U.S. patent application number 12/065257 was filed with the patent office on 2008-12-25 for accuracy of continuous glucose sensors.
This patent application is currently assigned to THEUNIVERSITY OF VIRGINIA PATENT FOUNDATION. Invention is credited to Christopher Ryan King, Boris P. Kovatchev.
Application Number | 20080314395 12/065257 |
Document ID | / |
Family ID | 37809192 |
Filed Date | 2008-12-25 |
United States Patent
Application |
20080314395 |
Kind Code |
A1 |
Kovatchev; Boris P. ; et
al. |
December 25, 2008 |
Accuracy of Continuous Glucose Sensors
Abstract
A method, apparatus, and a kit are capable of improving accuracy
of CGS devices using dynamic outputs of continuous glucose
sensors.
Inventors: |
Kovatchev; Boris P.;
(Charlottesville, VA) ; King; Christopher Ryan;
(Chicago, IL) |
Correspondence
Address: |
JACKSON & CO., LLP
6114 LA SALLE AVENUE, #507
OAKLAND
CA
94611-2802
US
|
Assignee: |
THEUNIVERSITY OF VIRGINIA PATENT
FOUNDATION
|
Family ID: |
37809192 |
Appl. No.: |
12/065257 |
Filed: |
August 29, 2006 |
PCT Filed: |
August 29, 2006 |
PCT NO: |
PCT/US06/33724 |
371 Date: |
August 29, 2008 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60713203 |
Aug 31, 2005 |
|
|
|
60815191 |
Jun 20, 2006 |
|
|
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Current U.S.
Class: |
128/898 |
Current CPC
Class: |
A61B 5/7278 20130101;
A61B 5/1495 20130101; A61B 5/7275 20130101; A61B 5/14532
20130101 |
Class at
Publication: |
128/898 |
International
Class: |
A61B 19/00 20060101
A61B019/00 |
Claims
1. A method for improving accuracy of a continuous glucose sensor
(CGS), comprising: calibrating the CGS at a first time; and
calibrating the CGS at a second time that is determined based upon
at least one of a dynamically monitored CGS value and a rate of CGS
change.
2. The method of claim 1, wherein the dynamically monitored CGS
value differs by at least 15 mg/dl before the second calibration
takes place.
3. The method of claim 1, wherein the dynamically monitored CGS
value differs by at least 20 mg/dl before the second calibration
takes place.
4. The method of claim 1, wherein the dynamically monitored CGS
value differs by at least 30 mg/dl before the second calibration
takes place.
5. The method of claim 1, further comprising: dynamically
monitoring the CGS value and the rate of CGS change over time.
6. The method of claim 5, further comprising: calculating the first
order time derivative of the monitored CGS value; determining
whether the absolute value of the first time derivative of the CGS
value is substantially less than 1; and maintaining the calibration
of the CGS at the first time when the absolute value of the first
time derivative of the CGS value is substantially less than 1.
7. The method of claim 6, further comprising: determining the
absolute change between the CGS at the second time and the CGS at
the first time calibration is greater than a pre-determined value
when the absolute value of the first time derivative of the CGS
value is substantially less than 1; and maintaining the calibration
of the CGS at the first time when the absolute change between the
CGS at the second time and the CGS at the first time calibration is
greater than a pre-determined value.
8. The method of claim 7, wherein the predetermined value is 30
mg/dl.
9. The method of claim 7, wherein the predetermined value is 40
mg/dl.
10. The method of claim 7, further comprising: recalibrating the
CGS when it is determined that the absolute change between the CGS
at the second time and the CGS at the first time calibration is
greater than a pre-determined value.
11. The method of claim 1, further comprising: improving the
accuracy of the CGS output by remedying a physiology time lag
between the blood glucose level and a glucose level in an
interstitial fluid that interacts with the blood glucose.
12. The method of claim 11, wherein the step of improving the
accuracy further comprises: deriving a mathematical equation
describing a time dependence of CGS output on the blood glucose
level; deriving the time dependence blood glucose level as a
function of the CGS output; and applying the derived time
dependence blood glucose level function to a set of CGS raw outputs
so as to predict the blood glucose level at a later time or
correcting the CGS output.
13. The method of claim 12, wherein the mathematical equation is
derived based on a model that includes a description of a diffusion
interaction between the blood glucose and glucose in the
interstitial fluid.
14. The method of claim 12, wherein the mathematical equation is
derived based on a model that includes a description of an
assumption of the glucose in the interstitial fluid.
15. The method of claim 1, wherein the second time that is
determined based upon both of the dynamically monitored CGS value
and the rate of CGS change.
16. A method for improving the accuracy of a continuous glucose
sensor, comprising: calibrating the continuous glucose sensor using
first blood glucose value and second blood glucose value; measuring
the first blood glucose value when the continuous glucose sensor
measures a corresponding first interstitial glucose value; and
measuring the second blood glucose value when the continuous
glucose sensor measures a corresponding second interstitial glucose
value that is different from the first interstitial glucose value
by a predetermined amount.
17. The method of claim 16, wherein the predetermined amount is at
least 15 mg/dl.
18. The method of claim 16, wherein the predetermined amount is at
least 20 mg/dl.
19. The method of claim 17, wherein the first and second glucose
data are obtained at different times.
20. The method of claim 17, wherein the second glucose data is
obtained through a decision making loop that comprises a
determination of a rate of CGS change based on a pre-determined
criterion.
21. The method of claim 20, wherein the pre-determined criterion
states that if the rate of CGS change is equal to or greater than a
pre-determined value, maintaining the CGS calibration with the
first glucose data.
22. The method of claim 21, wherein the pre-determined value is
1.
23. The method of claim 22, wherein the pre-determined criterion
further states that if the rate of CGS change is less than 1,
performing another decision based on another predetermined
value.
24. The method of claim 23, wherein said another pre-determined
criterion states that if the absolute difference between the CGS
and the calibrated CGS with the first blood glucose data is equal
to or less than a pre-determined difference value, maintaining the
CGS calibration with the first glucose data.
25. The method of claim 24, wherein said another pre-determined
criterion further states that if the absolute difference between
the CGS and the calibrated CGS with the first blood glucose data is
greater than the pre-determined difference value, performing
another calibration with the second blood glucose data.
26. The method of claim 17, further comprising: improving the
accuracy of the CGS output by remedying a physiology time lag
between the blood glucose level and a glucose level in an
interstitial fluid that interacts with the blood glucose.
27. The method of claim 26, wherein the step of improving the
accuracy further comprises: deriving a mathematical equation
describing a time dependence of CGS output on the blood glucose
level; deriving the time dependence blood glucose level as a
function of the CGS output; and applying the derived time
dependence blood glucose level function to a set of CGS raw outputs
so as to correct the CGS output for inherent time lags.
28. The method of claim 27, wherein the mathematical equation is
derived based on a model that includes a description of a diffusion
interaction between the blood glucose and glucose in the
interstitial fluid.
29. The method of claim 27, wherein the mathematical equation is
derived based on a model that includes a description of an
assumption of the glucose in the interstitial fluid.
30. The method of claim 27, wherein the time dependence blood
glucose level as a function of the CGS output is an inversed
function of the mathematical equation that describes the time
dependence of the CGS output on the blood glucose level.
31. A system for improving an accuracy of a continuous glucose
sensor, comprising: an accuracy improving module accessible to an
output of the continuous glucose sensor, further comprising: a
decision making mechanism capable of determining a calibration at a
time based upon at least one of a dynamically monitored output of
the continuous glucose sensor.
32. The system of claim 31, wherein the decision making mechanism
is capable of determining the calibration at the time that is based
upon the output of the continuous glucose sensor and a rate of
change of the output of the continuous glucose sensor.
33. The system of claim 31, wherein the accuracy improving module
further comprises: an initial request module capable of initiating
a calibration at a predetermined time sequence.
34. The system of claim 33, wherein the decision making mechanism
further comprises: a monitoring module capable of dynamically
monitoring the output from the continuous glucose sensor.
35. The system of claim 34, wherein the decision making mechanism
further comprises: a determination instruction stating that the
dynamically monitored output from the continuous glucose sensor
differs by at least 15 mg/dl before the second calibration takes
place.
36. The system of claim 34, wherein the decision making mechanism
further comprises: a determination instruction stating that the
dynamically monitored output from the continuous glucose sensor
differs by at least 20 mg/dl before the second calibration takes
place.
37. The system of claim 34, wherein the decision making mechanism
further comprises: a determination instruction stating that the
absolute rate of change is substantially equal to or greater than 1
before the second calibration takes place.
38. The system of claim 34, further comprising: a time lag
correction module capable of improving the accuracy of the CGS
output by remedying a physiology time lag between the blood glucose
level and a glucose level in an interstitial fluid that interacts
with the blood glucose.
