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BACKGROUND OF THE INVENTION
The present invention relates to a system and method for predicting blood
glucose level by means of computer analysis of blood glucose time-series
data of a diabetic.
Basically, insulin therapies for diabetics are executed by applying insulin
calculated based on a blood glucose level of a patient (diabetic). The
control of blood glucose level is mainly executed by an open circle method
in that the blood glucose level is simply measured or by a feedback method
in that an insulin administration amount is determined on the basis of the
blood glucose level measurement data by a doctor once or twice a month.
Furthermore, in some cases, the insulin administration amount is
controlled day by day on the basis of a predetermined insulin scale.
Doctors mainly have executed insulin treatments to patients as follows.
(1) On the basis of the blood glucose level measurement date, the doctor
determines the insulin administration amount twice a month. (2) On the
basis of the predetermined insulin administration amount to the blood
glucose level, the insulin is applied to a patient one or third a day.
However, these treatments may put the blood glucose level unstable since
they include a feedback having a large time lag. For example, the increase
of the insulin administration amount for decreasing the average of the
blood glucose level may invite low blood glucose level (hypoglycemia). On
the other hand, the decrease of the insulin administration amount may
invite high blood glucose level (hyperglycemia). Therefore, in order to
properly determine the insulin administration amount for a proper blood
glucose level control, it is necessary to execute a blood glucose level
control without time lag so as to decrease a daily change of the blood
glucose level and to finally put it within an allowable range.
SUMMARY OF THE INVENTION
It is an object of the present invention to provide a system and method for
predicting blood glucose level which system and method enables a
determination of a proper insulin administration amount without time lag,
and a prediction of a daily blood glucose on the basis of the blood
glucose level measured data.
The inventors of the present invention propose a method and system for
enabling a short-term prediction of the blood glucose level from a present
blood glucose by means of the Local Fuzzy Reconstruction Method disclosed
in U.S. Pat. No. 5,748,851.
An aspect of the present invention resides in a blood glucose level
predicting system which comprises a time series measurement data storing
section for storing blood glucose level measured data in a blood glucose
time series file to treat the data as time series data, a dynamics
estimating section for estimating a dynamics which most preferably
represents a phase characteristic of the time series data stored in the
time series measurement data storing section, a parameter storing section
for storing embedding a dimension n and a time delay .tau. of the dynamics
estimated in the dynamics estimating section as parameters for embedding
the estimated dynamics in multidimensional state space, a blood glucose
predicting section for predicting a near future value of the blood glucose
level by means of the Local Fuzzy Reconstruction Method on the basis of
the stored data of the blood glucose level data stored in the blood
glucose time series file and the parameters corresponding to the data and
for storing the predicted future value in a predicted blood glucose file,
and a display section for displaying the data of the blood glucose time
series file and the predicted blood glucose file.
Another aspect of the present invention resides in a blood glucose level
predicting method which comprises the steps of: preparing blood glucose
level data measured at latest and past time for use as time series data;
constructing an attractor by embedding the time series data in a
multidimensional space according to the Takens' Embedding Theorem;
selecting data vector z(T) on the attractor which includes the latest
blood glucose data; selecting a plurality of neighboring vectors x(i) on
the other trajectory passing through a neighbor space of the data vector
z(T) on the basis of a selecting reference that the Euclidean distance is
smaller than a predetermined value; selecting a data vector x(i+s) at s
steps future with respect to the data vector x(i) from the attractor;
estimating a predicted value z(T+s) at s steps future with respect to the
data vector z(T) by using the data vectors z(T), x(i) and x(i+s) by means
of the Local Fuzzy Reconstruction Method; and obtaining a predicted value
y(T+s) at s step future with respect to the predicted value z(T+s).
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a structural view showing a blood glucose level predicting system
of an embodiment according to the present invention.
FIGS. 2A to 2C are graphs each of which shows a part of time series data of
cases I, II and III.
FIGS. 3A to 3C are perspective views of attractors of FIGS. 2A to 2C
projected on the three dimensional space.
FIG. 4 is views showing detailed shape of the attractors on the three
dimensional space.
FIGS. 5A and 5B are explanatory views for explaining embedding of the time
series data on a n-dimensional reconstruction space.
