implements program code stored in a computer readable memory or
comprises a signal processor embodied in one or more programmable
IC chips.
[0065] According to another aspect, the present invention is
directed to a computer program product for use in conjunction with
a gas delivery device to control an amount of at least one gas X in
a subject's lung to attain a target end tidal partial pressure of a
gas X in the subject's lung, comprising program code for: [0066] a.
Obtaining input of a concentration of gas X in the mixed venous
blood entering the subject's pulmonary circulation for gas exchange
in one or more respective breaths [i] (C.sub.MVX[i]); [0067] b.
Obtaining input of a logistically attainable end tidal partial
pressure of gas X (PetX[i].sup.T) for a respective breath [i];
[0068] c. Obtaining input of a prospective computation of an amount
of gas X required to be inspired by the subject in an inspired gas
to target the PetX[i].sup.T for a respective breath [i] using
inputs required to compute a mass balance equation including
C.sub.MVX[i], wherein one or more values required to control the
amount of gas X in a volume of gas delivered to the subject is
output from the mass balance equation; and [0069] d. Controlling
the amount in a volume of gas delivered to the subject in a
respective breath [i] to target the respective PetX[i].sup.T based
on the prospective computation.
[0070] In one embodiment of the method, a concentration of gas X
(F.sub.IX) is computed to target or attain PetX[i].sup.T in a
respective breath [i].
[0071] Optionally, the mass balance equation is solved for
F.sub.IX.
[0072] It will be appreciated the computer program product may be
used in conjunction with a gas delivery device, to at least
partially implement a control system for carrying out one or more
embodiments of the method described herein.
[0073] The program code may be stored in a computer readable memory
or embodied in one or more programmable IC chips.
[0074] The present invention is also directed to the use of an
aforementioned method, apparatus or computer program product to:
[0075] a) Provide a controlled vasoactive stimulus for measurement
of vascular reactivity; [0076] b) Provide a controlled vasoactive
stimulus for measurement of cerebrovascular reactivity; [0077] c)
Provide a controlled vasoactive stimulus for measurement of liver,
kidney, heart or eye vascular reactivity; or [0078] d)
Simultaneously change the subjects end tidal partial pressures of
oxygen and carbon dioxide to selected values, for example to
potentiate a diagnosis or treat cancer,
[0079] According to another aspect, the present invention is
directed to a method of controlling an amount of at least one gas X
in a subject's lung to attain a targeted end tidal partial pressure
of the at least one gas X, comprising the steps of: [0080] a.
Obtaining input of a concentration of gas X in the mixed venous
blood entering the subject's pulmonary circulation for gas exchange
in one or more respective breaths [i] (C.sub.MVX[i]); [0081] b.
Obtaining input of a prospective computation of an amount of gas X
required to be Inspired by the subject in an inspired gas to target
the PetX[i].sup.T for a respective breath [i ] using inputs
required to compute a mass balance equation including C.sub.MVX[i],
wherein one or more values required to control the amount of gas X
in a volume of gas delivered to the subject is output from the mass
balance equation, the mass balance equation comprising terms
corresponding to ail or an application-specific subset of the terms
set forth in:
[0081] F 1 .times. X .function. [ i ] = ( P ET .times. X .function.
[ i ] T - P ET .times. X .function. [ i - 1 ] T ) ( FRC + V T ) + P
ET .times. X .function. [ i - 1 ] T ( FG 1 - T E ) - PB Q - ( 1 - s
) T F ( C MV .times. X .function. [ i ] - C P .times. X .function.
[ i ] ) FG 1 T B PB eq . .times. 1 F 1 .times. X .function. [ i ] =
P ET .times. X .function. [ i ] T ( FRC + V T ) - P ET .times. X
.function. [ i - 1 ] T ( FRC + V D ) - PB Q ( 1 - s ) T B ( C MV
.times. X .function. [ i ] - C P .times. X .function. [ i ] ) ( ( V
T - V D ) PB ) eq . .times. 2 ##EQU00001## [0082] c. Controlling
the amount of gas X in a volume of gas delivered to the subject in
a respective breath [i] to target the respective PetX[i].sup.T
based on the prospective computation.
[0083] The terms referred to the equations are defined herein.
[0084] In one embodiment of the method, a concentration of gas X
(F.sub.IX) is computed to target or attain PetX[i].sup.T in a
respective breath [i].
[0085] Optionally, the mass balance equation is solved for
F.sub.IX.
[0086] According to one embodiment, the gas inspired by the subject
in each respective breath [i] comprises a first inspired gas and a
second inspired neutral gas (as define hereafter), wherein a
selected volume of the first inspired gas is delivered in the first
part of a respective breath [i] followed by a second inspired
neutral gas for the remainder of the respective breath [i], the
volume of the first inspired gas selected so that intake of the
second inspired neutral gas at least fills the entirety of the
anatomic dead space.
[0087] The verb "target" used with reference to achieving a
logistically attainable PetX[i].sup.T value for a respective breath
[i] means "attain" with the relative precision pragmatically
demanded by the particular therapeutic or diagnostic application in
question or the sequence of targets sought to be attained in both
absolute and relative (between contiguous breaths) terms. For
example, as discussed below, by "tuning" values for certain inputs
into equation 1 or 2 (particularly functional residual capacity and
total metabolic consumption or production of gas X) a logistically
attainable end tidal partial pressure of gas X could be attained
with relative precision in one breath. The logistically attainable
PetX[i].sup.T value could theoretically be attained with a
clinically acceptable reduced precision by not tuning those values
or foregoing other optimizations, as described herein, for example,
by tuning total metabolic production or consumption of gas X
without tuning FRC, which would be expected to delay getting to the
target value more precisely by several breaths.
[0088] For purposes herein, it is understood that limitations of a
physiological or other nature may impinge on attaining a
PetX[i].sup.T. Given a logistically attainable target for which
parameters known to impinge on accuracy, that can be optimized
(described herein e.g. tuning FRC and total metabolic
consumption/production of gas X) are optimized, we have found that
a PetX[i].sup.T can be considered to be "attained" as a function of
the difference between the targeted value and a steady state value
measured for an individual. For example, assuming a measurement
error of +/- 2 mm. of Hg, in the case of CO.sub.2, for a
PetX[i].sup.T between 30 and 50 mmHg, a measured PetCO.sub.2 value
that is within 1 to 3 mm. of Hg of PetX[i].sup.T can be considered
to be "attained". Tuning to an extent that achieves a measured
value within this range will serve as an indicator as to whether
tuning has been successfully completed or should be continued.
However in principle, tuning may be iterated until the difference
between the measured and targeted PetX is minimized. However, for a
PetCO.sub.2[i].sup.T between 51 and 65 mmHg, a measured PetX value
that is within (i.e +/-) 1 to 5 mm. of Hg of PetCO.sub.2[i].sup.T
can be considered to be "attained" and the success of a given
tuning sequence can be judged accordingly.
[0089] In the case of oxygen, a measured PetO.sub.2 value that is
within 5-10% of PetO.sub.2[i].sup.T can be considered to be one
which has "attained" PetO.sub.2[i].sup.T, For example, if the
target PetO.sub.2 value is between 75 mm of Hg and 150 mm of Hg a
range of measured values that proportionately is within (i.e. |/-)
4 mm and 8 mm of Hg (5 and 10% of 75 respectively) to +/- 8 mm to
15 mm of Hg (5-10% of 150) can be considered to be attained
(similarly for a target of 100 mm of Hg, +/- 5-10 mm of Hg; and for
a PetO2[i].sup.T of 200 mm Hg, +/- 10-20 mm of Hg).
[0090] However, as described above, depending on the demands of the
application and the circumstances, a PetX[i].sup.T can be
considered to be "targeted" with a deliberately reduced precision
(as opposed to "attained" as a goal) if parameters known to impinge
on accuracy, that can be optimized (described herein e.g. tuning
FRC and total metabolic consumption/production of gas X) are
deliberately not optimized. The Invention as defined herein (not to
the exclusion of variations apparent to those skilled in the art)
is nevertheless exploited inasmuch as various aspects of the
invention described herein provide for a prospective targeting
system, a system that can be judiciously optimized (or not) to
accommodate a variety of circumstances and sub-optimal uses
thereof. A PetX[i].sup.T can be considered to have been "targeted"
by exploiting the invention as defined, in one embodiment, after
executing a sequence of tuning breaths, wherein the tuning sequence
optionally establishes that the optimizations defined herein make
the target "attainable".
[0091] According to another aspect, the present invention is also
directed to a preparatory method for using a gas delivery device to
control an amount of at least one gas X in a subject's lung to
attain a targeted end tidal partial pressure of the at least one
gas X, comprising the step of executing a sequence of "tuning"
breaths as described hereafter.
[0092] Optionally, one or more inputs for computation of
PetX[i].sup.T are " tuned" as defined below to adjust, as necessary
or desirable, estimated or measured values for FRC and/or total
metabolic production/consumption of gas X so as to reduce the
discrepancy between targeted and measured end tidal partial
pressure of gas X i.e. an actual value, optionally measured at the
mouth. Tuning is preferably done when a measured baseline steady
state value of PetX[i] is ascertained for a series of ensuing test
breaths.
[0093] According to one embodiment of the invention, an estimated
or measured value for the subject's functional residual capacity
(FRC) is tuned.
[0094] Optionally, FRC is tuned in a series of tuning breaths by:
[0095] a. changing the targeted end tidal partial pressure of gas X
between a tuning breath [i+x] and a previous tuning breath [i+x-1];
[0096] b. comparing the magnitude of the difference between the
targeted end tidal partial pressure of gas X for said tuning
breaths [i+x] and [i+x-1] with the magnitude of the difference
between the measured end tidal partial pressure of gas X for the
same tuning breaths to quantify any discrepancy in relative
magnitude; and [0097] c. adjusting the value of FRC in proportion
to the discrepancy to reduce the discrepancy in any subsequent
prospective computation of F.sub.IX.
[0098] Optionally, FRC is tuned in a series of tuning breaths in
which a sequence of end tidal partial pressures of gas X is
targeted at least once by: [0099] (a) obtaining input of a measured
baseline steady state value for PetX[i] for computing F.sub.IX at
start of a sequence; [0100] (b) selecting a target end tidal
partial pressure of gas X (PetX[i].sup.T) for at least one tuning
breath [i+x] wherein PetX[i+x].sup.R differs from
PetX[i+x-1].sup.T; and [0101] (c) comparing the magnitude of the
difference between the targeted end tidal partial pressure of gas X
for said tuning breaths [I+x] and [i+x-1] with the magnitude of the
difference between the measured end tidal partial pressure of gas X
for the same tuning breaths to quantify any discrepancy in relative
magnitude; [0102] (d) adjusting the value of FRC in proportion to
any discrepancy in magnitude to reduce the discrepancy in a
subsequent prospective computation of F.sub.IX including in any
subsequent corresponding tuning breaths[i+x-1] and [i+x] forming
part of an iteration of the sequence.
[0103] According to one embodiment of the invention, an estimated
or measured value of the subject's total metabolic production or
consumption of gas X is tuned.
[0104] Optionally, the total metabolic production or consumption of
gas X is tuned in a series of tuning breaths by comparing a
targeted end tidal partial pressure of gas X (PetX[i+x].sup.T) for
the at least one tuning breath [i+x] with a corresponding measured
end tidal partial pressure of gas X for the corresponding breath
[i+x] to quantify any discrepancy and adjusting the value of the
total metabolic production or consumption of gas X in proportion to
any discrepancy to reduce the discrepancy in any subsequent
prospective computation of F.sub.IX.
[0105] Optionally, the total metabolic consumption or production of
gas X is tuned in a series of tuning breaths in which a sequence of
end tidal partial pressures of gas X is targeted at least once by:
[0106] (a) obtaining input of a measured baseline steady state
value for PetX[i] for computing F.sub.IX at start of a sequence;
[0107] (b) targeting a selected target end tidal partial pressure
of gas X (PetX[i].sup.T) for each of a series of tuning breaths
[i+1 . . . i+n], wherein PetX[i].sup.T differs from the baseline
steady state value for PetX[i]; [0108] (c) comparing the targeted
end tidal partial pressure of gas X (PetX[i+x].sup.T for at least
one tuning breath [i+x] in which the targeted end tidal gas
concentration of gas X has been achieved without drift in a
plurality of prior breaths [1+x-1, 1+x-2 . . . ] with a
corresponding measured end tidal partial pressure of gas X for a
corresponding breath [i+x] to quantify any discrepancy and
adjusting the value of the total metabolic consumption or
production of gas X in proportion to the discrepancy to reduce the
discrepancy in a subsequent prospective computation of F.sub.IX
including in any subsequent corresponding tuning breath [i+x]
forming part of an iteration of the sequence.
[0109] All key inputs for computing F.sub.IX are itemized
below.
[0110] We have found that a prospective model which predicts an
F.sub.IX that is required to target a logistically attainable end
tidal partial pressure of a gas X is simplified and enhanced by
using a sequential gas delivery system (alternatively called a
sequential gas delivery device, or sequential rebreathing).
[0111] According to another embodiment, the apparatus according to
the invention is a "sequential gas delivery device" as defined
hereafter. The sequential gas delivery device optionally comprises
a partial rebreathing circuit or a sequential gas delivery circuit
as defined hereafter.
[0112] The rate of gas exchange between the subject's mixed venous
blood and alveoli for a respective breath [i] may be controlled by
providing a partial re-breathing circuit through which the subject
inspires a first gas in which the concentration of gas X is
F.sub.IX and a second gas having a partial pressure of gas X which
is substantially equivalent to the partial pressure of gas X in the
subject's end tidal expired gas prior to gas exchange in the
current respective breath [i] (the subject's last expired gas which
is made available for re-breathing) or a gas formulated in situ to
match a concentration of gas X which would have been exhaled in a
prior breath. Practically, this may be accomplished by setting the
rate of gas flow into the partial rebreathing circuit for a
respective breath [i] to be less than the patient's minute
ventilation or minute ventilation minus anatomic dead space
ventilation (i.e. such that the last inspired second gas at least
fills the anatomical dead space if not also part of the alveolar
space) and using this rate or the volume of inspired gas it
represents in a current breath to compute F.sub.IX for a respective
breath [i].
[0113] With reference to parameters used to compute terms in
equation 1 or 2, it is understood that phrases like "obtaining
input" and similar expressions are intended to be understood
broadly to encompass, without limitation, input obtained by or
provided by an operator of a gas delivery device through any form
of suitable hardware input device or via programming or any form of
communication or recordation that Is translatable into an
electronic signal capable of controlling the gas delivery
device.
[0114] According to another aspect, the invention is also directed
to a method of controlling an amount of at least one gas X in a
subject's lung to attain, preliminary to or during the course of a
diagnostic or therapeutic procedure, at least one target end tidal
partial pressure of a gas X.
[0115] A PetX[i] attained for any immediately previous breath [i-1]
is: [0116] a. alterable, prospectively, to any other logistically
attainable value, in one breath, using a method or apparatus
according to the invention; [0117] b. maintainable, prospectively,
without drift, in a respective breath [i] or in breath [i] and in
one or more subsequent breaths [i+1] . . . [i+n] using a method or
apparatus according to the invention.
[0118] According to one embodiment of the invention, a input of a
concentration of gas X in the mixed venous blood entering the
subject's lung for gas exchange in the respective breath
[i](C.sub.MVX[i]) can be obtained (e.g. predicted) by a
compartmental modelling of gas dynamics. "Compartmental modeling of
gas dynamics" means a method in which body tissues are modeled as
system of one or more compartments characterized in terms of
parameters from which the mixed-venous return of gas X can be
predicted. These parameters include the total number of
compartments, the fraction of the total cardiac output received by
the respective compartment, the respective compartment's storage
capacity for gas X and the fraction of the overall
production/consumption of gas X that can be assigned to the
compartment.
[0119] The total number of compartments (ncomp) in the model must
be known or selected, and then each compartment (k) is assigned a
fraction of the total cardiac output (qk), a storage capacity for
gas X (dXk), and a fraction of the overall production/consumption
rate of gas X (vXk). In general, the storage capacity for any gas X
in a compartment is known for an average subject of a particular
weight, and then scaled proportional to the actual weight of the
subject under test.
[0120] Modeling/predicting the mixed-venous return can be done for
any gas X using the following information: [0121] 1. A formula for
conversion of end-tidal partial pressures to blood content of gas X
(i.e. determining the content of the gas X in the pulmonary
end-capillary blood based on data with respect to partial
pressures). [0122] 2. the fraction of the overall
production/consumption of the gas X which occurs in the
compartment; [0123] 3. the storage capacity of the compartment for
gas X; [0124] 4. blood flow to/from the compartment.
[0125] Some examples of gas X include Isoflorane, carbon dioxide
and oxygen.
[0126] Compartmental modeling of gas dynamics may be simplified
using a single compartment model.
[0127] Means for controlling gas delivery typically include
suitable gas flow controllers for controlling the rate of flow of
one or more component gases. The gas delivery may be controlled by
a computer for example an integrated computer chip or an external
computer running specialized computer readable instructions via
which inputs, computations and other determinations of parameter
and controls are made/handled. The computer readable instructions
may be embodied in non-transitory computer readable medium which be
distributed as a computer program product.
[0128] It will be appreciated that logistically attainable target
values for end tidal partial pressures of gas X may be set for
respective breaths within a series breaths which are taken
preliminary to or as part of a diagnostic or therapeutic procedure.
Typically these values are defined in advance for the series or for
at least part of the series of breaths. As described below, these
individually logistically attainable values may be used to attain
values in multiple breaths that are not logistically attainable in
one breath.
[0129] The term "tuning" and related terms (e.g. tune, tuned etc.)
means that a value for an estimated or measured parameter that is
required to compute F.sub.IX is adjusted, as necessary or
desirable, to enable more precise computation of the F.sub.iX
required to achieve a PetX[i].sup.T, preferably based on observed
differences between the target PetX[i].sup.T set for one or more
respective breaths and actual PetX[i] value(s) obtained for the
respective breath(s), If any, such that post-adjustment observed
value(s) more closely match the respective target value(s). The
tuned parameter(s) can be understood to fall into two categories:
lung and non-lung related parameters. Preferably, the lung related
parameter is FRC. A step change in the end tidal partial pressure
of gas X is required to tune this parameter. Non-lung related
parameters are preferably tissue related parameters, preferably
those required for computing a compartmental model of gas dynamics,
preferably parameters governing total metabolic production or
consumption of gas X in the body or the overall cardiac output,
optionally parameters affecting assessment of the contribution of a
respective compartment to the mixed venous content of gas X,
preferably as a function of the production or consumption of gas X
in the respective compartment, the assigned storage capacity for
gas X in the respective compartment and the contribution of blood
flow from the respective compartment to the total cardiac output,
for example, by observing that a repeatedly targeted value does not
drift when attained. Drift can be defined in the negative or
considered to have been corrected for, for example, if an adjusted
value for a tissue related parameter results in a variation of no
greater than 1 to 2 mm of Hg (ideally approximately 1 mm of Hg or
less) between observed and targeted end tidal values of gas X for a
series of 5 consecutive breaths (i.e. where the end tidal partial
pressure of gas X is sought to be maintained for a series of
breaths e.g. 30 breaths and observed drift is corrected).
