CN113506632A - Method for estimating blood sugar of type I diabetes mellitus based on non-periodic sampling data - Google Patents

Method for estimating blood sugar of type I diabetes mellitus based on non-periodic sampling data Download PDF

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CN113506632A
CN113506632A CN202110635787.9A CN202110635787A CN113506632A CN 113506632 A CN113506632 A CN 113506632A CN 202110635787 A CN202110635787 A CN 202110635787A CN 113506632 A CN113506632 A CN 113506632A
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赵鹏
张洁
苑海涛
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Shandong Provincial Hospital Affiliated to Shandong First Medical University
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Abstract

A method for estimating blood sugar of type I diabetics based on non-periodic sampling data comprises the following steps: and establishing a blood sugar metabolism model of the type I diabetes, and converting the blood sugar metabolism model into a state space equation form. And establishing a filter based on the sampling data and an error dynamic model, wherein the measurement data comprises measurement noise. And analyzing the stability of the error dynamic model and designing the parameters of the filter. The method of the invention can realize the dynamic estimation of continuous blood sugar only by adopting non-periodic discrete measurement data, thereby reducing the blood sugar measurement frequency of patients, reducing the measurement cost and improving the blood sugar measurement experience.

Description

Method for estimating blood sugar of type I diabetes mellitus based on non-periodic sampling data
Technical Field
The application relates to a method for estimating blood sugar of type I diabetics based on non-periodic sampling data.
Background
Type 1 diabetes, the primary insulin-dependent diabetes, occurs mostly in children and adolescents, and also at various ages. The onset of the disease is rapid, the insulin in the body is absolutely insufficient, ketoacidosis is easy to occur, the satisfactory curative effect can be obtained only by using the insulin treatment, otherwise, the life is threatened. Particularly, in the operation process and the postoperative recovery process of type I diabetics, relatively strict monitoring on blood sugar is required to obtain an excellent effect, and currently, periodic sampling is mostly adopted, and then model training and prediction are carried out.
Disclosure of Invention
In order to solve the above problems, the present application discloses a method for estimating blood glucose of type I diabetics based on non-periodic sampling data, comprising the following steps:
establishing a blood sugar metabolism model of the type I diabetic, and converting the blood sugar metabolism model into a state space equation form;
establishing a filter and an error dynamic model based on sampling data, wherein the measurement data comprises measurement noise;
and analyzing the stability of the error dynamic model and designing the parameters of the filter.
Preferably, the blood glucose metabolism model is:
Figure BDA0003105103090000011
wherein G (t) is a blood glucose concentration,
Figure BDA0003105103090000012
is the derivative of G (t); gbIs the basal blood glucose concentration; i (t) is the concentration of insulin,
Figure BDA0003105103090000013
is the derivative of I (t); i isbIs the insulin basal value; x (t) is the insulin action effect;
Figure BDA0003105103090000021
is the derivative of X (t); u (t) is the amount of insulin injection in vitro; d (t) is the rate of absorption of blood glucose; p is a radical of2，p3，p4Are the model coefficients.
Preferably, let x1＝G(t)，x2＝X(t)，x3＝I(t)，x＝[x1，x2，x3]TAnd taking into account the discrete measurement output y (t)k) And measuring the noise v (t)k) The measurement is based on differential equation (1), deformed into the form of the following equation of state:
Figure BDA0003105103090000022
wherein the content of the first and second substances,
Figure BDA0003105103090000023
C＝[1 0 0]，Dv＝1，E＝[1 0 0]，
Figure BDA0003105103090000024
is the derivative of x.
Preferably, the following form filter is designed:
Figure BDA0003105103090000025
wherein x isfIs the state of the filter(s),
Figure BDA0003105103090000026
is xfA derivative of (a); y (t)k) Is a discrete measurement and is the input to the filter; t is tkIs the sampling instant; z is a radical off(t) is the output of the filter; the matrix F is a filter gain matrix;
let xe(t)＝x(t)-xf(t) and e (t) z (t) -zf(t) obtainable from (2) and (3):
Figure BDA0003105103090000027
where Δ f (t, x)f)＝f(Hx(t))-f(Hxf(t))；
The matrix F is designed to satisfy:
Figure BDA0003105103090000028
preferably, the following function is introduced:
Figure BDA0003105103090000029
wherein
Figure BDA00031051030900000210
t∈[tk，tk+1)，
Figure BDA00031051030900000211
The derivation and simplification operation of (6) can be obtained:
Figure BDA0003105103090000031
wherein
Figure BDA0003105103090000032
Figure BDA0003105103090000033
Y(t)(11)＝ATQ(t)+Q(t)A+ρ1(t)(Q1-Q2)
The sufficient condition that pi (t) < 0 is satisfied by using the convex combination technology is
Figure BDA0003105103090000034
Further, from (7) can be obtained
