CN113506632B - Non-periodic sampling data-based estimation method for blood sugar of type I diabetes patient - Google Patents
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- NOESYZHRGYRDHS-UHFFFAOYSA-N insulin Chemical compound N1C(=O)C(NC(=O)C(CCC(N)=O)NC(=O)C(CCC(O)=O)NC(=O)C(C(C)C)NC(=O)C(NC(=O)CN)C(C)CC)CSSCC(C(NC(CO)C(=O)NC(CC(C)C)C(=O)NC(CC=2C=CC(O)=CC=2)C(=O)NC(CCC(N)=O)C(=O)NC(CC(C)C)C(=O)NC(CCC(O)=O)C(=O)NC(CC(N)=O)C(=O)NC(CC=2C=CC(O)=CC=2)C(=O)NC(CSSCC(NC(=O)C(C(C)C)NC(=O)C(CC(C)C)NC(=O)C(CC=2C=CC(O)=CC=2)NC(=O)C(CC(C)C)NC(=O)C(C)NC(=O)C(CCC(O)=O)NC(=O)C(C(C)C)NC(=O)C(CC(C)C)NC(=O)C(CC=2NC=NC=2)NC(=O)C(CO)NC(=O)CNC2=O)C(=O)NCC(=O)NC(CCC(O)=O)C(=O)NC(CCCNC(N)=N)C(=O)NCC(=O)NC(CC=3C=CC=CC=3)C(=O)NC(CC=3C=CC=CC=3)C(=O)NC(CC=3C=CC(O)=CC=3)C(=O)NC(C(C)O)C(=O)N3C(CCC3)C(=O)NC(CCCCN)C(=O)NC(C)C(O)=O)C(=O)NC(CC(N)=O)C(O)=O)=O)NC(=O)C(C(C)CC)NC(=O)C(CO)NC(=O)C(C(C)O)NC(=O)C1CSSCC2NC(=O)C(CC(C)C)NC(=O)C(NC(=O)C(CCC(N)=O)NC(=O)C(CC(N)=O)NC(=O)C(NC(=O)C(N)CC=1C=CC=CC=1)C(C)C)CC1=CN=CN1 NOESYZHRGYRDHS-UHFFFAOYSA-N 0.000 claims description 21
- 239000011159 matrix material Substances 0.000 claims description 16
- WQZGKKKJIJFFOK-GASJEMHNSA-N Glucose Natural products OC[C@H]1OC(O)[C@H](O)[C@@H](O)[C@@H]1O WQZGKKKJIJFFOK-GASJEMHNSA-N 0.000 claims description 14
- 239000008103 glucose Substances 0.000 claims description 14
- 229940125396 insulin Drugs 0.000 claims description 11
- 102000004877 Insulin Human genes 0.000 claims description 10
- 108090001061 Insulin Proteins 0.000 claims description 10
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- 238000000338 in vitro Methods 0.000 claims description 2
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- 101000577696 Homo sapiens Proline-rich transmembrane protein 2 Proteins 0.000 description 1
- 206010023379 Ketoacidosis Diseases 0.000 description 1
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Abstract
A blood sugar estimation method for type I diabetes patients based on non-periodic sampling data comprises the following steps: and establishing a blood glucose metabolism model of the type I diabetes patient, and converting the blood glucose 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 parameters of the filter. The method can realize the dynamic estimation of continuous blood sugar by adopting non-periodic discrete measurement data, reduces the blood sugar measurement frequency of patients, reduces the measurement cost and improves the blood sugar measurement experience.
Description
Technical Field
The application relates to a blood sugar estimation method for type I diabetes patients based on aperiodic sampling data.
Background
Type 1 diabetes, primary insulin-dependent diabetes mellitus, occurs mostly in children and adolescents, and can also occur at various ages. The onset of the disease is relatively rapid, the insulin in the body is absolutely insufficient, ketoacidosis is easy to occur, and satisfactory curative effect can be obtained only by treating with insulin, otherwise, life is endangered. Particularly, in the operation process and the postoperative recovery process of the type I diabetes patient, the blood sugar is required to be monitored strictly so as to obtain good effects, and at present, periodic sampling is mostly adopted and then model training and prediction are carried out, but in the use process, due to various influencing factors, emergency conditions and other conditions, continuous periodic sampling is basically impossible, and when periodic data cannot be obtained, the accuracy of prediction is greatly reduced.
Disclosure of Invention
In order to solve the problems, the application discloses a method for estimating blood sugar of a type I diabetes patient based on aperiodic sampling data, which comprises the following steps:
establishing a blood glucose metabolism model of the type I diabetes patient, and converting the blood glucose metabolism model into a state space equation form;
establishing a filter based on sampling data and an error dynamic model, wherein the measuring data comprises measuring noise;
and analyzing the stability of the error dynamic model and designing parameters of the filter.