FIG. 6 is an explanatory view for explaining a dynamics from x(T) to x(T+s)
by means of the Local Reconstruction Method.
FIGS. 7A to 7C are graphs of membership functions in antecedent statement
in the Local Fuzzy Reconstruction Method.
FIG. 8 is a graph showing a prediction result of the case I.
DETAILED DESCRIPTION OF THE INVENTION
The inventors of the present invention found that the time series behavior
of the blood glucose level performs a chaotic phenomenon, on the basis of
the analysis as to the instability of the blood glucose level control.
Further, they proposed a method and system for enabling a short-term
prediction of the blood glucose level from a present blood glucose level
by means of the Local Fuzzy Reconstruction Method disclosed in U.S. Pat.
No. 5,748,851 which has been proposed by the inventors of this invention.
(Time Series Behavior and Chaotic Phenomena of Blood Glucose Level)
First, as to time series behavior and chaotic phenomena of blood glucose
level, the analyzed and proved contents will be discussed hereinafter.
The analyzed objects of the blood glucose level were ten diabetics
including five cases of insulin dependency type (IDDM) and five cases of
non-insulin dependency type (NIDDM). The data thereof were recorded day by
day for at least one year and a half and for at most ten years. FIGS. 2A
to 2C show time series data of one NIDDM case and two IDDM cases which
were put in a good control condition.
A percentage of HbA.sub.1c is employed as an index of a practical control
since it is practically known that the percentage of HbA.sub.1c generally
represents an average of the controlled blood glucose level for the past
one or two month. The percentage of HbA.sub.1c of the case I was stably
controlled within a range from 5 to 6% as shown in FIG. 2A. The percentage
of HbA.sub.1c of the case II was similarly controlled within a range from
5 to 6% as shown in FIG. 2B. The percentage of HbA.sub.1c of the case III
was controlled within a range from 9 to 11% as shown in FIG. 2C.
The case I is diagnosed to have a non insulin dependent type diabetes, so
that the blood glucose level control function is insufficiently executed
by means of intrinsic insulin secretion. The cases II and III are
diagnosed to have an insulin dependent type diabetes, so that intrinsic
insulin secretion is almost not executed and therefore the blood glucose
level control function due to the intrinsic insulin secretion almost does
not executed.
By executing the spectrum analysis as to the data of these three cases by
means of FFT (Fast Fourier Transform), each of frequency components
appeared in wide range. The self-correlation function of each frequency
component was converged to nearly zero according to the increase of time.
The maximum Lyapunov exponent thereof was positive. These results
represented that there was a possibility that these three cases perform
chaotic behaviors.
FIGS. 3A to 3C show attractors projected on the three-dimensional space as
to the three cases. The attractor of the case I had a cylindrical shape,
the attractor of the case II had a tetrahedron shape, and the attractor of
the case III had a ball shape. As to fractal dimension, the case I was
2.27, the case II was 2.73, and the case III was 3.54. This represented
that the fractal dimension increased according to the complexity of the
shape of the attractor.
As a result of the evaluation of the control level of the blood glucose
level by HbA.sub.1c, the evaluation of the cases I (cylindrical shape) and
II (tetrahedron shape) were good control similarly. It was deemed that the
difference of the shapes of the attractors was caused by the difference of
the self blood glucose level control ability between IDDM and NIDDM. Both
of the cases II and III were IDDM and were controlled by the continuous
insulin subcutaneous injection treatment (CSII). The control level of the
case II was good control, and that of the case III was poor control.
The result of the researches as to the other cases represented that all of
them perform chaotic behaviors. The shapes of the attractors thereof were
one of a cylindrical shape, a tetrahedron shape, a ball shape, or mixture
thereof.
As a result of the various researches in view of the variation of the
number of data and in the various viewpoints, it was deemed that the
attractors of the three shapes were formed based on a spiral shape shown
in FIG. 4 and the spiral shape is changed into one of the cylindrical
shape, the tetrahedron shape and the ball shape according to several
parameters and noises. Further, it was inferred that the parameters would
be dependent on the remaining of the blood glucose level control ability
by means of the intrinsic insulin secretion and the control level of the
blood glucose level from the other cases.
