An optimization method for insulin infusion rate in artificial pancreas

Abstract

The present application relates to the technical field of artificial pancreas, and particularly relates to an optimization method for insulin infusion rate in artificial pancreas, comprising the following steps: S1: establishing a blood glucose control mathematical model, calculating a general expression of insulin infusion rate containing an equivalent part and an equivalent linear equation of insulin concentration error; S2: improving a conventional linear insulin infusion rate method in a closed loop system of artificial pancreas, and proposing a nonlinear method capable of replacing the conventional linear insulin infusion rate, namely a non-smooth infusion rate; S3: optimizing an insulin infusion rate improvement gain parameter in the nonlinear method in step S2, so that the insulin concentration reaches an expected value more quickly, the required maximum infusion rate is smaller, and the consumed energy is also smaller. The optimization method can significantly improve the control speed of the insulin concentration, and the required maximum infusion rate is smaller and the consumed energy is also smaller.

Description

Technical Field

[0001] This invention relates to the field of control technology for artificial pancreas, and more particularly to a method for optimizing the insulin infusion rate in an artificial pancreas. Background Technology

[0002] Diabetes can cause vascular and nerve damage, leading to various complications that seriously threaten patients' health and lives. The total number of diabetes patients in my country has reached over 100 million and is rapidly increasing. Common types of diabetes are mainly divided into type 1 and type 2 diabetes. Type 1 diabetes patients experience earlier onset, larger blood sugar fluctuations, and more severe symptoms, significantly impacting their quality of life. To prevent the various complications caused by high blood sugar, type 1 diabetes patients need to rely entirely on insulin for blood sugar control. Insulin treatment methods generally include intravenous insulin injection and subcutaneous insulin injection using an insulin pen or insulin pump.

[0003] Based on doctors' and patients' experience, while daily insulin injections (once or several times a day) can help control blood sugar, the optimal insulin dose varies greatly from patient to patient, both on different days and at different times of the same day. Therefore, for patients with type 1 diabetes and poor liver function, conventional insulin infusion methods often fail to achieve stable blood sugar levels. Thanks to advancements in sensor and IoT technologies, sustainable glucose monitors are now used for blood sugar detection in diabetes. Furthermore, combining a subcutaneous insulin pump with a sustainable glucose monitor to create a wearable artificial pancreas can automatically secrete insulin based on blood sugar levels, effectively replacing the function of beta cells in the pancreas.

[0004] Too much insulin injected by an insulin pump can lead to hypoglycemia, while too little insulin can lead to hyperglycemia and subsequently diabetic ketoacidosis. Therefore, only by injecting appropriate insulin based on individual blood glucose levels can safe and stable blood glucose control be achieved. Thus, a key technology in artificial pancreas is the use of effective closed-loop control algorithms to precisely control the patient's blood glucose. The Proportional-Integral-Derivative (PID) algorithm is the earliest and most widely used control algorithm in artificial pancreas, and many intelligent control methods based on PID algorithms have subsequently been applied. For example, Chinese patent application CN104958077A discloses an intelligent control closed-loop artificial pancreas system, in which the fuzzy adaptive proportional-integral-derivative control algorithm uses proportional-integral-derivative algorithms to simulate the physiological transport process of insulin secretion by human β cells as the basic model, and uses fuzzy logic algorithms to continuously optimize the parameters in the basic model established by the proportional-integral-derivative algorithm, thereby intelligently controlling the insulin infusion device. For example, Chinese patent application CN106860955A discloses a method for closed-loop insulin pump infusion based on fuzzy adaptive proportional-integral calculus control. This method uses the blood glucose concentration of diabetic patients as the controlled object, real-time blood glucose measurements as the input to a PID controller, and the insulin pump injection volume as the output of the PID controller. Based on the real-time monitored blood glucose data, fuzzy logic reasoning is used to simulate the human decision-making process and continuously optimize the parameters in the PID prediction model. This allows the PID controller to accurately calculate the insulin injection time and volume, providing patients with near-normal blood glucose control and achieving optimal closed-loop control of the insulin pump infusion using the fuzzy adaptive PID control algorithm.

