U.S. patent application number 12/164522 was filed with the patent office on 2008-10-23 for method and device for predicting physiological values.
This patent application is currently assigned to Animas Technologies, LLC.. Invention is credited to Timothy C. Dunn, Yalia Jayalakshmi, Ronald T. Kurnik, Matthew J. Lesho, Jonathan James Oliver, Russell O. Potts, Janet A. Tamada, Steven Richard Waterhouse, Charles W. Wei.
Application Number | 20080262746 12/164522 |
Document ID | / |
Family ID | 27388938 |
Filed Date | 2008-10-23 |
United States Patent
Application |
20080262746 |
Kind Code |
A1 |
Dunn; Timothy C. ; et
al. |
October 23, 2008 |
METHOD AND DEVICE FOR PREDICTING PHYSIOLOGICAL VALUES
Abstract
The invention relates generally to methods, systems, and devices
for measuring the concentration of target analytes present in a
biological system using a series of measurements obtained from a
monitoring system and a Mixtures of Experts (MOE) algorithm. In one
embodiment, the present invention describes a method for measuring
blood glucose in a subject.
Inventors: |
Dunn; Timothy C.; (San
Francisco, CA) ; Jayalakshmi; Yalia; (Sunnyvale,
CA) ; Kurnik; Ronald T.; (Foster City, CA) ;
Lesho; Matthew J.; (San Mateo, CA) ; Oliver; Jonathan
James; (Oakland, CA) ; Potts; Russell O.; (San
Francisco, CA) ; Tamada; Janet A.; (Mountain View,
CA) ; Waterhouse; Steven Richard; (San Francisco,
CA) ; Wei; Charles W.; (Fremont, CA) |
Correspondence
Address: |
PHILIP S. JOHNSON;JOHNSON & JOHNSON
ONE JOHNSON & JOHNSON PLAZA
NEW BRUNSWICK
NJ
08933-7003
US
|
Assignee: |
Animas Technologies, LLC.
West Chester
PA
|
Family ID: |
27388938 |
Appl. No.: |
12/164522 |
Filed: |
June 30, 2008 |
Related U.S. Patent Documents
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Application
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Filing Date |
Patent Number |
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10626896 |
Jul 24, 2003 |
7405055 |
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12164522 |
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09911341 |
Jul 23, 2001 |
6653091 |
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10626896 |
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09405976 |
Sep 27, 1999 |
6326160 |
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09911341 |
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09241929 |
Feb 1, 1999 |
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09405976 |
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09198039 |
Nov 23, 1998 |
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09241929 |
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09163856 |
Sep 30, 1998 |
6180416 |
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09198039 |
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Current U.S.
Class: |
702/19 |
Current CPC
Class: |
Y10S 436/815 20130101;
A61B 5/441 20130101; Y10S 436/806 20130101; Y10T 436/115831
20150115; A61B 5/1486 20130101; Y10S 435/808 20130101; A61B 5/14532
20130101; Y10S 436/805 20130101; Y10S 435/817 20130101 |
Class at
Publication: |
702/19 |
International
Class: |
G06F 19/00 20060101
G06F019/00 |
Claims
1-24. (canceled)
25. One or more microprocessors for use in an analyte monitoring
system for measuring an amount of concentration of analyte present
in a biological system, said one or more microprocessors comprising
programming to control: providing two or more ranges of measurement
values, wherein said measurement values are indicative of amounts
or concentration of analyte present in the biological system:
identifying the range in which a selected measurement value falls,
and employing an algorithm for prediction of further measurement
values wherein said algorithm is optimized for performance in the
identified range.
26. The one or more microprocessors of claim 25, wherein a Mixtures
of Experts algorithm is used to determine said selected measurement
value and said Mixtures of Experts algorithm is trained using a
global training set.
27. The one more microprocessors of claim 25, wherein said
algorithm for prediction of further measurement values is a
Mixtures of Experts algorithm and said Mixtures of Experts
algorithm is trained using data from the identified range.
28. The one or more microprocessors of claim 25, wherein said or
more microprocessors are further programmed to control operation of
a sensing device that provides raw signal specifically related to
analyte amount or concentration in the biological system.
29. The one or more microprocessors of claim 28, wherein said one
or more microprocessors are further programmed to control
correlating the raw signal with a measurement value indicative of
analyte amount of concentration in the biological system.
30. The one or more microprocessors of claim 29, wherein for the
Mixtures of Experts algorithm the individual experts have a linear
form An = i = l n An i w i ( 1 ) ##EQU00023## wherein (An) is an
analyte of interest, n is the number of experts, An.sub.i is the
analyte predicted by Expert i; and w.sub.i is a parameter, and the
individual experts An.sub.i are further defined by the expression
shown as Equation (2) An i = j = l m a ij P j + z i ( 2 )
##EQU00024## wherein, An.sub.i is the analyte predicted by Expert
i; P.sub.j is one of m parameters, m is typically less then 100;
a.sub.ij are coefficients; and z.sub.i is a constant; and further
where the weighting value, w.sub.i, is defined by the formula shown
as Equation (3) w i = d i [ k = l n d k ] ( 3 ) ##EQU00025## where
e refers to the exponential function, d.sub.i is one of the
d.sub.k, d.sub.i and d.sub.k are parameter sets analogous to
Equation 2 used to determine the weight w.sub.i, the d.sub.k are
given by Equation 4 d k = j = l m .alpha. jk P j + .omega. k ( 4 )
##EQU00026## where a.sub.jk is coefficient, P.sub.j is one of m
parameters, and where .omega..sub.k is a constant.
31. The one or more microprocessors of claim 30, wherein the
analyte is glucose.
32. A method to measure an amount of concentration of analyte
present in a biological system, the method comprising: providing
two or more ranges of measurement values, in which said measurement
values are indicative of amounts or concentration of analyte
present in the biological system; identifying the range in which a
selected measurement value falls; and employing an algorithm to
predict further measurement values in the identified range.
33. The method of claim 32, in which the algorithm comprises: for
the Mixtures of Experts algorithm the individual experts have a
linear form An = i = l n An i w i ( 1 ) ##EQU00027## wherein (An)
is an analyte of interest, n is the number of experts, An.sub.i is
the analyte predicted by Expert i; and w.sub.i is a parameter, and
the individual experts An.sub.i are further defined by the
expression shown as Equation (2) An i = j = l m a ij P j + z i ( 2
) ##EQU00028## wherein, An.sub.i is the analyte predicted by Expert
i; P.sub.j is one of m parameters, m is typically less then 100;
a.sub.ij are coefficients; and z.sub.i is a constant; and further
where the weighting value, w.sub.i, is defined by the formula shown
as Equation (3) w i = d i [ k = l n d k ] ( 3 ) ##EQU00029## where
e refers to the exponential function, d.sub.i is one of the
d.sub.k, d.sub.i and d.sub.k are parameters sets analogous to
Equation 2 used to determine the weight w.sub.i, the d.sub.k are
given by Equation 4 d k = j = l m .alpha. jk P j + .omega. k . ( 4
) ##EQU00030## where a.sub.jk is coefficient, P.sub.j is one of m
parameters, and where .omega..sub.k is a constant.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a continuation-in-part of U.S. patent
application Ser. No. 09/241,929, filed 1 Feb. 1999, which is a
continuation-in-part of U.S. patent application Ser. No.
09/198,039, filed 23 Nov. 1998, which is a continuation-in-part of
U.S. patent application Ser. No. 09/163,856, filed 30 Sep. 1998,
all applications are herein incorporated by reference in their
entireties.
FIELD OF THE INVENTION
[0002] The invention relates generally to a method and device for
measuring the concentration of target chemical analytes present in
a biological system. More particularly, the invention relates to a
method and monitoring systems for predicting a concentration of an
analyte using a series of measurements obtained from a monitoring
system and a Mixtures of Experts (MOE) algorithm.
BACKGROUND OF THE INVENTION
[0003] The Mixtures of Experts model is a statistical method for
classification and regression (Waterhouse, S., "Classification and
Regression Using Mixtures of Experts, October 199.7, Ph.D. Thesis,
Cambridge University). Waterhouse discusses Mixtures of Experts
models from a theoretical perspective and compares them with other
models, such as, trees, switching regression models, modular
networks. The first extension described in Waterhouse's thesis is a
constructive algorithm for learning model architecture and
parameters, which is inspired by recursive partitioning. The second
extension described in Waterhouse's thesis uses Bayesian methods
for learning the parameters of the model. These extensions are
compared empirically with the standard Mixtures of Experts model
and with other statistical models on small to medium sized data
sets. Waterhouse also describes the application of the Mixtures of
Experts framework to acoustic modeling within a large vocabulary
speech recognition system.
[0004] The Mixtures of Experts model has been employed in protein
secondary structure prediction (Barlow, T. W., Journal Of Molecular
Graphics, 13 (3), p. 175-183, 1995). In this method input data were
clustered and used to train a series different networks.
Application of a Hierarchical Mixtures of Experts to the prediction
of protein secondary structure was shown to provide no advantages
over a single network.
[0005] Mixtures of Experts algorithms have also been applied to the
analysis of a variety of different kinds of data sets including the
following: human motor systems (Ghahramani, Z. and Wolpert, D. M.,
Nature, 386(6623):392-395, 1997); and economic analysis (Hamilton,
J. D. and Susmel, R., Journal of Econometrics, 64(1-2):307-333,
1994).
SUMMARY OF THE INVENTION
[0006] The present invention provides a method and device (for
example, a monitoring or sampling system) for continually or
continuously measuring the concentration of an analyte present in a
biological system. The method entails continually or continuously
detecting a raw signal from the biological system, wherein the raw
signal is specifically related to the analyte. A calibration step
is performed to correlate the raw signal with a measurement value
indicative of the concentration of analyte present in the
biological system. These steps of detection and calibration are
used to obtain a series of measurement values at selected time
intervals. Once the series of measurement values is obtained, the
method of the invention provides for the prediction of a
measurement value using a Mixtures of Experts (MOE) algorithm.
[0007] The raw signal can be obtained using any suitable sensing
methodology including, for example, methods which rely on direct
contact of a sensing apparatus with the biological system; methods
which extract samples from the biological system by invasive,
minimally invasive, and non-invasive sampling techniques, wherein
the sensing apparatus is contacted with the extracted sample;
methods which rely on indirect contact of a sensing apparatus with
the biological system; and the like. In preferred embodiments of
the invention, methods are used to extract samples from the
biological sample using minimally invasive or non-invasive sampling
techniques. The sensing apparatus used with any of the above-noted
methods can employ any suitable sensing element to provide the raw
signal including, but not limited to, physical, chemical,
electrochemical, photochemical, spectrophotometric, polarimetric,
calorimetric, radiometric, or like elements. In preferred
embodiments of the invention, a biosensor is used which comprises
an electrochemical sensing element.
[0008] In one particular embodiment of the invention, the raw
signal is obtained using a transdermal sampling system that is
placed in operative contact with a skin or mucosal surface of the
biological system. The sampling system transdermally extracts the
analyte from the biological system using any appropriate sampling
technique, for example, iontophoresis. The transdermal sampling
system is maintained in operative contact with the skin or mucosal
surface of the biological system to provide for continual or
continuous analyte measurement.
[0009] In a preferred embodiment of the invention, a Mixtures of
Experts algorithm is used to predict measurement values. The
general Mixtures of Experts algorithm is represented by the
following series of equations: where the individual experts have a
linear form:
An = i = 1 n An i w i ( 1 ) ##EQU00001##
wherein (An) is an analyte of interest, n is the number of experts,
An.sub.i is the analyte predicted by Expert i; and w.sub.i is a
parameter, and the individual experts An.sub.i are further defined
by the expression shown as Equation (2)
An i = j = 1 m a ij P j + z i ( 2 ) ##EQU00002##
wherein, An.sub.i is the analyte predicted by Expert i; P.sub.j is
one of m parameters, m is typically less than 100; a.sub.ij are
coefficients; and z.sub.i is a constant; and further where the
weighting value, w.sub.i, is defined by the formula shown as
Equation (3).
w i = d i [ k = 1 n d k ] ( 3 ) ##EQU00003##
where e refers to the exponential function and the d.sub.k (note
that the d.sub.i in the numerator of Equation 3 is one of the
d.sub.k) are a parameter set analogous to Equation 2 that is used
to determine the weights w.sub.i. The d.sub.k are given by Equation
4.
d k = j = 1 m .alpha. jk P j + .omega. k ( 4 ) ##EQU00004##
where .alpha..sub.jk is a coefficient, P.sub.j is one of m
parameters, and where .omega..sub.k is a constant.
[0010] Another object of the invention to use the Mixtures of
Experts algorithm of the invention to predict blood glucose values.
In one aspect, the method of the invention is used in conjunction
with an iontophoretic sampling device that provides continual or
continuous blood glucose measurements. In one embodiment the
Mixtures of Experts algorithm is essentially as follows: where the
individual experts have a linear form
BG=w.sub.1BG.sub.1+w.sub.2BG.sub.2+w.sub.3BG.sub.3 (5)
wherein (BG) is blood glucose, there are three experts (n=3) and
BG.sub.i is the analyte predicted by Expert i; w.sub.i is a
parameter, and the individual Experts BG.sub.i are further defined
by the expression shown as Equations 6, 7, and 8
BG.sub.1=p.sub.1(time)+q.sub.1(active)+r.sub.1(signal)+s.sub.1(BG|cp)+t.-
sub.1 (6)
BG.sub.2=p.sub.2(time)+q.sub.2(active)+r.sub.2(signal)+s.sub.2(BG|cp)+t.-
sub.2 (7)
BG.sub.3=p.sub.3(time)+q.sub.3(active)+r.sub.3(signal)+s.sub.3(BG|cp)+t.-
sub.3 (8)
wherein, BG.sub.i is the analyte predicted by Expert i; parameters
include, time (elapsed time since the sampling system was placed in
operative contact with said biological system), active (active
signal), signal (calibrated signal), and BG/cp (blood glucose value
at a calibration point); p.sub.i, q.sub.i, r.sub.i, and s.sub.i are
coefficients; and t.sub.i is a constant; and further where the
weighting value, w.sub.i, is defined by the formulas shown as
Equations 9, 10, and 11
w 1 = d 1 d 1 + d 2 + d 3 ( 9 ) w 2 = d 2 d 1 + d 2 + d 3 ( 10 ) w
3 = d 3 d 1 + d 2 + d 3 ( 11 ) ##EQU00005##
where e refers to the exponential function and d.sub.i is a
parameter set (analogous to Equations 6, 7, and 8) that are used to
determine the weights w.sub.i, given by Equations 9, 10, and 11,
and
d.sub.1=.tau..sub.1(time)+.beta..sub.1(active)+.gamma..sub.1(signal)+.de-
lta..sub.1(BG|cp)+.di-elect cons..sub.1 (12)
d.sub.2=.tau..sub.2(time)+.beta..sub.2(active)+.gamma..sub.2(signal)+.de-
lta..sub.2(BG|cp)+.di-elect cons..sub.2 (13)
d.sub.3=.tau..sub.3(time)+.beta..sub.3(active)+.gamma..sub.3(signal)+.de-
lta..sub.3(BG|cp)+.di-elect cons..sub.3 (14)
where .tau..sub.i, .beta..sub.i, .gamma..sub.i and .delta..sub.i
are coefficients, and where .di-elect cons..sub.i is a
constant.