As mentioned above, although the time series behavior of the blood glucose
level of diabetics is deemed to be irregular phenomena which were
considered as indeterministic phenomena subordinated to randomness, it was
solved that the time series behavior of the blood glucose level is a
deterministic chaos phenomenon which is governed by a distinct
determinism.
(Blood Glucose Level Prediction by Local Fuzzy Reconstruction Method)
When the behavior of any time series data is chaotic, it can be assumed
that the behavior follows a certain deterministic law. Then, if the
nonlinear deterministic regularity can be estimated, data in the near
future until losing the deterministic causality can be predicted from the
observed data at a certain time point because chaos has a sharp dependency
on initial condition.
A near future prediction from the viewpoint of the deterministic dynamical
system is based on the Takens' theorem for "reconstructing the attractor
in the state space and of the original dynamical system from single
observed time series data". The Takens+ theorem is summarized below.
From the observed time series data y(t), a vector x(t) is generated as
follows.
x(t)=(y(t), y(t-.tau.), y(t-2.tau.), . . . , y(t-(n-1).tau.))
where ".tau." represents a time delay. This vector indicates one point of
an n-dimensional reconstructed state space R.sup.n. Therefore, it is
possible to draw trajectory in the n-dimensional reconstructed state space
by changing "T". Assuming that the target system is a deterministic
dynamical system and that the observed time series data is obtained
through an observation system corresponding to C.sup.1 continuous mapping
from the state space of dynamical system to the 1-dimensional Euclidean
space R, the reconstructed trajectory is an embedding of the original
trajectory when "n" value is sufficiently large.
Namely, if any attractor has appeared in the original dynamical system,
another attractor, which remains the phase structure of the first
attractor, will appear in the reconstructed state space. "n" is usually
called an "embedding dimension".
In order that such reconstruction achieves "embedding", it has been proven
that the dimension "n" should satisfy the following condition, where "m"
represents the state space dimension of the original dynamical system.
n.gtoreq.2m+1
However, this is a sufficient condition. Depending on data, embedding can
be established even when "n" is less than 2m+1. Further, if n is greater
than 2d (n>2d) where d is a box count dimension of the attractor in the
original dynamical system, it is proven that the reconstructing operation
becomes an one-by-one projection.
Since it has been proved that the change of the blood glucose level is a
deterministic chaotic phenomenon, it is possible to predict a near future
value of the blood glucose level on the basis of an attractor which is
reconstructed in a reconstruction state space on the basis of the
treatment of the time series data of the blood glucose level according to
the Takens' embedding theorem.
Concretely, the blood glucose time series data y(t) observed at constant
sampling time intervals is embedded in an n-dimensional state space with
the embedding dimension n and the time delay .tau. by the Takens'
embedding theorem, as shown in FIG. 5A. This process is called
"reconstruction". Consequently the following vector is obtained.
x(t)=(y(t), y(t-.tau.), y(t-2.tau.), y(t-(n-1).tau.))
wherein j=1.about.L, L is the numbers of data of time series data y(t).
When this reconstruction is repeated on a number of observed data, a smooth
manifold consisting of a finite number of data vectors can be composed in
the n-dimensional reconstructed state space. FIG. 5B shows the attractor
trajectory obtained by embedding the time series data into
three-dimensional reconstructed state space.
With regard to the state space and attractor trajectory reconstructed by
the embedding procedure, the near-feature trajectory of the data vector
including the latest time series observed is presumed by using each
trajectory of that data vector and the neighboring on, thereby determining
the vector at s step ahead. That is, it is possible to obtain a predicted
value of the blood glucose level in a near future from the present blood
glucose data vector and the neighboring data vector thereof.
By plotting the data vector z(T) resulting from the latest observation in
the n-dimensional reconstructed state space and by replacing the
neighboring data vector with x(i), the state x(i+s) at s steps ahead is
already known as shown in FIG. 6 because x(i) is the past data. By using
this, the predicted value z(T+s) at s steps ahead with respect to the
present deta vector z(T) is obtained. Further, the predicted value y(t+s)
at s steps ahead with respect to the original time series data is obtained
from this predicted value z(T+s).