[0005] The control methods proposed in the aforementioned patents all utilize PID control algorithms to some extent. From a system stability analysis perspective, this algorithm ensures that the system tends to stabilize at an exponential convergence rate. However, to further improve the convergence speed of insulin concentration, it is often necessary to increase the infusion rate. However, an excessively high insulin infusion rate can lead to an infusion rate exceeding the subcutaneous tissue's absorption rate of insulin. This causes insulin to temporarily accumulate subcutaneously, forming indurations that cannot be properly absorbed, resulting in control saturation and control residue. The former prevents the blood glucose lowering rate from reaching the expected level during infusion, while the latter can lead to over-control after infusion, ultimately causing hypoglycemia. Therefore, how to further enhance the blood glucose lowering effect of the artificial pancreas without increasing the infusion rate is a crucial problem that current closed-loop artificial pancreas systems need to solve, and this is one of the main research topics of this patent. Summary of the Invention

[0006] The purpose of this invention is to improve the convergence speed of insulin concentration from the perspective of control algorithm, especially considering not increasing the maximum insulin infusion rate to avoid control saturation and control residue problems caused by excessive infusion rate, and also considering not consuming too much energy to extend the charging and usage time of the artificial pancreas. This invention uses a non-smooth insulin infusion rate to replace the traditional linear infusion rate method. The key is to provide an optimized range for the gain parameter to improve the closed-loop control performance of the artificial pancreas.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] An optimization method for insulin infusion rate in an artificial pancreas includes the following steps:

[0009] S1: Establish a mathematical model for blood glucose control, calculate the general expression for insulin infusion rate including the equivalent part, and the equivalent linear equation for insulin concentration error;

[0010] S2: By improving the conventional linear insulin infusion rate method in the artificial pancreas closed-loop system, a nonlinear method, namely non-smooth infusion rate, is proposed to replace the conventional linear insulin infusion rate.

[0011] S3: Optimize the insulin infusion rate improvement gain parameter in the nonlinear method in step S2 to make the insulin concentration reach the desired value faster, require a smaller maximum infusion rate, and consume less energy.

[0012] The mathematical model for blood glucose control in step S1 is as follows:

[0013]

[0014]

[0015]

[0016] Where G(t) represents the blood glucose concentration, in mg / dL. b Z(t) represents the baseline blood glucose level in mg / dL, and Z(t) represents the hypoglycemic effect of insulin in min. -1 d(t) represents the change in blood glucose concentration due to food intake, in mg·dL. -1 min -1 I(t) represents insulin concentration, in mU / L. b This represents the baseline insulin level, expressed in mU / L, and n represents the insulin decay rate coefficient, expressed in min. -1u(t) represents the insulin infusion rate, which is also the controller to be designed, in mU / min; VI represents the insulin distribution volume in L; and p1 represents the rate coefficient of glucose moving from the plasma space into the liver (mainly for storage) or into the periphery (mainly for oxidation), in min. -1 p2 represents the rate coefficient of decrease in the hypoglycemic effect of insulin, in minutes. -1 p3 represents the rate coefficient of plasma insulin's effect on the hypoglycemic effect of insulin, with units of L·mU. -1 ·min -2 .

[0017] The general expression for the insulin infusion rate, including the equivalent portion, in step S1 is as follows:

[0018]

[0019] Where u0 represents the equivalent insulin infusion rate, I d This indicates that the virtual insulin concentration is calculated within the inner ring of the artificial pancreas using the backstepping method. The equivalent linear equation for the insulin concentration error in step S1 is expressed as:

[0020]

[0021] Where I e The error in insulin concentration is expressed as I. e =II d .