[0011] In another embodiment for the prediction of blood glucose
values, the Mixtures of Experts algorithm is essentially as
follows: where the individual experts have a linear form
BG=w.sub.1BG.sub.1+w.sub.2BG.sub.2+w.sub.3BG.sub.3 (15)
wherein (BG) is blood glucose, there are three experts (n=3) and
BG.sub.i is the analyte predicted by Expert i; w.sub.i is a
parameter, and the individual Experts BG.sub.i are further defined
by the expression shown as Equations 16, 17, and 18
BG.sub.1=p.sub.1(time.sub.c)+q.sub.1(active)+r.sub.1(signal)+s.sub.1(BG|-
cp)+t.sub.1 (16)
BG.sub.2=p.sub.2(time.sub.c)+q.sub.2(active)+r.sub.2(signal)+s.sub.2(BG|-
cp)+t.sub.2 (17)
BG.sub.3=p.sub.3(time.sub.c)+q.sub.3(active)+r.sub.3(signal)+s.sub.3(BG|-
cp)+t.sub.3 (18)
wherein, BG.sub.i is the analyte predicted by Expert i; parameters
include, time.sub.c (elapsed time since calibration of said
sampling system), active (active signal), signal (calibrated
signal), and BG/cp (blood glucose value at a calibration point);
p.sub.i, q.sub.i, r.sub.i, and s.sub.i are coefficients; and
t.sub.i is a constant; and further where the weighting value,
w.sub.i, is defined by the formulas shown as Equations 19, 20, and
21
w 1 = d 1 d 1 + d 2 + d 3 ( 19 ) w 2 = d 2 d 1 + d 2 + d 3 ( 20 ) w
3 = d 3 d 1 + d 2 + d 3 ( 21 ) ##EQU00006##
where e refers to the exponential function and d.sub.i is a
parameter set (analogous to Equations 6, 7, and 8) that are used to
determine the weights w.sub.i, given by Equations 19, 20, and 21,
and
d.sub.1=.tau..sub.1(time.sub.c)+.beta..sub.1(active)+.gamma..sub.1(signa-
l)+.delta..sub.1(BG|cp)+.di-elect cons..sub.1 (22)
d.sub.2=.tau..sub.2(time.sub.c)+.beta..sub.2(active)+.gamma..sub.2(signa-
l)+.delta..sub.2(BG|cp)+.di-elect cons..sub.2 (23)
d.sub.3=.tau..sub.3(time.sub.c)+.beta..sub.3(active)+.gamma..sub.3(signa-
l)+.delta..sub.3(BG|cp)+.di-elect cons..sub.3 (24)
where .tau..sub.i, .beta..sub.i, .gamma..sub.i and .delta..sub.i
are coefficients, and where .di-elect cons..sub.i is a
constant.
[0012] Parameters can be substituted, and/or other parameters can
be included in these calculations, for example, time parameters can
be varied (e.g., as described above, elapsed time since the
sampling system was placed in contact with a biological system, or
elapsed time since the sampling system was calibrated) or multiple
time parameters can be used in the same equation where these
parameters are appropriately weighted. Further parameters include,
but are not limited to, temperature, ionophoretic voltage, and skin
conductivity. In addition, a calibration check can be used to
insure an efficacious calibration.
[0013] A further object of the invention to provide a method for
measuring an analyte, for example, blood glucose, in a subject. In
one embodiment, the method entails operatively contacting a glucose
sensing apparatus with the subject to detect blood glucose and thus
obtain a raw signal from the sensing apparatus. The raw signal is
specifically related to the glucose, and is converted into a
measurement value indicative of the subject's blood glucose
concentration using a calibration step. In one aspect of the
invention, the sensing apparatus is a near-IR spectrometer. In
another aspect of the invention, the sensing means comprises a
biosensor having an electrochemical sensing element.
[0014] It is also an object of the invention to provide a
monitoring system for continually or continuously measuring an
analyte present in a biological system. The monitoring system is
formed from the operative combination of a sampling means, a
sensing means, and a microprocessor means which controls the
sampling means and the sensing means. The sampling means is used to
continually or continuously extract the analyte from the biological
system across a skin or mucosal surface of said biological system.
The sensing means is arranged in operative contact with the analyte
extracted by the sampling means, such that the sensing means can
obtain a raw signal from the extracted analyte which signal is
specifically related to the analyte. The microprocessor means
communicates with the sampling means and the sensing means, and is
used to: (a) control the sampling means and the sensing means to
obtain a series of raw signals at selected time intervals during a
continual or continuous measurement period; (b) correlate the raw
signals with measurement values indicative of the concentration of
analyte present in the biological system; and (c) predict a
measurement value using the Mixtures of Experts algorithm. In one
aspect, the monitoring system uses an iontophoretic current to
extract the analyte from the biological system.
[0015] It is a further object of the invention to provide a
monitoring system for measuring blood glucose in a subject. The
monitoring system is formed from an operative combination of a
sensing means and a microprocessor means. The sensing means is
adapted for operative contact with the subject or with a
glucose-containing sample extracted from the subject, and is used
to obtain a raw signal specifically related to blood glucose in the
subject. The microprocessor means communicates with the sensing
means, and is used to: (a) control the sensing means to obtain a
series of raw signals (specifically related to blood glucose) at
selected time intervals; (b) correlate the raw signals with
measurement values indicative of the concentration of blood glucose
present in the subject; and (c) predict a measurement value using
the Mixtures of Experts algorithm.
[0016] In a further aspect, the monitoring system comprises a
biosensor having an electrochemical sensing element. In another
aspect, the monitoring system comprises a near-IR spectrometer.
[0017] Additional objects, advantages and novel features of the
invention will be set forth in part in the description which
follows, and in part will become apparent to those skilled in the
art upon examination of the following, or may be learned by
practice of the invention.
BRIEF DESCRIPTION OF THE DRAWINGS
[0018] FIG. 1A depicts a top plan view of an iontophoretic
collection reservoir and electrode assembly for use in a
transdermal sampling device constructed according to the present
invention.
[0019] FIG. 1B depicts the side view of the iontophoretic
collection reservoir and electrode assembly shown in FIG. 1A.
[0020] FIG. 2 is a pictorial representation of an iontophoretic
sampling device which includes the iontophoretic collection
reservoir and electrode assembly of FIGS. 1A and 1B.
[0021] FIG. 3 is an exploded pictorial representation of components
from a preferred embodiment of the automatic sampling system of the
present invention.
[0022] FIG. 4 is a representation of one embodiment of a bimodal
electrode design. The figure presents an overhead and schematic
view of the electrode assembly 433. In the figure, the bimodal
electrode is shown at 430 and can be, for example, a Ag/AgCl
iontophoretic/counter electrode. The sensing or working electrode
(made from, for example, platinum) is shown at 431. The reference
electrode is shown at 432 and can be, for example, a Ag/AgCl
electrode. The components are mounted on a suitable nonconductive
substrate 434, for example, plastic or ceramic. The conductive
leads 437 (represented by dotted lines) leading to the connection
pad 435 are covered by a second nonconductive piece 436 (the area
represented by vertical striping) of similar or different material
(e.g., plastic or ceramic). In this example of such an electrode
the working electrode area is approximately 1.35 cm.sup.2. The
dashed line in FIG. 4 represents the plane of the cross-sectional
schematic view presented in FIG. 5.
[0023] FIG. 5 is a representation of a cross-sectional schematic
view of the bimodal electrodes as they may be used in conjunction
with a reference electrode and a hydrogel pad. In the figure, the
components are as follows: bimodal electrodes 540 and 541; sensing
electrodes 542 and 543; reference electrodes 544 and 545; a
substrate 546; and hydrogel pads 547 and 548.
[0024] FIG. 6 depicts predicted blood glucose data (using the
Mixtures of Experts algorithm) versus measured blood glucose data,
as described in Example 2.
[0025] FIG. 7 depicts predicted blood glucose data (using the
Mixtures of Experts algorithm) versus measured blood glucose data,
as described in Example 4.
[0026] FIG. 8 presents a graph of the measured and predicted blood
glucose levels vs. time, as described in Example 4.
[0027] FIG. 9 depicts an exploded view of an embodiment of an
autosensor.
[0028] FIGS. 10A and 10B graphically illustrate the method of the
present invention used for decreasing the bias of a data set.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0029] Before describing the present invention in detail, it is to
be understood that this invention is not limited to particular
compositions or biological systems, as such may vary. It is also to
be understood that the terminology used herein is for the purpose
of describing particular embodiments only, and is not intended to
be limiting.
[0030] It must be noted that, as used in this specification and the
appended claims, the singular forms "a", "an" and "the" include
plural referents unless the content clearly dictates otherwise.
Thus, for example, reference to "an analyte" includes mixtures of
analytes, and the like.
[0031] All publications, patents and patent applications cited
herein, whether supra or infra, are hereby incorporated by
reference in their entirety.
[0032] Unless defined otherwise, all technical and scientific terms
used herein have the same meaning as commonly understood by one of
ordinary skill in the art to which the invention pertains. Although
any methods and materials similar or equivalent to those described
herein can be used in the practice for testing of the present
invention, the preferred materials and methods are described
herein.
[0033] In describing and claiming the present invention, the
following terminology will be used in accordance with the
definitions set out below.
1.0.0 DEFINITIONS
[0034] The terms "analyte" and "target analyte" are used herein to
denote any physiological analyte of interest that is a specific
substance or component that is being detected and/or measured in a
chemical, physical, enzymatic, or optical analysis. A detectable
signal (e.g., a chemical signal or electrochemical signal) can be
obtained, either directly or indirectly, from such an analyte or
derivatives thereof. Furthermore, the terms "analyte" and
"substance" are used interchangeably herein, and are intended to
have the same meaning, and thus encompass any substance of
interest. In preferred embodiments, the analyte is a physiological
analyte of interest, for example, glucose, or a chemical that has a
physiological action, for example, a drug or pharmacological
agent.
[0035] A "sampling device" or "sampling system" refers to any
device for obtaining a sample from a biological system for the
purpose of determining the concentration of an analyte of interest.
As used herein, the term "sampling" means invasive, minimally
invasive or non-invasive extraction of a substance from the
biological system, generally across a membrane such as skin or
mucosa. The membrane can be natural or artificial, and can be of
plant or animal nature, such as natural or artificial skin, blood
vessel tissue, intestinal tissue, and the like. Typically, the
sampling means are in operative contact with a "reservoir," or
"collection reservoir," wherein the sampling means is used for
extracting the analyte from the biological system into the
reservoir to obtain the analyte in the reservoir. A "biological
system" includes both living and artificially maintained systems.
Examples of minimally invasive and noninvasive sampling techniques
include iontophoresis, sonophoresis, suction, electroporation,
thermal poration, passive diffusion, microfine (miniature) lances
or cannulas, subcutaneous implants or insertions, and laser
devices. Sonophoresis uses ultrasound to increase the permeability
of the skin (see, e.g., Menon et al. (1994) Skin Pharmacology
7:130-139). Suitable sonophoresis sampling systems are described in
International Publication No. WO 91/12772, published 5 Sep. 1991.
Passive diffusion sampling devices are described, for example, in
International Publication Nos.: WO 97/38126 (published 16 Oct.
1997); WO 97/42888, WO 97/42886, WO 97/42885, and WO 97/42882 (all
published 20 Nov. 1997); and WO 97/43962 (published 27 Nov. 1997).
Laser devices use a small laser beam to burn a hole through the
upper layer of the patient's skin (see, e.g., Jacques et al. (1978)
J. Invest. Dermatology 88:88-93). Examples of invasive sampling
techniques include traditional needle and syringe or vacuum sample
tube devices.
[0036] The term "collection reservoir" is used to describe any
suitable containment means for containing a sample extracted from a
biological system. For example, the collection reservoir can be a
receptacle containing a material which is ionically conductive
(e.g., water with ions therein), or alternatively, it can be a
material, such as, a sponge-like material or hydrophilic polymer,
used to keep the water in place. Such collection reservoirs can be
in the form of a hydrogel (for example, in the form of a disk or
pad). Hydrogels are typically referred to as "collection inserts."
Other suitable collection reservoirs include, but are not limited
to, tubes, vials, capillary collection devices, cannulas, and
miniaturized etched, ablated or molded flow paths.
[0037] A "housing" for the sampling system can further include
suitable electronics (e.g., microprocessor, memory, display and
other circuit components) and power sources for operating the
sampling system in an automatic fashion.
[0038] A "monitoring system," as used herein, refers to a system
useful for continually or continuously measuring a physiological
analyte present in a biological system. Such a system typically
includes, but is not limited to, sampling means, sensing means, and
a microprocessor means in operative communication with the sampling
means and the sensing means.
[0039] The term "artificial," as used herein, refers to an
aggregation of cells of monolayer thickness or greater which are
grown or cultured in vivo or in vitro, and which function as a
tissue of an organism but are not actually derived, or excised,
from a pre-existing source or host.
[0040] The term "subject" encompasses any warm-blooded animal,
particularly including a member of the class Mammalia such as,
without limitation, humans and nonhuman primates such as
chimpanzees and other apes and monkey species; farm animals such as
cattle, sheep, pigs, goats and horses; domestic mammals such as
dogs and cats; laboratory animals including rodents such as mice,
rats and guinea pigs, and the like. The term does not denote a
particular age or sex. Thus, adult and newborn subjects, as well as
fetuses, whether male or female, are intended to be covered.
[0041] As used herein, the term "continual measurement" intends a
series of two or more measurements obtained from a particular
biological system, which measurements are obtained using a single
device maintained in operative contact with the biological system
over the time period in which the series of measurements is
obtained. The term thus includes continuous measurements.
[0042] The term "transdermal," as used herein, includes both
transdermal and transmucosal techniques, i.e., extraction of a
target analyte across skin or mucosal tissue. Aspects of the
invention which are described herein in the context of
"transdermal," unless otherwise specified, are meant to apply to
both transdermal and transmucosal techniques.
[0043] The term "transdermal extraction," or "transdermally
extracted" intends any noninvasive, or at least minimally invasive
sampling method, which entails extracting and/or transporting an
analyte from beneath a tissue surface across skin or mucosal
tissue. The term thus includes extraction of an analyte using
iontophoresis (reverse iontophoresis), electroosmosis,
sonophoresis, microdialysis, suction, and passive diffusion. These
methods can, of course, be coupled with application of skin
penetration enhancers or skin permeability enhancing technique such
as tape stripping or pricking with micro-needles. The term
"transdermally extracted" also encompasses extraction techniques
which employ thermal poration, electroporation, microfine lances,
microfine canulas, subcutaneous implants or insertions, and the
like.
[0044] The term "iontophoresis" intends a method for transporting
substances across tissue by way of an application of electrical
energy to the tissue. In conventional iontophoresis, a reservoir is
provided at the tissue surface to serve as a container of material
to be transported. Iontophoresis can be carried out using standard
methods known to those of skill in the art, for example, by
establishing an electrical potential using a direct current (DC)
between fixed anode and cathode "iontophoretic electrodes,"
alternating a direct current between anode and cathode
iontophoretic electrodes, or using a more complex waveform such as
applying a current with alternating polarity (AP) between
iontophoretic electrodes (so that each electrode is alternately an
anode or a cathode).
[0045] The term "reverse iontophoresis" refers to the movement of a
substance from a biological fluid across a membrane by way of an
applied electric potential or current. In reverse iontophoresis, a
reservoir is provided at the tissue surface to receive the
extracted material.
[0046] "Electroosmosis" refers to the movement of a substance
through a membrane by way of an electric field-induced convective
flow. The terms iontophoresis, reverse iontophoresis, and
electroosmosis, will be used interchangeably herein to refer to
movement of any ionically charged or uncharged substance across a
membrane (e.g., an epithelial membrane) upon application of an
electric potential to the membrane through an ionically conductive
medium.
[0047] The term "sensing device," "sensing means," or "biosensor
device" encompasses any device that can be used to measure the
concentration of an analyte, or derivative thereof, of interest.