(Blood Glucose Level Prediction by Local Fuzzy Reconstruction Method)
In the prediction of the blood glucose level by means of the local
reconstruction method, the transition from state x(i) to state x(i+s)
after s steps can be assumed to be dependent on the dynamics subjected to
determinism, wherein i.epsilon.N(z(T)), and N(z(T)) are the set of index i
of x(i) neighboring z(T). This dynamics can be described in the form below
.
IF x(T) is x(i) THEN x(T+s) is x(i+s) (1)
where x(i) is a set of the data vector neighboring z(T) in the
n-dimensional reconstruction state space, x(T+s) is a set representative
of a data vector at s step ahead x(T), and x(i) is a data vector
neighboring to x(T). Therefore, if the step S is a time when the
deterministic causality is still remained due to the sharp dependency to
an initial value of the chaos, it can be assumed that the dynamics from
the transition form state z(T) to state z(T+s) is approximately equivalent
to that from state x(i) to x(i+s).
When the attractor embedded in the n-dimensional reconstructed state space
is smoothly manifold, the trajectory from x(T) to x(T+s) is influenced by
the vector distance from x(T) to x(i). That is, it can be deemed that the
trajectory of x(i) affects the trajectory from z(T) to z(T+s) according to
the decrease of the distance of the x(t) to z(T).
As mentioned above, the following relations are established.
x(i)=(y(i), y(i-.tau.), y(i-2.tau.), y(i-(n-1).tau.))x(i+s)=(y(i+s),
y(i+s-.tau.), y(i+s-2.tau.), y(i+s-(n-1).tau.)) (2)
This formula can be rewritten as follows when focusing attention on the j
axis in the n-dimensional reconstructed state space.
IF aj(T) is yj(i) THEN aj(T+s) is y(i+s) (j=1.about.n) (3)
where aj(T) is the J-axis component of the neighboring value x(i) to z(T)
in n-dimensional reconstructed state space, aj(T+s) is the J-axis
component of x(i+s) in n-dimensional reconstruction state space, and n is
the dimension of embedding.
Also, the trajectory from x(T) to X(T+s) is influenced by vector distance
from z(T) to x(i). The attractor corresponding to the trajectory of the
vector is a smooth manifold, and therefore this influence is represented
by a nonlinear form. Hence, for rending a nonlinear characteristic, the
formula (3) can be expressed by the fuzzy function as follows:
IF aj(T)=yj(i) THEN aj(T+s)=yj(j+s) (j=1.about.n) (4)
Further, the following formula has been already established.
z(T)=(y(T, y(T-.tau.), y(T-2.tau.), y(T-(n-1).tau.))
Therefore, the j-axis component of z(T) in the n-dimensional reconstructed
state space becomes equal to yj(T).
Accordingly, the j-axis component of the predicted value z(T+s) of data
vector z(T+s) after s steps of z(T) is obtained as aj(T+s) by the fuzzy
inference with yj(T) substituted into aj(T) of formula (6). This method is
called the Local Fuzzy Reconstruction Method.
Explanation thereof is given below in a concrete example where the
dimension are of embedding n=3, the time delay .tau.=4, and the number
neighboring data vectors N=3. Let us assume each data vector as follows:
z(T)=(y1(T), y2(T-4), y3(T-8))
x(a)=(y1(a), y2(a-4), y3(a-8))
x(b)=(y1(b), y2(b-4), y3(b-8))
x(c)=(y1(c), y2(c-4), y3(c-8))
z(T+s)=(y1(T+s), y2(T+s-4), y3(T+s-8))
x(a+s)=(y1(a+s), y2(a+s-4), y3(a+s-8))
x(b+s)=(y1(b+s), y2(b+s-4), y3(b+s-8))
x(c+s)=(y1(c+s), y2(c+s-4), y3(c+s-8))
where x(a), x(b) and x(c) are neighboring data vectors to z(T). x(a+s),
x(b+s) and x(c+s) are data vectors s step ahead of x(a), x(b) and x(c),
respectively.
On this assumption, the fuzzy rule given in formula (4) can be represented
by formulas (5) to (7).