[0130] Tuning FRC is important for transitioning accurately between
end-tidal values. Tuning non-lung related parameters e.g. VCO2 is
important so that the steady state error between end-tidal values
is small. The tuning requirements depend on the goals of the
targeting sequence. For example, in the case of inducing a step
increase in the end-tidal partial pressure of CO2 from 40 mmHg to
50 mmHg, if attaining 50 mmHg in the first breath is important, FRC
is preferably tuned. If achieving 50 mmHg in the first breath is
not vital, but achieving this target in 20 breaths is all that may
matter, a non-lung related parameter such as VCO2 should be tuned.
If the goal of the end tidal targeting sequence is to achieve
50mmHg in one breath, and then maintain 50 mmHg for the ensuing 20
breaths, both FRC and a non-lung related parameter should be tuned.
If you don't care if you get to 50 mmHg In the first breath, and
then drift to 55 after 20 breaths, don't tune either.
[0131] The following are examples of end tidal values that would be
achieved for each combination. Assume transition is made on the
second breath (bold):
[0132] Tuned FRC (good transition), untuned VCO2 (bad steady state
error)--40, 50, 51, 52, 53, 54, 55, 55, 55. 55, 55, 55
[0133] Untuned FRC (bad transition), tuned VCO2 (no steady state
error)--40, 53, 56, 53, 52, 51, 50, 50, 50, 50, 50
[0134] Tuned FRC (good transition), tuned VCO2 (no steady state
error)--40, 50, 50, 50, 50, 50, 50, 50, 50
[0135] Untuned FRC (bad transition), untuned VCO2 (bad steady state
error)--40, 62, 60, 58, 57, 56, 55, 55, 55, 55.
[0136] For example, to achieve a progressively increasing end tidal
partial pressure of gas X where the actual or absolute values are
not of concern, only that the values keep increasing in each
breath, it would not be necessary to tune FRC or VCO2. However, to
transition from 40 to 50 mmHg (for example, where gas X is CO2),
though not necessarily in one breath, it would be preferable to
tune a non-lung related parameter e.g. VCO2 but not FRC. If it were
important to transition from 40 mmHg to 50 mmHg in one breath, but
not so important if the end tidal values drifted away from 50 mmHg
after the first breath, it would be important to tune FRG but not
VCO2 etc, Nevertheless, a target would be set for each respective
breath [i] and that target would be effectively attained with a
degree of accuracy and immediacy necessary for the application in
question. Accordingly, a tidal based model for targeting end tidal
partial pressure of a gas X provides a tunable flexible system for
attaining those targets in line with a wide variety of objectives
of the user.
[0137] It is to be understood that this tuning can be applied
independently to each of the gases that are being targeted, as each
gas can be targeted independently of the other gases.
[0138] An attainable target may be maintained in one or more
subsequent breaths by setting the target end tidal value for the
respective breath to be the same as PetX[i-1]. A target that is not
attainable in one breath may be obtained in a series of breaths [i]
. . . [i+n].
[0139] As suggested above and discussed below, it is possible that
a particular end tidal partial pressure is not logistically
attainable in one breath. If logistically attainable at all, such a
target may be logistically attained only after multiple breaths. In
contrast to methods requiring negative feedback, such as dynamic
end tidal forcing, in one aspect of the method of the present
invention this number of breaths may be pre-defined prospectively.
This number of breaths may also be minimized so that the ultimate
end tidal target is attained as rapidly as logistically feasible,
for example by simple computational trial and error with respect to
an incremented series of target. As described below, logistic
constraints could be seen as limitations to inhaling the amount of
the gas X that needs to be inhaled to reach a target concentration
on the next breath; this could be because of limitations of
available concentration X, or volume of inspired gas or both.
Mandatory constraints are at least those inherent in any method of
controlling the end tidal partial pressure of a gas X by way of
inhalation of concentrations of gas X in that F.sub.IX cannot be
less 0% and greater than 100% for any given breath. Constraints may
also be selected as a matter of operational necessity or
efficiency--so called "operational constraints" which may be
self-imposed but not mandatory in all cases. For example,
practically speaking, it may be inadvisable for safety reasons to
administer a gas X (especially where gas X Is not oxygen) in the
highest feasible concentrations due to patient safety risks
accompanying failure of the system. Accordingly, for safety reasons
it may be advisable for a component gas comprising gas X to have at
least 10% oxygen thereby defining an optional logistical limit of
the method. Therefore what is logistically achievable is understood
to be operationally limited by the composition of all the gas
sources to which the apparatus is connected at any point in time.
Furthermore, as described below, sequential gas delivery is
typically effected by delivering a gas of a first composition
followed by a neutral gas. The rate of flow and hence volume of the
first gas generally controlled to within certain parameters so that
the second gas at least fills the anatomic dead space. This is
operationally mandatory in the sense that not all values for this
parameter are workable, especially if a medically relevant target
end tidal partial pressure of gas X is sought lo be achieved in one
breath as opposed to incrementally over several breathes. What is
logistically attainable will be dictated by the extant rate of
flow, if unvaried, or liveried, by the range of logistically
practicable rates of flow. Hence, what is logistically attainable
may be tied to independently controlled parameters which may or may
not be varied. Hence, some of these operational parameters may be
mandatory in a particular context or in a universal sense (running
the system so that it always works without reset e.g, recalculation
of prospectively calculated F.sub.IX values for a dynamic set of
breaths of interest if the tidal volume falls outside established
controls.
[0140] According to one embodiment of the method, the model of gas
dynamics that is used to predict C.sub.MVX[i] in the mixed venous
blood entering the subject's lung for gas exchange in the
respective breath [i] estimates a value of C.sub.MVX[i]) by: (a)
dividing tissues to which the subject's arterial blood circulates
into one or more compartments (k): and (b) determining the
contribution of a respective compartment to the mixed venous
content of gas X as a function of the production or consumption of
gas X in the respective compartment, the assigned storage capacity
for gas X in the respective compartment and the contribution of
blood flow from the respective compartment to the total cardiac
output or pulmonary blood flow. For example, where gas X is carbon
dioxide the content of carbon dioxide in the mixed venous blood
leaving a compartment C.sub.vCO2.sub.k[i] is determined by
assigning to a compartment a fraction of the overall metabolic
carbon dioxide production (vco2.sub.k), a fraction of the total
cardiac output (q.sub.k) and a storage capacity for carbon dioxide
(dCO2.sub.k).
[0141] In contrast to a negative feedback system, the
afore-described system is a prospective end-tidal targeting system.
Prior to execution of an end-tidal targeting sequence, the tissue
model is used to predict the time course of the mixed-venous blood
gases that will result from ideal execution of the sequence.
[0142] The time course of predicted mixed-venous gases is used to
compute the series of inspired gas mixtures required to realize the
target end-tidal partial pressures of gases. In this way, assuming
that the end-tidal partial pressures of gases adhere to the targets
allows prediction of the mixed-venous gases, and prediction of the
mixed-venous gases allows a priori calculation of the inspired gas
mixtures required to accurately implement the end-tidal targets.
There is no requirement to modify the series of the inspired gas
mixtures calculated before execution of the sequence based on
deviations of the measured end-tidal partial pressures of gases
from the targets during execution of the sequence.
[0143] Instead, the system is tuned to obtain tuned values for
certain parameters before execution of the sequence so that the
end-tidal partial pressures of gases induced during sequence
execution closely adhere to the target functions without the need
for any feedback control. Optionally, the program code includes
code for directing a suitable gas delivery device such as a rapid
flow controller to deliver a gas X containing gas having an
F.sub.IX output from a mass balance equation. The term "gas
delivery means" by contrast to gas delivery device refers to a
discrete component of a gas delivery device that is used to control
the volume of gas delivered at a particular increment in time such
as a rapid Now controller.
[0144] It will be appreciated that each of the key method steps for
carrying out the invention can be functionally apportioned to
different physical components or different computer programs and
combinations of both. Furthermore a device according to the
invention will optionally comprise one or more physical components
in the form of a gas analyzer, a pressure transducer, a display, a
computer, a gas delivery device such as a rapid flow controller, a
gas channeling means (gas conduits/tubes), standard electronic
components making up a PCB, input devices for setting parameters
etc. The various means for carrying out these steps include without
limitation one in the same physical means, or different physical
means on different devices, the same device or the same device
component. Depending on the number of added gases these components
may multiplied or where possible shared.
[0145] In another aspect, the present invention is also directed to
a device comprising an integrated circuit chip configured for
carrying out the method, or a printed circuit board (comprising
discrete or integrated electronic components). The device
optionally Includes at least one gas delivery means such as a rapid
flow controller. The device optionally includes an input device for
inputting various parameters described herein. The parameters can
be input via a variety of means including, but not limited to, a
keyboard, mouse, dial, knob, touch screen, button, or set of
buttons.
[0146] It is understood that any input, computation, output, etc.
described herein can be accomplished by a variety of signal
processing means including, but not limited to, a programmable
processor, a programmable microcontroller, a dedicated integrated
circuit, a programmable integrated circuit, discrete analog or
digital circuitry, mechanical components, optical components, or
electrical components. For example, the signal processing steps
needed for executing the inputs, computations and outputs can
physically embodied in a field programmable gate array or an
application specific integrated circuit,
[0147] The term "blending" may be used to describe the act of
organizing delivery of one gas in conjunction with at least one
other and hence the term blending optionally encompasses physical
blending and coordinated release of individual gas components.
[0148] The term "computer" is used broadly to refer to any device
(constituted by one or any suitable combination of components)
which may be employed in conjunction with discrete electronic
components to perform the functions contemplated herein, including
computing and obtaining input signals and providing output signals,
and optionally storing data for computation, for example
inputs/outputs to and from electronic components and application
specific device components as contemplated herein. As contemplated
herein a signal processor or processing device in the form of a
computer may use machine readable instructions or dedicated
circuits to perform the functions contemplated herein including
without limitation by way of digital and/or analog signal
processing capabilities, for example a CPU, for example a dedicated
microprocessor embodied in an IC chip which may be integrated with
other components, for example in the form of a microcontroller. Key
inputs may include input signals from--a pressure transducer, a gas
analyzer, any type of input device for inputting a target end tidal
partial pressure of gas X (for example, a knob, dial, keyboard,
keypad, mouse, touch screen etc.), input from a computer readable
memory etc. Key outputs include output of the flow and/or
composition of gas required to a flow controller.
[0149] For example of a compartmental model for mixed venous blood
carbon dioxide dynamics may assign body tissues to k compartments
e.g. 5 compartments and assign the contribution of a respective
compartment to the mixed venous content of carbon dioxide as a
function of the production of carbon dioxide in the respective
compartment, the assigned storage capacity for carbon dioxide in
the respective compartment and the contribution of blood flow from
the respective compartment to the total cardiac output.
[0150] In one aspect, the present invention is directed to a
non-transitory computer readable memory device having recorded
thereon computer executable instructions for carrying out one or
more embodiments of the above-identified method. The invention is
not limited by a particular physical memory format on which such
instructions are recorded for access by a computer. Non-volatile
memory exists in a number of physical forms including non-erasable
and erasable types. Hard drives, DVDs/CDs and various types of
flash memory may be mentioned. The invention, in one broad aspect,
is directed to a non-transitory computer readable medium comprising
computer executable instructions for carrying out one or more
embodiments of the above-identified method. The instructions may
take the form of program code for controlling operation of an
electronic device, the program code including code for carrying out
the various steps of a method or control of an apparatus as defined
above.
[0151] A "gas delivery device" means any device that can make a gas
of variable/selectable composition available for inspiration. The
gas delivery apparatus may be used in conjunction with a ventilator
or any other device associated with a breathing circuit from which
the subject is able to inspire a gas of variable/controllable
composition without substantial resistance. Preferably, the
composition of the gas and/or flow rate is under computer control.
For example, such a device may be adapted to deliver at least one
gas (pure or pre-blended) at a suitable pre-defined rate of flow.
The rate of flow may be selectable using a form of input device
such a dial, lever, mouse, key board, touch pad or touch screen.
Preferably the device provides for one or more pure or blended
gases to be combined i.e. "a gas blender".
[0152] A "gas blender" means a device that combines one or more
stored (optionally stored under pressure or delivered by a pump)
gases in a pre-defined or selectable proportion for delivery a
selectable rate of flow, preferably under computer control. For
example or more stored gases may be combined with pumped room air
or a combination of pure or blended (each blended gas may have at
least 10% oxygen for safety) gases respectively contain one of
carbon dioxide, oxygen and nitrogen as the sole or predominant
component. Optionally, the selectable proportion is controlled
automatically using an input device, optionally by variably
controlling the flow of each stored gas (pure or pre-blended)
separately, preferably using rapid flow controllers, to enable
various concentrations or partial pressures of a gas X to be
selected at will within a pre-defined narrow or broad range. For
example, a suitable blender may employ one or more gas reservoirs,
or may be a high flow blender which blows gas past the mouth i.e.
in which gas that is not inspired is vented to the room.
[0153] A "partial rebreathing circuit" is any breathing circuit in
which a subject's gas requirements for a breath are made up in part
by a first gas of a selectable composition, and a rebreathed gas to
the extent that the first gas does not fully satisfy the subject's
volume gas requirements for the breath. The first gas must be
selectable in at least one of composition or amount. Preferably the
amount and composition of the first gas is selectable. The
rebreathed gas composition optionally consists of previously
exhaled gas that has been stored or a gas formulated to have the
same concentration of gas X as previously exhaled gas or a second
gas has a gas X concentration that is selected to correspond (i.e.
has the same concentration) as that of the targeted end tidal gas
composition for a respective breath [i].
[0154] Preferably the circuit is designed or employable so that the
subject receives the entirety of or a known amount of the first gas
in every breath or in a consecutive series of breaths forming part
of gas delivery regimen. In a general sense a re-breathed gas
serves a key role in that it does not contribute significantly to
the partial pressure gradient for gas flow between the lung and the
pulmonary circulation when intake of the gas at least fills the
entirety of the anatomic dead spar. Therefore, in the case of a
spontaneously breathing subject (whose tidal volume is not
controlled e.g. via a ventilator) the subject's unpredictable tidal
volume does not defeat prospective computation of the controlled
gas composition required to attain or target PetX[i] for a
respective breath [i].
[0155] Optionally, the "rebreathed gas" may be constituted by or
substituted by a prepared gas (in terms of its gas X content).
Thus, according to one embodiment of the invention, the second gas
has a gas X concentration that is selected to correspond to that of
the targeted end tidal gas composition for a respective breath [i].
The volume of the first inspired gas may also be adjusted (e.g.
reduced) to target PetX[i].sup.T for a respective breath [i] such
that the subject receives an optimal amount of a gas having a gas X
concentration that corresponds to PetX[i].sup.T.
[0156] As alluded to above, it will be appreciated that the gas X
content of a prepared gas can be formulated to represent a gas of a
"neutral" composition. Thus the total inspired gas for a respective
breath [i] will comprise a first inspired gas having a controlled
volume and gas X concentration (F.sub.IX) and a second gas which
has a gas X content whose contribution to establishing a partial
pressure gradient between the lung and pulmonary circulation is
optionally minimized. In a broader sense, the second inspired gas
content of gas X can be optimized to attain a targeted end tidal
concentration (for a universal set of circumstances) and in a
sub-optimal sense this concentration at least does not defeat the
ability to prospectively compute an F.sub.IX for the purposes of
attaining or targeting a PetX[i] for a respective breath [i] (i.e.
not knowing the subject's tidal volume for a respective breath [i]
will not preclude such computation).
[0157] "Prospectively" or a "prospective computation" means, with
reference to a determination of an amount of gas X required to be
inspired by the subject in an inspired gas to attain or target a
PetX[i].sup.T for a respective breath [i] (optionally computed in
terms of F.sub.IX), using inputs required to compute a mass balance
equation (preferably including C.sub.MVX[i]), without necessary
recourse to feedback to attain rapidly and repeatably. In contrast,
to a negative feedback system, which relies on ongoing measurements
of PetX[i] to provide feedback for continually adjusting computed
F.sub.IX values to minimize the discrepancy between target and
measured PetX[i] values, the system of the present invention is
adapted to attain logistically achievable end tidal values rapidly
and accurately (as defined herein) without recourse to feedback. As
discussed herein, a negative feedback system suffers from an
inherent trade-off between response time and stability. According
to the present invention, recourse to feedback is designed to be
unnecessary for the purpose of attaining logistically achievable
PetX targets rapidly and predictably.
[0158] Of further consideration are the delays associated with
measurement of the end-tidal partial pressures of gases which are
required for feedback into the system. Gas composition analysis is
performed by continuously drawing gas from proximal to the
subject's airway into a gas analyzer through a sampling catheter.
The gas analyzer returns a time varying signal of gas composition
which is, however, delayed from the actual ventilatory phase of the
subject by the travel time through the sampling catheter and the
response time of the gas analyzer. Therefore, at the start of any
inspiration, the end-tidal partial pressures of gases from the
immediately previous breath are not yet known. Where the sampling
catheters are long, such as in an MRI environment where the patient
is in the MRI scanner and the gas analyzers must be placed in the
control room, this delay can reach three or more breaths. As in any
negative feedback system, this delay in measuring the controlled
parameter will further destabilize and limit the response time of
the system.
[0159] A "sequential gas delivery device" means, with respect to
delivering a gas in successive respective breaths [i], a device for
delivery of a controlled gas mixture in the first part of a
respective breath [i] followed by a "neutral" gas in the second
part of the respective breath [i]. A controlled gas mixture is any
gas that has a controllable composition with respect to one or more
gases of interest used to compose it. Accordingly, where the gas of
interest is a gas X, the controlled gas mixture has an amount of
gas X, optionally defined in terms of a concentration of gas X
denoted as F.sub.IX. The controlled gas mixture may be referred to,
for convenience, as a first inspired gas. Gas inspired in any
breath is "neutral", inter alia, if it has the same composition as
gas expired by the subject in a previous breath. The term "neutral"
gas is used because the gas in question is one which has the same
partial pressure of one or more gases of interest as the blood, in
the alveoli, or in the pulmonary capillaries, and hence, upon
inspiration'into the alveolar space, in the second part of a
respective breath, this gas does not exchange any gas with the
pulmonary circulation. Unless otherwise defined explicitly or
implicitly a gas of interest is generally one for which the end
tidal partial pressure is sought to be controlled according to the
invention.