Preferred sensing devices for detecting blood analytes generally
include electrochemical devices and chemical devices. Examples of
electrochemical devices include the Clark electrode system (see,
e.g., Updike, et al., (1967) Nature 214:986-988), and other
amperometric, coulometric, or potentiometric electrochemical
devices. Examples of chemical devices include conventional
enzyme-based reactions as used in the Lifescan.RTM. glucose monitor
(Johnson and Johnson, New Brunswick, N.J.) (see, e.g., U.S. Pat.
No. 4,935,346 to Phillips, et al.).
[0048] A "biosensor" or "biosensor device" includes, but is not
limited to, a "sensor element" which includes, but is not limited
to, a "biosensor electrode" or "sensing electrode" or "working
electrode" which refers to the electrode that is monitored to
determine the amount of electrical signal at a point in time or
over a given time period, which signal is then correlated with the
concentration of a chemical compound. The sensing electrode
comprises a reactive surface which converts the analyte, or a
derivative thereof, to electrical signal. The reactive surface can
be comprised of any electrically conductive material such as, but
not limited to, platinum-group metals (including, platinum,
palladium, rhodium, ruthenium, osmium, and iridium), nickel,
copper, silver, and carbon, as well as, oxides, dioxides,
combinations or alloys thereof. Some catalytic materials,
membranes, and fabrication technologies suitable for the
construction of amperometric biosensors were described by Newman,
J. D., et al. (Analytical Chemistry 67(24), 4594-4599, 1995).
[0049] The "sensor element" can include components in addition to a
biosensor electrode, for example, it can include a "reference
electrode," and a "counter electrode." The term "reference
electrode" is used herein to mean an electrode that provides a
reference potential, e.g., a potential can be established between a
reference electrode and a working electrode. The term "counter
electrode" is used herein to mean an electrode in an
electrochemical circuit which acts as a current source or sink to
complete the electrochemical circuit. Although it is not essential
that a counter electrode be employed where a reference electrode is
included in the circuit and the electrode is capable of performing
the function of a counter electrode, it is preferred to have
separate counter and reference electrodes because the reference
potential provided by the reference electrode is most stable when
it is at equilibrium. If the reference electrode is required to act
further as a counter electrode, the current flowing through the
reference electrode may disturb this equilibrium. Consequently,
separate electrodes functioning as counter and reference electrodes
are most preferred.
[0050] In one embodiment, the "counter electrode" of the "sensor
element" comprises a "bimodal electrode." The term "bimodal
electrode" as used herein typically refers to an electrode which is
capable of functioning non-simultaneously as, for example, both the
counter electrode (of the "sensor element") and the iontophoretic
electrode (of the "sampling means").
[0051] The terms "reactive surface," and "reactive face" are used
interchangeably herein to mean the surface of the sensing electrode
that: (1) is in contact with the surface of an electrolyte
containing material (e.g. gel) which contains an analyte or through
which an analyte, or a derivative thereof, flows from a source
thereof; (2) is comprised of a catalytic material (e.g., carbon,
platinum, palladium, rhodium, ruthenium, or nickel and/or oxides,
dioxides and combinations or alloys thereof) or a material that
provides sites for electrochemical reaction; (3) converts a
chemical signal (e.g. hydrogen peroxide) into an electrical signal
(e.g., an electrical current); and (4) defines the electrode
surface area that, when composed of a reactive material, is
sufficient to drive the electrochemical reaction at a rate
sufficient to generate a detectable, reproducibly measurable,
electrical signal that is correlatable with the amount of analyte
present in the electrolyte.
[0052] An "ionically conductive material" refers to any material
that provides ionic conductivity, and through which
electrochemically active species can diffuse. The ionically
conductive material can be, for example, a solid, liquid, or
semi-solid (e.g., in the form of a gel) material that contains an
electrolyte, which can be composed primarily of water and ions
(e.g., sodium chloride), and generally comprises 50% or more water
by weight. The material can be in the form of a gel, a sponge or
pad (e.g., soaked with an electrolytic solution), or any other
material that can contain an electrolyte and allow passage
therethrough of electrochemically active species, especially the
analyte of interest.
[0053] The term "physiological effect" encompasses effects produced
in the subject that achieve the intended purpose of a therapy. In
preferred embodiments, a physiological effect means that the
symptoms of the subject being treated are prevented or alleviated.
For example, a physiological effect would be one that results in
the prolongation of survival in a patient.
[0054] A "laminate", as used herein, refers to structures comprised
of at least two bonded layers. The layers may be bonded by welding
or through the use of adhesives. Examples of welding include, but
are not limited to, the following: ultrasonic welding, heat
bonding, and inductively coupled localized heating followed by
localized flow. Examples of common adhesives include, but are not
limited to, pressure sensitive adhesives, thermoset adhesives,
cyanocrylate adhesives, epoxies, contact adhesives, and heat
sensitive adhesives.
[0055] A "collection assembly", as used herein, refers to
structures comprised of several layers, where the assembly includes
at least one collection insert, for example a hydrogel. An example
of a collection assembly of the present invention is a mask layer,
collection inserts, and a retaining layer where the layers are held
in appropriate, functional relationship to each other but are not
necessarily a laminate, i.e., the layers may not be bonded
together. The layers may, for example, be held together by
interlocking geometry or friction.
[0056] An "autosensor assembly", as used herein, refers to
structures generally comprising a mask layer, collection inserts, a
retaining layer, an electrode assembly, and a support tray. The
autosensor assembly may also include liners. The layers of the
assembly are held in appropriate, functional relationship to each
other:
[0057] The mask and retaining layers are preferably composed of
materials that are substantially impermeable to the analyte
(chemical signal) to be detected (e.g., glucose); however, the
material can be permeable to other substances. By "substantially
impermeable" is meant that the material reduces or eliminates
chemical signal transport (e.g., by diffusion). The material can
allow for a low level of chemical signal transport, with the
proviso that chemical signal that passes through the material does
not cause significant edge effects at the sensing electrode.
[0058] "Substantially planar" as used herein, includes a planar
surface that contacts a slightly curved surface, for example, a
forearm or upper arm of a subject. A "substantially planar" surface
is, for example, a surface having a shape to which skin can
conform, i.e., contacting contact between the skin and the
surface.
[0059] A "Mixtures of Experts (MOE)" algorithm is used in the
practice of the present invention. An example of a Mixtures of
Experts algorithm useful in connection with the present invention
is represented by the following equations, where the individual
experts have a linear form:
An = i = 1 n An i w i ( 1 ) ##EQU00007##
wherein (An) is an analyte of interest, n is the number of experts,
An.sub.i is the analyte predicted by Expert i; and w.sub.i is a
parameter, and the individual experts An.sub.i are further defined
by the expression shown as Equation (2)
An i = j = 1 m a ij P j + z i ( 2 ) ##EQU00008##
wherein, An.sub.i is the analyte predicted by Expert i; P.sub.j is
one of m parameters, m is typically less than 100; a.sub.ij are
coefficients; and z.sub.i is a constant; and further where the
weighting value, w.sub.i, is defined by the formula shown as
Equation (3).
w i = d i [ k = 1 n d k ] ( 3 ) ##EQU00009##
where e refers to the exponential function the d.sub.k (note that
the d.sub.i in the numerator of Equation 3 is one of the d.sub.k)
are a parameter set analogous to Equation 2 that is used to
determine the weights w.sub.i. The d.sub.k are given by Equation
4.
d k = j = 1 m .alpha. jk P j + .omega. k ( 4 ) ##EQU00010##
where .alpha..sub.jk is a coefficient, P.sub.j is one of m
parameters, and where .omega..sub.k is a constant.
[0060] The Mixtures of Experts algorithm is a generalized
predictive technology for data analysis. This method uses a
superposition of multiple linear regressions, along with a
switching algorithm, to predict outcomes. Any number of
input/output variables are possible. The unknown coefficients in
this method are determined by a maximum posterior probability
technique.
[0061] The method is typically implemented as follows. An
experimental data set of input/output pairs is assembled that spans
the expected ranges of all variables. These variables are then used
to train the Mixtures of Experts (that is, used to determine the
unknown coefficients). These coefficients are determined using, for
example, the Expectation Maximization method (Dempster, A. P., N.
M. Laird, and D. B. Rubin, J. Royal Statistical Society (Series
B-Methodological) 39:(1), 1977). Once these coefficients are known,
the Mixtures of Experts is easily applied to a new data set.
[0062] "Parameter" as used herein refers to an arbitrary constant
or variable so appearing in a mathematical expression that changing
it give various cases of the phenomenon represented (McGraw-Hill
Dictionary of Scientific and Technical Terms, S. P. Parker, ed.,
Fifth Edition, McGraw-Hill Inc., 1994). In the context of the
GlucoWatch.RTM. monitor (Cygnus, Inc., Redwood City, Calif.), a
parameter is a variable that influences the value of the blood
glucose level as calculated by an algorithm. For the Mixtures of
Experts algorithm, these parameters include, but are not limited
to, the following: time (e.g., elapsed time since the monitor was
applied to a subject; and/or elapsed time since calibration); the
active signal; the calibrated signal; the blood glucose value at
the calibration point; the skin temperature; the skin conductivity;
and the iontophoretic voltage. Changes in the values of any of
these parameters can be expected to change the value of the
calculated blood glucose value. Parameters can be substituted,
and/or other parameters can be included in these calculations, for
example, time parameters can be varied (e.g., is elapsed time since
the sampling system was placed in contact with a biological system,
or elapsed time since the sampling system was calibrated) or
multiple time parameters can be used in the same equation where
these parameters are appropriately weighted.
[0063] By the term "printed" as used herein is meant a
substantially uniform deposition of an electrode formulation onto
one surface of a substrate (i.e., the base support). It will be
appreciated by those skilled in the art that a variety of
techniques may be used to effect substantially uniform deposition
of a material onto a substrate, e.g., Gravure-type printing,
extrusion coating, screen coating, spraying, painting, or the
like.
[0064] "Bias" as used herein refers to the difference between the
expected value of an estimator and the true value of a parameter.
"Bias" is used in a statistical context, in particular, in
estimating the value of a parameter of a probability distribution.
For example, in the case of a linear regression wherein
y=mx+b, for x=a,
[0065] the bias at "a" equals (ma+b)-a.
[0066] "Decay" as used herein refers to a gradual reduction in the
magnitude of a quantity, for example, a current detected using a
sensor electrode where the current is correlated to the
concentration of a particular analyte and where the detected
current gradually reduces but the concentration of the analyte does
not.
2.0.0 GENERAL METHODS
[0067] The present invention relates to the analysis of data
obtained by use of a sensing device for measuring the concentration
of a target analyte present in a biological system. In preferred
embodiments, the sensing device comprises a biosensor. In other
preferred embodiments, a sampling device is used to extract small
amounts of a target analyte from the biological system, and then
sense and/or quantify the concentration of the target analyte.
Measurement with the biosensor and/or sampling with the sampling
device can be carried out in a continual manner. Continual
measurement allows for closer monitoring of target analyte
concentration fluctuations.
[0068] In the general method of the invention, a raw signal is
obtained from a sensing device, which signal is related to a target
analyte present in the biological system. The raw signal can be
obtained using any suitable sensing methodology including, for
example, methods which rely on direct contact of a sensing
apparatus with the biological system; methods which extract samples
from the biological system by invasive, minimally invasive, and
non-invasive sampling techniques, wherein the sensing apparatus is
contacted with the extracted sample; methods which rely on indirect
contact of a sensing apparatus with the biological system; and the
like. In preferred embodiments of the invention, methods are used
to extract samples from the biological sample using minimally
invasive or non-invasive sampling techniques. The sensing apparatus
used with any of the above-noted methods can employ any suitable
sensing element to provide the signal including, but not limited
to, physical, chemical, electrochemical, photochemical,
spectrophotometric, polarimetric, calorimetric, radiometric, or
like elements. In preferred embodiments of the invention, a
biosensor is used which comprises an electrochemical sensing
element.
[0069] In another embodiment of the invention, a near-IR glucose
sensing apparatus is used to detect blood glucose in a subject, and
thus generate the raw signal. A number of near-IR glucose sensing
devices suitable for use in the present method are known in the art
and are readily available. For example, a near-IR radiation
diffuse-reflection laser spectroscopy device is described in U.S.
Pat. No. 5,267,152 to Yang et al. Similar near-IR spectrometric
devices are also described in U.S. Pat. No. 5,086,229 to Rosenthal
et al. and U.S. Pat. No. 4,975,581 to Robinson et al. These near-IR
devices use traditional methods of reflective or transmissive near
infrared (near-IR) analysis to measure absorbance at one or more
glucose-specific wavelengths, and can be contacted with the subject
at an appropriate location, such as a finger-tip, skin fold,
eyelid, or forearm surface to obtain the raw signal.
[0070] The raw signal obtained using any of the above-described
methodologies is then converted into an analyte-specific value of
known units to provide an interpretation of the signal obtained
from the sensing device. The interpretation uses a mathematical
transformation to model the relationship between a measured
response in the sensing device and a corresponding analyte-specific
value (in the present invention, a Mixtures of Experts algorithm).
Thus, a calibration step is used herein to relate, for example, an
electrochemical signal (detected by a biosensor), or near-IR
absorbance spectra (detected with a near-IR detector) with the
concentration of a target analyte in a biological system.
[0071] The predicted analyte values can optionally be used in a
subsequent step to control an aspect of the biological system. In
one embodiment, predicted analyte values are used to determine
when, and at what level, a constituent should be added to the
biological system in order to control an aspect of the biological
system. In a preferred embodiment, the analyte value can be used in
a feedback control loop to control a physiological effect in the
biological system.
[0072] The above general methods can, of course, be used with a
wide variety of biological systems, target analytes, and/or sensing
techniques. The determination of particularly suitable combinations
is within the skill of the ordinarily skilled artisan when directed
by the instant disclosure. Although these methods are broadly
applicable to measuring any chemical analyte and/or substance in a
biological system, the invention is expressly exemplified for use
in a non-invasive, transdermal sampling system which uses an
electrochemical biosensor to quantify or qualify glucose or a
glucose metabolite.
[0073] 2.1.0 Obtaining the Raw Signal.
[0074] The raw signal can be obtained using any sensing device that
is operatively contacted with the biological system. Such sensing
devices can employ physical, chemical, electrochemical,
spectrophotometric, polarimetric, colorimetric, radiometric, or
like measurement techniques. In addition, the sensing device can be
in direct or indirect contact with the biological system, or used
with a sampling device which extracts samples from the biological
system using invasive, minimally invasive or non-invasive sampling
techniques. In preferred embodiments, a minimally invasive or
non-invasive sampling device is used to obtain samples from the
biological system, and the sensing device comprises a biosensor
with an electrochemical sensing element.
[0075] The analyte can be any specific substance or component in a
biological system that one is desirous of detecting and/or
measuring in a chemical, physical, enzymatic, or optical analysis.
Such analytes include, but are not limited to, amino acids, enzyme
substrates or products indicating a disease state or condition,
other markers of disease states or conditions, drugs of abuse,
therapeutic and/or pharmacologic agents (e.g., theophylline,
anti-HIV drugs, lithium, anti-epileptic drugs, cyclosporin,
chemotherapeutics), electrolytes, physiological analytes of
interest (e.g., urate/uric acid, carbonate, calcium, potassium,
sodium, chloride, bicarbonate (CO.sub.2), glucose, urea (blood urea
nitrogen) lactate/lactic acid, hydroxybutyrate, cholesterol,
triglycerides, creatine, creatinine, insulin, hematocrit, and
hemoglobin), blood gases (carbon dioxide, oxygen, pH), lipids,
heavy metals (e.g., lead, copper), and the like. In preferred
embodiments, the analyte is a physiological analyte of interest,
for example glucose, or a chemical that has a physiological action,
for example a drug or pharmacological agent.