Regarding the first axis of reconstructed state space,
IF a1(T) is y1(a) THEN a1(T+s) is y1(a+s)
IF a1(T) is y1(b) THEN a1(T+s) is y1(b+s)
IF a1(T) is y1(c) THEN a1(T+s) is y1(c+s) (5)
Regarding the second axis of the reconstructed state space,
IF b2(T) is y2(b-4) THEN a2(T+s) is y2(a+s-4)
IF b2(T) is y2(a-4) THEN a2(T+s) is y2(b+s-4)
IF a2(T) is y2(c-4) THEN a2(T+s) is y2(c+s-4) (6)
Regarding the third axis of the reconstructed state space,
IF a3(T) is y3(a-8) THEN a3(T+s) is y3(a+s-8)
IF a3(T) is y3(b-8) THEN a3(T+s) is y3(b+s-8)
IF a3(T) is y3(c-8) THEN a3(T+s) is y3(c+s-9) (7)
As shown in FIG. 7, a1(T), a2(T) and a3(T) represent the first, second and
third axes at step T, and a1(T+s), a2(T+s) and a3(T+s) represent the
respective axes at step T+s. Because x(a), x(b) and x(c) are neighboring
data vectors around z(T), each axis of the reconstructed state space in
the antecedent statement of fuzzy rule (5), (6) and (7) has the membership
function shown in FIG. 7. Note that the membership functions in the
subsequent are all of a crisp expression.
For the dynamics expressed by the above fuzzy rules and membership
functions, a fuzzy influence is conducted with the following taken as
input data:
a1(T)=y1(T), a2(T)=y2(T), a3(T)=y3(T).
In consequence, the following formula is obtained.
y1(T+s)=a1(T+s)
y2(T+s)=a2(T+s)
y3(T+s)=a3(T+s) (8)
Thus, the predicted value y1(T+s) at s steps ahead of the original time
series data y1(T) is obtained as a1(T+s).
As mentioned above, by utilizing the interpolation ability and the local
approximating ability of the Fuzzy Inference, the predicted value z(T+s)
is obtained. From this predicted value z(T+s), a predicted value y(t+s)
after s steps can be obtained.
In order to adapt the prediction employing the Local Fuzzy Reconstruction
Method to the prediction of the blood glucose level, the following steps
are executed: obtaining the data vector z(T) of the present blood glucose
level from an attractor constructed by embedding the time series data of
the blood glucose level in the multidimensional state space, obtaining a
plurality of neighboring vectors x(i) on the other trajectory passing
through a neighbor space of the data vector z(T) on the basis of a
selecting reference that the Euclidean distance is small, obtaining a data
vector x(i+s) at s steps future with respect to the data vector x(i) from
the attractor, obtaining a predicted value z(T+s) at s steps future with
respect to the data vector z(T) by using the data vectors z(T), x(i) and
x(i+s) by means of the Local Fuzzy Reconstruction Method; and obtaining a
time series blood glucose level predicted value y(t+s) at s steps future
with respect to the predicted value z(T+s).
(Prediction Experiments Under the Local Fuzzy Reconstruction Method)
The inventors of the present invention found that it is possible to predict
the blood glucose time series behavior in the near future by adapting the
blood glucose level measurement data into the chaos theorem, by means of
various experiments.
The experiments were to execute a blood glucose level prediction in one-day
future of each case by using a software employing the Local Fuzzy
Reconstruction Method. The prediction result obtained in the experiment
was shown in FIG. 8 upon being compared with actual measurement data. FIG.
8 shows a result as to the case I. As is clear from the data, the
prediction was executed with an error less than 20 mg/dl in average. This
result proved that this prediction had an accuracy applicable to a
practical use. The good results were obtained at to the other cases.
From the prediction result, when the prediction result is smaller than a
predetermined level, by preparing a proper program form slightly changing
the insulin administration amount which effectively functions at this
timing, it becomes possible to construct a best mode blood glucose level
control system without time lag.
(System for Predicting Near Future Blood Glucose Level by the Local Fuzzy
Reconstruction Method)
FIG. 1 shows a system structural view of the blood glucose level predicting
system according to the present invention.