[0160] A volume of gas that enters the alveolar space and exchanges
gas with the pulmonary circulation for a breath [i] may be defined
independently of a fixed tidal volume, for example by: [0161] a.
setting the rate of flow of a controlled gas mixture (also termed
fresh gas flow rate) in a rebreathing circuit to be less than the
patient's minute ventilation or minute ventilation minus anatomic
dead space ventilation (i.e. such that the last inspired second gas
at least fills the anatomical dead space if not also part of the
alveolar space); [0162] b. obtaining input of the rate of flow or
volume of the controlled gas mixture into the circuit for the
respective breath (this rate can be maintained from breath to
breath or varied) and computing the effective volume of alveolar
gas exchange for the respective breath based on the rate of fresh
gas flow for the respective breath.
[0163] According to one embodiment, the rebreathing circuit is a
sequential gas delivery circuit.
[0164] According to another embodiment, volume of gas that enters
the alveolar space and exchanges gas with the pulmonary circulation
is determined by utilizing a fixed tidal volume set for the
respective breath (e.g. using a ventilator) and subtracting a
volume corresponding to the subject's anatomic dead space
volume.
[0165] The F.sub.IX may be set independently of the concentration
of any other component of the inspiratory gas.
[0166] Optionally, a gas X and a gas Y are components of the
inspired gas and a target arterial concentration of gas X and a
target arterial concentration of a gas Y are selected for a
respective breath, independently of each other, and, if present,
independently of the concentration of any other component Z of the
inspiratory gas.
[0167] A mass balance equation that comprises terms "corresponding
to" all or an application-specific subset of the terms in equations
1 or 2 above means that the same underlying parameters are
accounted for.
[0168] According to one aspect of the invention (which may be
implemented in connection with any one or more of compatible
embodiments of the invention defined hereinabove), the invention is
directed to an apparatus for controlling an amount of at least one
gas X in a subject's lung to attain a series of targeted end tidal
partial pressures of at least one gas X (PetX.sup.T), the series of
targeted end tidal partial pressures of at least one gas X
(PetX.sup.T) adapted to stimulate a physiological response, the
apparatus comprising: [0169] (1) a gas delivery device; [0170] (2)
a control system for controlling the gas delivery device, wherein
the control system is adapted to target a series of PetX.sup.T
values for a respective series of intervals, the control system
including means for: [0171] a. Obtaining input of a series of
logistically attainable PetX.sup.T values for the series of
respective intervals; and [0172] b. Determining an amount of gas X
required to be inspired by the subject in an inspired gas to target
the PetX.sup.T for a respective interval: [0173] c. Controlling the
amount of gas X in a volume of gas delivered to the subject in a
respective interval to target the respective PetX.sup.T for the
interval.
[0174] The series of PetX.sup.T values preferably comprise at least
one of a set of PetX.sup.T. increments and a set of PetX.sup.T
decrements.
[0175] The term "interval" is used broadly to mean a time interval
of selected length, an interval defined by the duration of a
respective inspiratory cycle and a previous or ensuing expiratory
cycle, for example, a respective breath [i] defined by an
inspiratory cycle and the expiratory cycle which follows it, and/or
an interval defined by a pattern of a physiological response. The
term `pattern of a physiological response` means a pattern
sufficient to define a dose-response (stimulus-response)
relationship for a full range of the physiologic response or for at
least a part thereof that reveals a pattern of interest, wherein
the increments in dose or stimulus are selected to disclose the
true shape of the dose response curve. A portion of interest may of
diagnostic or medical interest to define a normal pattern of the
response for example to differentiate between variations in a
normal response for different groups e.g. ages, and optionally a
differential response e.g. particular range or prevalence of a
response or a different or pathologic response, associated with a
condition or disease. For example, a pattern may disclose a linear,
exponential or sigmoidal dose response curve for an individual or
group of common individuals selected from at least one of persons
having a `normal` physiological response and persons disclosing a
different or pathological physiological response. For example, a
pattern may disclose that a response is sigmoidal and not linear
(e.g. it is only linear over a certain range of the stimulus) when
a fuller range of the response is probed using a suitable range and
series of smaller changes in stimulus. For example, an interval of
diagnostic interest may be a fraction of the amount of time
required to observe the time course of the response wherein the
fraction is sufficiently small to obtain a set of values defining
the pattern of response. The ramp sequence may also be selected to
determine a time course of a full or partial range of a
physiological response by tracking signals signifying that a
particular condition, associated with a direct o indirect measure
of the response, has been met, the condition preferably of the type
satisfied by attainment or projected attainment of a threshold
amount change in a measurable parameter correlated with a
physiologic response to a stimulus comprising or consisting of an
increment or decrement in a subject's end tidal partial pressure of
gas X. A fraction or proportionate amount of a time period required
to observe a continuous time course of a physiological response or
satisfy a set threshold amount of change in the response (attained
or predicted to be attained based on a known or predictable
mathematical relationship between the stimulus--an increment or
decrement in PetX--and a measurable parameter that defines the time
course of the response), is then defined to be sufficient to
demarcate the end of a previous interval and the beginning of a
next ensuing interval. The time course may be selected to grade
individuals in terms of the overall appearance of the pattern
(measurement of a continuous variable) or differentiate between
populations with respect satisfying one or more individual criteria
(e.g. a discontinuous variable eliciting a yes/no answer).
[0176] A gas delivery device can be controlled to attain a series
of targeted end tidal partial pressures of at least one gas X
(PetX.sup.T) by the prospective model described herein; or by a
combination of a prospective model and feedback control (known as
dynamic end tidal forcing), for example, wherein the feedback loop
(e.g. using a PID controller) adds a control signal to adjust a
prospective determination of F.sub.IX; the control signal generated
based on the difference between the target and measured end tidal
values. Computation of FIX can be accomplished using the tidal
model equations herein by adapting the continuous flow equations
published by Robbins and Swanson.
[0177] According to one aspect of the invention (which may be
implemented in connection with any one or more of compatible
embodiments of the invention defined hereinabove), the invention is
directed to a method of controlling an amount of at least one gas X
in a subjects lung to attain at least one targeted end tidal
partial pressure of the at least one gas X, comprising the steps
of: [0178] a. Obtaining input of a logistically attainable end
tidal partial pressure of gas X (PetX[i].sup.T) for a series of
respective breaths [i]; [0179] b. Obtaining input of a prospective
computation of an amount of gas X required to be inspired by the
subject in art inspired gas to target the PetX[i].sup.T for a
respective breath [i] using inputs required to compute a mass
balance equation, wherein one or more values required to control
the amount of gas X in a volume of gas delivered to the subject is
output from the mass balance equation; and optionally [0180] c.
Controlling the amount gas X in a volume of gas delivered to the
subject in a respective breath [i] to target the respective
PetX[i].sup.T based on the prospective computation;
[0181] and wherein the respective PetX[i].sup.T for the series of
breaths [i] increases or decreases from the start of the series to
the end of the series (from PetX[i.sup.1].sup.T to
PetX[i.sup.n].sup.T) in accordance with a ramp sequence (as defined
below).
[0182] Optionally, the respective PetX[i].sup.T for the series of
breaths [i] increases every Nth breath in respective selected
increments ("Z") from the start of the series to the end of the
series (from PetX[i.sup.1].sup.T to PetX[i.sup.n].sup.T), wherein
either N equals 1 and Z is greater than 0 in each breath in the
series, or N is greater than 1 and Z may be zero in breaths which
arc not the Nth breath and Z is greater than 0 in every Nth
breath.
[0183] Optionally, the respective PetX[i].sup.T for the series of
breaths [i] decreases every Nth breath in respective selected
decrements (T) from the start of the series to the end of the
series (from PetX[i.sup.1].sup.T to PetX[i.sup.n].sup.T), wherein
either N equals 1 and Z is greater than 0, or N is greater than 1
and Z may be zero in breaths which are not the Nth breath and Z is
greater than 0 in every Nth breath
[0184] Accordingly, PetX[i].sup.T may change every Nth breath in
respective selected increments or decrements ("Z") from the start
of the series to the end of the series (from PetX[i.sup.1].sup.T to
PetX[i.sup.n].sup.T), wherein N equals 1 and Z is greater than 0.
In another embodiment, N is greater than 1 and Z may be zero in
breaths which are not the Nth breath.
[0185] Embodiments in which PetX[i.sup.1].sup.T increases include
the following. In one embodiment, "Z" is greater 0 and is the same
in each breath in the series (N=1). For example, N may equal 1 and
"Z" may equal 8. Therefore, for example, a target end tidal oxygen
concentration may increase every breath (N=1) from [i].sup.1 to
[i].sup.n from PetX[i.sup.1].sup.T=100 mm Hg to
PetX[i.sup.n].sup.T=180 mm Hg over the course of the next 10
contiguous breaths (respective targets in mm of Hg=108, 116, 124,
132, 140, 148, 156, 164, 172, 180). As another example, N may equal
5 and same end tidal target value may be maintained at the same
target for the 4 breaths in between each 5.sup.th breath such that
it would take approximately 50 breath to span the same range of end
tidal targets from [i].sup.1=PetX[i.sup.1].sup.T=100 mm Hg to
[i].sup.50=PetX[i.sup.50].sup.T=180 mm Hg. This same sequence may
be expressed another way i.e. Z is changing and for the series of
fifty breaths as follows: Z equals, respectively 0, 0, 0, 0, 8, 0,
0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0,
0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8 0, 0, 0, 0,
8.
[0186] In one embodiment, Z is selected to correspond to a selected
rate of change in a physiological response to a stimulus (the
stimulus being a correlate of PetX[i].sup.T such as the arterial
partial pressure of gas X (PaX)). The selected rate of change
corresponds to a rate wherein a targeted physiologic response is
substantially realized for each increment/decrement before the next
increment/decrement, such that successive measurements of the
response are substantially matched to an increment/decrement in a
change in stimulus. Accordingly, it is possible to plot the change
in response with respect to the change in PetX[i].sup.T with
substantial accuracy. For example, where the time course of the
response of a physiologic parameter is exponential, the rate of
change in PetX[i].sup.T may be selected such that three time
constants in the progress of the response (approximately 95%
response) are achieved before the next increment/decrement in
PetX[i].sup.T stimulus is given. A time interval for executing the
range in stimulus "R" or the range (extent) of the expected
response "r" may be selected and the target change per breath in
stimulus readily mathematically determined. For example, with
respect to ramping up PetCO.sub.2[i].sup.T from 35 to 50 mm of Hg
over a selected time period (e.g. approx. 5 minutes) increasing
PetCO.sub.2[i].sup.T approx. 0.25 mm Hg every breath may define a
suitable ramp sequence. Optionally, this rate may be corroborated.
Corroboratively, a greater than 95% CVR response to a change in
PaCO.sub.2 may be determined to be achieved in 16-18 seconds. Thus
increments of 1 mm of Hg every 16 second would be suitable.
Assuming a subject inhales 15 times per minute (1 breath every 4
seconds, this corresponds to 0.25 mm of Hg every breath.
Accordingly, according to one embodiment of the invention,
optionally, the time interval over which the response is measured
and the range of change in stimulus range may be input to
facilitate execution of a ramp sequence so that a series of
PetCO.sub.2[i].sup.T targets for the intervening breaths may be
correspondingly obtained.
[0187] Optionally, with respect to increases in
PetCO.sub.2[i].sup.T, N is advantageously 1, 2 or 3 breaths,
optionally 1 breath, and Z is the optionally the same for each
increase, depending on the total time interval for executing the
range In stimulus Z or desired response range optionally ranging
from 0.2 to 2 mm Hg. Optionally, with respect to increases in
PetO2[i].sup.T N is advantageously 1 to 5, optionally 1, and Z is
the optionally the same for each increase, Z ranging from 1 to 20
mm Hg. Simply by way of example, PetO.sub.2[i].sup.T may be
increased every Nth breath wherein N=1 and Z=8 for each successive
breath in the series e.g. ranging from 100 mm Hg to 350 mm Hg)
while PetCO2[i].sup.T is maintained constant, In another
embodiment, PetCO2[i].sup.T is increased each Nth breath e.g. from
35 mm Hg to 50 mm Hg (N=1, Z=0.25 for each successive breath in the
series) while PetO.sub.2[i].sup.T is maintained constant.
[0188] Advantageously, as regards such sequences, where the targets
are increased or decreased at a rate selected for observing a
substantial response to an increment or decrement in stimulus
(termed a "ramp sequence"); e.g. with respect to an exponential
response, optionally at least a response corresponding to two time
constants, optionally at least a 90-95% response or a response
corresponding to three time constants, optionally approximately
linearly with respect to time, the response (e.g. CVR) to a change
in the end tidal concentration of gas X e.g, carbon dioxide, is
substantially achieved within a given time increment e.g. spanning
4 breaths, and is optionally plotted (measurement may be more
frequent) approximately every 4 breaths, in contrast to making the
change in stimulus in one step, ideally, in one breath, in which
case, the continuous plotting of the response reveals the time
course of the response to the stimulus.
[0189] Accordingly the invention is also directed to an apparatus
for controlling an amount of at least one gas X in a subject's lung
to attain a targeted end tidal partial pressure of the at least one
gas X, comprising: [0190] (1) a gas delivery device; [0191] (2) a
control system for controlling the gas delivery device including
means for: [0192] a. Obtaining input of a concentration of gas X in
the mixed venous blood entering the subject's pulmonary circulation
for gas exchange in one or more respective breaths [i]
(C.sub.MVX[i]); [0193] b. Obtaining input of a logistically
attainable end tidal partial pressure of gas X (PetX[i].sup.T) for
a respective breath [i]; [0194] c. Obtaining input of a prospective
computation of an amount of gas X required to be inspired by the
subject in an inspired gas to target the PetX[i].sup.T for a
respective breath [i] using inputs required to compute a mass
balance equation including C.sub.MVX[i], wherein one or more values
required to control the amount of gas X in a volume of gas
delivered to the subject is output from the mass balance equation;
and [0195] d. Controlling the amount of gas X in a volume of gas
delivered to the subject in a respective breath [i] to target the
respective PetX[i].sup.T based on the prospective computation; and
optionally [0196] e. Inputting values for execution of a ramp
sequence (optionally via means for setting a cumulative time
interval for measuring the response and a range of the stimulus or
response to be canvassed, or optionally an increment or decrement Z
(in the example above 025 mm of Hg) for each a series of respective
breaths [i].sup.1 to [i].sup.n, and optionally N.
[0197] N may be fixed at 1 in which case Z will be greater than 0
or or N is greater than 1 and Z may be zero in breaths which are
not the Nth breath and Z is greater than 0 in every Nth breath.
BRIEF DESCRIPTION OF THE FIGURES
[0198] The invention will now be described with reference to the
figures, in which:
[0199] FIG. 1 is a schematic overview of the movement of blood and
the exchange of gases throughout the entire system.
[0200] FIG. 2 is a detailed schematic representation of the
movement of blood and the exchange of gases at the tissues.
[0201] FIG. 3 is a detailed schematic representation of the
movement of blood and the exchange of gases at the lungs when
sequential rebreathing is not employed.
[0202] FIG. 4 is a detailed schematic representation of the
movement of blood and the exchange of gases at the lungs when
sequential rebreathing is employed.
[0203] FIG. 5 is a schematic diagram of one embodiment of an
apparatus according to the invention that can be used to implement
an embodiment of a method according to the invention.
[0204] FIG. 6 is a graphic representation of a tuning sequence and
observed errors that can be used to tune model parameters.
[0205] FIG. 7 is a Table of abbreviations (Table 1) used in the
specification
[0206] FIGS. 8a arid 8b are graphical representations of changes in
target end tidal values of CO2 and response--mid-cerebral artery
blood flow velocity, for a slow responder and a fast responder as
revealed by a ramp sequence.
[0207] FIG. 9 is a graphical representation of blood flow responses
to PCO.sub.2 predicted for the model of a brain vascular territory
with a partially-stenosed vessel branch and a healthy branch in
parallel as revealed by a ramp sequence.
[0208] FIG. 10 is a graphical representation of a bold signal
response to PCO.sub.2 as revealed by a ramp sequence and
corresponding CVR maps for an axial slice at different PetCO2
ranges for a patient with moya moya disease.
[0209] FIG. 11 is a table showing a partial raw data set for 6
subjects according to Example 1.
DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT
[0210] The invention is described hereafter in terms of one or more
optional embodiments of a gas X, namely carbon dioxide and
oxygen.
Prospective Modelling
[0211] Mass balance equations of gases in the lung are
conventionally derived from a continuous flow model of the
pulmonary ventilation. In this model, ventilation is represented as
a continuous flow through the lungs, which enters and exits the
lungs through separate conduits. As a consequence, for example, the
anatomical dead space would not factor into the mass balance other
than to reduce the overall ventilatory flow into the alveolar
space. In reality, however, ventilation in humans is not
continuous, but tidal. Gas does not flow through the lungs, but
enters the lungs during a distinct inspiration phase of the breath
and exits during a subsequent expiration phase of the breath. In
each breath cycle, gas is inspired into the lungs via the airways
and expired from the lungs via the same airways through which gas
was inspired. One possible implication, for example, is that the
first gas inspired into the alveolar space in any breath is
residual gas which remains in the anatomical dead space following
the previous expiration. Continuous flow models neglect the
inspiration of residual gas from the anatomical dead space, and
therefore, since accounting for such a factor is generally
desirable, do not accurately represent the flux of gases in the
lungs.
[0212] As continuous flow models of pulmonary ventilation do not
correctly represent the flux of gases in the lungs, the end-tidal
partial pressures of gases induced from the inspiration of gas
mixtures computed from such a model will, necessarily, deviate from
the targets.
[0213] By contrast, according to one aspect of the present
invention, a mass balance equation of gases in the lungs is
preferably formulated in terms discrete respective breaths [i]
including respective discrete volumes corresponding to one or more
of the FRC, anatomic dead space, the volume of gas X transferred
between the pulmonary circulation and the lung in a respective
breath [i] and an individual tidal volume of a respective breath
[i]) is adaptable to account, for example, for inspiration of
residual gas from the anatomical dead space into the alveolar space
in each breath. Inasmuch as a tidal model more faithfully
represents the actual flux of gases in the lungs compared with the
conventional model, the induced end-tidal partial pressures of
gases, to an extent that the model is fully exploited, it will more
closely adhere to the targets compared with results achieved using
a continuous flow model.
[0214] Moreover, we have found that using a tidal model of
pulmonary ventilation, can be synergistically employed with a
sequential gas delivery system to facilitate closer adherence to
targets in both ventilated and spontaneously breathing subjects
without reliance on a negative feedback system.
[0215] According to the present invention, a prospective
determination of pulmonary ventilation and gas exchange with the
blood can efficiently exploited even in spontaneously breathing
subjects where the ventilatory parameters are highly variable and
difficult to measure.