39. A kit, comprising a continuous glucose sensor; a calibration
unit in a data communication with to the continuous glucose sensor
for calibrating the continuous glucose sensor; and a set of
instructions including instructions for instruction monitoring
monitored output from the continuous glucose sensor, and performing
first and second calibrations at first and second continuous
glucose sensor output values that differ by at least 15 mg/dl.
40. The kit of claim 39, wherein the calibration unit is
connectable to the continuous glucose sensor.
41. The kit of claim 39, wherein the calibration unit is an
integral member of the continuous glucose sensor.
42. The kit of claim 39, wherein the instruction further states
that the dynamically monitored output of the continuous glucose
sensor differs by at least 20 mg/dl before the second calibration
takes place.
43. The kit of claim 39, wherein the instruction further states
that an absolute rate of change of the output of the continuous
glucose sensor is less than 1 before the second calibration takes
place.
44. The kit of claim 39, wherein the accuracy improving mechanism
further comprises: a time lag correction module accessible to the
output of the continuous glucose sensor and capable of remedying a
physiology time lag.
45. A method for improving an accuracy of a continuous glucose
sensor, comprising: calibrating the CGS using a first blood glucose
level and a second blood glucose level different by a predetermined
amount from the first glucose data.
46. The method of claim 45, wherein the predetermined amount is at
least 15 mg/dl.
47. The method of claim 46, wherein the predetermined amount is at
least 20 mg/dl.
48. The method of claim 47, wherein the second glucose data is
obtained through a decision making loop that comprises a
determination of a rate of CGS change based on a pre-determined
criterion.
49. The method of claim 48, wherein the pre-determined criterion
states that if the rate of CGS change is equal to or greater than
1, maintaining the CGS calibration with the first glucose data.
50. A computer-readable medium having computer executable
instructions for performing the method set forth in claim 1.
51. A computer-readable medium having computer executable
instructions for performing the method set forth in claim 16.
52. A computer-readable medium having computer executable
instructions for performing the method set forth in claim 45.
53. A kit, comprising: a calibration unit for calibrating a
continuous glucose, the calibration unit comprising a blood glucose
sensor; and a set of instructions including instructions for
monitoring output from a continuous glucose sensor, and performing
first and second calibrations at first and second continuous
glucose sensor output values that differ by at least 15 mg/dl,
where the first and second calibrations comprise respectively first
and second determinations of blood glucose with the blood glucose
sensor.
Description
CROSS-REFERENCE TO RELATED PUBLICATIONS
[0001] This US patent application claims priority under 35 U.S.C.
119(e) from co-pending U.S. provisional application Ser. No.
60/713,203 filed Aug. 31, 2005, and Ser. No. 60/815,191 filed Jun.
20, 2006, the subject matter of each being incorporated herein by
reference in its entirety. The subject matter of each one of the
publications and the US provisional application in APPENDIX A
attached herewith is incorporated herein by reference in their
entirety.
TECHNICAL FIELD OF THE INVENTION
[0002] The present invention relates to the art of glucose
monitoring, and more particularly to methods and systems for
continuous glucose monitoring.
BACKGROUND OF THE INVENTION
[0003] Existing evidence, such as "National Diabetes Fact Sheet" by
American Diabetes Association, indicates that currently
approximately 18.2 million people in the U.S. have diabetes; and
diabetes is the sixth-leading cause of death in the U.S. One in
three Americans born in the year 2000 will develop Type 2 diabetes.
With the large number of diabetes patients, and with the incidence
of diabetes expected to increase, there is a continuously growing
need for accurate glucose monitoring systems to monitor glucose
levels. Continuous glucose sensors are designed to provide not only
real-time glucose levels at a single point in time, but also the
trend of a person's glucose levels based on analysis taking place
every certain period of time with minimal finger-sticks, leading to
improved glycemic/diabetes control.
[0004] Most contemporary continuous glucose sensors (hereafter
CGS), however, yield blood glucose (hereafter BG) estimates by
sampling interstitial glucose (hereafter IG) in interstitial fluid,
rather than BG due to the difficulty in directly measuring BG in
artery or blood vessels. A typical glucose (BG) estimation from IG
is produced from at least two consecutive approximation steps: 1)
Blood-to-interstitial glucose (BG-to-IG) transport; and 2)
Derivation of BG values from IG-related electrical current recorded
by the sensor. As a result, although CGS technology has made
dramatic strides, the development of accurate and reliable CGS
devices continues to face numerous challenges in terms of
calibration, sensitivity, stability, and physiological time lag
between blood and interstitial glucose concentrations. The
difference between BG and CGS readings arises from following major
factors: physiology, sensor calibration, noise, and engineering.
The physiological time lag and gradients are changing dynamically
with time, with BG levels, and across subjects; and the direct
frequent in vivo sampling of IG is extremely difficult.
Consequently, the evaluation of engineering performance of CGS is
left with a central problem: separating the portion of BG/CGS error
due to calibration, sensor noise, and BG/IG gradient.
[0005] Therefore, a method and apparatus are desired for improving
accuracy and reliability of CGS.
SUMMARY OF THE INVENTION
[0006] Various objects and advantages of the preferred embodiments
of the present invention will be appreciated based on this
disclosure. According to the preferred embodiments, the present
invention improves the accuracy and reliability of CGS by improving
the calibration of CGS sensors or remedying errors due to
physiological time lag or a combination thereof.
[0007] As an exemplary embodiment of the invention, a method for
improving accuracy of a continuous glucose sensor (CGS) is
disclosed herein. The method comprises: calibrating the CGS at a
first time; and changing the CGS calibration at a second time that
is determined based upon a dynamically monitored CGS value, a rate
of CGS change, and a predetermined criterion.
[0008] As another exemplary embodiment of the invention, a method
for improving accuracy of a continuous glucose sensor (CGS) is
disclosed herein. The method comprises: calibrating the CGS using a
first blood glucose data and a second blood glucose data different
from the first glucose data.
[0009] As yet another exemplary embodiment of the invention, a
continuous glucose sensing (CGS) device is disclosed herein. The
device comprises: first means for measuring interstitial glucose
level so as to obtain a CGS output; and a calibration module
accessible to the CGS output for improving accuracy of the CGS,
further comprising: a monitoring module accessible to the CGS
output for dynamically monitoring the CGS and a time derivative of
the CGS; and instructing another calibration event based on the
dynamic CGS value, the time derivative of the CGS value, and a
predetermined criterion.
[0010] As yet another exemplary embodiment of the invention, a
computer-readable medium having computer executable instructions
for performing a method for improving accuracy of a continuous
glucose sensor is disclosed, wherein the method comprises:
retrieving an initial blood glucose value and a CGS value obtained
in a measurement for the initial blood glucose value; monitoring
the CGS value and a time derivative of the CGS value over time;
determining whether to initiate another calibration based on the
monitored CGS values and the time derivative of the CGS value; and
calibrating the CGS if it is determined to initiate said another
calibration.
[0011] As yet another exemplary embodiment of the invention, a
computer-readable medium having computer executable instructions
for performing a method for improving accuracy of a continuous
glucose sensor is disclosed, wherein the method comprises:
retrieving a blood glucose value and a CGS value obtained in a
measurement for the initial blood glucose value at a first time;
and calibrating the CGS at a second time determined by a CGS value
at substantially the second time, a time derivative of the CGS, and
a predetermined criterion.
[0012] As yet another exemplary embodiment of the invention, a
system used for treating a disease associated with blood glucose is
disclosed herein. The system comprises: a continuous glucose device
of claim 300; means for delivering the CGS values to a disease
treating center that is capable of issuing a corresponding treating
instruction or taking a corresponding treating action.
[0013] Various objects and/or advantages of some preferred
embodiments of the invention can be, in some preferred examples,
achieved via the features of the independent claims attached
hereto. Additional preferred embodiments are further set forth in
the dependent claims. In the claims, only elements denoted by the
words "means for" are intended to be interpreted as means plus
function claims under 35 U.S.C. .sctn. 112, the sixth
paragraph.
BRIEF DESCRIPTION OF DRAWINGS
[0014] The preferred embodiments of the invention can be best
understood from the following detailed description taken in
conjunction with the accompanying drawings of which:
[0015] FIG. 1 schematically illustrates a method for measuring
blood glucose levels using a continuous glucose sensor according to
an example of the invention;
[0016] FIG. 2 is an exploded diagram showing the continuous glucose
sensor comprising a calibrator of FIG. 1;
[0017] FIG. 3 is a gram illustrates functional modules of the
calibrator and the time lag corrector according to an example of
the invention;
[0018] FIG. 4a is a block diagram of the calibration module
according to an example of the invention;
[0019] FIG. 4b is a flow chart of a calibration process according
to an example of the invention;
[0020] FIG. 5 illustrates therein the blood glucose differential
during calibration and the accuracy of the CGS improved by an
exemplary method of the invention;
[0021] FIG. 6 is a flow chart showing the steps executed for
improving the accuracy of the CGS using the time-lag correction
method of the invention;
[0022] FIG. 7 is a flow chart showing the steps executed for
calibrating the CGS according to yet another example of the
invention;
[0023] FIG. 8 is a diagram showing the improved CGS measurement
using an exemplary method of the invention;
[0024] FIG. 9 is another diagram showing the improved CGS
measurement using an exemplary method of the invention;
[0025] FIG. 10 is yet another diagram showing the improved CGS
measurement using an exemplary method of the invention;
[0026] FIG. 11 is a flow chart showing the steps executed for
improving the accuracy of the CGS according to yet another example
of the invention;
[0027] FIG. 12 is a diagram illustrating a system in which examples
of the invention can be implemented; and
[0028] FIG. 13 is a diagram showing an exemplary computing device
having computer-readable instructions in which example of the
invention can be implemented.
DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS
[0029] This invention provides a method and device for improving
accuracy of continuous glucose sensors by improving the calibration
of the CGS or by remedying errors arising from the physiological
time lag between BG and IG, or a combination thereof. In view of
many possible variations within the spirit of the invention, the
invention will be discussed in the following with reference to
specific examples. However, it will be appreciated by those skilled
in the art that the following discussion is for demonstration
purposes, and should not be interpreted as a limitation. Other
variations without departing from the spirit of the invention are
also applicable.
[0030] Inaccuracies of most current CGS devices are mainly
attributed to poor CGS calibration, physiology time lag, and random
errors. To reduce the inaccuracy of the CGS, an improved
calibration procedure is proposed. The reduction of inaccuracy can
alternatively be achieved by remedying the error related to
physiological time lag, which is also proposed in this invention.
In fact, the improved calibration procedure and the time lag remedy
procedure can alternatively be combined together so as to achieve a
better performance of CGS.
[0031] Referring to FIG. 1, a method of measuring glucose levels in
vivo according to an example of the invention is schematically
illustrated therein. Because of the large difficulty in directly
measuring glucose levels in blood vessels or arteries 102, CGS 100
detects blood glucose level by measuring the glucose level in
interstitial fluid 104 that interacts with blood vessels or
arteries; and associating the output value of the CGS to the blood
glucose level (the process is often referred to as calibration).
This indirect measurement stands on the proven basis that the blood
glucose level co-varies with the glucose level in the interstitial
fluid.
[0032] To improve the accuracy of CGS, accuracy improver 106 is
provided as shown in FIG. 2. The accuracy improver can improve the
accuracy of the CGS by improving the CGS calibration through an
optimal calibration recommendation (which will be discussed
afterwards), or by remedying the error related to the physiology
time lag (which will be discussed afterwards), or by a combination
thereof. Even though FIG. 2 shows that the accuracy improver is
included in the CGS (100) as a functional member, it is not
required to be so. In other examples, the accuracy improver can be
a stand-alone module or method that is separate from the CGS.
Specifically, the accuracy improver can be implemented in a device
in connection to the CGS output for improving the accuracy of the
CGS. Moreover, the accuracy module can be implemented in the form
of a sequence of computer-executable codes stored in a
computer-readable medium; or can be implemented in hardware of the
device, which will be detailed afterwards.
[0033] As an example of the invention, FIG. 3 schematically
illustrates an exploded view of the accuracy improver (106) in FIG.
2. In this particular example, the accuracy improver (106)
comprises CGS calibration module 108 and time lag correction module
110. The CGS calibration module, by performing an optimal
calibration recommendation cycle, is designated for improving the
calibration of the CGS, thus improving the overall accuracy of the
CGS. The time lag correction module (110) is designated for
remedying the error from the physiology time lag between the blood
glucose and interstitial glucose levels. Depending upon the
specific function of the accuracy improver as discussed above, the
accuracy improver may have only one or both of the CGS calibration
and time lag correction modules.
Improved CGS Calibration
[0034] It is known in the art that the accuracy of CGS calibration
depends on the rate of blood glucose (hereafter BG) change and the
BG value (BG(t)) at the time (t) of calibration. The rate of BG
change can be mathematically expressed as the time derivative of
BG(t): d(BG(t))/dt. Given the fact that calibrations with variant
inputs are better than those with single or non-varying inputs, the
CGS calibration of the invention uses variant inputs.
[0035] As an example, FIG. 4a is a diagram showing functional
modules of an exemplary CGS calibration (118) of FIG. 3. Referring
to FIG. 4a, CGS calibrator 118 comprises initial calibration module
111, storing module 113, reassigning module 115, and decision loop
module 117 that further comprises monitoring module 119, internal
request module 121, self-check initiation module 123, determining
module 125, and sensor calibration module 129.
[0036] The initial calibration module performs initial calibration
so as to obtain an initial calibration data pair SG(0) and BG(0)
from an initial measurement of BG(0). Storing module 113 couples to
the output of the initial calibration module 111 and stores the
initial calibration data pair SG(0) and BG(0). Monitoring module
119 connects to the output of the storing module and dynamically
monitors the CGS output SG(t) and the rate of SG(t) change
SG'(t)=dSG(t)/dt. Internal request module 121 connects to the
output of the monitor module and manages internal requests for
calibration. Self-check initiation module 123 is connected to the
output of the internal request module and designated for initiating
a self-check procedure for optimal calibration timing. In
connection with the output of self-check module 123, determining
module 125 makes decisions of whether to perform another
calibration by sensor calibration module 129 at the particular
time. The calibration data from the calibration after the decision
are reassigned to the CGS through reassign module 115.
[0037] It is noted that one or more above functional modules can be
incorporated into other functional modules in practice. In
particular, sensor calibration module 129 can be incorporated into
initial sensor calibration module 111 for performing CGS
calibration. Any of monitor module 119, internal request module
121, self-check module 123, and determining module 125 can be
incorporated into combined functional module(s).
[0038] An exemplary operation of the functional modules in FIG. 4a
so as to accomplish the desired optimal calibration recommendation
process of the invention is schematically illustrated in FIG. 4b.
Referring to FIG. 4b, an initial calibration is performed by
measuring the blood glucose level BG(0) at the initial time t so as
to obtain an initial CGS output SG(0) (step 112). This step can be
performed by initial calibration module 111 in FIG. 4a. The initial
pair of data BG(0) and SG(0) is recorded at step 114. This step can
be performed by storing module 113 in FIG. 4a. Such initial
calibration can be performed at a time recommended by the CGS
manufacture, or at a time determined by the user. The calibration
procedure then enters to calibration decision making loop 118 that
is administrated by decision loop module 117 as shown in FIG.
4a.
[0039] The calibration decision making loop starts from step 120
that monitors sensor values SG(t) and the rate of change SG'(t)
over time with SG'(t) being defined as the first order time
derivative of SG(t), that is SG'(t)=dSG(t)/dt. The dynamic
monitoring and derivation of the SG'(t) can be performed by monitor
module 119 in FIG. 4a. Upon receiving another calibration request
at a specific time t.sub.1 (step 122), a self-check procedure for
optimal calibration timing is initiated at step 124. This step
triggers the sequence of actions determining whether a calibration
should be performed or not performed at this time, e.g. 126 and 128
in FIG. 4b. The receiving of the calibration request and delivering
such request to initiate the self-check procedure can be
accomplished by the internal request module 121 in FIG. 4a; and the
self-check initiation can be accomplished by the self-check
initiation module 123 in FIG. 4a. It is noted that the internal
request for another calibration can be initiated at the time
defined by the manufacture, or alternatively, by a time defined by
the user, such as a doctor or even proper patients.
[0040] Following the initiation of the self-check procedure at step
124, it is determined whether |SG'(t.sub.1)|<1 at step 126. This
determination step can be performed by determination module 125 in
FIG. 4a. If |SG'(t.sub.1).gtoreq.1, the procedure flows back to
step 120 to continuously monitoring the SG(t) and SG'(t) values.
Otherwise, the procedure makes another determination of whether
|Sg(t.sub.1)-SG(t.sub.0)| is greater than d(mg/dl), wherein
d(mg/dl) is the pre-determined difference threshold between the
initial SG(0) and the CGS output at time t.sub.1 SG(t.sub.1). As an
example, d(mg/dl) can be 10 mg/dl or higher, such as 15 mg/dl or
higher, and more preferably 30 mg/dl or higher. Either one or both
of the determinations at steps 126 and 128 can be performed by
determination module 125 as shown in FIG. 4a. If
|Sg(t.sub.1)-SG(t.sub.0)| is equal to or less than d(mg/dl) at step
128, the procedure flows back to step 120. Otherwise, another
calibration is performed at step 130, by for example, sensor
calibration module 129 in FIG. 4a. The CGS calibration values are
reassigned at step 116 based on the recalibration at step 130, for
example, by respectively replacing the calibration values
SG(t.sub.0) and BG(t.sub.0) with the recalibrated values
SG(t.sub.1) and BG(t.sub.1). The reassigned calibration values are
stored at step 114. The above reassignment can be accomplished by
reassigning module 115 in FIG. 4a.