Figure BDA0003105103090000035
To (9) at [ tk，tk+1) The upper integral can be obtained
Figure BDA0003105103090000036
When in use
Figure BDA0003105103090000037
Then, the following can be obtained:
Figure BDA0003105103090000038
wherein the content of the first and second substances,
Figure BDA0003105103090000039
Figure BDA00031051030900000310
order to
Figure BDA00031051030900000311
And according to Schur complement theorem, a sufficient condition that xi < 0 is satisfied is
Figure BDA00031051030900000312
Thus, from (11) can be obtained
Figure BDA00031051030900000313
Synthesis of (10) and (13) gives
Figure BDA0003105103090000041
When ω (t) ≡ 0, v (t)k) Is not identical to 0, obtainable from (14)
V(tk+1)-V(tk)＜0
Figure BDA0003105103090000042
Namely, the error system (4) is gradually stable;
the operation of successive addition is carried out on the two ends of (14)
Figure BDA0003105103090000043
The error system (4) therefore satisfies H∞Performance index (5);
the optimal filter gain matrix is solved to obtain a filter gain matrix:
Figure BDA0003105103090000044
this application can bring following beneficial effect: the method of the invention can realize the dynamic estimation of continuous blood sugar only by adopting non-periodic discrete measurement data, thereby reducing the blood sugar measurement frequency of patients, reducing the measurement cost and improving the blood sugar measurement experience.
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The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the application and together with the description serve to explain the application and not to limit the application. In the drawings:
FIG. 1 is a graph of sampling times and corresponding sampling intervals;
FIG. 2 shows the actual blood glucose concentration of type I diabetic patients and the estimated values of the two methods;
FIG. 3 is an estimation error;
fig. 4 shows an estimation method.
Detailed Description
In order to clearly explain the technical features of the present invention, the present application will be explained in detail by the following embodiments in combination with the accompanying drawings.
As shown in FIGS. 1-3, the blood glucose estimation method based on non-periodic sampling data designed by the present invention is applied to blood glucose estimation of type I diabetic patients. For ease of testing and comparison, the experiments were presented in numerical simulation format, with the numerical calculation and simulation software selected as MATLAB. In the experiment, the coefficients in the blood sugar-insulin metabolism model (1) of the type I diabetes patient are selected to be p respectively2＝0.015，P3＝2×10-6，p4＝0.21，G b80. The model and the filter are obtained in the manner of fig. 4.
The method comprises the following specific steps:
s101, establishing a blood sugar metabolism model of the type I diabetic, and converting the blood sugar metabolism model into a state space equation form;
s102, establishing a filter and an error dynamic model based on sampling data, wherein the measurement data comprises measurement noise;
and S103, analyzing the stability of the error dynamic model, and designing parameters of the filter.
First, with reference to [1 ]]Yoneyama, "H ∞ filtering for sampled-data systems," 2009IEEE international Conference on Control and Automation, 2009, pp.1728-1733, doi: 10.1109/ICCA.2009.5410206. Comparing optimal H assuming equal sampling intervals∞Performance index. For comparison, assume a sampling interval of tk+1-tk∈[10，30]. By utilizing the method and the time-lag system method provided by the patent, the optimal H can be respectively obtained∞Performances 2.159 and 2.338, namely the performance of the method provided by the patent is superior to that of the time-lag system method.
Second, the estimated performance of the designed filter is evaluated. Given a sampling interval tk+1-tk∈[15，30]From equation (16), an optimal filter gain matrix is obtained as F*＝[0.9998，-0.0005，-0.0219]T. The patient started eating 30 minutes after an initial blood glucose value of 80 mg/dl. FIG. 1 shows the sampling time and sampling interval (min needs to be marked), and FIG. 2 shows the blood of type I diabetes patientsThe actual values of sugar concentration and the estimated values of both methods, the error of estimation, are shown in FIG. 3. It can be seen that the blood sugar estimation method of the non-periodic sampling data provided by the invention has an estimation error of about +/-0.5 mg/dl, has higher estimation precision and is superior to a time-lag system method (the estimation error is about +/-0.95 mg/dl).
The embodiments in the present specification are described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, for the system embodiment, since it is substantially similar to the method embodiment, the description is simple, and for the relevant points, reference may be made to the partial description of the method embodiment.
The above are merely examples of the present application and are not intended to limit the present application. Various modifications and changes may occur to those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the scope of the claims of the present application.