[0022] The conventional linear insulin infusion rate used in the artificial pancreas closed-loop system in step S2 is as follows:

[0023]

[0024] Where α>0 is the control gain parameter; by improving it, the non-smooth infusion rate has the following explicit structure:

[0025]

[0026] Where β>0 is the improved control gain parameter, p∈(0,1) is the power exponent parameter, and sig(x) function represents...

[0027] The method for optimizing the insulin infusion rate gain parameter β in step S3 is as follows: The improved control gain parameter β satisfies the following constraints:

[0028]

[0029]

[0030]

[0031] Among them, I e0 represents the initial value of the variable I e , represents the precision coefficient, and I ed represents the expected error precision of the insulin concentration system (the value of I ed is set by the engineer according to the precision of the hardware device. The closer θ and I ed are to 0, the higher the precision of the artificial pancreas control system). Then, compared with the conventional linear insulin infusion rate (1), the optimized non-smooth infusion rate (2) can still ensure that the insulin concentration reaches the expected value faster under the premise of a smaller maximum required insulin infusion rate.

[0032] The following proves the rationality of the above analysis from a theoretical perspective. Substitute the infusion rates (1) and (2) into the error equation respectively. Assume that the initial time is 0, and calculate the analytical solution of I e respectively to obtain:

[0033] The analytical solution of I e corresponding to the infusion rate (1): I e (t) = I e0 e -αt

[0034] Infusion rate (2): According to the above two equations, the I e driven by the two infusion rate methods can be calculated. The times for e0 to converge from the initial value I ed to the expected precision error I

[0035] are respectively: -1 The time corresponding to the infusion rate (1): t1 = α e0 ln|I -1 | - α ed ln|I

[0036] The time corresponding to the infusion rate (2): t2 = β -1 (1 - p) -1 (|I e0 | 1-p -|I ed | 1-p )

[0037] According to the above two equations, it can be calculated that if the infusion rate (2) is to complete the task faster, that is, t2 < t1, then the gain parameter β needs to satisfy β > α(1 - θ 1-p )|I e0 | 1-p [(p - 1)lnθ]-1 That is, β>β T For infusion rates (1) and (2), the infusion rate at the initial moment is the maximum infusion rate, so the maximum value of infusion rate (1) is |u 1,t＝0 |=|αI e0 The maximum value of infusion rate (2) is |u 2,t＝0 |=|βI e0 | p Calculations show that, to satisfy |u 2,t＝0 |<|u 1,t＝0 |, then β needs to satisfy β<α|I e0 | 1-p ,Right now If β can be found in (β) T ,β u If β takes values ​​within an interval, then it is necessary to prove that β... T <β u Established. β T <β u Equivalent to

[0038]

[0039] The above formula is equivalent to The following Lemma 1 proves that the inequality holds.

[0040] Lemma 1. For any real numbers θ and p satisfying θ∈(0,1) and p∈(0,1), the function

[0041] h(θ) = 1 - θ 1-p The value of +(1-p)lnθ is always less than 0.

[0042] By Lemma 1, since θ∈(0,1) and p∈(0,1), h(θ)<0 always holds, i.e., β T <β u This holds true consistently. Therefore, β can exist in (β... T ,β u The interval [β] takes values. It has been proven that when β∈(β... T ,β u When the optimized non-smooth infusion rate (2) is smaller than the maximum insulin infusion rate required, the insulin concentration can still reach the desired value faster.

[0043] In addition, this invention proposes another method for optimizing the control gain parameter β of insulin infusion rate, as follows:

[0044] The improved control gain parameter β satisfies the following constraints:

[0045]

[0046]

[0047]

[0048] Among them, I e0 represents the initial value of the variable I e and represents the precision coefficient, β T has the physical meaning that the stabilization time of the non-smooth infusion rate is not greater than the minimum gain parameter of the conventional linear infusion rate, β E has the physical meaning that the energy consumed by the non-smooth infusion rate is not more than the maximum gain parameter of the conventional linear infusion rate.