[0216] Where mechanical ventilation is employed, a prospective
model of pulmonary ventilation and gas exchange with the blood
envisages that the subject's ventilatory parameters can be
estimated or measured to a level of accuracy sufficient to employ
prospective control of the end-tidal partial pressures of one of
more gases.
[0217] According to one embodiment of the invention, a technique of
inspiratory gas delivery, sequential rebreathing, which, when using
a tidal model of the pulmonary ventilation, significantly reduces
or eliminates the dependence of the calculation of the inspired gas
composition to be delivered in each breath, and therefore the
actual end-tidal partial pressures of gases induced, on the
subject's ventilatory parameters.
[0218] In parallel to what we have observed from studies with
respect to the subject's ventilatory parameters, we have found that
when we run a set of standardized tuning sequences, our model of
the tissues more accurately reflects the actual dynamics of the gas
stored in the subject's tissues.. The model parameters may be
refined until the end-tidal partial pressures of gases induced by
execution of the tuning sequences sufficiently adhere to the
targets without the use of any feedback control.
Sequential Gas Delivery
[0219] Sequential rebreathing is a technique whereby two different
gases are inspired in each breath--a controlled gas mixture
followed by a "neutral" gas. A controlled gas mixture is any gas
that has a controllable composition. Gas inspired in any breath is
neutral if it has the same composition as gas expired by the
subject in a previous breath. Neutral gas is termed as such since
it has substantially the same partial pressures of gases as the
blood in the pulmonary capillaries, and hence, upon inspiration
into the alveolar space, does not substantially exchange any gas
with the pulmonary circulation. Optionally, the rebreathed gas has
a composition that is selected to correspond (i.e. have the same
gas X concentration as that of) the targeted end tidal gas
composition for a respective breath [i]. It will be appreciated
that a modified sequential gas delivery circuit in which the
subject exhales via a port leading to atmosphere and draws on a
second gas formulated by a second gas delivery device (e.g. a gas
blender) could be used for this purpose, for example where the
second gas is deposited in an open ended reservoir downstream of a
sequential gas delivery valve, for example within a conduit of
suitable volume as exemplified in FIG. 7 of U.S. Pat. No.
6,799,570.
[0220] Sequential rebreathing is implemented with a sequential gas
delivery breathing circuit which controls the sequence and volumes
of gases inspired by the subject. A sequential gas delivery circuit
may be comprised of active or passive valves and/or a computer or
other electronic moans to control the volumes of, and/or switch the
composition or source of, the gas inspired by the subject.
[0221] The controlled gas mixture is made available to the
sequential gas delivery circuit for inspiration, optionally, at a
fixed rate. On each inspiration, the sequential gas delivery
circuit ensures the controlled gas mixture is inspired first, for
example with active or passive valves that conned the subject's
airway to a source of the controlled gas mixture. The supply of the
controlled gas mixture is controlled so that it is reliably
depleted in each breath.
[0222] Once the supply of the controlled gas mixture is exhausted,
the sequential gas delivery circuit provides the balance of the
tidal volume from a supply of neutral gas exclusively, for example
with active or passive valves that connect the subject airway to
the subject's exhaled gas from a previous breath.
[0223] Gas expired in previous breaths, collected in a reservoir,
is re-inspired in a subsequent breath. Alternatively, the
composition of gas expired by the subject can be measured with a
gas analyzer and a gas with equal composition delivered to the
subject as neutral gas,
[0224] During inspiration of the neutral gas and expiration, the
supply of the controlled gas mixture for the next inspiration
accumulates at the rate it is made available to the sequential gas
delivery circuit. In this way, the subject inspires only a fixed
minute volume of the controlled gas mixture, determined by the rate
at which the controlled gas mixture is made available to the
sequential gas delivery circuit, independent of the subject's total
minute ventilation, and the balance of subject's the minute
ventilation is made up of neutral gas.
[0225] Examples of suitable sequential gas delivery circuits are
disclosed in US Patent Application No. 20070062534.
[0226] The fixed availability of the controlled gas mixture may be
accomplished by delivering a fixed flow rate of the controlled
mixture to a physical reservoir from which the subject inspires.
Upon exhaustion of the reservoir, the source of inspiratory gas is
switched, by active or passive means, to neutral gas from a second
gas source, for example a second reservoir, from which the balance
of the tidal volume is provided.
[0227] It is assumed that in each breath the volume of the neutral
gas inspired at least fills the subject's anatomical dead space.
Herein, all of the controlled gas mixture reaches the alveolar
space and any of the neutral gas that reaches the alveolar space
does not exchange gas with the circulation as it is already in
equilibrium with the pulmonary capillary blood.
[0228] Sequential gas delivery circuits may be imperfect in the
sense that a subject will inspire what is substantially entirety a
controlled gas mixture first. However, upon exhaustion of the
supply of the controlled gas mixture, when neutral gas is inspired,
an amount of controlled gas mixture is continually inspired along
with the neutral gas rather than being accumulated by the
sequential gas delivery circuit for the next inspiration (2). The
result is that the subject inspires exclusively controlled gas
mixture, followed by a blend of neutral gas and controlled gas
mixture. As a result of the imperfect switching of gases, a small
amount of the controlled gas mixture is inspired at the end of
inspiration and enters the anatomical dead space rather than
reaching the alveolar space. In practise, the amount of controlled
gas mixture lost to the anatomical dead space is small, and
therefore, the amount of controlled gas mixture that reaches the
alveolar space can still be assumed equal to the rate at which the
controlled gas mixture is made available to the sequential gas
delivery circuit for inspiration. Therefore, the method described
herein can be executed, as described, with imperfect sequential gas
delivery circuits.
[0229] A simple implementation of sequential rebreathing using a
gas blender and passive sequential gas delivery circuit is
described in references cited below (2; 3). Other implementations
of sequential gas delivery are described in patents (4-8).
[0230] The contents of all references set forth below are hereby
incorporated by reference,
[0231] Various implementations of sequential gas delivery have
described by Joseph Fisher et al, in the scientific and patent
literature.
[0232] As seen FIG. 1, which shows a high level overview of the
movement of blood and the exchange of gases throughout the entire
system, the majority of the total blood flow (Q) passes through the
pulmonary circulation. Upon transiting the pulmonary capillaries,
the partial pressures of gases in the pulmonary blood equilibrate
with the partial pressure of gases in the lungs (P.sub.RT[i])--the
result is partial pressures of gases in the pulmonary end-capillary
blood equal to the end-tidal partial pressures of gases in the
lungs. The blood gas contents of this blood (C.sub.p[i]) can then
be determined from these partial pressures. The remaining fraction
(s) of the total blood flow is shunted past the lungs and flows
directly from the mixed-venous circulation into the arterial
circulation without undergoing any gas exchange. Therefore, the gas
contents of the arterial blood (C.sub.a[i]) are a flow weighted
average of the pulmonary end-capillary blood with gas contents
equilibrated to that of the lungs, and the shunted blood with gas
contents which are equal to the mixed-venous blood entering the
pulmonary circulation (C.sub.MV[i]). The arterial blood flows
through the tissue capillary beds, where gases are exchanged
between the blood and the tissues. There are one or more tissue
capillary beds, each of which receives a fraction of the total
blood flow (q) and has unique production, consumption, storage, and
exchange characteristics for each gas. The gas contents in the
venous blood leaving each tissue (C.sub.v[i]) can be determined
from these characteristics. The gas contents of the mixed-venous
blood leaving the tissues (C.sub.MV(TG)[i]) are given by the flow
weighted average of the gas contents in the venous blood leaving
each tissue. The mixed-venous blood leaving the tissues enters the
pulmonary circulation after the recirculation delay (n.sub.R).
FIG. 2--The Tissues
[0233] As shown in FIG. 2, the total blood flow (Q) enters the
tissue capillary beds from the arterial circulation, where the gas
contents of the arterial blood (C.sub.a[i]) are modified by gas
exchange between the blood and the tissues. To obtain input of the
gas contents of the mixed-venous blood, the flow of blood through
the tissues is modelled as a system of one or more compartments
where each compartment represents a single tissue or group of
tissues. Each compartment is assumed to receive a fraction of the
total blood flow (q) and has a unique production or consumption (v)
of, and storage capacity (d) for, each gas. The content of gases in
the venous blood leaving each compartment (C.sub.v[i]) can be
determined from the arterial inflow of gases, and the assumed
production or consumption, and storage of the gas In the
compartment. The blood flows leaving each compartment unite to form
the mixed-venous circulation. Therefore, the gas contents of the
mixed-venous blood leaving the tissues (C.sub.MV(T)[i]) are given
by the flow weighted average of the gas contents in the venous
blood leaving each tissue.
[0234] FIG. 3--The Lungs (No Sequential Rebreathing)
[0235] As shown in FIG. 3, gas enters the lungs in two
ways--diffusion from the pulmonary circulation and inspiration
though the airways. The pulmonary blood flow is equal to the total
blood flow (Q) less the fraction (s) of the total blood flow that
is shunted past the lungs. The flux rate of gas between the lungs
and the pulmonary blood flow in a breath (VB[i]) is, by mass
balance, the product of the pulmonary blood flow and the difference
between the gas contents of the mixed-venous blood (C.sub.MV[i])
entering the pulmonary circulation and the gas contents of the
pulmonary end-capillary blood (C.sub.p[i]) leaving the pulmonary
circulation.
[0236] The starting volume of the lungs in any breath Is given by
the functional residual capacity (FRC'). This is the gas left over
in the lungs at the end of the previous expiration, and contains
partial pressures of gases equal to the target end-tidal partial
pressures from the previous breath (P.sub.ET[i-1].sup.T). The first
part of inspiration draws gas in the anatomical dead space
(V.sub.p) from the previous breath into the alveolar space. The
partial pressures of gases in this volume are equal to the target
end-tidal partial pressures from the previous breath. Subsequently,
a volume of a controlled gas mixture (VG.sub.1) with controllable
partial pressures of gases P.sub.1[i]) is inspired.
FIG. 4--The Lungs (Sequential Rebreathing)
[0237] As shown in FIG. 4, gas enters the lungs in two
ways--diffusion from the pulmonary circulation and inspiration
though the airways. The pulmonary blood flow is equal to the total
blood flow (Q) less the fraction (s) of the total blood flow that
is shunted past the lungs. f he flux rate of gas between the lungs
and the pulmonary blood flow in a breath VB[i]) is, by mass
balance, the product of the pulmonary blood flow and the difference
between the gas contents of the mixed-venous blood (C.sub.MV[i])
entering the pulmonary circulation and the gas contents of the
pulmonary end-capillary blood (C.sub.p[i]) leaving the pulmonary
circulation.
[0238] The starting volume of the lungs in any breath is given by
the functional residual capacity (FRC). This is the gas left over
in the lungs at the end of the previous expiration, and contains
partial pressures of gases equal to the target end-tidal partial
pressures from the previous breath (P.sub.ET[i-1].sup.T). The first
part of inspiration draws gas in the anatomical dead space
(V.sub.D) from the previous breath into the alveolar space. The
partial pressures of gases in this volume are equal to the target
end-tidal partial pressures from the previous breath. Subsequently,
a volume of a controlled gas mixture (VG.sub.1) with controllable
partial pressures of gases (P.sub.1[i]) is inspired. The average
volume of the controlled gas mixture inspired into the alveoli in
each breath (VG.sub.1) is given by the flow rate of the controlled
gas mixture (FG.sub.1) to the sequential gas delivery circuit
(SGDC) delivered over one breath period (T.sub.B). The balance of
the tidal volume (V.sub.T) is composed of a volume of neutral gas
(VG.sub.2). Where a sequential gas delivery circuit is used that
provides previously expired gas as neutral gas, this volume
contains partial pressures of gases equal to the target end-tidal
partial pressures from the previous breath.
FIG. 5--Apparatus
[0239] As shown in FIG. 5, according to one embodiment of an
apparatus according to the invention, the apparatus consists of a
gas blender (GB), a Hi-OX.sub.SR sequential gas delivery circuit
(SGDC), gas analyzers (GA), a pressure transducer (PT), a computer
(CPU), an input device (ID), and a display (DX). The gas blender
contains three rapid flow controllers which are capable of
delivering accurate mixes of three source gases (SG.sub.1,
SG.sub.2, SG.sub.3) to the circuit. The gases are delivered to the
circuit via a gas delivery tube connecting the outlet of the gas
blender to the inlet of the sequential gas delivery circuit. The
gas analyzers measure the partial pressures of gases at the airway
throughout the breath. The analyzers sample gas for analysis
proximal to the subject's airway via a sampling catheter. A small
pump is used to draw gases from the subjects airway through the gas
analyzers. The pressure transducer is used for measurement of the
breath period (T.sub.B) and end-tidal detection, and also connected
by a sampling catheter proximal to the subject's airway. The gas
analyzers and pressure transducer communicate with the computer via
analog or digital electrical signals. The computer runs a software
implementation of the end-tidal targeting algorithm and demands the
required mixtures from the blender via analog or digital electrical
signals. The operator enters the target end-tidal values and
subject parameters into the computer via the input device. The
display shows the measured and targeted end-tidal gases.
FIG. 6 Tuning
[0240] As illustrated in FIG. 6, with reference to examples of gas
X (oxygen and carbon dioxide) parameters representing inputs for
computation of F.sub.IX can be tuned so that the measured end-tidal
partial pressures of O2 (P.sub.RTO2[i].sup.M) and the measured
end-tidal partial pressures of CO2 (P.sub.FTCO2[i].sup.M) during
any sequence more closely reflect the target end-tidal partial
pressures of O2 (P.sub.ETO2[i].sup.T) and the target end-tidal
partial pressures of CO2 (P.sub.ETCO2[i].sup.T). To tune the system
parameters, standardized tuning sequences are run and the measured
results compared to the targets. The difference between measured
end-tidal partial pressures and the target end-tidal partial
pressures in the standardized tuning sequences can be used to
refine the estimates of some physiological parameters.
[0241] The tuning sequence optionally sets the target end-tidal
partial pressure of O2 (P.sub.FTO2[i].sup.T) at 5 mmHg above the
baseline end-tidal partial pressure of O2 (P.sub.ETO2.sub.0.sup.M)
throughout the sequence, and executes a 5 mmHg step-change in the
end-tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.T) from 5
mmHg above the baseline end-tidal partial pressure of CO2
(P.sub.ETCO2.sub.0.sup.M) to 10 mmHg above the baseline end-tidal
partial pressure of CO2 in breath 30 (i30) of the sequence.
[0242] Embodiments of mass balance equations: [0243] No SGD:
[0243] F 1 .times. X .function. [ i ] = P ET .times. X .function. [
i ] T ( FRC + V T ) - P ET .times. X .function. [ i - 1 ] T ( FRC +
V D ) - PB Q ( 1 - s ) T B ( C MV .times. X .function. [ i ] - C p
.times. X .function. [ i ] ) ( V T - V D ) PB ##EQU00002## [0244]
SGD:
[0244] F 1 .times. X .function. [ i ] = ( P ET .times. X .function.
[ i ] T - P ET .times. X .function. [ i - 1 ] T ) ( FRC + V T ) + P
ET .times. X .function. [ i - 1 ] T ( FG 1 T B ) - PB Q ( 1 - s ) T
B ( C MV .times. X .function. [ i ] - C p .times. X .function. [ i
] ) FG 1 T B PB ##EQU00003##
[0245] Abbreviations and terms are in FIG. 7.
Physiological Inputs
[0246] This section describes how to obtain measurements or
estimates of all the physiological inputs required to execute a
prospective end-tidal targeting sequence.
[0247] Subject weight, height, age, and sex:
[0248] Subject weight (IV), height (if), age (A), and sex (G) can
be obtained from a subject interview, an interview with a family
member, from an attending physician, or from medical records.
Weight and height can also be measured.
Bicarbonate:
[0249] The bicarbonate concentration ([HCO.sub.3]) can be obtained
from a blood gas measurement. If a blood gas measurement is not
available or possible, it can be estimated as the middle of the
normal range--24 mmol/L (9; 10).
Temperature:
[0250] Body temperature (T) can be obtained from a recent invasive
or non-invasive measurement. If a measurement is not available or
possible, it can be estimated as the middle of the normal range--37
C (11; 12).
Haemoglobin Concentration:
[0251] The haemoglobin concentration (Hb) can be obtained from a
blood gas measurement. If a blood gas measurement is not available
or possible, it can be estimated as the middle of the normal range
for the subject's sex (G): [0252] 15 g/dL for males [0253] 13 g/dL
for females (10; 13)
Shunt Fraction:
[0254] The intrapulmonary shunt fraction (s) can be measured using
a variety of invasive and non-invasive techniques (14-17). If
measurement is not available or possible, it can be estimated as
the middle of the normal range--0.05 (18; 19).
Cardiac Output:
[0255] The cardiac output (Q) can be measured using a variety of
invasive and non-invasive techniques (20-23). If measurement is not
available or possible, it can be estimated from the subject's
weight (W) according to the relationship:
Q=10(0.066W+1.4) (24)
Breath Period:
[0256] The breath period (T.sub.B) can be measured using a pressure
transducer (PT) or flow transducer (FT) proximal to the subject's
airway. Alternatively, the subject can be coached to breathe at a
predetermined rate using a metronome or other prompter. If the
subject is mechanically ventilated, this parameter can be
determined from the ventilator settings or ventilator operator.
Recirculation Time:
[0257] The number of breaths for recirculation to occur (n.sub.R)
can be measured using a variety of invasive and non-invasive
techniques (25-27). If measurement is not available or possible, it
can be estimated from the breath period (T.sub.B) and an average
recirculation time (0.3 min) (28) according to the
relationship:
n.sub.R=0.3/T.sub.B
Metabolic O2 Consumption:
[0258] The overall metabolic O2 consumption (VO2) can be measured
using a metabolic cart. If measurement is not available or
possible, it can be estimated from the subject's weight (W), height
(H), age (A), and sex (G) according to the relationship:
V .times. .times. O .times. .times. 2 = 10 W + 625 H - 5 A + 5
6.8832 .times. .times. for .times. .times. males ( 29 ) V .times. O
.times. .times. 2 = 10 W + 625 H - 5 A - 161 6.8832 .times. .times.
for .times. .times. females ##EQU00004##
Metabolic CO2 Production:
[0259] The overall metabolic CO2 production (VCO2) can be measured
using a metabolic cart. If measurement is not available or
possible, it can be estimated from the overall metabolic 02
consumption (VO2) and average respiratory exchange ratio (0.8 ml
CO2/ml O2) (30) according to the relationship:
VCO2=0.8VO2
Functional Residual Capacity:
[0260] The functional residual capacity (FRC) can be measured using
a variety of respiratory manoeuvres (31). If measurement is not
available or possible, it can be estimated from the subjects height
(H), age (A), and sex (G) according to the relationship:
FRC=(2.34H+0.01A-1,09)1000 for males
FRC=(2.24H+0.001A-1. 00)1000 for females (32)
Anatomical Dead Space:
[0261] The anatomical dead space (V.sub.D) can be measured using a
variety of respiratory manoeuvres (33-35). If measurement is not
available or possible, it can be estimated from the subject's
weight (W) and sex (G) according to the relationship:
V.sub.D=1.765W+32.16 for males
V.sub.D=1.913W+21.267 for females (36)
[0262] Rate at which the controlled gas mixture is made available
for inspiration when using a sequential gas delivery circuit
(SGDC)
[0263] When using a sequential gas delivery circuit (SGDC), the
rate at which the controlled gas mixture is made available for
inspiration (FG.sub.1) should be set so that the volume of the
neutral gas inspired in each breath (VG.sub.2) is greater than or
equal to the anatomical dead space (V.sub.D). The subject can be
coached to increase their ventilation and/or the availability of
the controlled gas mixture decreased until a sufficient volume of
the neutral gas is observed to be inspired in each breath.