[0041] After reassigning and recording, the calibration process
re-enters the decision making cycle 118, and repeat the above steps
114, 120, 122, 124, 126, 128, 130, and 116. The number of
calibration cycles can be determined by the default number of
calibrations suggested by the CGS manufacture, or alternatively, by
the user. As an example, a plurality of calibration cycles--e.g. 2
to 10, or more typically 3 to 4 calibration cycles can be performed
during the first 24 hours of CGS life.
[0042] The improved accuracy of CGS using the optimal calibration
method as discussed above can be validated by the following
experimental data and computer-simulations, as shown in FIG. 5.
Experimental Data
[0043] To test the accuracy of the CGS incorporating the accuracy
improvement method as discussed above, a measurement is conducted
on thirty-nine (39) subjects with type 1 diabetes mellitus (T1DM).
The 39 participants have the following statistics: average age 42.5
years with standard deviation (SD) of 12 (SD=12), average duration
of T1DM 21.6 years (SD=94), average HbAlc=7.4% (SD=0.8), 16
males.
[0044] The study was approved by the University of Virginia IRB
Subjects. The subjects were admitted to the general clinic research
center (GCRC) in the evening prior to the study. The participants'
BG levels were controlled overnight within euglycemic range of
100-150 mg/dl (55-8.3 mmol/l). A Minimed CGMS.TM. was attached to
each subject and was calibrated during the study in accordance with
the manufacturer's instructions. All CGMS.TM. were inserted in the
abdomen. Hyperinsulmemic clamps were performed in the morning. Each
clamp used constant insulin infusion rate of 1 mU/kg/min and
variable glucose infusion rate to achieve and maintain BG levels at
approximately 110 mg/dl (around 6 mmol/l). Subsequently, the
glucose infusion rate was reduced to permit a controlled decline in
BG of approximately 1 mg/dl/min until BG reached 50 mg/dl (around
2.8 mmol/l). Glucose infusion was then resumed to allow a recovery
to normal glucose levels. The euglycemic portion of the clamp study
varied in length from 70 to 210 minutes; and the duration of the BG
reduction procedure ranged from 30 to 60 minutes. The recovery
ranged from 30 to 60 minutes. Arterialized blood was achieved by
warming the hand to 50.degree. C. and was sampled every 5 minutes
for reference BG levels. To allow for insulin to reach its steady
state effect, the first 15 minutes of data after the beginning of
infusion were ignored. CGMS.TM. readings were synchronized with
reference BG.
Computer Simulation of Sensor Optimal Calibration
[0045] A recalibration of the sensor using 2 reference BG values
taken during the clamp study described above is computer-simulated,
as shown in FIG. 5 that presents the sensor error as a function of
the difference between the two BG values. The simulated
recalibration uses the standard linear calibration function of the
CGMS.TM.. The results from the recalibration are compared to the
sensors' own accuracy displayed during the experiment and to a
"perfect" calibration using all available reference BG values.
[0046] Referring to FIG. 5, the X-axis presents the distance
between two simulated calibration points in BG units (mg/dl); and
the Y-axis presents the mean absolute error (MAE) of the sensor
output with the two-point calibration. It can be seen in the figure
that MAE is high if the two calibration BGs are close by value. MAE
decreases rapidly when the difference approaches 20 mg/dl, and
slowly decreases thereafter. The upper horizontal line in the
figure represents the MAE of the sensor's own calibration; and the
lower horizontal line represents the MAE resulting from a "perfect"
calibration using all available reference points.
[0047] It can also be seen in the figure that the BG calibration
difference d with value larger than 30 mg/dl but lower than 40
mg/dl achieves excellent results; whereas the difference d with a
value larger than 40 mg/dl achieves "nearly-perfect" results. It is
worthwhile to point that the sensor calibration during the
experiment described above was always done in periods of steady BG
kept at euglycemia, thus the influence of BG rate of change was
minimal.
Correction of Physiology Time Lag
[0048] In addition to the calibration of CGS, physiology time lag
between BG and IG also causes inaccuracy in the CGS output. This
arises from the fact that most of current CGS devices doe not
directly measure the blood glucose levels, but the IG levels in the
interstitial fluids instead. CGS devices then convert the IG
readings into estimates of BG. Therefore, an improved conversion
method from IG to BG will lead to improved performance of CGS. An
object of the invention improves the conversion from IG to BG by
including the physiology time lag between the IG and BG levels.
Such improvement is accomplished through analyses and incorporation
of the time dependency between IG and BG. Specifically, a
mathematical model is established for describing the time
dependency among BG and IG or CGS output. Based upon the
established model, a mathematical equation is derived to
quantitatively express the time dependence of CGS output on
BG--that is CGS is a function of BG. This equation is then
converted so as to express BG as a function of CGS. The inverted
equation can thus be used to predict the BG level for given CGS
output values. In application, the inverted equation is applied to
the raw CGS data to produce accurate BG estimates.
Mathematical Model
[0049] Given the fact that glucose is a relatively small molecule,
it is believed that glucose can diffuse freely through capillary
wall, such as blood vessels and adipose tissues. Adipose tissue is
highly vascularized; and the interstitial fluid occupies a
relatively thin layer between cells. This fact implies that there
is no volume element that is very far from a cell surface, nor is
it very far from a capillary wall. Therefore, uptake and diffusion
of glucose in the interstitial fluid can be assumed to be
relatively topologically uniform.
[0050] The transportation behavior of the IG and BG according to
the invention is depicted in FIG. 1. Referring again to FIG. 1, the
transport behavior of glucose between interstitial fluid and blood
vessels (or adipose tissues) can be modeled as diffusion. IG in the
interstitial fluid also experiences consumption, which results in
amount and/or concentration reduction.
[0051] For deriving a mathematical diffusion equation, it is
assumed that the particular local interstitial environment in
question does not significantly contribute to the development of
the BG/time curve, therefore, the time dependence of BG level,
BG(t), evolves independently, and can be treated as an exogenous
variable in the system. This assumption is particularly safe
especially in hyperinsulinemic clamp situations where the BG level
is mostly controlled by the IV infusion of dextrose. It is further
assumed that the uptake of glucose follows either an IG independent
path, or one described by Michaelis-Menten kinetics, as expressed
respectively in equations 1a and 1b:
I G ( t ) . | UU = I G ( t ) t UU = - .alpha. ( t ) Eq . 1 a I G (
t ) . | MM = I G ( t ) t MM = - .alpha. ( t ) I G ( t ) Km + I G (
t ) Eq . 1 b ##EQU00001##
In the above equations, .alpha. is the uptake of glucose per unit
time per unit volume.
[0052] It is noted that equations 1a and 1b describe the explicit
time dependence. Other variables, such as insulin levels, exercise,
and the like, which may directly effect the glucose uptake BG and
IG, are not excluded from the equations. Km is a constant in
equation 1b; and it does not introduce additional fitable
parameters. In practice, Km can take those published values for the
activity of GLUI-4, asset forth in "Whole body glucose metabolism"
by Zierler K, in Am J Physiol. 276:E409-E426, 1999, the subject
matter of which is incorporated herein by reference in entirety. By
referring to Fick's Law, the change in IG(t) due to diffusion from
the blood can be described by equation 2:
I G ( t ) . | diffusion = .beta. .times. [ B G ( t ) - I G ( t ) ]
Eq . 2 ##EQU00002##
where .beta. is the permeability of the capillary wall to glucose.
Since there are no other clear sources or sinks of glucose in the
interstitial fluid, the net change of glucose can be derived by
adding equations 1a and 1b, which can be expressed as the following
equations 3a and 3b, wherein equation 3a corresponds to the uniform
uptake diffusion model, and equation 3b corresponds to the
Michaelis-Menten kinetic model.
I G ( t ) . | net - UU = I G ( t ) t net - UU = .beta. .times. [ B
G ( t ) - I G ( t ) ] - .alpha. ( t ) Eq . 3 a I G ( t ) . | net -
MM = I G ( t ) t net - MM = .beta. .times. [ B G ( t ) - I G ( t )
] - .alpha. ( t ) I G ( t ) Km + I G ( t ) Eq . 3 b
##EQU00003##
Mathematical Solutions for Equations 3a and 3b
[0053] Equation 3a is an ordinary differential equation that has
analytical solutions; while equation 3b is a non-linear
differential equation of the second type Abel equation that
requires numerical simulation. The analytical solution for equation
3a is expressed in the following equation 4:
I G ( t ) | net - UU = - .beta. t .times. [ .intg. 0 t [ .beta.