[0049] Compared with the conventional linear insulin infusion rate (1), the optimized non-smooth infusion rate (2) can still ensure that the insulin concentration reaches the expected value faster under the premise that the maximum insulin infusion rate required is smaller and the energy consumed is smaller.

[0050] The following proves the rationality of the above analysis from a theoretical perspective. It has been proven above that only when the gain β of the infusion rate (2) satisfies β > β T , there is t2 < t1. The energy consumption of the two infusion rates is calculated separately below. The general formula for the energy consumed by the infusion rate (1) over time is:

[0051]

[0052] Then, the energy consumed when the infusion rate (1) converges from I e0 to I ed can be calculated as

[0053]

[0054] The general formula for the energy consumed by the infusion rate (2) over time is:

[0055]

[0056] Then, according to the above formula, the energy consumed when the infusion rate (2) converges from I e0 to I ed can be calculated as

[0057]

[0058] According to the above expressions of E1 and E2, it can be calculated that to satisfy E2 < E1, the gain parameter β of the infusion rate (2) must satisfy β < 0.5α(1 - θ 2 )(1 + p)|I e0 | 1-p (1 - θ 1+p ) -1 , that is, β < βE If β can be found in (β) T ,β E If β takes values ​​within an interval, then it is necessary to prove that β... T <β E Established. β T <β E Equivalent to

[0059]

[0060] The above formula is equivalent to The following Lemma 2 proves that the inequality holds.

[0061] Lemma 2. For any positive real numbers θ and p belonging to (0,1), the function

[0062] l(θ) = 2(1-θ) 1+p (1-θ) 1-p )-(1+p)(1-p)(1-θ 2 )lnθ -1 The value is always less than 0.

[0063] By Lemma 2, the function l(θ) is always less than 0 on θ∈(0,1) and p∈(0,1), therefore β T <β E Therefore, β can be established in (β). T ,β E The interval [β] takes values. It has been proven that when β∈(β... T ,β E When β∈(β), the optimized non-smooth infusion rate (2) can still ensure that the insulin concentration reaches the desired value faster while consuming less energy. Further proof is given below for β∈(β) T ,β E When the infusion rate (2) is less than the maximum infusion rate (1), it is only necessary to prove that β E <β u That's all.

[0064] β E <β u Equivalent to

[0065]

[0066] Simplifying the above equation, we get We will now prove that k(θ) < 0 always holds true. Taking the first derivative of k(θ) with respect to θ, we get dk(θ) / dθ = 2(1+p)θ p (1-θ 1-pFrom the range of values ​​for θ and p, we know that dk(θ) / dθ>0, meaning k(θ) is an increasing function with respect to θ. Combined with k(1)=0, we know that k(θ)<0 always holds true. Therefore, β E <β u This holds true consistently. It has been proven that when β∈(β... T ,β E When the optimized non-smooth infusion rate (2) is lower than the maximum insulin infusion rate and consumes less energy, the insulin concentration can still reach the desired value faster.

[0067] The beneficial effects of this invention are:

[0068] 1. This invention addresses the insulin concentration control problem in a closed-loop artificial pancreas system by proposing a non-smooth insulin infusion rate method and its gain parameter optimization method. It innovatively proposes thresholds for three key gain parameters: the minimum gain parameter β such that the settling time of the non-smooth infusion rate is no greater than that of the conventional linear infusion rate. T The maximum value of the non-smooth infusion rate is no greater than the maximum gain parameter β of the conventional linear infusion rate. u The maximum gain parameter β, where the energy consumed by a non-smooth infusion rate is no more than that of a conventional linear infusion rate. E The paper also provides detailed mathematical expressions for these three parameters.