Tidal Volume:
[0264] The tidal volume (V) can be measured using a flow transducer
(FT) proximal to the subject's airway. If measurement is not
available or possible, in spontaneous breathers when using a
sequential gas delivery circuit (SGDC), it can be estimated from
the rate at which the controlled gas mixture (G.sub.1) is made
available for inspiration (FG.sub.1), the breath period (T.sub.B),
and the anatomical dead space (V.sub.D) according to the empirical
relationship:
If FG.sub.115000: V.sub.T=(0.75FG.sub.1+3750)T.sub.B+V.sub.D
else: V.sub.TFG.sub.1T.sub.R+V.sub.D
[0265] Alternatively, the subject can be coached or trained to
breathe to a defined volume using a prompter which measures the
cumulative inspired volume and prompts the subject to stop
inspiration when the defined volume has been inspired. If the
subject is mechanically ventilated, this parameter can be
determined from the ventilator settings or ventilator operator.
Target Sequence Input
[0266] The operator enters a target sequence of n breaths
consisting of a target end-tidal partial pressures of O2
(P.sub.ETO2[i].sup.T) and a target end-tidal partial pressure of
CO2 (P.sub.ETCO2[i].sup.T) for every breath (i) of the
sequence.
[0267] Calculation of the inspired gas composition to Induce target
end-tidal values
[0268] The partial pressure of O2 in the controlled gas mixture
(P.sub.1O2[i]) and the partial pressure of CO2 in the controlled
gas mixture (P.sub.1CO2[i]) required to induce the sequence of
target end-tidal partial pressures of O2 (P.sub.ETO2[i].sup.T) and
target end-tidal partial pressures of CO2 (P.sub.ETCO2[i].sup.T)
can be calculated by executing the steps outlined in sections 6-15
for every breath of the sequence (i, i=1 . . . n).
[0269] Calculate the Oand CO2 partial pressures of pulmonary
end-capillary blood
[0270] When sequential rebreathing is employed (2; 37; 38), we
assume that the partial pressure of O2 in pulmonary end-capillary
blood (P.sub.pO2[i]) is equal to the target end-tidal partial
pressure of O2 (P.sub.ETO2[i].sup.T), and the partial pressure of
CO2 in pulmonary end-capillary blood (P.sub.pCO2[i]) is equal to
the target end-tidal partial pressure of CO2 (P.sub.ETCO2[i
].sup.T) (39).
P.sub.pO2[i]=P.sub.ETO2[i].sup.T
P.sub.pCO2[i]=P.sub.ETCO2[i].sup.T
[0271] Various other formulas have been proposed to derive blood
gas partial pressures from end-tidal partial pressures. For
example, see (40; 41). Any of these relationships can be used in
place of the above equalities.
Calculate the pH Pulmonary End-Capillary Blood
[0272] The pH of the pulmonary end-capillary blood (pH[i]) can be
calculated from the Henderson-Hasselbalch equation using the blood
bicarbonate concentration ([HCO.sub.3]), the blood CO2 partial
pressure (P.sub.pCO2[i]), and the solubility of CO2 in blood (0.03
mmol/L/mmHg) (9).
pH .function. [ i ] = 6.1 + log .function. ( [ HCO 3 ] 0.03 P p
.times. CO .times. .times. 2 .function. [ i ] ) ##EQU00005##
Calculate the O2 Saturation of Pulmonary End-Capillary Blood
[0273] The O2 saturation of pulmonary end-capillary blood
(S.sub.pO2[i]) can be calculated from experimental equations using
the body temperature (T), the blood pH (pH[i]), the blood CO2
partial pressure (P.sub.pCO2[i]), and the blood O2 partial pressure
(P.sub.pO2[i]) (42).
S p .times. O .times. .times. 2 .function. [ i ] = 100 - 8532.2289
z + 2121.401 z 2 - 67.073989 z 3 + z 4 935960.87 - 31346.258 z +
2396.1674 z 2 - 67.104406 z 3 + z 4 ##EQU00006## .times. where
##EQU00006.2## .times. z = P p .times. O .times. .times. 2
.function. [ i ] 10 0.024 .times. ( 37 - r ) + 0.4 ( p .times.
.times. H .function. [ i ] - 7.4 ) + 0.06 ( log .times. .times. 4
.times. C - log .times. .times. P p .times. CO .times. .times. 2
.function. [ i ] ) ##EQU00006.3##
Calculate the O2 Content of Pulmonary End-Capillary Blood
[0274] The OL2 content of pulmonary end-capillary blood
(C.sub.pO2[i]) can be calculated from the O2 saturation of the
blood (S.sub.pO2[i]), the blood haemoglobin concentration (Hb), the
O2 carrying capacity of haemoglobin (1.36 ml/g), and the solubility
of O2 in blood (0.003 ml/dL/mmHg) (43).
C p .times. O .times. .times. 2 .function. [ i ] = 1.36 Hb S F
.times. O .times. .times. 2 .function. [ i ] 100 + 0.003 P p
.times. O .times. .times. 2 .function. [ i ] ##EQU00007##
[0275] Alternative derivations of pH, O2 saturation, and O2 content
are reviewed in detail in (44).
Calculate the CO2 Content of Pulmonary End-Capillary Blood
[0276] The CO2 content of pulmonary end-capillary blood
(C.sub.pCO2[i]) can be calculated from the blood haemoglobin
concentration (Hb), the O2 saturation of the blood (S.sub.pO2[i]),
the blood pH (pH[i]), and the blood CO2 partial pressure
(P.sub.pCO2[i]) (45).
C p .times. CO .times. .times. 2 .function. [ i ] - ( 1.0 - 0.02924
Hb ( 2.244 - 0.422 ( Sp .times. O .times. .times. 2 .function. [ i
] 100 ) ) ( 8.740 - pH .function. [ i ] ) ) C pl ##EQU00008##
where: C.sub.pi=0.0301P.sub.pCO2[i](1+10.sup.pH[i]-6.0)2.226
[0277] See also (46-48) for alternative calculations of CO2
content.
Calculate the O2 and CO2 Content of Arterial Blood
[0278] The arterial blood is a mixture of the pulmonary
end-capillary blood and the blood shunted past the lungs. The
percentage of the cardiac output (Q) that is shunted past the lungs
is given by the intrapulmonary shunt fraction (s).
[0279] The content of O2 in the arterial blood (C.sub.aO2[i]) is a
weighted average of the O2 content of the pulmonary end-capillary
blood (C.sub.pO2[i]) and the O2 content of the blood which is
shunted directly from the mixed venous circulation
(C.sub.MVO2[i]).
C.sub.aO2[i]=(1-s)C.sub.pO2[i]1 s-C .sub.MVO2[i]
[0280] The content of CO2 in the arterial blood (C.sub.aCO2[i]) is
a weighted average of the CO2 content of the pulmonary
end-capillary blood (C.sub.pCO2[i]) and the CO2 content of the
blood which is shunted directly from the mixed-venous circulation
(C.sub.MVCO2[i]).
C.sub.aCO2[i]=(1-s)C.sub.pCO2 +sC.sub.MVCO2[i]
Calculate the O2 Content of the Mixed-Venous Blood
[0281] Before returning to the venous circulation, the arterial
blood passes through the tissue capillary beds where O2 is consumed
and exchanged. This system can be modelled as a compartmental
system where each compartment (j) represents a single tissue or
group of tissues. Each compartment is assigned a storage capacity
for O2 (dO2.sub.j). Each compartment is also modelled as being
responsible fora fraction (vo2.sub.j) of the overall metabolic O2
consumption (VO2), and receiving a fraction (q.sub.j) of the total
cardiac output (Q). The content of O2 in the venous blood leaving a
compartment (C.sub.vO2.sub.j[i]) is equal to the content of O2 in
the compartment. Assuming an O2 model with n.sub.O2 compartments,
the O2 content of the venous blood leaving each compartment can be
calculated from the O2 content in the compartment during the
previous breath (C.sub.vO2.sub.j[i-1]), the compartment parameters,
and the period of the breath (T.sub.B).
[0282] For j=1 . . . n.sub.O2
C V .times. O .times. .times. 2 j .function. [ i ] = C V .times. O
.times. .times. 2 j .function. [ i - 1 ] + 100 T B d .times.
.times. O .times. .times. 2 j ( q j Q ( C a .times. O .times.
.times. 2 .function. [ i ] - C V .times. O .times. .times. 2 j
.function. [ i - 1 ] ) - vo .times. .times. 2 j V .times. .times. O
.times. .times. 2 ) ##EQU00009##
[0283] The values for a one compartment model (n.sub.O2=1) are
given below. The model assumes a single compartment with a storage
capacity for O2 (dO2.sub.k) proportional to the subjects weight (W)
(49).
TABLE-US-00001 J q.sub.J dO2.sub.J vo2.sub.J 1 1 (1500/70) W 1
[0284] The mixed-venous O2 content leaving the tissues
(C.sub.MV(T)O2[i]) is the sum of the O2 content leaving each
compartment (C.sub.vO2.sub.j[i]) weighted by the fraction of the
cardiac output (q.sub.j) received by the compartment.
C MV .function. ( T ) .times. O .times. .times. 2 .function. [ i ]
= j = 1 n .times. O .times. .times. 2 .times. q j C V .times. O
.times. .times. 2 j .function. [ i ] ##EQU00010##
[0285] Alternatively, since the storage capacity of O2 in the
tissues of the body is small, the O2 content of the mixed-venous
blood leaving the tissues (C.sub.MV(T)O2[i]) can be assumed to be
equal to the arterial inflow of O2 to the tissues
(QC.sub.4O2.sub.j[i]) less the overall metabolic O2 consumption of
the tissues (VO2) distributed over the cardiac output (Q).
C MV .function. ( T ) .times. O .times. .times. 2 j .function. [ i
] = Q C a .times. O .times. .times. 2 .function. [ i ] - V .times.
O .times. .times. 2 Q ##EQU00011##
[0286] The O2 content of the mixed-venous blood entering the
pulmonary circulation (C.sub.MVO2[i]) is equal to the O2 content of
the mixed-venous blood leaving the tissues delayed by the
recirculation time (C.sub.MV(T)O2[i-n.sub.R])
C.sub.MVO2[i]=C.sub.MV(T)O2[i-n.sub.R]
[0287] Other O2 model parameters are available from (49; 50).
Calculate the CO2 Content of the Mixed-Venous Blood
[0288] Before returning to the venous circulation, the arterial
blood passes through the tissue capillary beds where CO2 is
produced and exchanged. This system can be modelled as a
compartmental system where each compartment (k) represents a single
tissue or group of tissues. Each compartment is assigned a storage
capacity for CO2 (dCO2.sub.k). Each compartment is also modelled as
being responsible for a fraction (vco2.sub.k) of the overall
metabolic CO2 production (VCO2), and receiving a fraction
(q.sub.k)of the total cardiac output (Q). The content of CO2 in the
venous blood leaving a compartment (C.sub.vCO2.sub.k[i]) is equal
to the content of CO2 in the compartment. Assuming a CO2 model with
n.sub.CO2, compartments, the CO2 content of the venous blood
leaving each compartment can be calculated from the CO2 content in
the compartment during the previous breath (C.sub.vCO2.sub.j[i-1]),
the compartment parameters, and the period of the breath
(T.sub.B).
[0289] For k=1 . . . n.sub.CO2
C V .times. CO .times. .times. 2 k .function. [ i ] - C V .times.
CO .times. .times. 2 k .function. [ i - 1 ] + 100 T B d .times.
.times. CO .times. .times. 2 k ( vco .times. .times. 2 k V .times.
.times. CO .times. .times. 2 - q k Q ( C V .times. CO .times.
.times. 2 k .function. [ i - 1 ] - C a .times. CO .times. .times. 2
.function. [ i ] ) ) ##EQU00012##
[0290] The values for a five compartment model n.sub.CO2-5) are
given below (51). The model assumes each compartment has a storage
capacity for CO2 (dCO2.sub.k) proportional to the subjects weight
(W).
TABLE-US-00002 k q.sub.k dCO2.sub.k vco2.sub.k 1 0.04 (225/70) W
0.11 2 0.14 (902/70) W 0.28 3 0.16 (9980/70) W 0.17 4 0.15
(113900/70) W 0.15 5 0.51 (3310/70) W 0.29
[0291] The values for a one compartment model (N.sub.CO2=1) are
given below. The model assumes a single compartment with a storage
capacity for CO2 (dCO2.sub.k) proportional to the subjects weight
(W). The storage capacity for the single compartment is calculated
as the average of the storage capacity for each compartment of the
multi-compartment model weighted by the fraction of the cardiac
output assigned to the compartment.
TABLE-US-00003 k q.sub.k dCO2.sub.k vco2.sub.k 1 1 (20505/70) W
1
[0292] The mixed-venous CO2 content leaving the tissues
(C.sub.MV(T)CO2[i]) is the sum of the CO2 content leaving each
compartment (C.sub.vCO2.sub.k[i]) weighted by the fraction of the
cardiac output (q.sub.k) received by the compartment.
C MV .function. ( T ) .times. CO .times. .times. 2 .function. [ i ]
= k = 1 n .times. CO .times. .times. 2 .times. q k C V .times. CO
.times. .times. 2 k .function. [ i ] ##EQU00013##
[0293] The CO2 content of the mixed-venous blood entering the
pulmonary circulation (C.sub.MVCO2[i]) is equal to the CO2 content
of the mixed-venous blood leaving the tissues delayed by the
recirculation time (C.sub.MV(T)CO2[i-n.sub.k])
C.sub.MVCO2[i]=C.sub.MV(T)CO2[i-n.sub.R]
[0294] Other CO2 model parameters are available from (49; 52).
Calculate PIO2 and PICO2 to Deliver with No Sequential Gas Delivery
Circuit
[0295] On each inspiration, a tidal volume (V.sub.T) of gas is
inspired into the alveoli. When the subject is not connected to a
sequential gas delivery circuit, gas is inspired in the following
order: a) the gas in the anatomical dead space (V.sub.D) is
re-inspired with a partial pressure of O2 equal to the target
end-tidal partial pressure of O2 from the previous breath
(P.sub.ETO2[i].sup.T) and a partial pressure of CO2 equal to the
target end-tidal partial pressure of CO2 from the previous breath
(P.sub.ETCO2[i].sup.T): b) a volume of controlled gas mixture
(VG.sub.1) with controllable partial pressure of O2 (P.sub.1O2[i])
and controllable partial pressure of CO2 (P.sub.1CO2[i]). This
inspired gas mixes with the volume of gas in the functional
residual capacity (FRC) with a partial pressure of O2 and CO2 equal
to the target end-tidal partial pressures from the previous
breath.
[0296] A volume of O2 is transferred between the alveolar space and
the pulmonary circulation (VB.sub.P2[i]). The rate of O2 transfer
between the alveolar space and the pulmonary circulation depends on
the product of the cardiac output (Q) less the intrapulmonary shunt
fraction (s), and the difference between the mixed-venous O2
content entering the pulmonary circulation (C.sub.MVO2[i]) and the
pulmonary end-capillary O2 content (C.sub.pO2[i]) leaving the
pulmonary circulation. This transfer occurs over the breath period
(T.sub.B).
VB.sub.O2[i]-Q(1-s)T.sub.B(C.sub.MVO2[i]-C.sub.pO2[i])
[0297] A volume of CO2 is transferred between the alveolar space
and the pulmonary circulation (VB.sub.CO2[i]). The rate of CO2
transfer between the alveolar space and the pulmonary circulation
depends on the product of the cardiac output (Q) less the
intrapulmonary shunt fraction (s), and the difference between the
mixed-venous CO2 content entering the pulmonary circulation
(C.sub.MVCO2[i]) and the pulmonary end-capillary CO2 content
(C.sub.pCO2[i]) leaving the pulmonary circulation. This transfer
occurs over the breath period (T.sub.B).
VB.sub.CO2[i]=Q(1-s)T.sub.B(C.sub.MVCO2[i]-C.sub.pCO2[i])
[0298] The average volume of the controlled gas mixture inspired
into the alveoli in each breath (VG.sub.1) is given by the tidal
volume (V.sub.T) less the anatomical dead space (V.sub.D).
VG.sub.1=V.sub.T-V.sub.D
[0299] The end-tidal partial pressure O2 (P.sub.ETO2[i].sup.T) is
simply the total volume of O2 in the alveolar space, divided by the
total volume of the alveolar space. The end-tidal partial pressure
CO2 (P.sub.ETCO2[i].sup.T) is simply the total volume of CO2 in the
alveolar space, divided by the total volume of the alveolar
space.
P ET .times. O .times. .times. 2 .function. [ i ] T = ( P ET
.times. O .times. .times. 2 .function. [ i - 1 ] T FRC O .times.
.times. 2 .times. .times. in .times. .times. FRC + P ET .times. O
.times. .times. 2 .function. [ i - 1 ] T V D O .times. .times. 2
.times. .times. re .times. - .times. inspired from .times. .times.
V D + P I .times. O .times. .times. 2 .function. [ i ] ( V T - V D
) O .times. .times. 2 .times. .times. in .times. .times. con -
trolled .times. .times. gas mixture + PB Q ( 1 - s ) T B ( C MV
.times. O .times. .times. 2 .function. [ i ] - C p .times. O
.times. .times. 2 .function. [ i ] ) O .times. .times. 2 .times.
.times. transfered .times. .times. into .times. .times. lung
.times. .times. from .times. .times. the .times. .times.
circulation .times. .times. ( VB O .times. .times. 2 ) ) V T + FRC
Total .times. .times. volume .times. .times. of .times. .times. the
.times. .times. alveolar .times. .times. space ##EQU00014## P ET
.times. C .times. O .times. .times. 2 .function. [ i ] T = ( P ET
.times. CO .times. .times. 2 .function. [ i - 1 ] T FRC CO .times.