Preferably, the blood glucose metabolism model is:
wherein G (t) is the blood glucose concentration,is the derivative of G (t); g b Is the basal blood glucose concentration; i (t) is insulin concentration, < >>Is the derivative of I (t); i b Is the basal value of insulin; x (t) is insulin action effect; />Is the derivative of X (t); u (t) is the amount of insulin injected in vitro; d (t) is the blood glucose absorption rate; p is p 2 ，p 3 ，p 4 Is a model coefficient.
Preferably, let x 1 ＝G(t)，x 2 ＝X(t)，x 3 ＝I(t)，x＝[x 1 ，x 2 ，x 3 ] T And taking into account the discrete measurement output y (t k ) And measurement noise v (t) k ) The measurement is based on differential equation (1), deformed into the form of the following state equation:
wherein,C＝[1 0 0]，D v ＝1，E＝[1 0 0]，/>is the derivative of x.
Preferably, the following form of filter is designed:
wherein x is f Is the state of the filter and,is x f Is a derivative of (2); y (t) k ) Is a discrete measurement and is the input to the filter; t is t k Is the sampling moment; z f (t) is the output of the filter; the matrix F is a filter gain matrix;
let x e (t)＝x(t)-x f (t) and e (t) =z (t) -z f (t) obtainable from (2) and (3):
wherein Δf (t, x f )＝f(Hx(t))-f(Hx f (t))；
The matrix F design satisfies:
preferably, the following function is introduced:
wherein the method comprises the steps oft∈[t k ，t k+1 )，/>
And (3) deriving and simplifying the step (6) to obtain:
wherein the method comprises the steps of
Y(t) (11) ＝A T Q(t)+Q(t)A+ρ 1 (t)(Q 1 -Q 2 )
The sufficient condition for pi (t) <0 to be established by utilizing the convex combination technology is that
And further from (7)
Pair (9) is at [ t ] k ，t k+1 ) Upper integral can be obtained
When (when)The method comprises the following steps of:
wherein,
order theAnd according to Schur's supplementary quotients, the full condition for the establishment of the Xi <0 is that
Thus, from (11)
Is obtained by integrating (10) and (13)
When ω (t) ≡0, v (t) k ) At 0.ident.0, from (14)
V(t k+1 )-V(t k )＜0
Namely, the error system (4) is gradually stabilized;
the two ends of the (14) are subjected to continuous addition operation to obtain
The error system (4) thus satisfies H ∞ Performance index (5);
the optimal filter gain matrix is obtained by solving the filter gain matrix:
the application has the following beneficial effects: the method can realize the dynamic estimation of continuous blood sugar by adopting non-periodic discrete measurement data, reduces the blood sugar measurement frequency of patients, reduces the measurement cost and improves the blood sugar measurement experience.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the application and do not constitute a limitation on the application. In the drawings:
FIG. 1 shows sampling time and corresponding sampling interval;
FIG. 2 is an actual value of blood glucose concentration and an estimated value of two methods for type I diabetics;
FIG. 3 is an estimation error;
fig. 4 is an estimation method.
Detailed Description
In order to clearly illustrate the technical features of the present solution, the present application will be described in detail below with reference to the following detailed description and the accompanying drawings.
As shown in fig. 1-3, the blood glucose estimation method based on non-periodic sampling data designed by the application is applied to blood glucose estimation of type I diabetics. For ease of testing and comparison, the experiments were presented in a numerical simulation, with the numerical calculation and simulation software being selected as MATLAB. In the experiment, the coefficients in the blood sugar-insulin metabolism model (1) of the type I diabetes patient are selected as p respectively 2 ＝0.015，P 3 ＝2×10 -6 ，p 4 ＝0.21，G b =80. The model and filter are obtained in the manner of fig. 4.
The specific steps are as follows:
s101, establishing a blood glucose metabolism model of a type I diabetes patient, and converting the blood glucose metabolism model into a state space equation form;
s102, establishing a filter based on sampling data and an error dynamic model, wherein measurement data comprise measurement noise;
s103, analyzing the stability of the error dynamic model, and designing parameters of a filter.
First, with document [1]Yoneyama, "H+_ filtering for sampled-data systems," 2009IEEE lnternational Conference on Control and Automation,2009,pp.1728-1733, doi:10.1109/ICCA.2009.5410206. Assuming the same sampling interval, comparing the optimal H ∞ Performance index. For comparison, assume that the sampling interval is t k+1 -t k ∈[10，30]. By utilizing the method and the time-lag system method provided by the patent, the optimal H can be obtained respectively ∞ Performance 2.159 and 2.338, the performance of the proposed method is superior to the time-lapse system method.
Next, the estimated performance of the designed filter is evaluated. Given a sampling interval t k+1 -t k ∈[15，30]From equation (16), the optimal filter gain matrix is found to be F * ＝[0.9998，-0.0005，-0.0219] T . The initial value of blood glucose in the patient was 80mg/dl and after 30 minutes feeding was started. Fig. 1 shows the sampling time and sampling interval (min is required), fig. 2 shows the actual blood glucose concentration of the type I diabetes patient and the estimated blood glucose concentration of the type I diabetes patient by two methods, and the estimated blood glucose concentration is shown in fig. 3. It can be seen that the blood sugar estimation method of the non-periodic sampling data provided by the application has 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).