[0076] In order to facilitate detection of the analyte, an enzyme
can be disposed in the collection reservoir, or, if several
collection reservoirs are used, the enzyme can be disposed in
several or all of the reservoirs. The selected enzyme is capable of
catalyzing a reaction with the extracted analyte (e.g., glucose) to
the extent that a product of this reaction can be sensed, e.g., can
be detected electrochemically from the generation of a current
which current is detectable and proportional to the concentration
or amount of the analyte which is reacted. A suitable enzyme is
glucose oxidase which oxidizes glucose to gluconic acid and
hydrogen peroxide. The subsequent detection of hydrogen peroxide on
an appropriate biosensor electrode generates two electrons per
hydrogen peroxide molecule which create a current which can be
detected and related to the amount of glucose entering the device.
Glucose oxidase (GOx) is readily available commercially and has
well known catalytic characteristics. However, other enzymes can
also be used, so long as they specifically catalyze a reaction with
an analyte or substance of interest to generate a detectable
product in proportion to the amount of analyte so reacted.
[0077] In like manner, a number of other analyte-specific enzyme
systems can be used in the invention, which enzyme systems operate
on much the same general techniques. For example, a biosensor
electrode that detects hydrogen peroxide can be used to detect
ethanol using an alcohol oxidase enzyme system, or similarly uric
acid with urate oxidase system, urea with a urease system,
cholesterol with a cholesterol oxidase system, and theophylline
with a xanthine oxidase system.
[0078] In addition, the oxidase enzyme (used for hydrogen
peroxidase-based detection) can be replaced with another redox
system, for example, the dehydrogenase-enzyme NAD-NADH, which
offers a separate route to detecting additional analytes.
Dehydrogenase-based sensors can use working electrodes made of gold
or carbon (via mediated chemistry). Examples of analytes suitable
for this type of monitoring include, but are not limited to,
cholesterol, ethanol, hydroxybutyrate, phenylalanine,
triglycerides, and urea. Further, the enzyme can be eliminated and
detection can rely on direct electrochemical or potentiometric
detection of an analyte. Such analytes include, without limitation,
heavy metals (e.g., cobalt, iron, lead, nickel, zinc), oxygen,
carbonate/carbon dioxide, chloride, fluoride, lithium, pH,
potassium, sodium, and urea. Also, the sampling system described
herein can be used for therapeutic drug monitoring, for example,
monitoring anti-epileptic drugs (e.g., phenytion), chemotherapy
(e.g., adriamycin), hyperactivity (e.g., ritalin), and
anti-organ-rejection (e.g., cyclosporin).
[0079] In particularly preferred embodiments, a sampling device is
used to obtain continual transdermal or transmucosal samples from a
biological system, and the analyte of interest is glucose. More
specifically, a non-invasive glucose monitoring device is used to
measure changes in glucose levels in an animal subject over a wide
range of glucose concentrations. The sampling method is based on
transdermal glucose extraction and the sensing method is based on
electrochemical detection technology. The device can be contacted
with the biological system continuously, and automatically obtains
glucose samples in order to measure glucose concentration at
preprogrammed intervals.
[0080] Sampling is carried out continually by non-invasively
extracting glucose through the skin of the patient using an
iontophoretic current. More particularly, an iontophoretic current
is applied to a surface of the skin of a subject. When the current
is applied, ions or charged molecules pull along other uncharged
molecules or particles such as glucose which are drawn into a
collection reservoir placed on the surface of the skin. The
collection reservoir may comprise any ionically conductive material
and is preferably in the form of a hydrogel which is comprised of a
hydrophilic material, water and an electrolyte. The collection
reservoir may further contain an enzyme which catalyzes a reaction
between glucose and oxygen. The enzyme is preferably glucose
oxidase (GOx) which catalyzes the reaction between glucose and
oxygen and results in the production of hydrogen peroxide. The
hydrogen peroxide reacts at a catalytic surface of a biosensor
electrode, resulting in the generation of electrons which create a
detectable biosensor current (raw signal). Based on the amount of
biosensor current created over a given period of time, a
measurement is taken, which measurement is related to the amount of
glucose drawn into the collection reservoir over a given period of
time. In a preferred embodiment the reaction is allowed to continue
until substantially all of the glucose in the collection reservoir
has been subjected to a reaction and is therefore no longer
detectable, and the total biosensor current generated is related to
the concentration of glucose in the subject.
[0081] When the reaction is complete, the process is repeated and a
subsequent measurement is obtained. More specifically, the
iontophoretic current is again applied, glucose is drawn through
the skin surface into the collection reservoir, and the reaction is
catalyzed in order to create a biosensor current. These sampling
(extraction) and sensing operations are integrated such that
glucose from interstitial fluid directly beneath the skin surface
is extracted into the hydrogel collection pad where it contacts the
GOx enzyme. The GOx enzyme converts glucose and oxygen in the
hydrogel to hydrogen peroxide which diffuses to a Pt-based sensor
and reacts with the sensor to regenerate oxygen and form electrons.
The electrons generate an electrical signal that can be measured,
analyzed, and correlated to blood glucose.
[0082] A generalized method for continual monitoring of a
physiological analyte is disclosed in International Publication No.
WO 97/24059, published 10 Jul. 1997, which publication is
incorporated herein by reference. As noted in that publication, the
analyte is extracted into a reservoir containing a hydrogel which
is preferably comprised of a hydrophilic material of the type
described in International Publication No. WO 97/02811, published
30 Jan. 1997, which publication is incorporated herein by
reference. Suitable hydrogel materials include polyethylene oxide,
polyacrylic acid, polyvinylalcohol and related hydrophilic
polymeric materials combined with water to form an aqueous gel.
[0083] In the above non-invasive glucose monitoring device, a
biosensor electrode is positioned on a surface of the hydrogel
opposite the surface contacting the skin. The sensor electrode acts
as a detector which detects current generated by hydrogen peroxide
in the redox reaction, or more specifically detects current which
is generated by the electrons generated by the redox reaction
catalyzed by the platinum surface of the electrode. The details of
such electrode assemblies and devices for iontophoretic extraction
of glucose are disclosed in International Publication No. WO
96/00110, published 4 Jan. 1996, and International Publication No.
WO 97/10499, published 2 Mar. 1997, which publications are also
incorporated herein by reference.
[0084] Referring now to FIGS. 1A and 1B, one example of an
iontophoretic collection reservoir and electrode assembly for use
in a transdermal sensing device is generally indicated at 2. The
assembly comprises two iontophoretic collection reservoirs, 4 and
6, each having a conductive medium 8, and 10 (preferably hydrogel
pads), respectively disposed therein. First (12) and second (14)
ring-shaped iontophoretic electrodes are respectively contacted
with conductive medium 8 and 10. The first iontophoretic electrode
12 surrounds three biosensor electrodes which are also contacted
with the conductive medium 8, a working electrode 16, a reference
electrode 18, and a counter electrode 20. A guard ring 22 separates
the biosensor electrodes from the iontophoretic electrode 12 to
minimize noise from the iontophoretic circuit. Conductive contacts
provide communication between the electrodes and an associated
power source and control means as described in detail below. A
similar biosensor electrode arrangement can be contacted with the
conductive medium 10, or the medium can not have a sensor means
contacted therewith.
[0085] Referring now to FIG. 2, the iontophoretic collection
reservoir and electrode assembly 2 of FIGS. 1A and 1B is shown in
exploded view in combination with a suitable iontophoretic sampling
device housing 32. The housing can be a plastic case or other
suitable structure which preferably is configured to be worn on a
subjects arm in a manner similar to a wrist watch. As can be seen,
conductive media 8 and 10 (hydrogel pads) are separable from the
assembly 2; however, when the assembly 2 and the housing 32 are
assembled to provide an operational iontophoretic sampling device
30, the media are in contact with the electrodes to provide a
electrical contact therewith.
[0086] A power source (e.g., one or more rechargeable or
nonrechargeable batteries) can be disposed within the housing 32 or
within the straps 34 which hold the device in contact with a skin
or mucosal surface of a subject. In use, an electric potential
(either direct current or a more complex waveform) is applied
between the two iontophoretic electrodes 12 and 14 such that
current flows from the first iontophoretic electrode 12, through
the first conductive medium 8 into the skin or mucosal surface, and
then back out through the second conductive medium 10 to the second
iontophoretic electrode 14. The current flow is sufficient to
extract substances including an analyte of interest through the
skin into one or both of collection reservoirs 4 and 6. The
electric potential may be applied using any suitable technique, for
example, the applied current density may be in the range of about
0.01 to 0.5 mA/cm.sup.2. In a preferred embodiment, the device is
used for continual or continuous monitoring, and the polarity of
iontophoretic electrodes 12 and 14 is alternated at a rate of about
one switch every 10 seconds to about one switch every hour so that
each electrode is alternately a cathode or an anode. The housing 32
can further include an optional temperature sensing element (e.g.,
a thermistor, thermometer, or thermocouple device) which monitors
the temperature at the collection reservoirs to enable temperature
correction of sensor signals. The housing can also include an
optional conductance sensing element (e.g., an integrated pair of
electrodes) which monitors conductance at the skin or mucosal
surface to enable data screening correction or invalidation of
sensor signals.
[0087] After a suitable iontophoretic extraction period, one or
both of the sensor electrode sets can be activated in order to
detect extracted substances including the analyte of interest.
Operation of the iontophoretic sampling device 30 can be controlled
by a controller 36 (e.g., a microprocessor), which interfaces with
the iontophoretic electrodes, the sensor electrodes, the power
supply, the optional temperature and/or conductance sensing
elements, a display and other electronics. For example, the
controller 36 can include a programmable a controlled circuit
source/sink drive for driving the iontophoretic electrodes. Power
and reference voltage are provided to the sensor electrodes, and
signal amplifiers can be used to process the signal from the
working electrode or electrodes. In general, the controller
discontinues the iontophoretic current drive during sensing
periods. A sensor confidence loop can be provided for continually
monitoring the sampling system to insure proper operations.
[0088] User control can be carried out using push buttons located
on the housing 32, and an optional liquid crystal display (LCD) can
provide visual prompts, readouts and visual alarm indications. The
microprocessor generally uses a series of program sequences to
control the operations of the sampling device, which program
sequences can be stored in the microprocessor's read only memory
(ROM). Embedded software (firmware) controls activation of
measurement and display operations, calibration of analyte
readings, setting and display of high and low analyte value alarms,
display and setting of time and date functions, alarm time, and
display of stored readings. Sensor signals obtained from the sensor
electrodes can be processed before storage and display by one or
more signal processing functions or algorithms which are stored in
the embedded software. The microprocessor can also include an
electronically erasable, programmable, read only memory (EEPROM)
for storing calibration parameters, user settings and all
downloadable sequences. A serial communications port allows the
device to communicate with associated electronics, for example,
wherein the device is used in a feedback control application to
control a pump for delivery of a medicament.
[0089] Further, the sampling system can be pre-programmed to begin
execution of its signal measurements (or other functions) at a
designated time. One application of this feature is to have the
sampling system in contact with a subject and to program the
sampling system to begin sequence execution during the night so
that it is available for calibration immediately upon waking. One
advantage of this feature is that it removes any need to wait for
the sampling system to warm-up before calibrating it.
2.1.1 Exemplary Embodiments of the Sampling System
[0090] An exemplary method and apparatus for sampling small amounts
of an analyte via transdermal methods is described below in further
detail. The method and apparatus are used to detect and/or quantify
the concentration of a target analyte present in a biological
system. This sampling is carried out in a continual manner, and
quantification is possible even when the target analyte is
extracted in sub-millimolar concentrations. Although the method and
apparatus are broadly applicable to sampling any chemical analyte
and/or substance, the sampling system is expressly exemplified for
use in transdermal sampling and quantifying or qualifying glucose
or a glucose metabolite.
[0091] Accordingly, in one aspect, an automatic sampling system is
used to monitor levels of glucose in a biological system. The
method can be practiced using a sampling system (device) which
transdermally extracts glucose from the system, in this case, an
animal subject. Transdermal extraction is carried out by applying
an electrical current or ultrasonic radiation to a tissue surface
at a collection site. The electrical current or ultrasonic
radiation is used to extract small amounts of glucose from the
subject into a collection reservoir. The collection reservoir is in
contact with a biosensor which provides for measurement of glucose
concentration in the subject.
[0092] In the practice, a collection reservoir is contacted with a
tissue surface, for example, on the stratum corneum of a patient's
skin. An electrical or ultrasonic force is then applied to the
tissue surface in order to extract glucose from the tissue into the
collection reservoir. Extraction is carried out continually over a
period of about 1-24 hours, or longer. The collection reservoir is
analyzed, at least periodically, to measure glucose concentration
therein. The measured value correlates with the subject's blood
glucose level.
[0093] More particularly, one or more collection reservoirs are
placed in contact with a tissue surface on a subject. The
collection reservoirs are also contacted with an electrode which
generates a current (for reverse iontophoretic extraction) or with
a source of ultrasonic radiation such as a transducer (for
sonophoretic extraction) sufficient to extract glucose from the
tissue into the collection reservoir.
[0094] The collection reservoir contains an ionically conductive
liquid or liquid-containing medium. The conductive medium is
preferably a hydrogel which can contain ionic substances in an
amount sufficient to produce high ionic conductivity. The hydrogel
is formed from a solid material (solute) which, when combined with
water, forms a gel by the formation of a structure which holds
water including interconnected cells and/or network structure
formed by the solute. The solute may be a naturally occurring
material such as the solute of natural gelatin which includes a
mixture of proteins obtained by the hydrolysis of collagen by
boiling skin, ligaments, tendons and the like. However, the solute
or gel forming material is more preferably a polymer material
(including, but not limited to, polyethylene oxide, polyvinyl
alcohol, polyacrylic acid, polyacrylamidomethylpropanesulfonate and
copolymers thereof, and polyvinyl pyrrolidone) present in an amount
in the range of more than 0.5% and less than 40% by weight,
preferably 8 to 12% by weight when a humectant is also added, and
preferably about 15 to 20% by weight when no humectant is added.
Additional materials may be added to the hydrogel, including,
without limitation, electrolyte (e.g., a salt), buffer, tackifier,
humectant, biocides, preservatives and enzyme stabilizers. Suitable
hydrogel formulations are described in International Publication
Nos. WO 97/02811, published 30 Jan. 1997, and WO 96/00110,
published 4 Jan. 1996, each of which publications are incorporated
herein by reference in their entireties.
[0095] Since the sampling system must be operated at very low
(electrochemical) background noise levels, the collection reservoir
must contain an ionically conductive medium that does not include
significant electrochemically sensitive components and/or
contaminants. Thus, the preferred hydrogel composition described
hereinabove is formulated using a judicious selection of materials
and reagents which do not add significant amounts of
electrochemical contaminants to the final composition.
[0096] In order to facilitate detection of the analyte, an enzyme
is disposed within the one or more collection reservoirs. The
enzyme is capable of catalyzing a reaction with the extracted
analyte (in this case glucose) to the extent that a product of this
reaction can be sensed, e.g., can be detected electrochemically
from the generation of a current which current is detectable and
proportional to the amount of the analyte which is reacted. A
suitable enzyme is glucose oxidase which oxidizes glucose to
gluconic acid and hydrogen peroxide. The subsequent detection of
hydrogen peroxide on an appropriate biosensor electrode generates
two electrons per hydrogen peroxide molecule which create a current
which can be detected and related to the amount of glucose entering
the device (see FIG. 1). Glucose oxidase (Gox) is readily available
commercially and has well known catalytic characteristics. However,
other enzymes can also be used, so long as they specifically
catalyze a reaction with an analyte, or derivative thereof (or
substance of interest), to generate a detectable product in
proportion to the amount of analyte so reacted.