.times. 2 .times. .times. in .times. .times. FRC + P ET .times. CO
.times. .times. 2 .function. [ i - 1 ] T V D CO .times. 2 .times.
.times. re .times. - .times. inspired from .times. .times. V D + P
I .times. CO .times. .times. 2 .function. [ i ] ( V T - V D ) CO
.times. .times. 2 .times. .times. in .times. .times. con - trolled
.times. .times. gas mixture + PB Q ( 1 - s ) T B ( C MV .times. CO
.times. .times. 2 .function. [ i ] - C p .times. CO .times. 2
.function. [ i ] ) CO .times. .times. 2 .times. .times. transfered
.times. .times. into .times. .times. lung .times. .times. from
.times. .times. the .times. .times. circulation .times. .times. (
VB CO .times. .times. 2 ) .times. ) V T + FRC Total .times. .times.
volume .times. .times. of .times. .times. the .times. .times.
alveolar .times. .times. space ##EQU00014.2##
[0300] Since all of these volumes and partial pressures are either
known, or can be estimated, the partial pressure of O2 in the
controlled gas mixture (P.sub.1O2[i]) and the partial pressure of
CO2 in the controlled gas mixture (P.sub.1CO2[i]) can be set to
induce target end-tidal partial pressures.
[0301] In some cases, some of the terms (braced terms in the
numerator of the above equations) contributing to the target
end-tidal partial pressure of O2 (P.sub.ETO2[i].sup.T) or the
target end-tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.T) may
be neglected. For example, in most cases, the O2 or CO2 re-inspired
from the anatomical dead space (V.sub.D) is small compared to the
O2 or CO2 in the other volumes that contribute to the end-tidal
partial pressures. In a case where the volume of O.sub.2 or
CO.sub.2 in the controlled gas mixture is very large, for example
when trying to induce a large increase in the target end-tidal
partial pressures, the O.sub.2 or CO.sub.2 transferred into the
lung from the circulation may be comparatively small and neglected.
Neglecting any terms of the mass balance equations will decrease
computational complexity at the expense of the accuracy of the
induced end-tidal partial pressures of gases.
[0302] After re-arranging the above equations for the partial
pressure of O2 in the controlled gas mixture and the partial
pressure of CO2 in the controlled gas mixture, simplification, and
grouping of terms:
P I .times. O .times. .times. 2 .function. [ i ] = P ET .times. O
.times. .times. 2 .function. [ i ] T ( FRC + V T ) - P ET .times. O
.times. .times. 2 .function. [ i - 1 ] T ( FRC + V D ) - PB Q ( 1 -
s ) T B ( C MV .times. O .times. .times. 2 .function. [ i ] - C p
.times. O .times. .times. 2 .function. [ i ] ) V T - V D
##EQU00015## P I .times. CO .times. .times. 2 .function. [ i ] = P
ET .times. CO .times. .times. 2 .function. [ i ] T ( FRC + V T ) -
P ET .times. CO .times. .times. 2 .function. [ i - 1 ] T ( FRC + V
D ) - PB Q ( 1 - s ) T B ( C MV .times. CO .times. .times. 2
.function. [ i ] - C p .times. C ) V T - V D ##EQU00015.2##
[0303] These equations can be used to calculate the partial
pressure of O2 in the controlled gas mixture (P.sub.1O2[i]) and the
partial pressure of CO2 in the controlled gas mixture
(P.sub.1CO2[i]) required to Induce a target end-tidal partial
pressure of O2 (P.sub.ETO2[i]) and target end-tidal partial
pressure of CO2 (P.sub.prCO2[i].sup.T) where the target end-tidal
partial pressure of O2 from the previous breath
(P.sub.ETO2[i-1].sup.T), the target end-tidal partial pressure of
CO2 from the previous breath (P.sub.ETCO2[i-1].sup.T), the
functional residual capacity (FRC), the anatomical dead space
(V.sub.D), tidal volume (V.sub.T), the breath period (T.sub.B),
cardiac output (Q), intrapulmonary shunt fraction (s), mixed-venous
content of O2 entering the pulmonary circulation (C.sub.MVO2[i]),
mixed-venous content of CO2 entering the pulmonary circulation
(C.sub.MVCO2[i]), pulmonary end-capillary content of O2
(C.sub.pO2[i]), and pulmonary end-capillary content of CO2
(C.sub.pCO2[i]) are either known, calculated, estimated, measured,
or predicted.
[0304] Notice that the partial pressure of O2 in the controlled gas
mixture (P.sub.1O2[i]) and the partial pressure of CO2 in the
controlled gas mixture (P.sub.1CO2[i]) required to induce a target
end-tidal partial pressure of O2 (P.sub.ETO2[i].sup.T) or a target
end-tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.T) depends
strongly on the tidal volume (V.sub.T), anatomical dead space (
V.sub.D) and the functional residual capacity (FRC).
[0305] It is often useful in practise to maintain the end-tidal
partial pressures of gases steady for a predefined number of
breaths or period of time. This is a special case of inducing
target end-tidal partial pressures of gases where the target
end-tidal partial pressure of a gas in a breath is equal to the
target end-tidal partial pressure of said gas from the previous
breath.
P.sub.ETO2[i].sup.T=P.sub.ETO2[i-1].sup.T OR
P.sub.ETCO2[i].sup.T=P.sub.ETCO2[i-1].sup.T
[0306] Herein, the above general equations for calculating the
composition of the controlled gas mixture reduce to the
following:
P I .times. O .times. .times. 2 .function. [ i ] = P ET .times. O
.times. .times. 2 .function. [ i ] T ( V T - V D ) - PB Q ( 1 - s )
T B ( C MV .times. O .times. .times. 2 .function. [ i ] - C p
.times. O .times. .times. 2 .function. [ i ] ) V T - V D
##EQU00016## P I .times. CO .times. .times. 2 .function. [ i ] = P
ET .times. CO .times. .times. 2 .function. [ i ] T ( V T - V D ) -
PB Q ( 1 - s ) T B ( C MV .times. CO .times. .times. 2 .function. [
i ] - C p .times. CO .times. .times. 2 .function. [ i ] ) V T - V D
##EQU00016.2##
[0307] Notice, these equations still require the estimation,
measurement, or determination of many of the subject's ventilatory
or pulmonary parameters, namely, tidal volume (V.sub.T), functional
residual capacity (FRC), breath period (T.sub.B), and anatomical
dead space (V.sub.D). Therefore, in the absence of sequential
rebreathing, the calculation of the partial pressure of O.sub.2 in
the controlled gas mixture (P.sub.1O2[i]) and the partial pressure
of CO2 in the controlled gas mixture (P.sub.1CO2[i]) required to
induce a target end-tidal partial pressure of O.sub.2
(P.sub.ETO2[i].sup.T) and a target end-tidal partial pressure of
CO.sub.2 (P.sub.ETCO2[i].sup.T) is highly dependant on the subjects
ventilatory and pulmonary parameters. However, some of these
parameters, namely functional residual capacity (FRC) and the
anatomical dead space (V.sub.D), can be measured or estimated prior
to execution of the targeting sequence, and can be reasonably
assumed not to change over the course of the experiment. Other
parameters, namely tidal volume (V.sub.T) and breath period
(T.sub.B), while normally highly variable, are very well controlled
and stable in mechanically ventilated subjects.
[0308] This method, therefore, is optional, especially where a
simpler approach is preferred, and the subjects ventilation can be
reasonably controlled or predicted.
[0309] It will be recognized that the volumes and partial pressures
required to calculate the partial pressure of O.sub.2 in the
controlled gas mixture (P.sub.1O2[i]) and the partial pressure of
CO.sub.2 in the controlled gas mixture (P.sub.1CO2[i]) may need to
be corrected for differences In temperature or presence of water
vapour between the lung and the conditions under which they are
measured, estimated, or delivered. The corrections applied will
depend on the conditions under which these volumes and partial
pressures are measured, estimated, or delivered. All volumes and
partial pressures should be corrected to body temperature and
pressure saturated conditions. A person skilled in the art will be
comfortable with these corrections.
[0310] A person skilled in the art will also recognize the
equivalence between partial pressures and fractional
concentrations.sub.-- Any terms expressed as partial pressures can
be converted to fractional concentrations and vice versa, For
example, the partial pressure of O2 in the controlled gas mixture
(P.sub.1O2[i]) and the partial pressure of CO2 in the controlled
gas mixture (P.sub.1CO2[i]) may be converted a fractional
concentration of O2 in the controlled gas mixture (F.sub.1O2[i])
and a fractional concentration of CO2 in the controlled gas mixture
(F.sub.1CO2[i]).
F I .times. O .times. 2 .function. [ i ] = P I .times. O .times. 2
.function. [ i ] PB ##EQU00017## F I .times. CO .times. 2
.function. [ i ] = P I .times. CO .times. .times. 2 .function. [ i
] PB ##EQU00017.2##
Calculate PIO2 and PICO2 to Deliver to a Sequential Gas Delivery
Circuit
[0311] On each inspiration, a tidal volume (V.sub.T)of gas is
inspired Into the alveoli. When the subject is connected to a
sequential gas delivery circuit (SGDC) that collects previously
expired gas in a reservoir for later inspiration as neutral gas
(ex. Hi-Ox.sub.SR), gas is inspired in the following order a) the
gas in the anatomical dead space (V.sub.D) is re-inspired with a
partial pressure of O2 equal to the target end-tidal partial
pressure of O2 from the previous breath (P.sub.ETO2[i].sup.T) and a
partial pressure of CO2 equal to the target end-tidal partial
pressure of CO.sub.2 from the previous breath
(P.sub.ETCO2[i-1].sup.T); b) a volume of controlled gas mixture
(VG.sub.1) with controllable partial pressure of O.sub.2
(P.sub.1O2[i]) and controllable partial pressure of CO2
(P.sub.1CO2[i]): c) a volume of neutral gas (VG.sub.2) with a
partial pressure of O2 and CO2 equal to the target end-tidal
partial pressures from the previous breath. This inspired gas mixes
with the volume of gas in the functional residual capacity (FRC)
with a partial pressure of O2 and CO2 equal to the target end-tidal
partial pressures from the previous breath.
[0312] A volume of O2 is transferred between the alveolar space and
the pulmonary circulation (VB.sub.n2[i]). The rate of O2 transfer
between the alveolar space and the pulmonary circulation depends on
the product of the cardiac output (Q) less the intrapulmonary shunt
fraction (s), and the difference between the mixed-venous O2
content entering the pulmonary circulation C.sub.MVO2[i]) and the
pulmonary end-capillary O2 content (C.sub.pO2[i]) leaving the
pulmonary circulation. This transfer occurs over the breath period
(T.sub.B).
VB.sub.O2[i]=Q(1-s)T.sub.B(C.sub.MVO2[i]-C.sub.pO2[i])
[0313] A volume of CO2 is transferred between the alveolar space
and the pulmonary circulation (VB.sub.CO02[i]). The rate of CO2
transfer between the alveolar space and the pulmonary circulation
depends on the product of the cardiac output (Q) less the
intrapulmonary shunt fraction (s), and the difference between the
mixed-venous CO2 content entering the pulmonary circulation
(C.sub.MVCO2[i]) and the pulmonary end-capillary CO2 content
(C.sub.pC2[i]) leaving the pulmonary circulation. This transfer
occurs over the breath period (T.sub.B).
VB.sub.CO2[i]=Q(1-s)T.sub.B(C.sub.MVCO2[i]-C.sub.pCO2[i])
[0314] Assuming a neutral gas at least fills the subjects
anatomical dead space (V.sub.D), the average volume of the
controlled gas mixture inspired into the alveoli in each breath
(VG.sub.1) is given by the rate at which the controlled gas mixture
is made available for inspiration (FG.sub.1) delivered over a
single breath period (T.sub.B):
VG.sub.1=FG.sub.1T.sub.B
[0315] The average volume of neutral gas that is inspired into the
alveoli in each breath is given by the tidal volume ( V.sub.T) less
the volume of inspired controlled gas mixture (VG.sub.1) and the
volume of gas that remains in the anatomical dead space
(V.sub.D):
VG.sub.2=V.sub.T-V.sub.D-FG.sub.1T.sub.B
[0316] The end-tidal partial pressure O2 (P.sub.ETO2[i].sup.T) is
simply the total volume of O2 in the alveolar space, divided by the
total volume of the alveolar space. The end-tidal partial pressure
CO2 ( P.sub.FTCO2[i].sup.T) is simply the total volume of CO2 in
the alveolar space, divided by the total volume of the alveolar
space.
P ET .times. O .times. .times. 2 .function. [ i ] T = ( O .times.
.times. 2 .times. .times. in .times. .times. FRC P ET .times. O
.times. .times. 2 .function. [ i - 1 ] T FRC .times. + .times. O
.times. .times. 2 .times. .times. rc-inspired .times. .times. from
.times. .times. V D P ET .times. O .times. .times. 2 .function. [ i
- 1 ] T V D .times. .times. + .times. O .times. .times. 2 .times.
.times. in .times. .times. controlled .times. .times. gas .times.
.times. mixture P 1 .times. O .times. .times. 2 .function. [ i ] (
FG 1 T B ) .times. + .times. O .times. .times. 2 .times. .times. in
.times. .times. neutral .times. .times. gas P ET .times. O .times.
.times. 2 .function. [ i - 1 ] T ( V T - V D - FG 1 .times. +
.times. O .times. .times. 2 .times. .times. transfered .times.
.times. into .times. .times. lung .times. .times. from .times.
.times. the .times. .times. circulation PB Q ( 1 - s ) T B ( C MV
.times. O2 [ i ] - C p ) .times. 2 .function. [ i ] ) V T + FRC
Total .times. .times. volume .times. .times. of .times. .times. the
.times. .times. alveolar .times. .times. space ##EQU00018##
[0317] Since all of these volumes and partial pressures are either
known, or can be estimated, the partial pressure of O2 in the
controlled gas mixture (P.sub.1O2[i]) and the partial pressure of
CO2 in the controlled gas mixture (P.sub.1CO2[i]) can be set to
induce target end-tidal partial pressures.
[0318] In some cases, some of the terms (braced terms in the
numerator of the above equations) contributing to the target
end-tidal partial pressure of O2 (P.sub.ETO2[i].sup.T) or the
target end-tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.T) may
be neglected. For example, in most cases, the O.sub.2 or CO.sub.2
re-inspired from the anatomical dead space (V.sub.D) is small
compared to the O.sub.2 or CO.sub.2 in the other volumes that
contribute to the end-tidal partial pressures. In the case where
the volume of O2 or CO2 in the controlled gas mixture is very
large, for example when trying to induce a large increase in the
target end-tidal partial pressures, the O2 or CO2 transferred into
the lung from the circulation may be comparatively small and
neglected. Neglecting any terms of the mass balance equations will
decrease computational complexity at the expense of the accuracy of
the induced end-tidal partial pressures of gases.
[0319] After re-arranging the above equations for the partial
pressure of O2 in the controlled gas mixture and the partial
pressure of CO2 in the controlled gas mixture, simplification, and
grouping of terms:
P I .times. O .times. .times. 2 .function. [ i ] = ( P ET .times. O
.times. .times. 2 .function. [ i ] T - P ET .times. O2 .function. [
i - 1 ] T ) ( FRC + V T ) + .times. P ET .times. O .times. .times.
2 .function. [ i - 1 ] T ( FG 1 T B ) - PB Q ( 1 - s ) .times. T B
( C MV .times. O .times. .times. 2 .function. [ i ] - C p .times. O
.times. .times. 2 .function. [ i ] ) FG 1 T B ##EQU00019## P I
.times. CO .times. .times. 2 .function. [ i ] = ( P ET .times. O
.times. .times. 2 .function. [ i ] T - P ET .times. CO .times.
.times. 2 .function. [ i - 1 ] T ) ( FRC + V T ) + .times. P ET
.times. CO .times. .times. 2 .function. [ i - 1 ] T ( FG 1 T B ) -
PB Q ( 1 - s ) .times. T B ( C M .times. .times. V .times. CO
.times. .times. 2 .function. [ i ] - C p .times. C FG 1 T B
##EQU00019.2##
[0320] The above equations can be used to calculate the partial
pressure of O2 in the controlled gas mixture (P.sub.1O2[i]) and the
partial pressure of CO2 in the controlled gas mixture
(P.sub.1CO2[i]) required to induce a target end-tidal target
partial pressure of O2 (P.sub.ETO2[i].sup.T) and a target end-tidal
partial pressure of CO2 (P.sub.ETCO2[i].sup.T) where the target
end-tidal partial pressure of O2 from the previous breath
(P.sub.ETO2[i-1].sup.T), the target end-tidal partial pressure of
CO2 from the previous breath (P.sub.ETCO2[i-1].sup.T, the
functional residual capacity (FRC), tidal volume (V.sub.T), rate at
which the controlled gas mixture Is made available for inspiration
(FG.sub.1), the breath period (T.sub.B), cardiac output (Q),
intrapulmonary shunt fraction (s), recirculation time (n.sub.R),
mixed-venous content of O2 entering the pulmonary circulation
(C.sub.MVO2[i]), mixed-venous content of CO2 entering the pulmonary
circulation (C.sub.MVCO2[i]), pulmonary end-capillary content of O2
(C.sub.PO2[i]), and pulmonary end-capillary content of
CO.sub.PCO2[i]) are either known, calculated, estimated, measured,
or predicted.
[0321] Notice that where this form sequential rebreathing is
employed, the anatomical dead space (V.sub.n) does not factor into
the above equations and end-tidal targeting is independent of its
measurement or estimation. Notice also that the tidal volume
(V.sub.T) appears only in summation with the functional residual
capacity (FRC), Since the tidal volume is, in general, small
compared to the functional residual capacity
(V.sub.T.ltoreq.0.1.FRC), errors in measurement or estimation of
the tidal volume have little effect on inducing target end-tidal
partial pressures of gases. In fact, the above equations can be
used with the tidal volume term omitted completely with little
effect on results.
[0322] It is often useful in practise to maintain the end-tidal
partial pressures of gases steady for a predefined number of
breaths or period of time. This is a special case of inducing
target end-tidal partial pressures of gases where the target
end-tidal partial pressure of a gas in a breath is equal to the
target end-tidal partial pressure of said gas from the previous
breath.
P.sub.ETO2[i].sup.T=P.sub.ETP2[i-1].sup.T OR
P.sub.ETCO2[i].sup.T=P.sub.ETCO2[i].sup.T
[0323] Herein, the above general equations for calculating the
composition of the controlled gas mixture reduce to the
following:
P I .times. O .times. .times. 2 .function. [ i ] = P ET .times. O
.times. .times. 2 .function. [ i ] T FG 1 - PB Q ( 1 - s ) ( C MV
.times. O .times. .times. 2 .function. [ i ] - C p .times. O
.times. .times. 2 .function. [ i ] ) FG 1 ##EQU00020## P I .times.