A self-checked blood glucose input section 1 shown in FIG. 1 sends a
measurement value of the blood glucose level measured by a diabetic day by
day by means of a communication means such as internet communication,
PHS(personal handy-phone system), on-line personal computer communication,
pocket pager, or facsimile. A blood glucose time series file 2 is a part
of an external storage system of a computer system equipped in a medical
center. The blood glucose time series file 2 stores the self-checked blood
glucose data sent from the blood glucose input section 1 as time series
data by each patient. A dynamics estimating section 3 estimates a dynamics
which most preferably represents a phase characteristic of each time
series data stored in the file 2. The estimation of the dynamics is
executed to predict one step future functioning as a parameter for
embedding into a multi-dimensional state space, that is, an initial value
for embedding an early half of the file by each patient. The dynamics
estimating section 3 executes to predict one step future value in case
that the data of early half plus one (early half+1) is known. After the
reputation of this process until a newest data, the best performance
process is selected, and "the embedding dimension n" and "the time delay
.tau." of the best performance process are selected.
The estimation of the dynamics is executed when the self-checked data is
damped to a predetermined amount and when the predicting performance is
degraded due to the change of the dynamics such that the change of the
blood glucose level of the patient moved from poor control to fair control
or good control.
The optimum embedding parameter file 4 stores "the embedding dimension n"
and "the time delay .tau." obtained at the dynamics estimating section 3
as a parameter for each patient.
The blood glucose predicting section 5 executes a prediction of the blood
glucose level at 1 to s step ahead (future) in such a manner to pick up
the blood glucose level measurement data of a selected patient from the
blood glucose time series file 2, to select an optimum embedding parameter
corresponding to the picked-up data from the parameter file 4, and to
predict the near future value of the blood glucose level on the basis of
the selected data and the parameters by means of the Local Fuzzy
Reconstruction Method.
The prediction of the blood glucose level by the above-mentioned system
according to the present invention is executed by the following manner:
preparing measured data of blood glucose level (newest latest and past)
for use as time series data; constructing an attractor by embedding the
time series data in a multidimensional space according to the Takens'
embedding theorem; selecting data vector z(T) on the attractor which
vector (attractor) includes the latest blood glucose level data; selecting
a plurality of neighboring vectors x(i) on the other trajectory passing
through a neighbor space of the data vector z(T) on the basis of a
selecting reference that the Euclidean distance is small; selecting a data
vector x(i+s) at s steps future with respect to the data vector x(i) from
the attractor; estimating (inferring) a predicted value z(T+s) at s steps
future with respect to the data vector z(T) by using the data vectors
z(T), x(i) and x(i+s) by means of the Local Fuzzy Reconstruction Method;
and obtaining a predicted value y(T+s) at s step future with respect to
the predicted value z(T+s).
A predicted blood glucose file 6 stores the blood glucose level dada
predicted at the blood glucose predicting section 5 for each patient. An
insulin administration amount input section 7 sends the amount of the
insulin practically administrated to the patient, by means of a
communication means such as internet, PHS, on-line personal computer
communication, packet pager, or facsimile to a medical center. An insulin
administration amount time series file 8 is a part of an external storage
system of a computer system equipped in the medical center. The insulin
administration amount time series file 8 stores the insulin administration
amount data sent from the insulin administration amount input section 7 as
time series data by each patient. A display section 9 displays data for
each patient upon searching the data from the blood glucose time series
file 2, the predicted blood glucose file 6 and the insulin administration
amount time series file 8 to provide necessary information for the
treatment for diabetic to a doctor. The display section 9 also displays
information representative of degree of certainty of the prediction and
degree of errors of the prediction, in addition to the present actual
value of the blood glucose level, the near future predicted value of the
blood glucose level and a history of the insulin administration.
With the thus arranged system, it is possible that a doctor decides a
proper insulin administration amount from the predicted blood glucose
level based on the dynamics of the change of the blood glucose level of
each patient. This realizes a time lag less control of blood glucose
level. Therefore, it is possible to keep the change of the blood glucose
level within an allowable range in a long period while decreasing the
magnitude of the change of the blood glucose level by each day. Further,
it is possible that a patient positively utilizes the self-checked data
and a doctor provides a daily instruction to the patient on the basis of
the predicted blood glucose level. This functions that the patient
improves motivation as to the self-check of the blood glucose level.
It will understood that a recording medium storing the blood glucose level
predicting method according to the present invention may be utilized in
various microcomputers to assist insulin therapy for diabetics.
The contents of Japanese Patent Application No. 10-93783, with a filing
date of Apr. 7, 1998 in Japan, are hereby incorporated by reference.
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