.times. B G ( s ) - .alpha. .times. I G ( ts ) ] st s ] Eq . 4
##EQU00004##
By assuming that .alpha. and .beta. are constant over time,
equation 4 can be reduced to the following equation 6 using the
Delta-tau notation as presented in the following equation 5:
.DELTA. .tau. ( f ( t ) ) .ident. f ( t ) - - .beta. ( t - .tau. )
f ( .tau. ) Eq . 5 I G ( t ) = I G ( .tau. ) - .beta. ( t - .tau. )
+ l = 0 .infin. ( - 1 .beta. ) l .DELTA. .tau. ( B G l - .alpha. /
.beta. ) Eq . 6 ##EQU00005##
[0054] By removing the higher order derivative terms of BG(t) in
equation 6, equation 6 can then be reduced to a form to which a
Kalman recursion analysis based on Kalman filtering/smoothing
technique are applicable. An exemplary of such technique is set
forth in "Optimal Control and Estimation" New York: Dover
Publications, 1994 37, the subject matter of which is incorporated
herein by reference in entirety, wherein a "state-space model" and
recursion process are used. The recursion process is attached
herein in Appendix B. Using the "state-space model" and with the
assumption that CGS readings are uniformly spaced by a small time
.zeta., a state-space model for dependence of CGS output and IG can
be described in the following equation 9.
C G S ( t i ) = calibration .times. I G ( t i ) + R .times. w 0 ,
wherein I G ( t i ) = - .beta. .tau. .times. I G ( t i - .xi. ) + f
( t i ) + Q .times. w s ; and wherein f ( t i ) = j = 0 .infin. ( -
1 .beta. ) j .DELTA. .tau. ( B G ( t ) j - .alpha. / .beta. ) . Eq
. 9 ##EQU00006##
[0055] A state-space model for CGS output including the BG
evolution can be expressed as the following equation 10.
B G i + 1 B G . i + 1 B G i + 1 B G i B G . i B G i I G i .alpha. =
[ 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 1 0 0 0 0 0 1 - 1 .beta. 1 .beta. 2 - - .beta. -
.beta. .beta. - .beta. .beta. 2 - .beta. - 1 .beta. 0 0 0 0 0 0 0 1
] .times. B G i B G . i B G i B G i - 1 B G . i - 1 B G i - 1 I G i
- 1 .alpha. + Q .times. w s 0 0 0 0 . 0 0 0 Equation 10
##EQU00007##
[0056] A state-space model for CGS output including the BG
evolution and linear projection can be expressed as the following
equation 11.
[ B G i + 1 B G . i + 1 B G i + 1 I G i + 1 .alpha. ] = [ 1 0 0 0 0
1 0 0 0 0 1 0 0 .beta. 0 0 1 - .beta. - 0 0 0 0 1 ] .times. [ B G i
B G . i B G i I G i .alpha. ] + Q .times. w s [ 0 0 0 0 ] Eq . 11
##EQU00008##
[0057] Inversion of equations 3a and 3b can be similarly performed
given the estimates of consumption, permeability, IG, and the rate
of change of IG. The inversed equations of 3a and 3b are
respectively presented as the following equations 12a and 12b:
B G ( t ) = I G ( t ) . + .alpha. ( t ) .beta. + I G ( t ) Eq . 12
a B G ( t ) = I G ( t ) . .beta. + I G ( t ) .times. [ 1 + .alpha.
/ .beta. Km + I G ( t ) ] Eq . 12 b ##EQU00009##
[0058] Equations 12a and 12b indicate that the use of CGS becomes
important to provide accurate estimates of the rate of change of
IG. Presentations of the inversed equations 12a and 12b are also
possible, which are expressed as following equations 13 and 14.
[ I G ( t i ) I G ( t i - 1 ) C G S ( t i + 1 ) ] = [ 0 0 calib 1 0
0 0 0 0 ] .times. [ I G ( t i - 1 ) I G ( t i - 2 ) C G S ( t i ) ]
+ [ 0 0 C G S ( t i + 1 ) ] + Q .times. w s [ 1 0 0 ] Eq . 13 f ( t
i ) = [ 1 - - .beta. 0 ] .times. [ I G ( t i ) I G ( t i - 1 ) C G
S ( t i + 1 ) ] + R .times. w 0 Eq . 14 ##EQU00010##
[0059] It is noted that the observation in the above described
model is the function of BG(t) that defined in equation 7. If one
accepts a polynomial smoothing/interpolation formula to describe
the course of BG(t), then it, too can be linearly inverted, as
shown in the attached Appendix C.
Algorithmic Implementation
[0060] The above described mathematical model and equations can
then be applied to the CGS readings for remedying the physiology
time lag between IG(t) and BG(t) by predicting BG levels using CGS
outputs. An exemplary procedure of the invention is presented in
the flow chart of FIG. 6.
[0061] Referring to FIG. 6, the mathematical model as discussed
above is developed at step 132. The model describes the dynamics
among BG(t), IG(t), and CGS output SG(t). Based upon the model
developed at step 132, the first mathematical equation is reduced
so as to find out SG(t) as a function of BG(t). This first equation
is preferably developed using Fick's law of diffusion and
Michaelis-Menten consumption. The first equation is then inversed
so as to estimate the dynamics of BG(t) as a function of CGS output
SG(t) at step 136. The inversed equation can then be applied to the
CGS raw data to improve the accuracy of the CGS readings at step
138. An exemplary application of the inversed equation to the raw
CGS data at step 138 is illustrated in FIG. 7.
[0062] Referring to FIG. 7, sets of raw data are obtained at step
140. The data sets comprise CGS outputs SG(t.sub.i), sample time
Tm(t.sub.i), and parameters Par (.alpha., .beta., calib), wherein
parameter calib is a parameter presented in equation 9 as
calibration. The raw CGS data are preferably preprocessed (though
not required) at step 142. Specifically, the CGS raw data are
processed by initial regression and/or filtering to smooth CGS raw
data. This step is important in that the investigation showed that
the raw CGS data current suffer from noise and random spikes that
need to be filtered out in order to improve the accuracy of the
inverted model equation. There are many ways to regress and/or
filter the CGS data. For example, the raw CGS data can be filtered
based upon clinically observed BG rate-of-change in combination
with a Bayesian estimation technique. In another example, the raw
CGS output can be processed with a Kalman filter based methods of
equations 10 and 11 that produce optimal estimation with the
assumption that the evolution of BG meets its limitations.
[0063] Given the pre-processed CGS data (or directly the raw CGS
data without the above pre-processing), the rate of change (time
derivative) of CGS output is calculated at step 144. A unique
feature of the CGS output is the ability to estimate the derivative
of their outputs. However, because of the observation and
systematic noise and wandering sensor sensitivity, it is observed
that such instant raw estimates are rarely optimal. Instead, a
short-interval polynomial smoothing technique using exponential
weights can produce better results, as indicated by experiments.
Then the IG proportionality coefficients are applied to CGS at step
146, followed by application of the inverted model as described
above to estimate the BG level at step 148.
Software Implementation
[0064] The process as described with reference to FIG. 7 can be
implemented in many ways, one of which is in software. As an
example, the above process can be implemented in a real-time
version, which can be of particular usage for the application
directly into CGS outputs so as to convert the raw CGS outputs into
BG estimates, and produce real-time results. A set of real-time
implementation program codes is attached herein as appendix D.
Alternatively, the process can be implemented as a retrospective
version that is of particular usage for performing retrospective
improvement of CGS accuracy; and is applicable to CGS that do not
display real-time data. A set of program codes for the
retrospective implementation is attached herein as appendix E. It
is noted that for ease of reference, the beginning of each line
numbers is removed. A linearized version of the parameters is
employed in favor of the computation speed. It will be appreciated
by those skilled in the art that the program codes presented in
appendices D and E are based on for demonstration purposes, and
should not be interpreted as a limitation. Many other variations
without departing from the spirit of the invention are also
applicable.
Testing of the Method
[0065] The above described process for remedying the physiology
time lag between BG and CGS output has been evaluated on data
acquired during a study performed at the University of Virginia
General Clinical Research Center (GCRC), which was an "add-on"
project to ongoing NIH research grant (RO1 DK 51562, Principal
Investigator Boris Kovatchev). The add-on study was sponsored by
Abbott Diabetes Care (P.I. William Clarke) to perform a direct
comparison between two CGS: Abbott Navigator.TM. and Minimed CGMS.
The development and testing of the model were among the objectives
of the add-on study.
Subjects for the Study
[0066] Sixteen subjects with TIDM (11 male, 5 female, age 42 with
standard deviation (SD) of 3 years, duration of diabetes 20 year
with SD of 3 years. Informed consent was obtained from each.
Subjects were admitted to the General Clinical Research Center in
the evening prior to the study following a physical examination. A
CGS system, the Freestyle Navigator.TM. was applied to each subject
for approximately 12 hours prior to the initiation of the data
recording, in accordance with the manufacturer's instructions and
calibrated as recommended. All systems were inserted in the
abdomen. No BG reference vs. CGS comparisons was made until the
next morning. Study Protocol is defined as that identical
hyperinsulinemic clamps were performed on two consecutive days:
[0067] On each day the hyperinsulinemic clamp used constant insulin
infusion rate of 40 mU/kg/min and variable glucose infusion rate to
achieve and maintain BG levels at approximately 110 mg/dl.