CO .times. .times. 2 .function. [ i ] = P ET .times. CO .times.
.times. 2 .function. [ i ] T FG 1 - PB Q ( 1 - s ) ( C M .times.
.times. V .times. CO .times. .times. 2 .function. [ i ] - C p
.times. CO .times. .times. 2 .function. [ i ] FG 1
##EQU00020.2##
[0324] Notice, these equations do not require the estimation,
measurement, or determination of any of the subject's ventilatory
or pulmonary parameters, namely, tidal volume (V.sub.T), functional
residual capacity (FRC), breath period (T.sub.B), or anatomical
dead space (V.sub.D).
[0325] The reduced or eliminated sensitivity of the equations to
the subject's ventilatory parameters makes this method useful in
practise with spontaneously breathing subjects. It is, however, not
limited to spontaneously breathing subjects, and may also be used
in mechanically ventilated subjects.
[0326] A person skilled in the art will recognize that the volumes
and partial pressures required to calculate the partial pressure of
O2 in the controlled gas mixture (P.sub.1O2[i]) and the partial
pressure of CO2 in the controlled gas mixture (P.sub.1CO2[i]) may
need to be corrected for differences in temperature or presence of
water vapour between the lung and the conditions under which they
are measured, estimated, or delivered. The corrections applied will
depend on the conditions under which these volumes and partial
pressures are measured, estimated, or delivered. All volumes and
partial pressures should be corrected to body temperature and
pressure saturated conditions. A person skilled in the art will be
comfortable with these corrections.
[0327] A person skilled in the art will also recognize the
equivalence between partial pressures and fractional
concentrations. Any terms expressed as partial pressures can be
converted to fractional concentrations and vice-versa. For example,
the partial pressure of O2 in the controlled gas mixture
(P.sub.1O2[i])and the partial pressure of CO2 in the controlled gas
mixture (P.sub.1CO2[i]) may be converted a fractional concentration
of O2 in the controlled gas mixture (F.sub.1CO2[i]) and a
fractional concentration of CO2 in the controlled gas mixture
(F.sub.1CO2[i]).
F I .times. O .times. .times. 2 .function. [ i ] - P I .times. O
.times. .times. 2 .function. [ i ] PB ##EQU00021## F I .times. CO
.times. .times. 2 .function. [ i ] = P I .times. CO .times. .times.
2 .function. [ i ] PB ##EQU00021.2##
[0328] Determine if targets are logistically feasible
[0329] In practise, many different Implementations of gas delivery
devices and sequential gas delivery circuits may be used. In
general, it is logistically feasible to induce the target end-tidal
partial pressures for the current breath (P.sub.ETO2[i].sup.T,
P.sub.ETCO2[].sup.T) if: [0330] 1) The required partial pressures
of gases in the controlled gas mixture are physically realizable:
[0331] a) 0.ltoreq.P.sub.1O2[i].ltoreq.PB [0332] b)
0.ltoreq.P.sub.1CO2[i].ltoreq.PB [0333] c)
P.sub.1O2[i]+P.sub.1CO2[i]<PB [0334] 2) The gas delivery device
is capable of delivering a controlled mixture of the desired
composition at the required flow rate
[0335] Where sequential rebreathing is carried out with a
Hi-Ox.sub.SR sequential gas delivery circuit and a gas blender:
[0336] Assuming 11.sub.SB source gases (SG.sub.1, SG.sub.n.sub.G)
are blended to deliver the required mixture to the Hi-Ox.sub.SR
sequential gas delivery circuit (SGDC). Each gas (m) contains a
known fractional concentration of O2 (fo2.sub.m) and a known
fractional concentration of CO2 (fco2.sub.m). The flow rate of each
gas (FSG.sub.m[i]) required to deliver the total desired flow rate
of the controlled gas (FG.sub.1) with the required partial pressure
of O2 (P.sub.1O2[i]) and the required partial pressure of CO2
(P.sub.1CO2[i]) can be determined by solving the following set of
equations:
m = 1 n SG .times. FSG m .function. [ i ] = FG 1 ##EQU00022## m = 1
n S .times. G .times. fo .times. .times. 2 m FSG m .function. [ i ]
= P I .times. O .times. .times. 2 .function. [ i ] P .times. B FG 1
##EQU00022.2## m = 1 n S .times. G .times. fco .times. .times. 2 m
FSG m .function. [ i ] = P I .times. CO .times. .times. 2
.function. [ i ] PB FG 1 ##EQU00022.3##
[0337] The target end-tidal partial pressures for the current
breath (P.sub.ETO2[i].sup.T, P.sub.ETCO2[i].sup.T) are logistically
feasible if: [0338] 1) 0.ltoreq.PO2[i].ltoreq.PB [0339] 2)
0.ltoreq.P.sub.1CO2[i].ltoreq.PB [0340] 3)
P.sub.1O2[i]+P.sub.1CO2[i].ltoreq.PB [0341] 4) There exists a
solution to the above system of equations, and [0342] 5)
FSG.sub.m[i].gtoreq.0.A-inverted.m [0343] 6) The gas blender is
capable of delivering a controlled mixture of the desired
composition at the required flow rate
[0344] It is therefore required that n.sub.SG.gtoreq.3. It is
computationally optimal to have n.sub.SG=3.
[0345] One possible set of gases is: [0346] SG.sub.1:
fco2,.sub.1=0, fo2.sub.1=1 [0347] SG.sub.2: fco.2.sub.2=1,
fo2.sub.2=0 [0348] SG3 fco2.sub.3=0, fo2.sub.3=0
[0349] It may enhance the safety of the system to use gases with a
minimal concentration of O2 and maximum concentration of CO2. In
this case, a possible set of gases is: [0350] SG.sub.1:
fco2.sub.1=0, fo2.sub.1=0.1 [0351] SG.sub.2: fco2.sub.2=0.4,
fo2.sub.2=0.1 [0352] SG.sub.3, fco2.sub.3=0, fo2.sub.3=1
[0353] The balance of the source gases when not entirely composed
of O2 and CO2 can be made up of any gas or combination of gases,
which may vary depending on the context. The balance of the source
gases is most often made up of N2 because it is physiologically
inert.
[0354] Adjusting parameters to make logistically infeasible targets
logistically feasible:
[0355] It may occur that inducing a target end-tidal partial
pressure of O2 (P.sub.ETO2[i].sup.T) or a target end-tidal partial
pressure of CO2 (P.sub.ETCO2[i].sup.T) in a given breath is not
logistically feasible. This may occur because the partial pressure
of O2 in the controlled gas mixture (P.sub.1O2[i]) or the partial
pressure of CO2 in the controlled gas mixture (P.sub.1CO2[o])
required to induce the target end-tidal partial pressure of O2 or
the target end-tidal partial pressure of CO2 is either not
physically realizable, or there does not exist a blend of the
current source gases (SG.sub.1, SG.sub.n.sub.G) resulting in the
required tho partial pressure of O2 in the controlled gas mixture
and the required partial pressure of CO2 in the controlled gas
mixture. If the composition of the controlled gas mixture is not
physically realizable for a given set of targets, the targets may
be modified and/or the rate at which the controlled gas mixture is
made available to the circuit (FG.sub.1)modified, or where
applicable, the tidal volume ( V.sub.T) modified, until the
composition is physically realizable. If the composition of the
controlled gas mixture is physically realizable for a given set of
targets, but no combination of the source gases results in the
required composition, the targets may be modified and/or the rate
at which the controlled gas mixture is made available to the
circuit modified, or where applicable, the tidal volume (V.sub.T)
modified, and/or different source gases used.
[0356] If P.sub.1O2[i]<0--The target end-tidal partial pressure
of O2 (P.sub.ETO2[i].sup.T) in not logistically feasible because
the partial pressure of O2 in the controlled gas mixture
(P.sub.1O2[i]) required to induce the target end-tidal partial
pressure of O2 is not physically realizable, To make induction of
the target logistically feasible, increase the target end-tidal
partial pressure of O2. Alternatively, where sequential rebreathing
is used, the rate at which the controlled gas mixture is made
available to the circuit (FG.sub.1) may be modified. Where
sequential rebreathing is not used, the tidal volume (V.sub.T) may
be modified.
[0357] If P.sub.1O2[i]>PB--The target end-tidal partial pressure
of O2 (P.sub.ETO2[i].sup.T) is not logistically feasible because
the partial pressure of O2 in the controlled gas mixture
(P.sub.1O2[i]) required to induce the target end-tidal partial
pressure of O2 is not physically realizable. To make induction of
the target logistically feasible, decrease the target end-tidal
partial pressure of O2. Alternatively, where sequential rebreathing
is used, the rate at which the controlled gas mixture is made
available to the circuit (FG.sub.1) may be modified. Where
sequential rebreathing Is not used, the tidal volume (V.sub.T) may
be modified.
[0358] If P.sub.1CO2[i]<0--The target end-tidal partial pressure
of CO2 (P.sub.ETCO2[i].sup.T) is not logistically feasible because
the partial pressure of CO2 in the controlled gas mixture
(P.sub.1CO2[i]) required to induce the target end-tidal partial
pressure of CO2 is not physically realizable. To make induction of
the target logistically feasible, decrease the target end-tidal
partial pressure of CO2. Alternatively, where sequential
rebreathing is used, the rate at which the controlled gas mixture
is made available to the circuit (FG.sub.1) may be modified. Where
sequential rebreathing is not used, the tidal volume (V.sub.T) may
be modified.
[0359] If P.sub.1CO2[i]>PB--The target end-tidal partial
pressure of CO2 (P.sub.ETCO2[i].sup.T) is not logistically feasible
because the partial pressure of CO2 in the controlled gas mixture
(P.sub.1CO2[i])required to induce the target end-tidal partial
pressure of CO2 is not physically realizable. To make Induction of
the target logistically feasible, decrease the target end-tidal
partial pressure of CO2. Alternatively, where sequential
rebreathing is used, the rate at which the controlled gas mixture
is made available to the circuit (FG.sub.1) may be modified. Where
sequential rebreathing is not used, the tidal volume (V.sub.T) may
be modified.
[0360] If P.sub.1O2[i]+P.sub.1CO2[i]>PB--The combination of the
target end-tidal partial pressure of O2 (P.sub.ETO2[i].sup.T) and
the target end-tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.T)
is not logistically feasible because the combination of the partial
pressure of O2 in the controlled gas mixture P.sub.1O2[i]) and the
partial pressure of CO2 in the controlled gas mixture
(P.sub.1CO2[i]) required to induce the targets is not physically
realizable. To make induction of the targets logistically feasible,
decrease the target end-tidal partial pressure of O2 and/or the
target end-tidal partial pressure of CO2. Alternatively, where
sequential rebreathing is used, the rate at which the controlled
gas mixture is made available to the circuit (FG.sub.1) may be
modified. Where sequential rebreathing is not used, the tidal
volume (V.sub.T) may be modified.
[0361] If there does not exist a solution to the above system of
equations, or there exists a solution for which FSG.sub.m[i]<0
for any m, then the current source gases (SG.sub.1, SG.sub.m.sub.G)
cannot be blended to create the controlled gas mixture. Different
source gases must be used to induce the end-tidal target of O2
(P.sub.ETO2[i].sup.T) and the end-tidal target of CO2
(P.sub.ETCO2[i].sup.T), or the desired targets must be changed.
Alternatively, it may be possible to modify the rate at which the
controlled gas mixture is made available to the circuit (FG.sub.1)
until the partial pressure of O2 in the controlled gas mixture
(P.sub.1O2[i]) and the partial pressure of CO2 in the controlled
gas mixture (P.sub.1CO2[i]) required to induce the targets are
realizable with the current source gases.
[0362] Often, the rate at which the controlled gas mixture is made
available to the circuit (FG.sub.1) is modified to make a target
end-tidal partial pressure of O2 (P.sub.ETO2[i].sup.T) or a target
end-tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.T)
logistically feasible to induce. However, the rate at which the
controlled gas mixture is made available to the circuit should not
be increased to a rate beyond which the subject fails to
consistently exhaust the supply of the controlled gas mixture in
each breath. This maximal rate varies between subjects. However, it
is not necessary that the rate at which the controlled gas mixture
is made available to the circuit be the same in every breath.
Therefore, the rate at which the controlled gas mixture is made
available to the circuit may be set to some basal value for most
breaths, and only increased in particular breaths in which the
inducing the target end-tidal partial pressures is not logistically
feasible at the basal rate of flow. The basal rate at which the
controlled gas mixture is made available to the circuit should be a
rate at which the subject can comfortably, without undo ventilatory
effort, exhaust the supply of the controlled gas mixture in each
breath. The maximal rate at which the controlled gas mixture is
made available to the circuit should be the maximum rate at which
the subject can consistently exhaust the supply of the controlled
gas mixture in each breath with a maximal ventilatory effort. The
subject may be prompted to increase their ventilatory effort In
breaths where the rate at which the controlled gas mixture is made
available to the circuit is increased.
Initializing the System
[0363] Let the index [0] represent the value of a variable for all
breaths before the start of the sequence (all values of
i.ltoreq.0). To initialize the system, the subject is allowed to
breathe freely, without intervention, until the measured end-tidal
partial pressure of O2 (P.sub.ETCO2.sup.M) and the 5measured end
tidal partial pressure of CO2 (P.sub.ETCO2.sup.M) are stable--these
are taken as the baseline partial pressure of O2
(P.sub.ETO2.sub.0.sup.M) and the baseline partial pressure of CO2
(P.sub.ETCO2.sub.0).The measured end-tidal partial pressures are
considered stable when there is less than .+-.5 mmHg change in the
measured end-tidal partial pressure of O2 and less than .+-.2 mmHg
change in the measured end-tidal partial pressure of CO2 over 3
consecutive breaths. The rest of the variables are Initialized by
assuming the whole system has equilibrated to a steady state at the
baseline end-tidal partial pressures.
[0364] Assume that end-tidal partial pressures are equal to the
baseline measurements: [0365]
P.sub.ETO2[0].sup.T=P.sub.ETO2.sub.0.sup.M [0366]
P.sub.ETCO2[0].sup.T=P.sub.ETCO2.sub.0.sup.M
[0367] Assume pulmonary end-capillary partial pressures are equal
to end-tidal partial pressures: [0368]
P.sub.pO2[0]=P.sub.ETO2[0].sup.T [0369] P.sub.pC O2[0]=P.sub.ETCO
2[0].sup.T
[0370] Calculate O2 blood contents assuming steady state:
[0371] Pulmonary end-capillary O2 saturation:
pH .function. [ 0 ] = 6.1 + log .function. ( [ HCO 3 ] 0.03 P P
.times. CO .times. .times. 2 .function. [ 0 ] ) ##EQU00023## S p
.times. O .times. 2 .function. [ 0 ] = 100 ( - 8532.2289 z .times.
1 .times. .times. 2121.401 z 2 - 67.073989 z 3 + z ) 4 935960.87 -
31346.258 z + 2396.1674 z 1 - 67.104406 z 3 + z 4 ##EQU00023.2##
where .times. .times. z = P P .times. O .times. .times. 2
.function. [ 0 ] 10 0.024 ( 37 - T ) + 0.4 ( p .times. .times. 11
.function. [ 0 ] - 7.4 + 0.06 ( log .times. .times. 40 - logP P
.times. CO .times. .times. 2 .function. [ 0 ] ) ##EQU00023.3##
[0372] Pulmonary end-capillary O2 content
C p .times. O .times. .times. 2 .function. [ 0 ] = 1 .times. .36 Hb
S p .times. O .times. 2 .function. [ 0 ] 100 + 0.003 P p .times. O
.times. .times. 2 .function. [ 0 ] ##EQU00024##
[0373] Mixed-venous O2 content:
C MV .function. ( T ) .times. O .times. .times. 2 .function. [ 0 ]
= C p .times. O .times. 2 .function. [ 0 ] - VO .times. .times. 2 (
1 - s ) Q ##EQU00025## C MV .times. O .times. 2 .function. [ 0 ] =
C MV .function. ( T ) .times. O .times. .times. 2 .function. [ 0 ]
##EQU00025.2##
[0374] Arterial O2 content:
[0375] C.sub.aO[0]=(1-s)C.sub.pO2[0]+sC.sub.MVO2[0]
[0376] O2 content of each compartment In the model
[0377] For j=1 . . . n.sub.O2
C V .times. O .times. .times. 2 j .function. [ 0 ] = C 4 .times. O
.times. .times. 2 .function. [ 0 ] - vo .times. .times. 2 j VO
.times. .times. 2 q 1 Q ##EQU00026##
[0378] Calculate CO2 blood contents assuming steady state:
[0379] Pulmonary end-capillary CO2 content
C p .times. CO .times. .times. 2 .function. [ 0 ] = ( 1.0 - 0.02924
Hb ( 2 . 2 .times. 4 .times. 4 - 0 .times. .422 ( Sp .times. O
.times. .times. 2 .function. [ 0 ] 100 ) ) ( 8.740 - pH .function.
[ 0 ] ) ) C pl ##EQU00027## C pi = 0.0301 P p .times. CO .times.
.times. 2 .function. [ 0 ] ( 1 + 10 pH .function. [ 0 ] - 6.10 )
2.226 ##EQU00027.2##
[0380] Mixed-venous CO2 content
C MV .function. ( T ) .times. CO2 .function. [ 0 ] = C p .times.
CO2 .function. [ 0 ] + VCO2 ( 1 - s ) Q ##EQU00028## C MV .times.
CO .times. .times. 2 .function. [ 0 ] = C MV .function. ( T )
.times. CO .times. .times. 2 .function. [ 0 ] ##EQU00028.2##
[0381] Arterial CO2 content
[0382] C.sub.aCO2[0]=(1-s)C.sub.pCO2[0]+C.sub.MVCO2[0]
[0383] CO2 content of each compartment In the model:
[0384] For k=1 . . . n.sub.CO2
C V .times. CO .times. 2 k .function. [ 0 ] = C a .times. CO
.times. 2 .function. [ 0 ] + vco .times. 2 k VCO .times. .times. 2
q k Q ##EQU00029##
[0385] Tuning the system
[0386] The parameters of the system can be tuned so that the
measured end-tidal partial pressures of O2 (P.sub.ETO2[i].sup.M)
and the measured end-tidal partial pressures of CO2
(P.sub.ETCO2[i].sup.M) during any sequence more closely reflect the
target end-tidal partial pressures of O2 (P.sub.ETO2[i].sup.T) and
target end-tidal partial pressures of CO2 (P.sub.ETCO 2[i].sup.T).