[0097] In like manner, a number of other analyte-specific enzyme
systems can be used in the sampling system, which enzyme systems
operate on much the same general techniques. For example, a
biosensor electrode that detects hydrogen peroxide can be used to
detect ethanol using an alcohol oxidase enzyme system, or similarly
uric acid with urate oxidase system, cholesterol with a cholesterol
oxidase system, and theophylline with a xanthine oxidase
system.
[0098] The biosensor electrode must be able to detect the glucose
analyte extracted into the one or more collection reservoirs even
when present at nominal concentration levels. In this regard,
conventional electrochemical detection systems which utilize
glucose oxidase (GOx) to specifically convert glucose to hydrogen
peroxide, and then detect with an appropriate electrode, are only
capable of detecting the analyte when present in a sample in at
least mM concentrations. In contrast, the sampling system allows
sampling and detection of small amounts of analyte from the
subject, wherein the analyte is detected at concentrations on the
order of 2 to 4 orders of magnitude lower (e.g., .mu.M
concentration in the reservoir) than presently detectable with
conventional systems.
[0099] Accordingly, the biosensor electrode must exhibit
substantially reduced background current relative to prior such
electrodes. In one particularly preferred embodiment, an electrode
is provided which contains platinum (Pt) and graphite dispersed
within a polymer matrix. The electrode exhibits the following
features, each of which are essential to the effective operation of
the biosensor: background current in the electrode due to changes
in the Pt oxidation state and electrochemically sensitive
contaminants in the electrode formulation is substantially reduced;
and catalytic activity (e.g., non-electrochemical hydrogen peroxide
decomposition) by the Pt in the electrode is reduced.
[0100] The Pt-containing electrode is configured to provide a
geometric surface area of about 0.1 to 3 cm.sup.2, preferably about
0.5 to 2 cm.sup.2, and more preferably about 1 cm.sup.2. This
particular configuration is scaled in proportion to the collection
area of the collection reservoir used in the sampling system,
throughout which the extracted analyte and/or its reaction products
will be present. The electrode is specially formulated to provide a
high signal-to-noise ratio (S/N ratio) for this geometric surface
area not heretofore available with prior Pt-containing electrodes.
For example, a Pt-containing electrode constructed for use in the
sampling system and having a geometric area of about 1 cm.sup.2
preferably has a background current on the order of about 20 nA or
less (when measured with buffer solution at 0.6V), and has high
sensitivity (e.g., at least about 60 nA/.mu.M of H.sub.2O.sub.2 in
buffer at 0.6V). In like manner, an electrode having a geometric
area of about 0.1 cm.sup.2 preferably has a background current of
about 2 nA or less and sensitivity of at least about 6 nA/.mu.M of
H.sub.2O.sub.2; and an electrode having a geometric area of about 3
cm.sup.2 preferably has a background current of about 60 nA or less
and sensitivity of at least about 180 nA/.mu.M of H.sub.2O.sub.2,
both as measured in buffer at 0.6V. These features provide for a
high S/N ratio, for example a S/N ratio of about 3 or greater. The
electrode composition is formulated using analytical- or
electronic-grade reagents and solvents which ensure that
electrochemical and/or other residual contaminants are avoided in
the final composition, significantly reducing the background noise
inherent in the resultant electrode. In particular, the reagents
and solvents used in the formulation of the electrode are selected
so as to be substantially free of electrochemically active
contaminants (e.g., anti-oxidants), and the solvents in particular
are selected for high volatility in order to reduce washing and
cure times.
[0101] The Pt powder used to formulate the electrode composition is
also substantially free from impurities, and the Pt/graphite
powders are evenly distributed within the polymer matrix using, for
example, co-milling or sequential milling of the Pt and graphite.
Alternatively, prior to incorporation into the polymer matrix, the
Pt can be sputtered onto the graphite powder, colloidal Pt can be
precipitated onto the graphite powder (see, e.g., U.K. patent
application number GB 2,221,300, published 31 Jan. 1990, and
references cited therein), or the Pt can be adsorbed onto the
graphite powder to provide an even distribution of Pt in contact
with the conductive graphite. In order to improve the S/N ratio of
the electrode, the Pt content in the electrode is lower relative to
prior Pt or Pt-based electrodes. In a preferred embodiment, the
overall Pt content is about 3-7% by weight. Although decreasing the
overall amount of Pt may reduce the sensitivity of the electrode,
the inventors have found that an even greater reduction in
background noise is also achieved, resulting in a net improvement
in signal-to-noise quality.
[0102] The Pt/graphite matrix is supported by a suitable binder,
such as an electrochemically inert polymer or resin binder, which
is selected for good adhesion and suitable coating integrity. The
binder is also selected for high purity, and for absence of
components with electrochemical background. In this manner, no
electrochemically sensitive contaminants are introduced into the
electrode composition by way of the binder. A large number of
suitable such binders are known in the art and are commercially
available, including, without limitation, vinyl, acrylic, epoxy,
phenoxy and polyester polymers, provided that the binder or binders
selected for the formulation are adequately free of electroactive
impurities.
[0103] The Pt/graphite biosensor electrodes formulated above
exhibit reduced catalytic activity (e.g., passive or
non-electrochemical hydrogen peroxide degradation) relative to
prior Pt-based electrode systems, and thus have substantially
improved signal-to-noise quality. In preferred Pt/graphite
electrode compositions, the biosensor exhibits about 10-25% passive
hydrogen peroxide degradation.
[0104] Once formulated, the electrode composition is affixed to a
suitable nonconductive surface which may be any rigid or flexible
material having appropriate insulating and/or dielectric
properties. The electrode composition can be affixed to the surface
in any suitable pattern or geometry, and can be applied using
various thin film techniques, such as sputtering, evaporation,
vapor phase deposition, or the like; or using various thick film
techniques, such as film laminating, electroplating, or the like.
Alternatively, the composition can be applied using screen
printing, pad printing, inkjet methods, transfer roll printing, or
similar techniques. Preferably, the electrode is applied using a
low temperature screen print onto a polymeric substrate. The
screening can be carried out using a suitable mesh, ranging from
about 100-400 mesh.
[0105] As glucose is transdermally extracted into the collection
reservoir, the analyte reacts with the glucose oxidase within the
reservoir to produce hydrogen peroxide. The presence of hydrogen
peroxide generates a current at the biosensor electrode that is
directly proportional to the amount of hydrogen peroxide in the
reservoir. This current provides a signal which can be detected and
interpreted by an associated system controller to provide a glucose
concentration value for display. In particular embodiments, the
detected current can be correlated with the subject's blood glucose
concentration so that the system controller may display the
subject's actual blood glucose concentration as measured by the
sampling system. For example, the system can be calibrated to the
subject's actual blood glucose concentration by sampling the
subject's blood during a standard glucose tolerance test, and
analyzing the blood glucose using both a standard blood glucose
monitor and the sampling system. In this manner, measurements
obtained by the sampling system can be correlated to actual values
using known statistical techniques.
[0106] In one preferred embodiment, the automatic sampling system
transdermally extracts the sample in a continual manner over the
course of a 1-24 hour period, or longer, using reverse
iontophoresis. More particularly, the collection reservoir contains
an ionically conductive medium, preferably the hydrogel medium
described hereinabove. A first iontophoresis electrode is contacted
with the collection reservoir (which is in contact with a target
tissue surface), and a second iontophoresis electrode is contacted
with either a second collection reservoir in contact with the
tissue surface, or some other ionically conductive medium in
contact with the tissue. A power source provides an electric
potential between the two electrodes to perform reverse
iontophoresis in a manner known in the art. As discussed above, the
biosensor selected to detect the presence, and possibly the level,
of the target analyte (glucose) within a reservoir is also in
contact with the reservoir.
[0107] In practice, an electric potential (either direct current or
a more complex waveform) is applied between the two iontophoresis
electrodes such that current flows from the first electrode through
the first conductive medium into the skin, and back out from the
skin through the second conductive medium to the second electrode.
This current flow extracts substances through the skin into the one
or more collection reservoirs through the process of reverse
iontophoresis or electroosmosis. The electric potential may be
applied as described in International Publication No. WO 96/00110,
published 4 Jan. 1996.
[0108] As an example, to extract glucose, the applied electrical
current density on the skin or tissue is preferably in the range of
about 0.01 to about 2 mA/cm.sup.2. In a preferred embodiment, in
order to facilitate the extraction of glucose, electrical energy is
applied to the electrodes, and the polarity of the electrodes is
alternated at a rate of about one switch every 7.5 minutes (for a
15 minute extraction period), so that each electrode is alternately
a cathode or an anode. The polarity switching can be manual or
automatic.
[0109] Any suitable iontophoretic electrode system can be employed,
however it is preferred that a silver/silver chloride (Ag/AgCl)
electrode system is used. The iontophoretic electrodes are
formulated using two critical performance parameters: (1) the
electrodes are capable of continual operation for extended periods,
preferably periods of up to 24 hours or longer; and (2) the
electrodes are formulated to have high electrochemical purity in
order to operate within the present system which requires extremely
low background noise levels. The electrodes must also be capable of
passing a large amount of charge over the life of the
electrodes.
[0110] In an alternative embodiment, the sampling device can
operate in an alternating polarity mode necessitating the presence
of a first and second bimodal electrodes (FIGS. 5, 540 and 541) and
two collection reservoirs (FIGS. 5, 547 and 548). Each bi-modal
electrode (FIG. 4, 430; FIGS. 5, 540 and 541) serves two functions
depending on the phase of the operation: (1) an electro-osmotic
electrode (or iontophoretic electrode) used to electrically draw
analyte from a source into a collection reservoir comprising water
and an electrolyte, and to the area of the electrode subassembly;
and (2) as a counter electrode to the first sensing electrode at
which the chemical compound is catalytically converted at the face
of the sensing electrode to produce an electrical signal.
[0111] The reference (FIGS. 5, 544 and 545; FIG. 4, 432) and
sensing electrodes (FIGS. 5, 542 and 543; FIG. 4, 431), as well as,
the bimodal electrode (FIGS. 5, 540 and 541; FIG. 4, 430) are
connected to a standard potentiostat circuit during sensing. In
general, practical limitations of the system require that the
bimodal electrode will not act as both a counter and iontophoretic
electrode simultaneously.
[0112] The general operation of an iontophoretic sampling system is
the cyclical repetition of two phases: (1) a reverse-iontophoretic
phase, followed by a (2) sensing phase. During the reverse
iontophoretic phase, the first bimodal electrode (FIG. 5, 540) acts
as an iontophoretic cathode and the second bimodal electrode (FIG.
5, 541) acts as an iontophoretic anode to complete the circuit.
Analyte is collected in the reservoirs, for example, a hydrogel
(FIGS. 5, 547 and 548). At the end of the reverse iontophoretic
phase, the iontophoretic current is turned off. During the sensing
phase, in the case of glucose, a potential is applied between the
reference electrode (FIG. 5, 544) and the sensing electrode (FIG.
5, 542). The chemical signal reacts catalytically on the catalytic
face of the first sensing electrode (FIG. 5, 542) producing an
electrical current, while the first bi-modal electrode (FIG. 5,
540) acts as a counter electrode to complete the electrical
circuit.
[0113] At the end of the sensing phase, the next iontophoresis
phase begins. The polarity of the iontophoresis current is reversed
in this cycle relative to the previous cycle, so that the first
bi-modal electrode (FIG. 5, 540) acts as an iontophoretic anode and
the second bi-modal electrode (FIG. 5, 541) acts as an
iontophoretic cathode to complete the circuit. At the end of the
iontophoretic phase, the sensor is activated. The chemical signal
reacts catalytically on the catalytic face of the second sensing
electrode (FIG. 5, 543) producing an electrical current, while the
second bi-modal electrode (FIG. 5, 541) acts as a counter electrode
to complete the electrical circuit.
[0114] The iontophoretic and sensing phases repeat cyclically with
the polarity of the iontophoretic current alternating between each
cycle. This results in pairs of readings for the signal, that is,
one signal obtained from a first iontophoretic and sensing phase
and a second signal obtained from the second phase. These two
values can be used (i) independently as two signals, (ii) as a
cumulative (additive) signal, or (iii) the signal values can be
added and averaged.
[0115] If two active reservoirs are used for analyte detection (for
example, where both hydrogels contain the GOx enzyme), a sensor
consistency check can be employed that detects whether the signals
from the reservoirs are changing in concert with one another. This
check compares the percentage change from the calibration signal
for each reservoir, then calculates the difference in percentage
change of the signal between the two reservoirs. If this difference
is greater than a predetermined threshold value (which is commonly
empirically determined), then the signals are said not to be
tracking one another and the data point related to the two signals
can be, for example, ignored.
[0116] The electrode described is particularly adapted for use in
conjunction with a hydrogel collection reservoir system for
monitoring glucose levels in a subject through the reaction of
collected glucose with the enzyme glucose oxidase present in the
hydrogel matrix.
[0117] The bi-modal electrode is preferably comprised of Ag/AgCl.
The electrochemical reaction which occurs at the surface of this
electrode serves as a facile source or sink for electrical current.
This property is especially important for the iontophoresis
function of the electrode. Lacking this reaction, the iontophoresis
current could cause the hydrolysis of water to occur at the
iontophoresis electrodes causing pH changes and possible gas bubble
formation. The pH changes to acidic or basic pH could cause skin
irritation or burns. The ability of an Ag/AgCl electrode to easily
act as a source of sink current is also an advantage for its
counter electrode function. For a three electrode electrochemical
cell to function properly, the current generation capacity of the
counter electrode must not limit the speed of the reaction at the
sensing electrode. In the case of a large sensing electrode, the
ability of the counter electrode to source proportionately larger
currents is required.
[0118] The design of the sampling system provides for a larger
sensing electrode (see for example, FIG. 4) than previously
designed. Consequently, the size of the bimodal electrode must be
sufficient so that when acting as a counter electrode with respect
to the sensing electrode the counter electrode does not become
limiting the rate of catalytic reaction at the sensing electrode
catalytic surface.
[0119] Two methods exist to ensure that the counter electrode does
not limit the current at the sensing electrode: (1) the bi-modal
electrode is made much larger than the sensing electrode, or (2) a
facile counter reaction is provided.
[0120] During the reverse iontophoretic phase, the power source
provides a current flow to the first bi-modal electrode to
facilitate the extraction of the chemical signal into the
reservoir. During the sensing phase, the power source is used to
provide voltage to the first sensing electrode to drive the
conversion of chemical signal retained in reservoir to electrical
signal at the catalytic face of the sensing electrode. The power
source also maintains a fixed potential at the electrode where, for
example hydrogen peroxide is converted to molecular oxygen,
hydrogen ions, and electrons, which is compared with the potential
of the reference electrode during the sensing phase. While one
sensing electrode is operating in the sensing mode it is
electrically connected to the adjacent bimodal electrode which acts
as a counter electrode at which electrons generated at the sensing
electrode are consumed.
[0121] The electrode sub-assembly can be operated by electrically
connecting the bimodal electrodes such that each electrode is
capable of functioning as both an iontophoretic electrode and
counter electrode along with appropriate sensing electrode(s) and
reference electrode(s), to create standard potentiostat
circuitry.
[0122] A potentiostat is an electrical circuit used in
electrochemical measurements in three electrode electrochemical
cells. A potential is applied between the reference electrode and
the sensing electrode. The current generated at the sensing
electrode flows through circuitry to the counter electrode (i.e.,
no current flows through the reference electrode to alter its
equilibrium potential). Two independent potentiostat circuits can
be used to operate the two biosensors. For the purpose of the
present sampling system, the electrical current measured at the
sensing electrode subassembly is the current that is correlated
with an amount of chemical signal.