[0069] 2. Artificial pancreas engineers can optimize the conventional linear infusion rate using the method proposed in this invention to further improve the performance of the closed-loop system from an algorithmic perspective. It is known that excessive insulin infusion rates can cause control saturation and control residue, which severely affect the blood glucose lowering effect. The method proposed in this invention can be used to set parameters that satisfy β∈(β... T ,β u This allows for a further increase in insulin concentration response speed without excessively increasing the insulin infusion rate. Furthermore, parameters can be set to satisfy β∈(β... T ,β E This allows for a further increase in the response speed of insulin concentration without consuming more energy. Attached Figure Description

[0070] Figure 1 This is a schematic diagram of a closed-loop system for an artificial pancreas, as proposed in this invention, for optimizing the insulin infusion rate in an artificial pancreas.

[0071] Figure 2 This invention presents a method for optimizing insulin infusion rate in an artificial pancreas, showing insulin concentration curves driven by linear and non-smooth infusion rates, along with a magnified view of these curves.

[0072] Figure 3This is a graph showing the equivalent infusion rate curves driven by linear and non-smooth infusion rates, along with a magnified view, in the method for optimizing insulin infusion rate in an artificial pancreas proposed in this invention. Detailed Implementation

[0073] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0074] Content not described in detail in this specification is prior art known to those skilled in the art. For example... Figure 1 As shown, a method for optimizing insulin infusion rate parameters in an artificial pancreas includes the following steps:

[0075] S1: Establish a mathematical model for blood glucose control, calculate the general expression for insulin infusion rate including the equivalent part, and the equivalent linear equation for insulin concentration error;

[0076] S2: By improving the conventional linear insulin infusion rate method in the artificial pancreas closed-loop system, a nonlinear method, namely non-smooth infusion rate, is proposed to replace the conventional linear insulin infusion rate.

[0077] S3: Optimize the insulin infusion rate improvement gain parameter in the nonlinear method in step S2 to make the insulin concentration reach the desired value faster, require a smaller maximum infusion rate, and consume less energy.

[0078] The mathematical model for blood glucose control in step S1 is as follows:

[0079]

[0080]

[0081]

[0082] Where G(t) represents the blood glucose concentration, in mg / dL. b Z(t) represents the baseline blood glucose level in mg / dL, and Z(t) represents the hypoglycemic effect of insulin in min. -1 d(t) represents the change in blood glucose concentration due to food intake, in mg·dL. -1 min -1 I(t) represents insulin concentration, in mU / L. b This represents the baseline insulin level, expressed in mU / L, and n represents the insulin decay rate coefficient, expressed in min. -1u(t) represents the insulin infusion rate, which is also the controller to be designed, in mU / min; VI represents the insulin distribution volume in L; and p1 represents the rate coefficient of glucose moving from the plasma space into the liver (mainly for storage) or into the periphery (mainly for oxidation), in min. -1 p2 represents the rate coefficient of decrease in the hypoglycemic effect of insulin, in minutes. -1 p3 represents the rate coefficient of plasma insulin's effect on the hypoglycemic effect of insulin, with units of L·mU. -1 ·min -2 .

[0083] The general expression for the insulin infusion rate, including the equivalent portion, in step S1 is as follows:

[0084]

[0085] Where u0 represents the equivalent insulin infusion rate, I d This indicates that the virtual insulin concentration was calculated in the inner ring of the artificial pancreas using the backstepping method.

[0086] The equivalent linear equation for the insulin concentration error in step S1 is expressed as:

[0087]

[0088] Where I e The error in insulin concentration is expressed as I. e =II d .

[0089] The conventional linear insulin infusion rate used in the artificial pancreas closed-loop system in step S2 is as follows:

[0090]

[0091] Where α>0 is the control gain parameter; by improving it, the non-smooth infusion rate has the following explicit structure:

[0092]

[0093] Where β>0 is the improved control gain parameter, p∈(0,1) is the power exponent parameter, and sig(x) function represents...