To tune the system parameters, standardized tuning sequences are
run and the measured results compared to the targets. The
difference between measured end-tidal partial pressures and the
target end-tidal partial pressures in the standardized tuning
sequences can be used to refine the estimates of some physiological
parameters.
[0387] Example tuning sequence:
[0388] The tuning sequence sets the target end-tidal partial
pressure of O2 (P.sub.ETO 2[i].sup.T) at 5 mmHg above the baseline
end-tidal partial pressure of O2 (P.sub.ETO2.sub.0.sup.M)
throughout the sequence, and executes a 5 mmHg step-change in the
end-tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.T) from 5
mmHg above the baseline end-tidal partial pressure of CO2
(P.sub.ETCO2.sub.0.sup.M) to 10 mmHg above the baseline end-tidal
partial pressure of CO2 in breath 30 (i=30) of the sequence. [0389]
P.sub.ETO2[i].sup.T=P.sub.ETO2.sub.0.sup.M+5 i=1..60 [0390]
P.sub.ETCO2[i].sup.T=P.sub.ETCO2.sub.0.sup.M+5 i=1..29 [0391]
P.sub.ETCO2[i].sup.T=P.sub.ETCO2.sub.0.sup.M+10 i=30..60
[0392] The estimate of the functional residual capacity (FRC) can
be refined as a function of the difference between the actual step
change induced in the end-tidal
CO2(P.sub.ETCO2[30].sub.M-P.sub.ETCO2[29].sup.M) and the target
step-change (P.sub.ETCO2[30].sup.T-P.sub.ETCO2[29].sup.T=5) in
breath 30 (i-30).
FRC=FRC.sub.0+.alpha.((P.sub.ETCO2[30].sup.M-P.sub.ETCO2[29
].sup.M)-P.sub.ETCO[30].sup.T-P.sub.ETCO2[29].sup.T)) .alpha.=200
ml/mmHg
[0393] In general, the correction factor (a) can range from 50-500
ml/mmHg. Lower values of the correction factor will produce a more
accurate estimate of the functional residual capacity (FRC) while
requiring more tuning iterations. Higher values will reduce the
number of tuning iterations but may cause the refined estimate of
the parameter to oscillate around the optimal value.
[0394] The estimate of the overall metabolic O2 consumption (VO2)
can be refined as a function of the difference between the target
end-tidal partial pressure of O2 (P.sub.ETO2[60].sup.T) and the
measured end-tidal partial pressure of O2 (P.sub.ETO2[60].sup.M) in
breath 60 (i=60). [0395]
VO2=VO2.sub.0-.beta.(P.sub.ETO2[60].sup.M-P.sub.ETO)2[60].sup.T)
.beta.=10 ml//min/mmHg
[0396] In general, the correction factor (.beta.) can range from
5-200 ml/min/mmHg. Lower values of the correction factor will
produce a more accurate estimate of the overall metabolic O2
consumption (VO2) while requiring more tuning iterations. Higher
values will reduce the number of tuning iterations but may cause
the refined estimate of the parameter to oscillate around the
optimal value.
[0397] The estimate of the overall metabolic CO2 production (VCO2)
can be refined as a function of the difference between the target
end-tidal partial pressure of CO2 (P.sub.ETCO2[29].sup.T) and the
measured end-tidal partial pressure of CO2 (P.sub.ETCO2[29].sup.M)
in breath 29 (i=29). [0398]
VCO2=VCO2.sub.0+.gamma.(P.sub.ETCO2[29].sup.M-P.sub.ETCO2[29].sup.T)
.gamma.=10 ml/min/mmHg
[0399] Alternatively. the estimate of the overall metabolic CO2
production (VCO2) can be refined as a function of the difference
between the target end-tidal partial pressure of CO2
(P.sub.ETCO2[60].sup.T) and the measured end-tidal partial pressure
of CO2 (P.sub.ETCO2[60].sup.M) in breath 60 (i=60)
VCO2=VCO2.sub.0+.gamma.(P.sub.ETCO2[60].sup.M-P.sub.ETCO2[60].sup.T)
.gamma.=10 ml/min/mmHg
[0400] In general, the correction factor (y) can range from 5-200
ml/min/mmHg. Lower values of the correction factor will produce a
more accurate estimate of the overall metabolic CO2 production
(VCO2) while requiring more tuning iterations. Higher values will
reduce the number of tuning iterations but may cause the refined
estimate of the parameter to oscillate around the optimal
value.
[0401] General requirements of a tuning sequence:
[0402] In breaths where the target end-tidal partial pressures of
gases are transitioning between values, the estimate of the
functional residual capacity (FRC) determines the magnitude of the
change induced in the actual end-tidal tidal partial pressures of
gases. The estimate of the overall metabolic O2 consumption (VO2)
influences the induced/measured end-tidal partial pressure of O2
(P.sub.ETO2[i].sup.M) in steady state. Similarly, the estimate of
the overall metabolic CO2 production (VCO2) influences the
induced/measured end-tidal partial pressure of CO2
(P.sub.ETCO2[i].sup.M) in steady state.
[0403] It therefore follows that a difference between the measured
change in the end-tidal partial pressure of O2
(P.sub.ETO2[i].sup.M-P.sub.ETO2[i].sup.M) and the targeted change
in the end-tidal partial pressure of O2
(P.sub.ETO2[i].sup.T-P.sub.ETO2[i].sup.T) in breaths where the
target end-tidal partial pressure of O2 Is not equal to the target
end-tidal partial pressure of O2 from the previous breath
(P.sub.ETO2[i ].sup.T.noteq.P.sub.ETO2[i-1), or a difference
between the measured change in the end-tidal partial pressure of
CO2 (P.sub.ETCO2[i].sup.M-P.sub.ETCO2[i-1].sup.M) and the targeted
change in the end-tidal partial pressure of CO2
(P.sub.ETCO2[i].sup.T-P.sub.ETCO2.upsilon.i-1].sup.T) in breaths
where the target end-tidal partial pressure of CO2 is not equal to
the target end-tidal partial pressure of CO2 from the previous
breath (P.sub.ETCO2[i].sup.T.noteq.P.sub.ETCO2[i-1].sup.T), reflect
errors in the estimate of the functional residual capacity
(FRC).
[0404] Conversely, differences between the target end-tidal partial
pressure of O2 (P.sub.ETO2[i].sup.T) and the measured end-tidal
tidal partial pressure of O2 (P.sub.ETO2[i].sup.M) in breaths at
the end of a long (20 breath) period of constant target end-tidal
partial pressures of O2 (P.sub.ETO2[i].sup.T=P.sub.ETO2[i-1].sup.T)
reflect errors in the overall metabolic O2 consumption (VO2). It is
assumed that the measured end-tidal partial pressures of O2 will
have stabilized (less than .+-.5 mmHg change in the measured
end-tidal partial pressure of O2 over 3 consecutive breaths),
although not necessarily at the target end-tidal partial pressure
of O2, after 20 breaths of targeting the same end-tidal partial
pressures of O2.sub.-- If, however, the measured end-tidal partial
pressure of O2 has not stabilized after 20 breaths of targeting the
same end-tidal partial pressures of O2, a longer duration of
targeting the same end-tidal partial pressure of O2 should be used
for tuning the overall metabolic consumption of O2.
[0405] Differences between the target end-tidal partial pressure of
CO2 (P.sub.ETCO2[i].sup.T) and the measured end-tidal tidal partial
pressure of CO2 (P.sub.ETCO2[i].sup.M) in breaths at the end of a
long (20 breath) period of constant target end-tidal partial
pressures of CO2 (P.sub.ETCO2[i].sup.T=P.sub.ETCO2[i-1].sup.T)
reflect errors in the overall metabolic CO2 production (VCO2). It
is assumed that the measured end-tidal partial pressures of CO2
will have stabilized (less than .+-.2 mmHg change in the measured
end-tidal partial pressure of CO2 over 3 consecutive breaths),
although not necessarily at the target end-tidal partial pressure
of CO2, after 20 breaths of targeting the same end-tidal partial
pressures of CO2. If, however, the measured end-tidal partial
pressure of CO2 has not stabilized after 20 breaths of targeting
the same end-tidal partial pressures of CO2, a longer duration of
targeting the same end-tidal partial pressure of CO2 should be used
for tuning the overall metabolic production of CO2.
[0406] The tuning sequence described above is only an example of
one sequence that can be used to tune the estimates of the
physiological parameters.
[0407] The functional residual capacity (FRC) can be tuned by
observing the difference between the measured change in the
end-tidal partial pressure of O2
(P.sub.ETO2[i].sup.M-P.sub.ETO2[i].sup.m) and the targeted change
in the end-tidal partial pressure of O2
(P.sub.ETO2[i].sup.T-P.sub.ETO2[i-1].sup.T) in breaths where the
target end-tidal partial pressure of O2 is not equal to the target
end-tidal partial pressure of O2 from the previous breath
(P.sub.ETO2[i].sup.T.noteq.P.sub.ETO2[i-1].sup.T), or a difference
between the measured change in the end-tidal partial pressure of
CO2 (P.sub.ETCO2[i].sup.M-P.sub.ETCO2[i-1].sup.M) and the targeted
change in the end-tidal partial pressure of CO2
(P.sub.ETCO2[i].sup.T-P.sub.ETCO2[i-1].sup.T) in breaths where the
target end-tidal partial pressure of CO2 is not equal to the target
end-tidal partial pressure of CO2 from the previous breath
(P.sub.ETCO2[i].sup.T.noteq.P.sub.ETCO2[i-1].sup.T). Therefore, any
sequence that targets the induction of a change in the end-tidal
partial pressure of O2, or a change in the end-tidal partial
pressure of CO2, can be used to tune the estimate of the functional
residual capacity.
[0408] The overall metabolic consumption of O2 (VO2) can be tuned
by observing the difference between the target end-tidal partial
pressure of O2 (P.sub.ETO2[i].sup.T) and the measured end-tidal
tidal partial pressure of O2 (P.sub.ETO2[i].sup.M) in breaths at
the end of a long (20 breath) period of constant target end-tidal
partial pressures of O2 (P.sub.ETO2[i].sup.T=P.sub.ETO2[i].sup.T).
It is assumed that the measured end-tidal partial pressures of O2
will have stabilized (less than t5 mmHg change in the measured
end-tidal partial pressure of O2 over 3 consecutive breaths),
although not necessarily at the target end-tidal partial pressures
of O2, after 20 breaths of targeting the same end-tidal partial
pressures of O2. If, however, the measured end-tidal partial
pressure of O2 has not stabilized after 20 breaths of targeting the
same end-tidal partial pressures of O2, a longer duration of
targeting the same end-tidal partial pressure of O2 should be used
for tuning the overall metabolic consumption of O2Therefore, any
sequence that targets to maintain the end-tidal partial pressure of
O2 constant for a sufficiently long duration may be used to tune
the estimate of the overall metabolic consumption of O2.
[0409] The overall metabolic production of CO2 (VCO2) can be tuned
by observing the difference between the target end-tidal partial
pressure of CO2 (P.sub.ETCO2[i].sup.T) and the measured end-tidal
tidal partial pressure of CO2 (P.sub.ETCO2[i].sup.M) in breaths at
the end of a long (20 breath) period of constant target end-tidal
partial pressures of CO2
(P.sub.ETCO2[i].sup.T=P.sub.ETCO2[i-1].sup.T). It is assumed that
the measured end-tidal partial pressures of CO2 will have
stabilized (less than .+-.2 mmHg change in the measured end-tidal
partial pressure of CO2 over 3 consecutive breaths), although not
necessarily at the target end-tidal partial pressure of CO2, after
20 breaths of targeting the same end-tidal partial pressures of
CO2. if, however, the measured end-tidal partial pressure of CO2
has not stabilized after 20 breaths of targeting the same end-tidal
partial pressures of CO2, a longer duration of targeting the same
end-tidal partial pressure of CO2 should be used for tuning the
overall metabolic production of CO2. Therefore, any sequence that
targets to maintain the end-tidal partial pressure of CO2 constant
fora sufficiently long duration may be used to tune the estimate of
the overall metabolic production of CO2.
[0410] it is not required that all parameter estimates are tuned in
the same sequence. Tuning of all parameters in the example sequence
is done only for convenience. Different tuning sequences may be
used to tune the estimates of different individual, or groups of,
parameters.
[0411] Embodiments of mass balance equations:
[0412] No SGD:
F I .times. X .function. [ i ] = P ET .times. X .function. [ i ] T
( FRC V T ) - P ET .times. X .function. [ i - 1 ] T ( FRC + V D ) -
.times. PB Q ( 1 - s ) T B ( C MV .times. X .function. [ i ] - C p
.times. X .function. [ i ] ( V T - V D ) PB ##EQU00030##
[0413] SGD:
F I .times. X .function. [ i ] = ( P ET .times. X .function. [ i ]
T - P ET .times. X .function. [ i - 1 ] T ( FRC + V T ) + P ET
.times. X .function. [ i - 1 ] T .times. ( FG 1 T B ) - PB Q ( 1 -
s ) T B ( C MV .times. X .function. [ i ] - FG 1 T B PB
##EQU00031##
[0414] As seen in FIGS. 8a and 8b a ramp sequence reveals the
sigmoidal nature of a pattern of a physiological
response--mid-cerebral artery blood flow velocity--showing its
sigmoidal nature over different time courses depending on whether
the subject is a fast or slow responder.
[0415] FIG. 9 blood flow responses to PCO.sub.2 predicted for the
model of a brain vascular territory with a partially-stenosed
vessel branch and a healthy branch in parallel. Where there is some
blood flow resistance upstream from the branches, it causes the
partially-stenosed vessel to encroach on its vasodilatory reserve
by an auto-regulatory mechanism. A vasodilatory stimulus such as in
increase in arterial CO.sub.2 will stimulate all vessels to dilate,
but those vessels that have already dilated in response to the
increase in upstream resistance have a reduced range of response.
The solid red line in FIG. 9 depicts the sigmoidal response of a
normal branch. The dotted blue line depicts the response of the
partially stenosed vessel branch when coupled in parallel with the
normal vessel branch, showing steal in hypercapnia and reverse
steal in hypocapnia. The slopes of the straight fines show the
predicted CVR values for PCO.sub.2 stimulus ranges 40-45 and 40-60
mmHg. The filled circle marks the resting blood flow et resting
PCO.sub.2 and the open circles show the measured responses for a
healthy territory (solid circles and line) and a territory perfused
via a stenosed vessel (dotted circles and line).
[0416] FIG. 9 illustrates the sigmoidal relationship between
regional blood flow and PCO.sub.2 predicts that CVR in a vascular
territory with adequate vasodilatory reserve will be greater for
increases In PCO.sub.2 from 40 to 45 rnmHg vs. Increases from 40 to
50 mmHg. By contrast, a vascular territory downstream from a
hemodynamically significant stenosis may have a positive CVR when
the PCO.sub.2 change is in a range where some vasodilatory reserve
is preserved, but, with a greater stimulus range such as 40-50 mmHg
PCO.sub.2, these vessels reach their vasodilatory limit and the
continued vasodilatory capacity In other regions will induce
steal.
[0417] The model outlined in FIG. 9 was investigated a
comprehensive manner by using it to predict the change in CBF
region by region in response to graded changes in PETCO.sub.2 in a
patient with steno-occlusive disease.
[0418] FIG. 10 shows an example of the development of steal with
hypercapnia, and reverse steal (Robin Hood effect) with hypocapnia
[Lassen, 1968 #16325]. Both of these conditions were observed in
the same patient, confirming that steal and reverse steal are a
function of the changes taking place in the parallel branches of
the vascular bed with intact cerebral autoregulation. The CVR map
in response to a hypercapnic change in PETCO.sub.2 from 30 to 50
mmHg is shown in FIG. 10A and colour coded with the scale shown. We
interpret the blue colour of the right MCA territory as signifying
a vascular bed with reduced vasodilatory reserve (presumably as a
result of MCA stenosis). The CVR maps for an axial slice at
different PETCO.sub.2 ranges for a 18 year old male patient with
moya moya disease affecting the right MCA territory are divided as
follows (A) CVR map calculated for a hypocapnic PETCO.sub.2 change
from 40 to 30 mmHg. (B) CVR map calculated for a hypercapnic
PETCO.sub.2 change from 30 to 40 mmHg, (C) CVR map calculated fora
hypercapnic PETCO.sub.2 change from 40 to 50 mmHg. (D) CVR map
calculated for a hypocapnic PETCO.sub.2 change from 50 to 40 mmHg.
(E) CVR map calculated over the full hypercapnic PETCO.sub.2 change
from 30 to 50 mmHg. In this subject, inducing a reduction of
PETCO.sub.2 from 40 mmHg to 30 mmHg produces a robust constriction
in the healthy left brain territory and a decrease in the blood
flow and BOLD signal (FIG. 10, CVR A). The CVR is color coded as
before, but with the convention that its sign follows the BOLD
change, so the CVR map is predominantly blue in the `normal`
vascular beds. However, a careful inspection of FIG. 10 (CVR A)
shows some yellow and orange colouration in the right MCA
territory, indicating areas of increasing blood flow and CVR due to
reverse steal, as predicted by the model demonstrated in FIG. 9.
With another change in the direction of the stimulus, the
hypercapnic increase in PETCO.sub.2 from 30 to 40 mmHg produces a
large increase in flow in the healthy left MCA region, but a lesser
increase in the compromised right MCA region (FIG. 10, CVR B).
Within this range of PETCO.sub.2 hypercapnia, the right MCA
territory demonstrates some vasodilatory reserve. Nevertheless, as
predicted and illustrated in FIG. 9, further hypercapnia to 50 mmHg
results in a greater steal and the CVR values are negative, and the
map is coloured blue (FIG. 10, CVR C). Finally, our conceptual
model predicts that withdrawal of the vasodilatory stimulus will
abolish the steal and induce a reverse steal via the Robin Hood
effect. Once again, this result is observed in FIG. 10 (CVR D);
this CVR map is virtually the reverse image of the CVR map
calculated for the full range of 30 to 50 mmHg change in
PETCO.sub.2 (FIG. 10, CVR E). In FIG. 10 the BOLD signal vs. time
is presented for the whole brain, an average value of all
voxels.
EXAMPLE 1
[0419] An apparatus according to the invention was used to target
end tidal gas concentrations of CO.sub.2 and O.sub.2 in 35
subjects. We targeted the following sequence (values attained in
brackets): normocapnia (60 seconds a PetCO.sub.2=40 mm Hg, SD=1 mm;
PetO.sub.2=100 mm Hg, SD=2 mm), Hypercapnia (60 seconds at
PetCO.sub.2=50mm Hg, SD=1 mm; PetO.sub.2=100mm Hg, SD=2mm),
normocapnia (100seconds), hypercapnia (180 seconds), and
normocapnia (110 seconds). FIG. 11, comprises a partial raw data
set for 6 subjects.
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