[0123] With regard to continual operation for extended periods of
time, Ag/AgCl electrodes are provided herein which are capable of
repeatedly forming a reversible couple which operates without
unwanted electrochemical side reactions (which could give rise to
changes in pH, and liberation of hydrogen and oxygen due to water
hydrolysis). The Ag/AgCl electrodes of the present sampling system
are thus formulated to withstand repeated cycles of current passage
in the range of about 0.01 to 1.0 mA per cm.sup.2 of electrode
area. With regard to high electrochemical purity, the Ag/AgCl
components are dispersed within a suitable polymer binder to
provide an electrode composition which is not susceptible to attack
(e.g., plasticization) by components in the collection reservoir,
e.g., the hydrogel composition. The electrode compositions are also
formulated using analytical- or electronic-grade reagents and
solvents, and the polymer binder composition is selected to be free
of electrochemically active contaminants which could diffuse to the
biosensor to produce a background current.
[0124] Since the Ag/AgCl iontophoretic electrodes must be capable
of continual cycling over extended periods of time, the absolute
amounts of Ag and AgCl available in the electrodes, and the overall
Ag/AgCl availability ratio, can be adjusted to provide for the
passage of high amounts of charge. Although not limiting in the
sampling system described herein, the Ag/AgCl ratio can approach
unity. In order to operate within the preferred system which uses a
biosensor having a geometric area of 0.1 to 3 cm.sup.2, the
iontophoretic electrodes are configured to provide an approximate
electrode area of 0.3 to 1.0 cm.sup.2, preferably about 0.85
cm.sup.2. These electrodes provide for reproducible, repeated
cycles of charge passage at current densities ranging from about
0.01 to 1.0 mA/cm.sup.2 of electrode area. More particularly,
electrodes constructed according to the above formulation
parameters, and having an approximate electrode area of 0.85
cm.sup.2, are capable of a reproducible total charge passage (in
both anodic and cathodic directions) of 270 mC, at a current of
about 0.3 mA (current density of 0.35 mA/cm.sup.2) for 48 cycles in
a 24 hour period.
[0125] Once formulated, the Ag/AgCl electrode composition is
affixed to a suitable rigid or flexible nonconductive surface as
described above with respect to the biosensor electrode
composition. A silver (Ag) underlayer is first applied to the
surface in order to provide uniform conduction. The Ag/AgCl
electrode composition is then applied over the Ag underlayer in any
suitable pattern or geometry using various thin film techniques,
such as sputtering, evaporation, vapor phase deposition, or the
like, or using various thick film techniques, such as film
laminating, electroplating, or the like. Alternatively, the Ag/AgCl
composition can be applied using screen printing, pad printing,
inkjet methods, transfer roll printing, or similar techniques.
Preferably, both the Ag underlayer and the Ag/AgCl electrode are
applied using a low temperature screen print onto a polymeric
substrate. This low temperature screen print can be carried out at
about 125 to 160.degree. C., and the screening can be carried out
using a suitable mesh, ranging from about 100-400 mesh.
[0126] In another preferred embodiment, the automatic sampling
system transdermally extracts the sample in a continual manner over
the course of a 1-24 hour period, or longer, using sonophoresis.
More particularly, a source of ultrasonic radiation is coupled to
the collection reservoir and used to provide sufficient
perturbation of the target tissue surface to allow passage of the
analyte (glucose) across the tissue surface. The source of
ultrasonic radiation provides ultrasound frequencies of greater
than about 10 MHz, preferably in the range of about 10 to 50 MHz,
most preferably in the range of about 15 to 25 MHz. It should be
emphasized that these ranges are intended to be merely illustrative
of the preferred embodiment; in some cases higher or lower
frequencies may be used.
[0127] The ultrasound may be pulsed or continuous, but is
preferably continuous when lower frequencies are used. At very high
frequencies, pulsed application will generally be preferred so as
to enable dissipation of generated heat. The preferred intensity of
the applied ultrasound is less than about 5.0 W/cm.sup.2, more
preferably is in the range of about 0.01 to 5.0 W/cm.sup.2, and
most preferably is in the range of 0.05 to 3.0 W/cm.sup.2.
[0128] Virtually any type of device may be used to administer the
ultrasound, providing that the device is capable of producing the
suitable frequency ultrasonic waves required by the sampling
system. An ultrasound device will typically have a power source
such as a small battery, a transducer, and a means to attach the
system to the sampling system collection reservoir. Suitable
sonophoresis sampling systems are described in International
Publication No. WO 91/12772, published 5 Sep. 1991, the disclosure
of which is incorporated herein by reference.
[0129] As ultrasound does not transmit well in air, a liquid medium
is generally needed in the collection reservoir to efficiently and
rapidly transmit ultrasound between the ultrasound applicator and
the tissue surface.
[0130] Referring now to FIG. 3, an exploded view of the key
components from a preferred embodiment of an autosensor is
presented. The sampling system components include two
biosensor/iontophoretic electrode assemblies, 304 and 306., each of
which have an annular iontophoretic electrode., respectively
indicated at 308 and 310, which encircles a biosensor 312 and 314.
The electrode assemblies 304 and 306 are printed onto a polymeric
substrate 316 which is maintained within a sensor tray 318. A
collection reservoir assembly 320 is arranged over the electrode
assemblies, wherein the collection reservoir assembly comprises two
hydrogel inserts 322 and 324 retained by a gel retaining layer
326.
[0131] Referring now to FIG. 9, an exploded view of the key
components from another embodiment of an autosensor for use in an
iontophoretic sampling device is presented. The sampling system
components include, but are not limited to, the following: a
sensor-to-tray assembly comprising two bimodal electrode assemblies
and a support tray 904; two holes 906 to insure proper alignment of
the support tray in the sampling device; a plowfold liner 908 used
to separate the sensors from the hydrogels 912 (for example, during
storage); a gel retaining layer 910; a mask layer 914 (where the
gel retaining layer, hydrogels, and mask layer form a collection
assembly, which can, for example, be a laminate); and a patient
liner 916.
[0132] The components shown in exploded view in FIGS. 3 and 9 are
intended for use in, for example, an automatic sampling device
which is configured to be worn like an ordinary wristwatch. As
described in International Publication No. Wo 96/00110, published 4
Jan. 1996, the wristwatch housing (not shown) contains conductive
leads which communicate with the iontophoretic electrodes and the
biosensor electrodes to control cycling and provide power to the
iontophoretic electrodes, and to detect electrochemical signals
produced at the biosensor electrode surfaces. The wristwatch
housing can further include suitable electronics (e.g.,
microprocessor, memory, display and other circuit components) and
power sources for operating the automatic sampling system.
[0133] Modifications and additions to the embodiments of FIGS. 3
and 9 will be apparent to those skilled in the art in light of the
teachings of the present specification. The laminates and
collection assemblies described herein are suitable for use as
consumable components in an iontophoretic sampling device.
[0134] In one aspect, the electrode assemblies can include bimodal
electrodes as shown in FIG. 4 and described above.
[0135] Modifications and additions to the embodiments shown in
FIGS. 3 and 9 will be apparent to those skilled in the art.
[0136] 2.2.0 Converting to an Analyte-Specific Value.
[0137] The raw signal is then converted into an analyte-specific
value using a calibration step which correlates the signal obtained
from the sensing device with the concentration of the analyte
present in the biological system. A wide variety of calibration
techniques can be used to interpret such signals. These calibration
techniques apply mathematical, statistical and/or pattern
recognition techniques to the problem of signal processing in
chemical analyses, for example, using neural networks, genetic
algorithm signal processing, linear regression, multiple-linear
regression, or principal components analysis of statistical (test)
measurements.
[0138] One method of calibration involves estimation techniques. To
calibrate an instrument using estimation techniques, it is
necessary to have a set of exemplary measurements with known
concentrations referred to as the calibration set (e.g., reference
set). This set consists of S samples, each with m instrument
variables contained in an S by m matrix (X), and an S by 1 vector
(y), containing the concentrations. If a priori information
indicates the relationship between the measurement and
concentration is linear, the calibration will attempt to determine
an S by 1 transformation or mapping (b), such that y=Xb, is an
optimal estimate of y according to a predefined criteria. Numerous
suitable estimation techniques useful in the practice of the
invention are known in the art. These techniques can be used to
provide correlation factors (e.g., constants), which correlation
factors are then used in a mathematical transformation to obtain a
measurement value indicative of the concentration of analyte
present in the biological system at the times of measurement.
[0139] In one particular embodiment, the calibration step can be
carried out using artificial neural networks or genetic algorithms.
The structure of a particular neural network algorithm used in the
practice of the invention can vary widely; however, the network
should contain an input layer, one or more hidden layers, and one
output layer. Such networks can be trained on a test data set, and
then applied to a population. There are an infinite number of
suitable network types, transfer functions, training criteria,
testing and application methods which will occur to the ordinarily
skilled artisan upon reading the instant specification.
[0140] The iontophoretic glucose sampling device described
hereinabove typically uses one or more "active" collection
reservoirs (e.g., each containing the GOx enzyme) to obtain
measurements. In one embodiment, two active collection reservoirs
are used. An input value can be obtained from these reserviors by,
for example, taking an average between signals from the reservoirs
for each measurement time point or using a summed value. Such
inputs are discussed in greater detail below. In another
embodiment, a second collection reservoir can be provided which
does not contain, for example, the GOx enzyme. This second
reservoir can serve as an internal reference (blank) for the
sensing device, where a biosensor is used to measure the "blank"
signal from the reference reservoir which signal can then be used
in, for example, a blank subtraction step.
[0141] In the context of such a sampling device an algorithm, in a
preferred embodiment a Mixtures of Experts algorithm, could use the
following inputs to provide a blood glucose measurement: time (for
example, time since monitor was applied to a subject, and/or time
since calibration); signal from an active reservoir; signal from a
blank reservoir; averaged (or a cumulative) signal from two active
reservoirs; calibration time; skin temperature; voltage; normalized
background; raw data current; peak or minimum value of a selected
input, e.g., current, averaged signal, calibrated signal; discrete
value points of a selected input, e.g., current, averaged signal,
calibrated signal; integral average temperature, initial
temperature, or any discrete time temperature; skin conductivity,
including, but not limited to, sweat value, iontophoretic voltage,
baseline value, normalized baseline value, other background values;
relative change in biosensor current or iontophoretic voltage
(relative to calibration) as an indicator of decay; alternate
integration ranges for calculating nanocoulomb (nC) values, e.g.,
using an entire biosensor time interval, or alternative ranges of
integration (for example, using discrete time points instead of
ranges, break out intervals from the total sampling time interval,
or full integration of the interval plus partial integration of
selected portions of the interval); and, when operating in the
training mode, measured glucose (use of exemplary inputs are
presented in Examples 1 and 2). Further, a calibration ratio check
is described in Example 4 that is useful to insure that the
calibration has been efficacious, and that the calibration
demonstrates a desired level of sensitivity of the sampling
system.
[0142] 2.3.0 Predicting Measurements
[0143] The analyte-specific values obtained using the above
techniques are used herein to predict target analyte concentrations
in a biological system using a Mixtures of Experts (MOE)
analysis.
[0144] The Mixtures of Experts algorithm breaks up a non-linear
prediction equation into several linear prediction equations
("Experts"). An "Expert" routine is then used to switch between the
different linear equations. In the equations presented below, the w
(weighting) factor determines the switch by weighting the different
Experts with a number between 0 and 1, with the restriction
that:
i = 1 n w i = 1 ##EQU00011##
[0145] The Mixtures of Experts algorithm of the present invention
is based on the ideal case presented in Equation 1, where the
individual experts have a linear form:
An = i = 1 n An i w i ( 1 ) ##EQU00012##
wherein (An) is an analyte of interest, n is the number of experts,
An.sub.i is the analyte predicted by Expert i; and w.sub.i is a
parameter. The number of experts is chosen based on the quality of
the fit of the model, subject to the requirement that it is
desirable to use the least number of experts possible. The number
of experts is preferably less than 100, and more preferably less
than 30. In most cases, selection of the fewest possible experts is
desirable.
[0146] The individual Experts An.sub.i are further defined by the
expression shown as Equation (2).
An i = j = 1 m a ij P j + z i ( 2 ) ##EQU00013##
wherein, An.sub.i is the analyte predicted by Expert i; P.sub.j is
one of m parameters, m is typically less than 100; a.sub.ij are
coefficients; and z.sub.i is a constant.
[0147] The weighting value, w.sub.i, is defined by the formula
shown as Equation (3).
w i = d i [ k = 1 n d k ] ( 3 ) ##EQU00014##
where e refers to the exponential function and the d.sub.k (note
that the d.sub.i in the numerator of Equation 3 is one of the
d.sub.k) are a parameter set analogous to Equation 2 that is used
to determine the weights w.sub.i. The d.sub.k are given by Equation
4.
d k = j = 1 m .alpha. jk P j + .omega. k ( 4 ) ##EQU00015##
where .alpha..sub.jk is a coefficient, P.sub.j is one of m
parameters, and where .omega..sub.k is a constant.
[0148] The Mixtures of Experts method described by the above
equations is supplied with a large data base of empirically
obtained information about the parameters defined by the equations.
By employing a linear regression function, the equations are
simultaneously solved for the values of all coefficients and
constants. In other words, the algorithm is trained to be
predictive for the value of An (the analyte) given a particular set
of data. A preferred optimization method to determine the
coefficients and constants is the Expectation Maximization method
(Dempster, A. P., N. M. Laird, and D. B. Rubin, J. Royal
Statistical Society (Series B-Methodological) 39:(1), 1977). Other
optimization methods include the Levenburg-Marquardt algorithm
(Marquardt, D. W., J. Soc. Ind. Appl. Math. 11:p 431-441, 1963) and
the Simplex algorithm (Nelder, J. A., and Mead, R., Computer
Journal 7:p 308, 1965).
[0149] In the context of blood glucose monitoring with an
iontophoretic sampling device, the MOE algorithm allows for the
accurate prediction of glucose concentration. In this regard,
during a typical iontophoretic measuring cycle, iontophoretic
extraction of the analyte is carried out for a suitable amount of
time, for example about 1 to 30 minutes, after which time the
extracted analyte is detected for a suitable amount of time, for
example about 1-30 minutes. An application of the Mixtures of
Experts algorithm to a specific set of parameters for glucose
monitoring is presented in Example 1.
[0150] In the context of blood glucose monitoring with an
iontophoretic sampling device, the Mixtures of Experts algorithm
allows for the accurate prediction of blood glucose
concentrations.
[0151] 2.4.0 Algorithm Modifications
[0152] A further aspect of the present invention is the
modification of the Mixtures of Experts (MOE) algorithm. The MOE
can be modified in a number of ways including, but not limited to,
the following modifications: using different groups of selected
inputs (see above); adapting the algorithm by modifying the
training set; using different algorithms or modifications of the
MOE for different ranges of analyte detection; using different
statistical distributions in the Mixtures of Experts; rejection of
selected expert(s); and, switching algorithms.
[0153] 2.4.1 Adapting the Algorithm
[0154] The Mixtures of Experts (MOE) is trained using sets of data
that contain patterns. Those patterns, represented in a training
data set, typically give good performance. Accordingly, training
MOE with a wide variety of patterns improves the predictive
performance of MOE, for example, using a variety of blood glucose
patterns that occur in diabetics patients to obtain parameters that
represent the patterns. In this case the selected patterns are used
to develop an appropriate training set for MOE and then the
parameters generated from that training set are used to test data
representing a variety of patterns. In one embodiment, a "global"
training set may be augmented by providing a training data set
developed from an individual subject's blood glucose data taken
over several (or many) days. Such an individual pattern is
potentially useful to customize the algorithm to that subject. The
parameters generated from using a training set including such an
individual patterns is then tested in the same individual to
determine whether the expanded training data set provides better
predicted values. In an alternative embodiment, a selected
percentage of the global training set can be used with the
individual's training set (rather than using the entire global
training set).