[0094] The method for optimizing the insulin infusion rate improvement control gain parameter β in step S3 is as follows: The improvement control gain parameter β satisfies the following constraints:

[0095]

[0096]

[0097]

[0098] Among them, I e0 represents the initial value of the variable I e ; represents the precision coefficient, and I ed represents the expected error precision of the insulin concentration system (the value of I ed is set by the engineer according to the precision of the hardware device. The closer θ and I ed are to 0, the higher the precision of the artificial pancreas control system). Then, compared with the conventional linear insulin infusion rate (1), the optimized non-smooth infusion rate (2) can ensure that the insulin concentration reaches the expected value faster under the premise of a smaller maximum required insulin infusion rate.

[0099] The following proves the rationality of the above analysis from a theoretical perspective. Substitute the infusion rates (1) and (2) into the error equation respectively. Assume that the initial time is 0, and calculate the analytical solution of I e respectively to obtain:

[0100] The analytical solution of I e corresponding to the infusion rate (1): I e (t) = I e0 e -αt

[0101] The infusion rate (2): According to the above two equations, the I e driven by the two infusion rate methods can be calculated. The times for e0 to converge from the initial value I ed to the expected precision error I

[0102] are respectively: -1 The time corresponding to the infusion rate (1): t1 = α e0 ln|I -1 | - α ed ln|I

[0103] The time corresponding to the infusion rate (2): t2 = β -1 (1 - p) -1 (|I e0 | 1-p - |I ed | 1-p )

[0104] According to the above two equations, it can be calculated that if the infusion rate (2) is to complete the task faster, that is, t2 < t1, then the gain parameter β needs to satisfy β > α(1 - θ 1-p )|Ie0 | 1-p [(p-1)lnθ] -1 That is, β>β T For infusion rates (1) and (2), the infusion rate at the initial moment is the maximum infusion rate, so the maximum value of infusion rate (1) is |u 1,t＝0 |=|αI e0 The maximum value of infusion rate (2) is |u 2,t＝0 |=|βI e0 | p Calculations show that, to satisfy |u 2,t＝0 |<|u 1,t＝0 |, then β needs to satisfy β<α|I e0 | 1-p ,Right now If β can be found in (β) T ,β u If β takes values ​​within an interval, then it is necessary to prove that β... T <β u Established.

[0105] β T <β u Equivalent to

[0106]

[0107] The above formula is equivalent to The following Lemma 1 proves that the inequality holds.

[0108] Lemma 1. For any real numbers θ and p satisfying θ∈(0,1) and p∈(0,1), the function

[0109] h(θ) = 1 - θ 1-p The value of +(1-p)lnθ is always less than 0.

[0110] By Lemma 1, since θ∈(0,1) and p∈(0,1), h(θ)<0 always holds, i.e., β T <β u This holds true consistently. Therefore, β can exist in (β... T ,β u The interval [β] takes values. It has been proven that when β∈(β... T ,β u When the optimized non-smooth infusion rate (2) is smaller than the maximum insulin infusion rate required, the insulin concentration can still reach the desired value faster.

[0111] In addition, this invention proposes another method for optimizing the control gain parameter β of insulin infusion rate, as follows:

[0112] The improved control gain parameter β satisfies the following constraints:

[0113]

[0114]

[0115]

[0116] where, I e0 represents the initial value of the variable I e , represents the precision coefficient, and the physical meaning of β T is that the stabilization time of the non-smooth infusion rate is not greater than the minimum gain parameter of the conventional linear infusion rate, and the physical meaning of β E is that the energy consumed by the non-smooth infusion rate is not more than the maximum gain parameter of the conventional linear infusion rate.

[0117] Compared with the conventional linear insulin infusion rate (1), the optimized non-smooth infusion rate (2) can still ensure that the insulin concentration reaches the expected value faster under the premise that the maximum insulin infusion rate required is smaller and the energy consumed is smaller.