Subsequently, the glucose infusion rate was reduced to permit a
controlled decline in BG levels of approximately 1 mg/dl/min until
the BG level reached 40 mg/dl. The euglycemic clamp portion of the
study varied in length from 70 to 210 minutes, while the duration
of the BG reduction procedure ranged from 30 to 60 minutes.
Arterialized blood was sampled every 5 minutes and reference BG
levels were determined using a Beckman Glucose Analyzer (Beckman
Instruments, Inc, Fullerton, Calif.). Freestyle Navigator.TM.
glucose readings were recorded each minute and were synchronized
with reference BG with a precision of 30 seconds. Reference and
Navigator.TM. rates and direction of BG change were calculated at
five-minute intervals. This procedure resulted in 29 clamp data
sets for the 16 participants in the study.
Software Used for Analysis
[0068] Numerical analysis was conducted using R 2.1.1, which is an
open-source free programming language and suite for statistic
analysis (http//www.r-project.org). Beyond the base packages, the
"odesolve," "fields," and "dsel" packages and their dependencies
from CRAN repositories were used Microsoft Excel was used to
produce graphs.
Results
[0069] Equation 12a was applied to the unfiltered Navigator.TM. raw
data with parameters found via nonlinear least squares. Each data
run begins at the start of descent into hypoglycemia. Table 1
presents a summary of the results for all 29 clamp events. It can
be seen that the average RMS error of the Navigator.TM. was reduced
more than 3-folds; and the % RMS error was reduced more that
5-folds. In addition, the correlation between reference and sensor
BG was improved by the model:
TABLE-US-00001 TABLE 1 BG prediction using a method of the
invention Navigator .TM. RMS error (mg/dl) 8.1 27.3 RMS % error
10.6 55.1 Pearson Correlation 0.995 0.940
[0070] FIG. 8 to FIG. 10 depicts the results. Specifically, FIG. 8
shows the average of the 29 events matched at the nadir with
five-minute data intervals. The solid diamond symbols are reference
BG recorded by the Beckman analyzer. The solid squares are the data
of the Navigator.TM.. The open squares are the Navigator.TM.
corrected by a method of the invention. It can be seen in the
figure that the model-corrected data are much closer to reference
BG than the original Navigator.TM. outputs. FIG. 9 and FIG. 10 show
two individual patients with one-minute data interval. In both
cases, a correction of the Navigator.TM. data by a method of the
invention (open squares) results in improved tracing of reference
BG.
A Combined Accuracy Improvement Method and Device
[0071] As discussed above, the accuracy of the CGS output can be
improved by an example of the invention through an improved
calibration method. Alternatively, CGS accuracy can also be
improved by remedying the physiology time lag between the BG and
IG. In another example of the invention, the above two correction
methods can be combined so as to further improve the CGS accuracy.
FIG. 11 illustrates a flow chart for performing a combined accuracy
improving process in accordance with another example of the
invention.
[0072] Referring to FIG. 11, the combined process starts from
calibrating the CGS using the method as described above with
reference to FIG. 4. System errors can be eliminated or reduced.
The CGS outputs from the calibrated CGS are preprocessed at step
152 by filtering and/or smoothing the calibrated CGS output. This
step can be performed using the same or different method as
described at step 142 in FIG. 7. It is noted that this step, though
preferred, is not required. From the pre-process, sensor noise
and/or minor random fluctuations in the CGS outputs and the first
order time derivative can be removed or reduced. The first order
time derivations of CGS outputs SG(t.sub.i) are calculated at step
144. The IG proportionality coefficient are then applied to the CGS
outputs followed by the application of the inverted model equations
to estimate the BG level, as described with reference to FIG. 6,
which will not be repeated herein.
[0073] Table 2 shows the accuracy improvement using the methods
according to example of the invention by comparing the CGS outputs
obtained from the methods of the invention and the CGS outputs in a
typical CGS in the art without employing the methods of the
invention. The CGS outputs obtained from the typical CGS in the art
are referenced in "Evaluating the accuracy of continuous glucose
monitoring sensors: continuous glucose error grid analysis
illustrated by therasense freestyle navigator data," by B
Kovatchev, L Gonder Frederick, D Cox, and W Clarke, Diabetes Care,
vol. 27, pp 1922-1928, 2004.
TABLE-US-00002 TABLE 2 CG_EGA Accuracy Results Accuracy Benign
Error MAE MAPE Zone % % % mg/dl % N Panel A: Original calibration
Hypoglycemia 50 0 50 27.9 50.1 376 Euglycemia 96.4 0.2 3.4 20.4
22.6 532 Panel B: d = 30 mg/dl calibration Hypoglycemia 86.7 4.8
8.5 10.9 19.8 376 Euglycemia 93.4 2.6 3.9 13.6 14.9 532 Panel C: BG
and SG (CGS output) compensation Hypoglycemia 100 0 0 4.9 8.4 376
Euglycemia 99.4 0.6 0 7.9 8.4 532
[0074] Panel A of Table 2 presents the continuous glucose
error-grid analysis (CG-EGA) of the accuracy of Minimed CGMS.TM.
during the clamp study described above, stratified by hypoglycemia
and euglycemia. The clinically accurate sensor readings were 50.0%
during hypoglycemia and 96.4% during euglycemia. The large
difference between these percentages is primarily due to the more
demanding clinical accuracy standards. For hypoglycemia events:
while for steady euglycemic state there is a large clinical
tolerance for sensor errors. During clinically dangerous and
rapidly developing conditions, such as hypoglycemia, the sensor is
desired to meet higher standards in order to provide accurate
feedback for appropriate and timely treatment decision. The CG-EGA
reflects this distinction. Further, the MAE and the mean absolute
percent error (MAPE) are included in Table 1 and stratified by BG
range as well.
[0075] The panel B in Table 2 presents the CG-EGA, MAE and MAPE of
a sensor re-calibrated by two reference BGs that are 30 mg/dl apart
(e.g. differential d is 30 mg/dl), which is a clinically reasonable
differential in the studied BG range. It can be seen that the
percent of CG-EGA accurate readings increases from 50% to 86.7%,
while MAE is reduced from 27.9 to 10.9 mg/dl during hypoglycemia.
Improvement in MAE and MAPE is observed during euglycemia as
well.
[0076] The panel C of Table 2 presents the CG-EGA, MAE and MAPE of
the SIG vs. BG estimated after sensor re-calibration. It can be
seen that the "accuracy" of SIG following BG fluctuation is
high--nearly 100%, which signifies an excellent theoretical limit
for potential sensor accuracy.
[0077] Examples of the invention can be implemented in many ways.
For example, it can be implemented as a functional member of a
continuous glucose sensor, or can be implemented as a standalone
module associated with the continuous glucose sensor. In either
instance, examples of the invention can be implemented as a set of
program codes of software installed in a computing device, or a set
of computer-executable codes of a hardware device coupled to the
continuous glucose sensor. Regardless the implementation media,
example of the invention can be associated with individual
continuous glucose sensors for improving the accuracy of the
individual glucose sensors. Alternatively, examples of the
invention can be implemented in such a way that the real-time CGS
data, along with related errors and error correction parameters and
data, can be transmitted to an error processing center. The
transmission may or may not be with the glucose data. In this way,
a generalized continuous glucose sensing system can be
established.
[0078] FIG. 12 diagrammatically illustrates an exemplary system in
which examples of the invention can be implemented. Referring to
FIG. 12, clinic setup 158 provides a place for doctors (e.g. 164)
to diagnose patients (e.g. 160) with diseases related with glucose.
Continuous glucose sensor (or sensing device incorporating glucose
testing function) 162 can be used to monitor and/or test the
glucose levels of the patient. Such monitor and/or test can be
short term (e.g. clinical visit) or long term (e.g. clinical stay
or family). The continuous glucose sensor incorporates therein an
example of the accuracy improvement methods as discussed above. The
CGS outputs with improved accuracy can be used by the doctor for
appropriate actions, such as insulin injection or food feeding for
the patient, or other appropriate actions. Alternatively, the CGS
output with improved accuracy can be delivered to computer terminal
168 for instant or future analyses. The delivery can be through
cable or wireless or any other suitable medium. The CGS output with
improved accuracy from the patient can also be delivered to a
portable device, such as PDA 166. The CGS outputs with improved
accuracy can be delivered to a glucose monitoring center 172 for
processing and/or analyzing. Such delivery can be made accomplished
through many ways, such as network connection 170, which can be
wired or wireless.
[0079] In addition to the CGS outputs with improved accuracy,
errors, parameters for accuracy improvements, and any accuracy
related information can be delivered, such as to computer 168,
and/or data processing center 172 for performing error analyses.
This can provide a centralized accuracy monitoring and/or accuracy
enhancement for glucose centers, due to the importance of the
glucose sensors.\
[0080] As discussed earlier, examples of the invention can also be
implemented in a standalone computing device associated with the
target continuous glucose sensors. An exemplary computing device in
which examples of the invention can be implemented is schematically
illustrated in FIG. 13. Although such devices are well known to
those of skill in the art, a brief explanation will be provided
herein for the convenience of other readers.