In this specification, each embodiment is described in a progressive manner, and identical and similar parts of each embodiment are all referred to each other, and each embodiment mainly describes differences from other embodiments. In particular, for system embodiments, since they are substantially similar to method embodiments, the description is relatively simple, as relevant to see a section of the description of method embodiments.
The foregoing is merely exemplary of the present application and is not intended to limit the present application. Various modifications and variations of the present application will be apparent to those skilled in the art. Any modification, equivalent replacement, improvement, etc. which come within the spirit and principles of the application are to be included in the scope of the claims of the present application.
Claims (2)
1. A blood sugar estimation method for type I diabetes patients based on non-periodic sampling data is characterized in that: the method comprises the following steps:
establishing a blood glucose metabolism model of the type I diabetes patient, and converting the blood glucose metabolism model into a state space equation form;
establishing a filter based on sampling data and an error dynamic model, wherein the measuring data comprises measuring noise;
analyzing the stability of the error dynamic model and designing parameters of a filter;
wherein, the blood glucose metabolism model is:
wherein G (t) is the blood glucose concentration,is the derivative of G (t); g b Is the basal blood glucose concentration; i (t) is the insulin concentration,is the derivative of I (t); i b Is the basal value of insulin; x (t) is insulin action effect; />Is the derivative of X (t); u (t) is the amount of insulin injected in vitro; d (t) is the blood glucose absorption rate; p is p 2 ,p 3 ,p 4 Is a model coefficient;
let x 1 ＝G(t),x 2 ＝X(t),x 3 ＝I(t),x＝[x 1 ,x 2 ,x 3 ] T And taking into account the discrete measurement output y (t k ) And measurement noise v (t) k ) The measurement is based on differential equation (1), deformed into the form of the following state equation:
wherein,C＝[1 0 0]，D v ＝1，E＝[1 0 0]，/>is the derivative of x;
the following form filter is designed:
z f (t)＝Ex f (t) (3)
wherein x is f Is the state of the filter and,is x f Is a derivative of (2); y (t) k ) Is a discrete measurement and is the input to the filter; t is t k Is the sampling moment; z f (t) is the output of the filter; the matrix F is a filter gain matrix;
let x e (t)＝x(t)-x f (t) and e (t) =z (t) -z f (t) obtainable from (2) and (3):
wherein Δf (t, x f )＝f(Hx(t))-f(Hx f (t))；
The matrix F design satisfies:
when the error system (4) is stabilized gradually, the error system (4) satisfies H ∞ And (5) obtaining an optimal filter gain matrix, and determining an estimated value of the blood sugar of the type I diabetes patient based on the filter output corresponding to the optimal filter gain matrix.
2. The method for estimating blood glucose in type I diabetes based on non-periodically sampled data of claim 1, wherein:
the following functions were introduced:
wherein the method comprises the steps of
Wherein x is e (t) is the estimation error, Q 1 And Q 2 The method is a positive definite matrix with proper dimension, can be given in advance, and can be searched by algorithms such as an interior point method; ζ (t) is equivalent to ρ (t), i.e., ζ (t) =ρ (t);
and (3) deriving and simplifying the step (6) to obtain:
wherein the method comprises the steps of
Y(t) (11) ＝A T Q(t)+Q(t)A+ρ 1 (t)(Q 1 -Q 2 )
Wherein e (t) is the estimated error and x e (t) is equivalent, i.e. e (t) =x e (t); ω (t) is the disturbance signal, here equivalent to d (t), i.e., ω (t) =d (t); b (B) ω Is a disturbance input matrix, takes the value as
The sufficient condition for making pi (t) <0 be satisfied by the convex combination technique is that
Wherein,τ 1 and τ 2 Respectively the upper and lower bounds of the sampling interval, i.e. 0<τ 1 ≤t k+1 -t k ≤τ 2 ,k∈N，ε ij (i, j e {1,2 }) and γ are both normal numbers; i is a unit matrix of appropriate dimension;
and further from (7)
Pair (9) is at [ t ] k ,t k+1 ) Upper integral can be obtained
When (when)The method comprises the following steps of:
wherein,
order theAnd according to Schur's index, make Xi<A sufficient condition for 0 to be satisfied is
Wherein P is 1 And P 2 All are positive definite matrices;
thus, from (11)
Is obtained by integrating (10) and (13)
When ω (t) ≡0, v (t) k ) At 0.ident.0, from (14)
V(t k+1 )-V(t k )<0
Namely, the error system (4) is gradually stabilized;
the two ends of the (14) are subjected to continuous addition operation to obtain
The error system (4) thus satisfies H ∞ Performance index (5);
the optimal filter gain matrix is obtained by solving the filter gain matrix:
wherein,gamma is a positive constant.
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