Claims (5)

1. A method for estimating blood sugar of type I diabetics based on non-periodic sampling data is characterized by comprising the following steps: the method comprises the following steps:
establishing a blood sugar metabolism model of the type I diabetic, and converting the blood sugar metabolism model into a state space equation form;
establishing a filter and an error dynamic model based on sampling data, wherein the measurement data comprises measurement noise;
and analyzing the stability of the error dynamic model and designing the parameters of the filter.
2. The method for estimating blood glucose in type I diabetics based on non-periodic sampling data according to claim 1, wherein the method comprises the following steps:
the blood glucose metabolism model is:
Figure FDA0003105103080000011
wherein G (t) is a blood glucose concentration,
Figure FDA0003105103080000012
is the derivative of G (t); gbIs the basal blood glucose concentration; i (t) is the concentration of insulin,
Figure FDA0003105103080000013
is the derivative of I (t); i isbIs the insulin basal value; x (t) is the insulin action effect;
Figure FDA0003105103080000014
is the derivative of X (t); u (t) is the amount of insulin injection in vitro; d (t) is the rate of absorption of blood glucose; p is a radical of2,p3,p4Are the model coefficients.
3. The method for estimating blood glucose in type I diabetics based on non-periodic sampling data according to claim 2, wherein the method comprises the following steps:
let x1＝G(t),x2＝X(t),x3＝I(t),x＝[x1,x2,x3]TAnd taking into account the discrete measurement output y (t)k) And measuring the noise v (t)k) The measurement is based on differential equation (1), deformed into the form of the following equation of state:
Figure FDA0003105103080000015
wherein the content of the first and second substances,
Figure FDA0003105103080000021
C＝[1 0 0]，Dv＝1，E＝[1 0 0]，
Figure FDA0003105103080000022
is the derivative of x.
4. The method for estimating blood glucose in type I diabetics based on non-periodic sampling data according to claim 3, wherein the method comprises the following steps:
the following form filter is designed:
Figure FDA0003105103080000023
wherein x isfIs the state of the filter(s),
Figure FDA0003105103080000024
is xfA derivative of (a); y (t)k) Is a discrete measurement and is the input to the filter; t is tkIs the sampling instant; z is a radical off(t) is the output of the filter; the matrix F is a filter gain matrix;
let xe(t)＝x(t)-xf(t) and e (t) z (t) -zf(t) obtainable from (2) and (3):
Figure FDA0003105103080000025
where Δ f (t, x)f)＝f(Hx(t))-f(Hxf(t))；
The matrix F is designed to satisfy:
Figure FDA0003105103080000026
5. the method for estimating blood glucose in type I diabetics based on non-periodic sampling data according to claim 4, wherein the method comprises the following steps:
the following function is introduced:
Figure FDA0003105103080000027
wherein
Figure FDA0003105103080000028
The derivation and simplification operation of (6) can be obtained:
Figure FDA0003105103080000029
wherein
Figure FDA0003105103080000031
Figure FDA0003105103080000032
Y(t)(11)＝ATQ(t)+Q(t)A+ρ1(t)(Q1-Q2)
The sufficient condition that II (t) < 0 is satisfied by utilizing the convex combination technology is
Figure FDA0003105103080000033
Further, from (7) can be obtained
Figure FDA0003105103080000034
To (9) at [ tk，tk+1) The upper integral can be obtained
Figure FDA0003105103080000035
When in use
Figure FDA0003105103080000036
Then, the following can be obtained:
Figure FDA0003105103080000037
wherein the content of the first and second substances,
Figure FDA0003105103080000038
Figure FDA0003105103080000039
order to
Figure FDA00031051030800000310
And according to Schur complement theorem, a sufficient condition that xi < 0 is satisfied is
Figure FDA00031051030800000311
Thus, from (11) can be obtained
Figure FDA00031051030800000312
Synthesis of (10) and (13) gives
Figure FDA00031051030800000313
When ω (t) ≡ 0, v (t)k) Is not identical to 0, obtainable from (14)
V(tk+1)-V(tk)＜0
Figure FDA0003105103080000041
Namely, the error system (4) is gradually stable;
the operation of successive addition is carried out on the two ends of (14)
Figure FDA0003105103080000042
The error system (4) therefore satisfies H∞Performance index (5);
the optimal filter gain matrix is solved to obtain a filter gain matrix:
Figure FDA0003105103080000043
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