[0081] Referring to FIG. 13, in its most basic configuration,
computing device 174 typically includes at least one processing
unit 180 and memory 176. Depending on the exact configuration and
type of computing device, memory 176 can be volatile (such as RAM),
non-volatile (such as ROM, flash memory, etc.) or some combination
of the two.
[0082] Additionally, device 174 may also have other features and/or
functionality. For example, the device could also include
additional removable and/or non-removable storage including, but
not limited to, magnetic or optical disks or tape, as well as
writable electrical storage media. Such additional storage is the
figure by removable storage 182 and non-removable storage 178.
Computer storage media includes volatile and nonvolatile, removable
and non-removable media implemented in any method or technology for
storage of information such as computer readable instructions, data
structures, program modules or other data. The memory, the
removable storage and the non-removable storage are all examples of
computer storage media. Computer storage media includes, but is not
limited to, RAM, ROM, EEPROM, flash memory or other memory
technology, CDROM, digital versatile disks (DVD) or other optical
storage, magnetic cassettes, magnetic tape, magnetic disk storage
or other magnetic storage devices, or any other medium which can be
used to store the desired information and which can accessed by the
device. Any such computer storage media may be part of, or used in
conjunction with, the device.
[0083] The device may also contain one or more communications
connections 184 that allow the device to communicate with other
devices (e.g. other computing devices). The communications
connections carry information in a communication media.
Communication media typically embodies computer readable
instructions, data structures, program modules or other data in a
modulated data signal such as a carrier wave or other transport
mechanism and includes any information delivery media. The term
"modulated data signal" means a signal that has one or more of its
characteristics set or changed in such a manner as to encode
information in the signal. By way of example, and not limitation,
communication media includes wired media such as a wired network or
direct-wired connection, and wireless media such as acoustic, RF,
infrared and other wireless media. As discussed above, the term
computer readable media as used herein includes both storage media
and communication media.
[0084] It will be appreciated by those of skill in the art that a
new and useful method for improving accuracy of continuous glucose
sensing devices and system using the same have been discussed
herein. In view of the many possible embodiments to which the
principles of this invention may be applied, however, it should be
recognized that the embodiments described herein with respect to
the drawing figures are meant to be illustrative only and should
not be taken as limiting the scope of invention. Those of skill in
the art will recognize that the illustrated embodiments can be
modified in arrangement and detail without departing from the
spirit of the invention. Therefore, the invention as described
herein contemplates all such embodiments as may come within the
scope of the following claims and equivalents thereof.
APPENDIX A
Subject Matter of the Following Publications and US Provisional
Application are Incorporated Herein by Reference in Entirety
[0085] 1. Santiago J V: Lessons from the Diabetes Control and
Complications Trial. Diabetes 1993, 42 1549-1554. [0086] 2. B.
Feldman, R B.about.azgS, Schwartz, and R. Weinstein, "A continuous
glucose sensor based on wired enzyme technology and results from a
3 day trial in patients with type 1 diabetes," Diabetes Technol
Ther, vol 5, pp 769-7'78, 2003, [0087] 3. D Klonoff, "Continuous
glucose monitoring: Roadmap for 21st century diabetes therapy,"
Diabetes Care, vol 28, pp 1231-1239, 2005. [0088] 4. E Cheyne, D.
Cavan, and D. Kerr, "Perfo.about.mance of continuous glucose
monitoring system during controlled hypoglycemia in healthy
volunteers," Diabetes Technol Ther, vol 4, pp 60'7-613, 2002 [0089]
5. M Boyne, D Silver, J. Kaplan, and C. Saudek, "Timing of changes
in interstitial and venous blood glucose measured with a continuous
subcutaneous glucose sensor;" Diabetes, vol 52, pp 2790-2794, 2003,
[0090] 6. P T Stout, J R. Racchini, and M. E Hilgers, "A novel
approach to mitigating the physiological lag between blood and
interstitial fluid glucose measurements," Diabetes Technol Ther,
vol. 6, pp. 635-644, 2004 [0091] 7. E. Kulcu, J. Tamada, G. Reach,
R Potts, and M. Lesho, "Physiological differences between
interstitial glucose and blood glucose measured in human subjects,"
Diabetes Care, vol 26, pp 2405-2409, 2003, [0092] 8. A Schoonen and
K Wientjes, "A model for transport of glucose in adipose tissue to
a microdialysis probe," Diabetes Technol Ther, vol. 5, pp. 589-598,
2003 [0093] 9. G. M Steil, K Rebrin, F Hariri, S Jinagonda, S
Tadros, C Darwin, and M F Saad, "Interstitial fluid glucose
dynamics during insulin induced hypoglycaemia," Diabetologia, vol
48, pp. 1833-1840, 2005, [0094] 10. K Rebrin and G Steil, "Can
interstitial glucose assessment replace blood glucose
measurements?" Diabetes Technol Ther, vol. 2, pp. 461472, 2000,
[0095] 11. Kovatchev, L Gonder Frederick, D Cox, and W Clarke,
"Evaluating the accuracy of continuous glucose monitoring sensors:
continuous glucose erIor grid analysis illustrated by therasense
freestyle navigator data," Diabetes Care, vol. 27, pp 1922-1928,
2004 [0096] 12. W Clarke, D. Cox, L Gonder Frederick, W Carter, and
S Pohl, "Evaluating clinical accuracy of systems for
self-monitoring of blood glucose," Diabetes Care, vol. 10, pp
622-628.1987, [0097] 13. Hanefeld M: Postprandial hyperglycemia:
noxious effects on the vessel wall International Journal
oj'Clinical Practice, 2002, Supplement 129: 45-50 [0098] 14.
Esposito K, Giugliano D, Nappo F, Martella K, for the Campanian
Postprandial Hyperglycemia Study Group. Circulation, 2004, 110:
214-219 [0099] 15. Quaglim L, Piconi L, Assalone R, Martinelli L,
Motz E, Ceriello A: Intermittent I-Iigh Glucose Enhances Apoptosis
Related to Oxidative Stress in Human Umbilical Vein Endothelial
Cells The Role of protein Kinase C and NAD(P)H-Oxidase Activation
Diabetes, 2003, a: 2795-2804. [0100] 16. Van der Does F E. De
Neeling J N, Snoek F J, Kostense P I, Grootenhuis P A, Bouter L M,
and R J Heine: Symptoms and well-being in relation to glycemic
control in type I1 diabetes Diabetes Care, 1996, u: 204-210 [0101]
17. De Sonnaville J J. Snoek F J Colly L P, Deville W. Wijkel D
Heine R J: Well-being and symptoms in relation to insulin therapy
in type 2 diabetes. Diabetes Care, 1998, a:919-24, [0102] 18. Cox D
J, Gonder-Frederick L A, McCall A, et al The effects of glucose
fluctuation on cognitive function and QOL: the functional costs of
hypoglycaemia and hype.about.glycaemia among adults with type 1 or
type 2 diabetes International Journal ojClinical Practice, 2002,
Supplement 129: 20-26 [0103] 19. Hirsh I B, Brownlee M: Should
minimal blood glucose variability become the gold standard of
glycemic control? J of Diabete.about. and Its Complications, 2005,
D: 178-181 [0104] 20. Reichard P, Phil M Mortality and treatment
side effects during long-term intensified conventional insulin
treatment in the Stockholm Diabetes Intervention study Diabetes 43:
313-317, 1994 [0105] 21. The Diabetes Control and Complications
Trial Research Group The effect of intensive treatment of diabetes
on the development and progression of long-term complications of
insulin-dependent diabetes mellitus N Engl J Med 329: 978-986, 1993
[0106] 22. Gross T M, Bode B W, Einhorn D, Kayne D M, Reed I H,
White N H, Masttototaro J J: Performance evaluation of the MiMed
continuous glucose monitoring system during patient home use
Diabetes Technol Thel 2000; 2:49-56 [0107] 23. Tav.about.iDs R,
Shoaibi A: The public health impact of the MiniMed Continuous
Glucose Monitoring System (CGMSO): an assessment of the literature
Diabetes Technol Ther 2004; 6:518-522 [0108] 24. Chico A,
Vidal-Rios P, Subiia M, Novials A: The continuous glucose
monitoring system is useful for detecting unrecognized
hypoglycemias in patients with type 1 and type 2 diabetes but is
not better than frequent capillary glucose measurements for
improving metabolic control Diabetes Care 26:1153-, 1157, 2003
[0109] 25. Masbototaro J: The MiniMed Continuous Glucose Monitoring
System (CGMS). J Pediatt Endocrinol Metab 12:751-758, 1999 [0110]
26. Feldman B, Brazg R, Schwartz S, Weinstein R: A continuous
glucose sensor based on wired enzyme technology--results from a
3-day trial in patients with type 1 diabetes Diabetes Technol Thel
2003; 5(5):769-79 [0111] 27. Pickup J: Sensitive glucose sensing in
diabetes Lancet 355:426-427, 2000 [0112] 28. Gerzitsen M, Jansen J
A, Lutterman J A: Performance of subcutaneously implanted glucose
sensors for continuous monitoring Neth J Med 54:167-179, 1999
[0113] 29. Boyne, Silver, Kaplan, & Saudek: Timing of Changes
in Interstitial and Venous Blood Glucose Measured With a Continuous
Subcutaneous Glucose Sensor Diabetes 52: 2790-2794, 2003 [0114] 30.