[0118] The following proves the rationality of the above analysis from a theoretical perspective. It has been proved above that only when the gain β of the infusion rate (2) satisfies β > β T , there is t2 < t1. The energy consumption of the two infusion rates is calculated separately below. The general formula for the energy consumed by the infusion rate (1) over time is:

[0119]

[0120] Then, the energy consumed when the infusion rate (1) converges from I e0 to I ed is

[0121]

[0122] The general formula for the energy consumed by the infusion rate (2) over time is:

[0123]

[0124]

[0125] Then, according to the above formula, the energy consumed when the infusion rate (2) converges from I e0 to I ed is

[0126]

[0127] Based on the above expressions of E1 and E2, it can be calculated that to satisfy E2 < E1, the gain parameter β of the infusion rate (2) must satisfy β < 0.5α(1 - θ 2 )(1 + p)|I e0 | 1-p (1 - θ 1+p ) -1 , that is, β < β E . If β can take values in the interval (β T , β E ), it is also necessary to prove that β T < β E holds. β T < β E is equivalent to

[0128]

[0129] The above is equivalent to The following gives a lemma 2 to prove that this inequality holds.

[0130] Lemma 2. For any positive real numbers θ and p belonging to the interval (0, 1), the function

[0131] l(θ) = 2(1 - θ 1+p )(1 - θ 1-p ) - (1 + p)(1 - p)(1 - θ 2 )lnθ -1 is always less than 0. <00OO567>From Lemma 2, it can be seen that the function l(θ) is always less than 0 when θ ∈ (0, 1) and p ∈ (0, 1). Therefore, β T < β E holds. So β can take values in the interval (β T , β E ). It has thus been proven that when β ∈ (β T , β E ), the optimized non - smooth infusion rate (2) can still ensure that the insulin concentration reaches the expected value faster while consuming less energy. Next, it is further proved that when β ∈ (β T , β E ), the maximum infusion rate of the infusion rate (2) is also less than that of the infusion rate (1). To prove this, it only needs to prove that β E < β u is sufficient.

[0133] β E < β u is equivalent to

[0134]

[0135] Simplifying the above formula gives We will now prove that k(θ) < 0 always holds true. Taking the first derivative of k(θ) with respect to θ, we get dk(θ) / dθ = 2(1+p)θ p (1-θ 1-p From the range of values ​​for θ and p, we know that dk(θ) / dθ>0, meaning k(θ) is an increasing function with respect to θ. Combined with k(1)=0, we know that k(θ)<0 always holds true. Therefore, β E <β u This holds true. Therefore, β E <β u This holds true consistently. It has been proven that when β∈(β... T ,β E When the optimized non-smooth infusion rate (2) is lower than the maximum insulin infusion rate and consumes less energy, the insulin concentration can still reach the desired value faster.

[0136] The effectiveness of the algorithm proposed in this application is verified using simulation software. Assume that a type 1 diabetic patient experiences a significant rise in blood glucose after eating. To quickly lower blood glucose, the insulin concentration in the patient's body should be increased from 15 mU / L to 50 mU / L in the shortest possible time, i.e., I(0) = 15 mU / L. d =50mU / L, I e0 = -35 mU / L. The equivalent form of a conventional linear infusion rate is known to be u1 = -αI. e Assuming the engineer sets the gain parameter α to α = 0.08, and the expected error accuracy of the insulin concentration system is set to I... ed =5 mU / L, then the accuracy coefficient θ = 0.1429 can be calculated. Based on the above information, assuming the exponential parameter of the non-smooth infusion rate is 0.7, then according to the following expression...