[0155] Further, the data comprising a training data set can be
specifically chosen to optimize performance of the MOE under
specific conditions. Such optimization may include, for example,
using diverse data sets or selecting the best data to represent a
specific condition. For example, different training data sets based
on data obtained from a variety of races can be used to train the
MOE to optimize predictive performance for individual members of
the different races represented by different data sets.
[0156] Finally, MOE is typically trained with values chosen in a
selected range (e.g., blood glucose values in the range of 40-400
mg/dl). However, the MOE can be trained with data sets that fall
outside of the selected range.
[0157] 2.4.2 Algorithm Optimized for Different Ranges
[0158] The MOE can be optimized for predictive performance in
selected ranges of data. Depending on the range different MOEs may
be invoked for prediction of analyte values (see "Switching
Algorithms" below). Alternatively, different algorithms can be used
for prediction of values in selected ranges of analyte detection.
For example, MOE may be used for prediction of glucose values in a
range of 40-400 mg/dl; however, at low and high ends of glucose
values a specifically defined function can be applied to the data
in order to get preferred values. Such preferred values may, for
example, be useful in the situation where under-prediction is more
desirable than over-prediction (e.g., at low blood glucose values).
In this case a modification of MOE may be used or an specific
algorithm may be optimized for prediction in the selected range
using, for example, a non-linear distribution function that
emphasizes predicting low blood glucose (BG) in the range
BG.ltoreq.100.
[0159] 2.4.3 Employing Different Distribution Functions
[0160] When calculating the weights used in the MOE algorithm a
selected distribution is used. One exemplary distribution is a
Gaussian distribution (Example 3) that weighs deviations relative
to the square of difference from the mean. However, other
distributions can be used to improve predictive function of the
algorithm. For example, a Laplacian distribution function was used
in the calculations presented in Example 4. The Laplacian
distribution has longer tails than a Gaussian distribution, and
weighs deviations relative to the absolute difference from the
mean. Other distribution functions can be used as well including,
but not limited to, Cauchy distribution or a specific distribution
function devised (or calculated) based on specific data sets
obtained, for example, from different individuals or different
groups of individuals (e.g., different races).
[0161] 2.4.4 Rejecting Experts
[0162] When multiple experts are used in the MOE each expert can be
inspected to determine if, for example, one or more of the experts
is providing incongruous values. When such an expert is identified
(e.g., in the calculation of a particular data point) the expert
may be eliminated for that calculation and the weights of the
remaining experts readjusted appropriately. Inspection of the
experts can be carried out by a separate algorithm and can, for
example, be based on whether the value predicted by the expert
falls outside of a designated range. If the value falls outside of
a designated range, the expert may be eliminated in that
calculation. For example, Example 3 describes the use of three
experts (BG.sub.1, BG.sub.2, and BG.sub.3) in an MOE for prediction
of blood glucose values, wherein a weighted average is used to
calculate the final blood glucose value. However, each of these
three experts can be inspected to determine if one (or more) of
them does not make sense (e.g., is providing a stochastic or
out-lying value significantly different from the other two
experts). The expert providing the incongruous value is disregarded
and the weights of the other two experts are readjusted
accordingly.
[0163] 2.4.5 Switching Algorithms
[0164] In yet another aspect of the present invention, prediction
of the concentration of an analyte can be accomplished using
specialized algorithms, where the specialized algorithms are useful
for predictions in particular situations (e.g., particular data
sets or ranges of predicted values) and where the algorithm used
for performing the calculations is determined based on the
situation. In this case a "switch" can be used to employ one (or
more) algorithm rather than another (or more) algorithm. For
example, a global MOE algorithm can be the switch used to selected
one of three different MOE algorithms. In one embodiment such a
global MOE algorithm may be used to determine a blood glucose
value. The blood glucose value is determined, by the algorithm, to
fall into one of three ranges (for example, low, normal, and high).
For each range there is an separate MOE algorithm that optimizes
the prediction for values in the particular range. The global MOE
algorithm then selects the appropriate MOE algorithm based on the
value and the selected MOE performs a new prediction of blood
glucose values based on the original input values but optimized for
the range into which the value was predicted (by the global MOE) to
fall. As a further illustration, inputs to determine a blood
glucose value are provided to a global MOE which determines that
the value is a low-value. The inputs are then directed to a
Low-Value Optimized MOE to generate a more accurate predicted blood
glucose value.
[0165] Specialized algorithms may be developed to be used in
different parts of a range of analyte signal spectrum or other
input values (e.g., high signal/low signal; high BGCal/low BGCal;
high/low calratio; high/low temp; etc., for all variables used in
the prediction). A global algorithm can be used to decide which
region of the spectrum the analyte signal is in, and then the
global algorithm switches the data to the appropriate specialized
algorithm.
[0166] In another embodiment, an algorithm other than the MOE can
be used as the switch to choose among a set of MOE algorithms, or
an MOE can be used as the switch to choose among a set of other
algorithms. Further, there can be multiple levels of specialized
switching (which can be graphically represented for instance by
branched tree-diagrams).
[0167] Following here are several specific, non-limiting examples,
of the uses of switching in the practice of the present invention
when blood glucose values are being determined.
[0168] In one embodiment, variables are identified that explicitly
represent signal decay, for example, a switch based on elapsed time
since calibration (early or late) or the value of Calratio at CAL
(high or low). An exemplary switch of this type is represented by
elapsed time since calibration where, for example, the algorithm
described in Example 3 may be trained independently with inputs
from an early phase of sensor use and inputs from a late phase
sensor use (e.g., the total useful life of a sensor element may be
split into two-halves--early and late). Then, depending on the time
since calibration that selected input values are being obtained (an
exemplary switch), the input values are directed to an MOE
algorithm that was trained on data from the appropriate phase
(i.e., either early or late). Such a switch is useful to help
correct for error based in sensor decay.
[0169] Another exemplary switch of this type is represented by the
value of Calratio at the calibration point. Calratio is described
in Example 4. The Calratio is a measure of sensor sensitivity.
Accordingly, if desired the Calratio range can be divided into two
halves (high and low ranges). The algorithm described in Example 3
may be trained independently with inputs from the high and low
ranges of the Calratio. A switch is then based on the Calratio
values to direct the inputs to the MOE algorithm that is trained
with the appropriate data set (i.e., data sets corresponding to
inputs from high and low Calratio ranges).
[0170] 2.5.0 Decreasing the Bias of a Data Set
[0171] In addition to the MOE algorithm described in the present
specification, following here is a description of a method to alter
data used to generate a training data set so as to correct slope,
intercept (and resultant bias) introduced by the limited range of
data input. This invention provides a useful correction for any
asymmetric data input that gives a bias to resultant predictions.
In this method, the values of a data set are used to create a
second data set that mirrors the first, i.e., positive values
become negative values (opposite signs). The two data sets are then
used as the training data set. This transformation of the
asymmetrical data set results in a forced symmetry of the data
comprising the training set.
[0172] The following is a non-limiting example of this method for
the correction of bias using blood glucose level determination. In
the blood glucose value determinations described herein there is an
inherent bias (manifested by a slope of <1 and a positive
intercept, e.g., FIG. 10A; in the figure, pBG is predicted blood
glucose and mBG is directly measured blood glucose--measured, for
example, using a HemoCue.RTM. meter) introduced into the prediction
function. This is in part due to the fact that there are no blood
glucose levels of <40 mg/dl used in the data input training set.
The data input for training the MOE algorithm, used to predict
blood glucose levels, uses, for example, the following variables:
elapsed time since calibration, average signal, calibrated signal,
and the blood glucose at the calibration point (see, e.g., Examples
3 and 4). The value that these inputs predict and try to match is
directly measured blood glucose. The allowed range for blood
glucose is 40-400 mg/dl. Due to this limited range of blood
glucose, the resultant function predictions (i.e., via the MOE)
result in an inherent bias, slope <1 and positive intercept when
plotting predicted blood glucose (y-axis variable, pBG, FIG. 10A)
versus directly measured blood glucose (x-axis variable, mBG, FIG.
10A).
[0173] The method of the present invention circumvents this problem
by augmenting the original input data set with a data set
comprising the same elapsed time since calibration, but with values
of the average signal (in nanocoulombs) and directly measured blood
glucose both of the opposite sign relative to the original, real
data set. The calibrated signal is then calculated using the
opposite sign data. In this way the input data is doubled and is
now symmetric around the origin (FIG. 10B; in the figure, pBG is
predicted blood glucose and mBG is directly measured blood
glucose--measured, for example, using a HemoCue.RTM. meter). In
FIG. 10B the dotted lines represent the slopes predicted from the
single data set with which they are associated. The solid line
between the two dashed lines represents the corrected slope based
on use of the original data set and the opposite sign data set to
train the algorithm.
[0174] The value of this approach when plotting predicted blood
glucose (using MOE) versus measured blood glucose can be seen by
examining the results presented in the following table.
TABLE-US-00001 Original Data Set & Opposite Sign Original Data
Set Data Set Deming Slope* 0.932 1.042 Deming Intercept* 12.04
-5.63 Bias 50 mg/dl 8.64 -3.53 Bias 80 mg/dl 6.6 -2.27 Bias 100
mg/dl 5.24 -1.43 Bias 150 mg/dl 1.84 0.67 Bias 200 mg/dl -1.56 2.77
*Based on orthogonal regression with a variance ratio equal to
two.
[0175] As the results in this table demonstrate, the bias reducing
method of the present invention has a slope closer to 1, an
intercept closer to zero, and the bias values are, in general,
closer to zero.
[0176] Accordingly, one aspect of the present invention is a method
for decreasing the bias of a data set. The method involves
generating a second data set that has values opposite in sign of
the original data set and using this first and second data set as a
combined data set to train the algorithm (e.g., MOE).
EXAMPLES
[0177] The following examples are put forth so as to provide those
of ordinary skill in the art with a complete disclosure and
description of how to make and use the devices, methods, and
formulae of the present invention, and are not intended to limit
the scope of what the inventor regards as the invention. Efforts
have been made to ensure accuracy with respect to numbers used
(e.g., amounts, temperature, etc.) but some experimental errors and
deviations should be accounted for. Unless indicated otherwise,
parts are parts by weight, molecular weight is weight average
molecular weight, temperature is in degrees Centigrade, and
pressure is at or near atmospheric.
Example 1
Application of the "Mixtures of Experts" to Glucose Monitoring
[0178] This example describes the use of a Mixtures of Experts
(MOE) algorithm to predict blood glucose data from a series of
signals.
[0179] In the present example, a GlucoWatch.RTM. monitor was used
to collect data and the following variables were chosen to generate
data sets for the MOE algorithm:
[0180] 1) elapsed time (time), elapsed time since the
GlucoWatch.RTM. monitor was applied to the subject, i.e., elapsed
time since the sampling system was placed in operative contact with
the biological system;
[0181] 2) active signal (active), in this example, the value of the
active parameter corresponded to the nanoamp signal that was
integrated over the sensing time-interval to give the active
parameter in nanocoulombs (nC);
[0182] 3) calibrated signal (signal), in this example was obtained
by multiplying an active by a constant, where the constant was
defined as the blood glucose level at the calibration point divided
by the active value at the calibration point. For example, as
follows:
signal = BG / cp active / cp ( active ) ##EQU00016##
where the slope of the line active versus blood glucose had a
non-zero intercept and the offset took into account that the
intercept was not zero. In the alternative, the constant could be
as follows:
signal = BG / cp ( active / cp + offset ) ( active + offset )
##EQU00017##
where the offset takes into account the intercept value.
[0183] 4) blood glucose value at the calibration point (BG/cp) was
determined by direct blood testing.
[0184] Other possible variables include, but are not limited to,
temperature, iontophoretic voltage (which is inversely proportional
to skin resistance), and skin conductivity.
[0185] Large data sets were generated by collecting signals using a
transdermal sampling system that was placed in operative contact
with the skin. The sampling system transdermally extracted the
analyte from the biological system using an appropriate sampling
technique (in this case, iontophoresis). The transdermal sampling
system was maintained in operative contact with the skin to provide
a near continual or continuous stream of signals.
[0186] The basis of the Mixtures of Experts was to break up a
non-linear prediction equation (Equation 5, below) into several
Expert prediction equations, and then to have a routine to switch
between the different linear equations. For predicting blood
glucose levels, three separate linear equations (Equations 6, 7,
and 8) were used to represent blood glucose, with the independent
variables discussed above of time, active, signal, blood glucose at
a calibration point (BG/cp), and a constant (t.sub.i).
[0187] The switching between equations 6, 7, and 8 was determined
by the parameters w.sub.1, w.sub.2, and w.sub.3 in equation 5,
which was further determined by the parameters d.sub.1, d.sub.2,
and d.sub.3 as given by equations 9-14, where the individual
experts had a linear form:
BG=w.sub.1BG.sub.1+w.sub.2BG.sub.2+w.sub.3BG.sub.3 (5)
wherein (BG) was blood glucose, there are three experts (n=3);
BG.sub.1 was the analyte predicted by Expert i; and w.sub.i was a
parameter, and the individual Experts BG.sub.i were further defined
by the expression shown as Equations 6, 7, and 8
BG.sub.1=p.sub.1(time)+q.sub.1(active)+r.sub.1(signal)+s.sub.1(BG|cp)+t.-
sub.1 (6)
BG.sub.2=p.sub.2(time)+q.sub.2(active)+r.sub.2(signal)+s.sub.2(BG|cp)+t.-
sub.2 (7)
BG.sub.3=p.sub.3(time)+q.sub.3(active)+r.sub.3(signal)+s.sub.3(BG|cp)+t.-
sub.3 (8)
wherein, BG.sub.i was the analyte predicted by Expert i; parameters
include, time (elapsed time), active (active signal), signal
(calibrated signal), and BG/cp (blood glucose value at a
calibration point); p.sub.i, q.sub.i, r.sub.i, and s.sub.i were
coefficients; and t.sub.i was a constant; and further where the
weighting value, w.sub.i, was defined by the formulas shown as
Equations 9, 10, and 11
w 1 = d 1 d 1 + d 2 + d 3 ( 9 ) w 2 = d 2 d 1 + d 2 + d 3 ( 10 ) w
3 = d 3 d 1 + d 2 + d 3 ( 11 ) ##EQU00018##
where e referred to the exponential function and d.sub.i was a
parameter set (analogous to Equations 6, 7, and 8) that were used
to determine the weights w.sub.i, given by Equations 9, 10, and 11,
and
d.sub.1=.tau..sub.1(time)+.beta..sub.1(active)+.gamma..sub.1(signal)+.de-
lta..sub.1(BG|cp)+.di-elect cons..sub.1 (12)
d.sub.2=.tau..sub.2(time)+.beta..sub.2(active)+.gamma..sub.2(signal)+.de-
lta..sub.2(BG|cp)+.di-elect cons..sub.2 (13)
d.sub.3=.tau..sub.3(time)+.beta..sub.3(active)+.gamma..sub.3(signal)+.de-
lta..sub.3(BG|cp)+.di-elect cons..sub.3 (14)
where .tau..sub.i, .beta..sub.i, .gamma..sub.i and .delta..sub.i
were coefficients, and where .di-elect cons..sub.i is a
constant.
[0188] To calculate the above parameters an optimization method was
applied to the algorithm (Equations 5-14) and the large data set.
The optimization method used was the Expectation Maximization
method (Dempster, A. P., N. M. Laird, and D. B. Rubin, J. Royal
Statistical Society (Series B-Methodological) 39:(1), 1977), but
other methods may be used as well.
[0189] The parameters in these equations were determined such that
the posterior probability of the actual glucose was maximized.
Example 2
Prediction of Measurement Values I
[0190] Iontophoretic extraction of glucose was carried out using a
GlucoWatch.RTM. monitor which employs (i) a low-level iontophoretic
current to extract glucose through patient's skin, and (ii) an
electrochemical biosensor to detect the extracted glucose.