Philip J Stout, Joel R Racchini, Michael E Hilgers: A Novel
App.about.oachto Mitigating the Physiological Lag Between Blood and
Interstitial Fluid Glucose Measurements Diabetes Technol Ther 2004
6:5, 635-644 [0115] 31. Schoonen & Wientjes: A Model for
Transport of Glucose in Adipose Tissue to a Microdialysis Probe
Diabetes Technol Ther 2003 5:4,589-59% [0116] 32. A S Popel
Analysis of capillary-tissue diffusion in multicapillary systems
Mathematical Biosciences, 39: 187-211, 19'78, [0117] 33. G. M.
Steil, K. Rebrin, F Hariri, S Jinagonda, S Tadros, C Darwin and M F
Saad, Interstitial fluid glucose dynamics during insulin-induced
hypoglycaemia Diabetologia 48:7, published online. DOI:
10.1007/s00125-,005-1852-x [0118] 34. Zierler K: Whole body glucose
metabolism Am J Physiol 276:E409-E426, 1999 [0119] 35. Palfreyman R
W, Clark A E, Denton R M, Holman G D, Kozka I S: Kinetic resolution
of the separate GLUT 1 and GLUT4 glucose transport activities in 3
13-L1 cells Biochem J. 284:275-,282, 1992. [0120] 36. Stengel R F:
Optimal Control and Estimation New York: Dover Publications, 1994
[0121] 37. Knobbe E J, Buckingham B: The extended Kalman filter f o
c.about.ontinuous glucose monitoring Diabetes Technol Ther 2005;
7:15-27, [0122] 38. Palerm Cesx C., Willis John P., Desemone James,
Bequette B Wayne: Hypoglycemia Prediction and Detection Using
Optimal Estimation Diabetes Technol Ther 2005; 7:3-14, [0123] 39.
"G M. Steil, K Rebrin, F Hariri, S Jinagonda, S Tadros, C Darwin
and M F. Saad. Interstitial fluid glucose dynamics du.about.ingin
sulin-induced hypoglycaemia Diabetologia 48:7, published online.
DOI: 101007/s00125-005-1852-x" [0124] 40. International Patent
Application Serial No. PCTiUS20051013792, entitled "Method, System
and Computer. Program Product for Evaluating the Accuracy of Blood
Glucose Monitoring SensorsiDevices," filed Apr. 21, 2005, [0125]
41. U.S. provisional application Ser. No. 60/815,191 to Kovatchev
et al. filed Jun. 20, 2006;
APPENDIX B
Kalman Recursion
Appendix A: Kalman Recursions
[0126] If we assume that our data follows a system of the form of
A1.1, where x is a hidden system state vector, y is an observation
vector, w.sub.s is system noise with covariance matrix Q, w.sub.O
is observation noise with covariance matrix R, and the F, G, H
matrices define system transitions, then the system is said to be a
state space model.
x.sub.i+1=Fx.sub.i+Gz.sub.i+w.sub.s
y.sub.i=Hx.sub.i+w.sub.o A1.1)
The Kalman filter is a two step process. First, one-step-ahead
predictions are made. Second, a correction to that prediction is
made based upon new measurements. Let us introduce to notation of
{circumflex over (X)}.sub.i,j meaning "the estimate of x at i given
the measurements up to and including j." Assuming that we have
current estimates of x and the error covariance of that estimate,
P, we can write the first step as A1.2. In order to correct the
estimates, we then calculate the Kalman gain in A1.3, and update
the estimates in A1.4 using the new measurement, y.
{circumflex over (x)}.sub.i|i-1=F{circumflex over
(x)}.sub.i-1|i-1+G{circumflex over (z)}.sub.i-1
{circumflex over (P)}.sub.i=FP.sub.i-1F.sup.T+Q A1.2)
K.sub.i={circumflex over (P)}.sub.iH.sup.T(H{circumflex over
(P)}.sub.iH.sup.T/R).sup.-1 A1.3)
{circumflex over (x)}.sub.i|i={circumflex over
(x)}.sub.i|i-1+K.sub.i(y.sub.i-H{circumflex over
(x)}.sub.i|i-1)
P.sub.i=(I-K.sub.iH){circumflex over (P)}.sub.i A1.4)
APPENDIX C
Recursion Process
[0127] X I = B G i , interpj A2 .7 ) diagonal ( X k I ) = B G k ^
A2 .8 ) ##EQU00011##
[0128] The diagonal operator can be written as in A2.9, which
reduces A2.8 to A2.10. Furthermore, by again concatenating the
first q+1 column vectors we can form the desired matrix A2.1 in A
2.11.
C i .ident. { C [ ii ] = 1 , else C [ ij ] = 0 } , diagonal ( A ) =
j = 1 n C j Ae j T A2 .9 ) B G k ^ = { i = 1 n C i X k ( X T W i X
) - 1 X T W j } B G , { } .ident. M k A2 .10 ) B G ~ = k = 0 q M k
B G e k A2 .11 ) ##EQU00012##
[0129] Finally, by inserting A2.11 into A2.3 we arrive at A 2.12, a
linear system which can be solved by methods such as QR
decomposition.
f ( t ) + .alpha. / .beta. = { ( I - .delta. B S ) k = 0 q M k ( -
1 / .beta. ) k } B G A2 .12 ) ##EQU00013##
APPENDIX D
Program Codes of Real-Time Implementation
Version 1: Real-Time Application:
[0130] 1 GetNewBGPreds<-function(Nav,times,par) { #needs times
in minutes to make the parameters work right #remove missing values
2 times[!is,.na(Nav)]->times;Nav[!is.na(Nav)1->Nav; #second
apply the calibration parameter
3 Navipar [[31]->Nav;
[0131] #third, create arrays to hold estimates of IG, and dot IG 4
rep(O., times=length(Nav))->Idot; Nav->IG; #fourth, create
estimates of dot IG in the time before much data has been collected
5 (IG[2]-IG[ll)/(times [Z1-times ill)->Idot 121; 6 #linear
interpolation 7 data frame(y=IG[1:3],x=times[1:31)->td; 8
lm(y-x,data=td)->tx;t xScoefficients
[2]->tx;attr(tx,"names")<-NULL; tx->Idot [3] 9 data frame
(y=IG[1:4],x=times [1:4])->td; 10
lm(y-x,data=td)->tx;tx$coefficients [2]->tx;attr (tx,
"namesw)<-NULL; tx->Idot [4]; #fifth, create estimates using
splines over the CGS data 11 for (i in 5:length(Nav)) ( 12 times
[(i-4):(i)]->tt;Nav[(i-4):(i) 1->td; 13 smooth
spline(x=tt,y=td,df=1)->temp; 14 predict (temp,times
[i],deriv=1)$ y-2Idot [i]; 15 predict (temp, times [l])
Sy->IG[il; 16 } #sixth, apply the main formula 17 IG+Idotkpar
[[2]]+par [[1]]->NewBG; #seventh, return the result
18 NewBG)
APPENDIX E
Program Codes of Retrospective Implementation
Version 2: Retrospective Correction:
[0132] In addition to the real-time implementation, one can
introduce an artificial delay by extending the time over which each
spline is interpolated in line 12 from "(i-4):(i)" to
"(i-4):(i+4)." In purely retrospective analysis, one can use the
more simple form given next.
19 GetOldBGPreds<-function(Nav,times,par) { #eliminate missing
values 20 times [!is .na (Nav)]->times;
21 Nav [!is .na (Nav) 1->Nav;
[0133] #apply calibration parameter
22 par [[3] 1 *Nav->Nav;
[0134] #create a smoothing spline regression over all the data 23
sreg (times, Nav)->Navfit; #use it to predict IG 24 predict
(Navfit,times)->IG; #use it to predict dot IG 25
predict(Navfit,times,deriv=1)->Idot; #apply main formula
26 (Idot)*par [[2]]+par [[I] 1+IG->BGpreds;
[0135] #return predictions
27 BGpreds)
[0136] Finally, if the full Michaelis-Menton form of the equation 3
is desired, then one can simply replaces "par [[1]]" with
"par[[1]]*IG/(126.+IG)" in lines 17 and 27. R contains many other
smoothing and interpolation facilities, and the use of sreg, smooth
spline, and lm can be substituted with many of them, although the
input/output format is frequently different.
* * * * *