Iontophoresis was carried out for 3 minute intervals and
electrochemical detection was carried out for 7 minute intervals to
result in 10 minute measurement cycles--thus generating collections
of data (data sets) as described in Example 1.
[0191] The data that were used for this analysis were obtained by
diabetic subjects each wearing a GlucoWatch.RTM. monitor over a 14
hour period. The MOE inputs consisted of the following parameters
(described in Example 1): time, active, signal, blood glucose at a
calibration point (BG/cp). These training data were used to
determine the unknown parameters in the MOE using the Expectation
Maximization Method. The output of the MOE algorithm was the
measured value of blood glucose. Using a three hour time point for
calibrating the GlucoWatch.RTM. monitor, the mean percentage error
(MPE) between the actual blood glucose and the calculated (MOE
predicted) blood glucose was 13%.
[0192] In a diabetic study consisting of 61 patients, the diabetic
subjects' blood glucose ranged from 23-389 mg/dl. A protocol was
followed whereby a subject (who had fasted since the previous
midnight) came to a test site where the GlucoWatch.RTM. monitor was
applied to the subject, started, and calibrated. Over the next 14
hours, the subject had normal meals and a finger prick blood sample
was taken every 20 minutes for glucose determination ("actual
glucose"). Blood glucose levels were measured using the
HemoCue.RTM. meter (HemoCue AB, Sweden), which has an accuracy of
.+-.10%.
[0193] A plot of the glucose levels predicted by the Mixtures of
Experts algorithm (based on the data described above) versus the
actual blood glucose levels is presented in FIG. 6 (a Correlation
Plot). Analysis of the data shown in FIG. 6 showed a slope of 0.88,
an intercept of 14, and a correlation coefficient of R=0.93. There
were N=1,348 points comprising the Correlation Plot.
[0194] These statistical results, along with the MPE=0.13
(discussed above), show the excellent predictive capabilities of
the GlucoWatch.RTM. monitor and the Mixtures of Experts
algorithm.
Example 3
[0195] Another Application of the "Mixtures of Experts" to Glucose
Monitoring
[0196] This example describes the use of a Mixtures of Experts
(MOE) algorithm to predict blood glucose data from a series of
signals.
[0197] In the present example, a GlucoWatch.RTM. monitor was used
to collect data and the following variables were chosen to generate
data sets for the MOE algorithm:
[0198] 1) time since calibration (time.sub.c), the elapsed time
since the calibration step was carried out for the GlucoWatch.RTM.
monitor (in hours);
[0199] 2) active signal (active), in this example, the value of the
active parameter corresponded to the averaged signal from two
active reservoirs, where each reservoir provided a nanoamp signal
that was integrated over the sensing time-interval, the two values
were then added and averaged to give the active parameter in
nanocoulombs (nC);
[0200] 3) calibrated signal (signal), in this example was obtained
as follows:
signal = BG / cp ( active / cp + offset ) ( active + offset )
##EQU00019##
where the offset takes into account the intercept value.
[0201] 4) blood glucose value at the calibration point (BG/cp), in
mg/dl, was determined by direct blood testing.
[0202] Other possible variables include, but are not limited to,
temperature, iontophoretic voltage (which is inversely proportional
to skin resistance), and skin conductivity.
[0203] Large data sets were generated by collecting signals using a
transdermal sampling system that was placed in operative contact
with the skin. The sampling system transdermally extracted the
analyte from the biological system using an appropriate sampling
technique (in this case, iontophoresis). The transdermal sampling
system was maintained in operative contact with the skin to provide
a near continual or continuous stream of signals.
[0204] The basis of the Mixtures of Experts was to break up a
non-linear prediction equation (Equation 15, below) into several
Expert prediction equations, and then to have a routine to switch
between the different linear equations. For predicting blood
glucose levels, three separate linear equations (Equations 16, 17,
and 18) were used to represent blood glucose, with the independent
variables discussed above of time, active, signal, blood glucose at
a calibration point (BG/cp), and a constant (t.sub.i).
[0205] The switching between Equations 16, 17, and 18 was
determined by the parameters w.sub.1, w.sub.2, and w.sub.3 in
equation 5, which was further determined by the parameters d.sub.1,
d.sub.2, and d.sub.3 as given by equations 9-14, where the
individual experts had a linear form:
BG=w.sub.1BG.sub.1+w.sub.2BG.sub.2+w.sub.3BG.sub.3 (15)
wherein (BG) was blood glucose, there are three experts (n=3);
BG.sub.i was the analyte predicted by Expert i; and w.sub.i was a
parameter, and the individual Experts BG.sub.i were further defined
by the expression shown as Equations 16, 17, and 18
BG.sub.1=p.sub.1(time.sub.c)+q.sub.1(active)+r.sub.1(signal)+s.sub.1(BG|-
cp)+t.sub.1 (16)
BG.sub.2=p.sub.2(time.sub.c)+q.sub.2(active)+r.sub.2(signal)+s.sub.2(BG|-
cp)+t.sub.2 (17)
BG.sub.3=p.sub.3(time.sub.c)+q.sub.3(active)+r.sub.3(signal)+s.sub.3(BG|-
cp)+t.sub.3 (18)
wherein, BG.sub.i was the analyte predicted by Expert i; parameters
include, times (elapsed time since calibration), active (active
signal), signal (calibrated signal), and BG/cp (blood glucose value
at a calibration point); p.sub.i, q.sub.i, r.sub.i, and s.sub.i
were coefficients; and t.sub.i was a constant; and further where
the weighting value, w.sub.i, was defined by the formulas shown as
Equations 19, 20, and 21
w 1 = d 1 d 1 + d 2 + d 3 ( 19 ) w 2 = d 2 d 1 + d 2 + d 3 ( 20 ) w
3 = d 3 d 1 + d 2 + d 3 ( 21 ) ##EQU00020##
where e referred to the exponential function and d.sub.i was a
parameter set (analogous to Equations 16, 17, and 18) that were
used to determine the weights w.sub.i, given by Equations 19, 20,
and 21, and
d.sub.1=.tau..sub.1(time.sub.c)+.beta..sub.1(active)+.gamma..sub.1(signa-
l)+.delta..sub.1(BG|cp)+.di-elect cons..sub.1 (22)
d.sub.2=.tau..sub.2(time.sub.c)+.beta..sub.2(active)+.gamma..sub.2(signa-
l)+.delta..sub.2(BG|cp)+.di-elect cons..sub.2 (23)
d.sub.3=.tau..sub.3(time.sub.c)+.beta..sub.3(active)+.gamma..sub.3(signa-
l)+.delta..sub.3(BG|cp)+.di-elect cons..sub.3 (24)
where .tau..sub.i, .beta..sub.i, .gamma..sub.i, and .delta..sub.i
were coefficients, and where .di-elect cons..sub.i is a
constant.
[0206] To calculate the above parameters an optimization method was
applied to the algorithm (Equations 15-24) and the large data set.
The optimization method used was the Expectation Maximization
method (Dempster, A. P., N. M. Laird, and D. B. Rubin, J. Royal
Statistical Society (Series B-Methodological) 39:(1), 1977), but
other methods may be used as well.
[0207] The parameters in these equations were determined such that
the posterior probability of the actual glucose was maximized.
Example 4
Prediction of Measurement Values II
[0208] A. Calibration Ratio Check
[0209] In order to insure an efficacious calibration of the
sampling system, the value of the following ratio was found to fall
in a selected range:
CalRatio = BG / cp ( active / cp + offset ) ##EQU00021##
where the offset takes into account the intercept value. The range
is established using standard error minimization routines to
evaluate a large population of calibration points, and thereby
determine the CalRatio values which result in accurate blood
glucose predictions. In one embodiment, the preferred CalRatio
range of values was between 0.00039 and 0.01. In the CalRatio,
BG/cp was the blood glucose concentration at the calibration point
(or calibration time), active was the input prediction at the
calibration point, and offset was a constant offset. The offset
value was established empirically using standard error minimization
routines to evaluate a number of potential offset values for a
large data set, and thereby select the one that, results in the
most accurate prediction of blood glucose.
[0210] The CalRatio check provides a screen for valid or
efficacious calibration readings. If the CalRatio falls outside of
the range of selected values, then the calibration was rejected and
the calibration was re-done. Low values of this ratio indicated low
sensitivity of glucose detection.
[0211] B. Prediction of Values
[0212] GlucoWatch.RTM. monitors (Cygnus, Inc., Redwood City,
Calif., USA) were applied to the lower forearm of human subjects
with diabetes (requiring insulin injection). Iontophoretic
extraction of glucose was carried out using the GlucoWatch.RTM.
monitor which employs (i) a low-level iontophoretic current to
extract glucose through patient's skin, and (ii) an electrochemical
biosensor to detect the extracted glucose.
[0213] The subjects were 18 years of age, or older, and consisted
of both males and females from a broad ethnic cross-section.
Iontophoresis was carried out for 3 minute intervals and
electrochemical detection was carried out for 7 minute intervals to
result in 10 minute measurement cycles--thus generating collections
of data (data sets) as described in Example 3. As described in
Example 3, the active measurement was the averaged signal from two
active reservoirs, for example, a first electrode acts as the
cathode during the first 10 minute cycle (3 minutes of
iontophoresis, followed by 7 minutes of sensing) and a second
electrode acts as the cathode during the second 10 minute cycle.
The combined cycle requires 20 minutes, and the combined cathode
sensor data is used as a measure of the glucose extracted (an
averaged "active signal", see Example 3). This 20 minute cycle is
repeated throughout operation of the GlucoWatch.RTM. monitor.
[0214] In addition, subjects obtained two capillary blood samples
per hour, and the glucose concentration was determined using a
HemoCue.RTM. clinical analyzer (HemoCue AB, Sweden). The blood
glucose measurement obtained at three hours was used as a single
point calibration, which was used to calculate the extracted blood
glucose for all subsequent GlucoWatch.RTM. monitor
measurements.
[0215] The data that were used for this analysis were obtained by
diabetic subjects each wearing two GlucoWatch.RTM. monitors over a
14 hour period. The MOE inputs consisted of the following
parameters (described in Example 3): time.sub.c, active, signal,
blood glucose at a calibration point (BG/cp). For the calibrated
signal:
signal = BG / cp ( active + offset ) ( active / cp + offset )
##EQU00022##
where (i) active/cp was the input prediction at the calibration
point, and (ii) the offset and takes into account the fact that
when predicted blood glucose is plotted vs. active, there is a
non-zero y-intercept. The optimized value of the offset that was
used was a constant value of 1000 nC. The signal that is used in
the Mixtures of Experts algorithm is temperature compensated by
applying an Arrhenius type correction to the raw signal data to
account for skin temperature fluctuations.
[0216] Finally, in order to eliminate potential outlier points,
various screens were applied to the raw and integrated sensor
signals. The purpose of these screens were to determine whether
certain environmental, physiological or technical conditions
existed during a measurement cycle that could result in an
erroneous reading. The screens that were used measured the averaged
signal (active), iontophoretic voltage, temperature, and skin
surface conductance. If any of these measurements deviated
sufficiently from predefined behavior during a measurement, then
the entire measurement was excluded. For example, if the skin
surface conductance exceeded a set threshold, which indicated
excessive sweating (sweat contains glucose), then this potentially
erroneous measurement was excluded. These screens enable very noisy
data to be removed, while enabling the vast majority of points
(>87%) to be accepted.
[0217] The Mixtures of Experts was further customized in the
following way. When the weights were updated using equations 19-24
(Example 3), a Laplacian distribution function was used. The
Laplacian distribution has longer tails than a Gaussian
distribution, and weighs deviations relative to the absolute
difference from the mean, whereas a Gaussian distribution weighs
deviations relative to the square of difference from the mean (P.
McCullagh and J. A. Nelder, Generalized Linear Models, Chapman and
Hall, 1989; and W. H. Press, S. A. Teukolsky, W. T. Vetterling and
B. P. Flannery, Numerical Recipes in C. Cambridge University Press,
Cambridge, 1992). In addition, the individual blood glucose values
were weighted by the inverse of the value of the blood glucose at
the calibration point. Both of these modifications result in
increased accuracy of predictions, especially at low blood glucose
levels.
[0218] The training data were used to determine the unknown
parameters in the Mixtures of Experts using the Expectation
Maximization Method. The Mixtures of Experts algorithm was trained
until convergence of the weights was achieved. The output of the
MOE algorithm was the measured value of blood glucose. Using a
three hour time point for calibrating the GlucoWatch.RTM. monitor,
the mean percentage error (MPE) between the actual blood glucose
and the calculated (MOE predicted) blood glucose was 14.4%.
[0219] In a diabetic study consisting of 91 GlucoWatch.RTM.
monitors, the diabetic subjects' blood glucose ranged from 40-360
mg/dl. A protocol was followed whereby a subject (who had fasted
since the previous midnight) came to a test site where two
GlucoWatch.RTM. monitors were applied to the subject, started, and
calibrated. Over the next 14 hours, the subject had normal meals
and a finger prick blood sample was taken every 20 minutes for
glucose determination ("actual glucose"). Blood glucose levels were
measured using the HemoCue.RTM. meter (HemoCue AB, Sweden), which
has an accuracy of +10%.
[0220] A plot of the glucose levels predicted by the Mixtures of
Experts algorithm (based on the data described above) versus the
actual blood glucose levels is presented in FIG. 7 (a Correlation
Plot). Also shown in FIG. 7 is the orthogonal least squares line
(A. Madansky, The Fitting of Straight Lines When both Variables are
Subject to Error, J. American Statistical Association 54:173-206,
1959; D. York, Least-Squares Fitting of a Straight Line, Canadian
Journal of Physics 44:1079-1986, 1966; W. A. Fuller, Measurement
Error Models, Wiley, New York, 1987; and W. H. Press, S. A.
Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipes
in C. Cambridge University Press, Cambridge, 1992) with an error
variance ratio (defined as the error in the dependent variable
divided by the error of the independent variable) of 2.05. This
variance error ratio corrects the linear regression line (which
assumes zero error in the independent variable) for the true error
in both independent and dependent variables.
[0221] The variance ratio was determined as follows. Each subject
was required to wear two GlucoWatch.RTM. monitors. Then, at each
time point, the difference between the two watches was determined,
squared and divided by 2. The resulting values were averaged over
the total number of time points used. Fifty pairs of watches, each
with 42 time points, were used for this calculation. The error
variance for the HemoCue.RTM. was obtained from clinical data
published in the literature. The GlucoWatch.RTM. monitor error
variance was calculated to be 150 (standard deviation=12 mg/dl) and
the HemoCue.RTM. error variance was calculated to be 73 (standard
deviation=8.5 mg/dl), giving the error ratio of 2.05.
[0222] Analysis of the data shown in FIG. 7 showed a slope of 1.04,
an intercept of approximately -10.7 mg/dl, and a correlation
coefficient of R=0.89.
[0223] It is also instructive to examine graphs of the measured and
predicted blood glucose levels vs. time. One such graph is shown in
FIG. 8 (in the legend of FIG. 8: solid diamonds are measurements
obtained using the GlucoWatch.RTM. monitor; open circles are blood
glucose concentrations as determined using HemoCue.RTM.; and the
"star" symbol represents blood glucose concentration at the
calibration point). FIG. 8 indicates the excellent capabilities of
the GlucoWatch.RTM. monitor and the Mixtures of Experts algorithm
in calibrating the device.
[0224] These statistical results, along with the MPE=14.4%
(discussed above), show the excellent predictive capabilities of
the GlucoWatch.RTM. monitor and the Mixtures of Experts
algorithm.
[0225] Although preferred embodiments of the subject invention have
been described in some detail, it is understood that obvious
variations can be made without departing from the spirit and the
scope of the invention as defined by the appended claims.
* * * * *