[0137]

[0138]

[0139]

[0140] These key threshold parameters, β, can be calculated one by one. T =0.1761, β E =0.2009, β u =0.2324. From the above, it can be seen that using a non-smooth infusion rate u2 = -βsig(I) e ) p If the gain parameter β is set to satisfy β∈(β T ,β uIf this is achieved, the insulin concentration response speed can be further improved without excessively increasing the insulin infusion rate; if the gain parameter β is set to satisfy β∈(β T ,β E This allows for a further increase in the response speed of insulin concentration without excessive energy consumption. Because β... E <β u In this simulation, we can assume that β = 0.2. The simulation results are shown below. Figure 2 and Figure 3 . Figure 2 The graphs show insulin concentration curves driven by linear and non-smooth infusion rates, along with magnified views of their parts. As can be seen from the graphs, the insulin concentration driven by the optimized method can reach 45 mU / L more quickly, thus achieving the target accuracy of 5 mU / L. Figure 3 The graphs show the equivalent infusion rate curves driven by linear and non-smooth infusion rates, along with their magnified local views. As can be seen from the graphs, the maximum value of the optimized insulin equivalent infusion rate is smaller than the linear infusion rate before optimization. Therefore, the optimization method proposed in this invention can significantly improve the performance of the closed-loop system.

Claims

1. A system for performing an optimization method for insulin infusion rate in an artificial pancreas, characterized in that, The optimization method performed by the system includes the following steps: S1: Establish a mathematical model for blood glucose control, calculate the general expression for insulin infusion rate including the equivalent part, and the equivalent linear equation for insulin concentration error; The blood glucose control mathematical model in S1 is as follows: Where G(t) represents the blood glucose concentration, in mg / dL. This represents the baseline blood glucose level, expressed in mg / dL. This indicates the hypoglycemic effect of insulin, measured in minutes. -1 , This indicates the change in blood glucose concentration due to food intake, expressed in mg·dL. -1 min -1 , This indicates insulin concentration, expressed in mU / L. This represents the baseline insulin level, expressed in mU / L, and n represents the insulin decay rate coefficient, expressed in min. -1 , This represents the insulin infusion rate, which is also the controller to be designed, and is expressed in mU / min. This represents the distribution volume of insulin, expressed in liters (L). The rate coefficient representing the rate at which glucose moves from the plasma space into the liver or into the periphery, measured in minutes. -1 , This represents the rate of decrease in the hypoglycemic effect of insulin, expressed in minutes. -1 , This represents the rate coefficient of plasma insulin's effect on the hypoglycemic effect, expressed in L·mU. -1 ·min -2 ; The general expression for the insulin infusion rate, which includes the equivalent portion, in S1 is as follows: Where u0 represents the equivalent insulin infusion rate, I d This indicates that the virtual insulin concentration was calculated in the inner ring of the artificial pancreas using the backstepping method; The equivalent linear equation for the insulin concentration error in S1 is expressed as follows: Where I e The error in insulin concentration is expressed as I. e =II d ; S2: By improving the conventional linear insulin infusion rate method in the artificial pancreas closed-loop system, a nonlinear method, namely non-smooth infusion rate, is proposed to replace the conventional linear insulin infusion rate. The conventional linear insulin infusion rate used in the artificial pancreas closed-loop system in S2 is: in To control the gain parameter, the non-smooth infusion rate is improved by having the following explicit structure: in To improve the control gain parameters, For the power exponent parameter, Function representation ; S3: Optimize the insulin infusion rate improvement gain parameter in the nonlinear method in step S2 to make the insulin concentration reach the desired value faster, require a smaller maximum infusion rate, and consume less energy.

2. The system for optimizing the insulin infusion rate in an artificial pancreas according to claim 1, characterized in that, In step S3, the insulin infusion rate is improved by controlling the gain parameter. The optimization method is as follows: Improve control gain parameters The following constraints must be satisfied: in, Representing variables initial value, Indicates the precision coefficient. This represents the expected error accuracy of the insulin concentration system. The physical meaning is that the settling time of a non-smooth infusion rate is no greater than the minimum gain parameter of a conventional linear infusion rate. The physical meaning is that the maximum value of the non-smooth infusion rate is not greater than the maximum gain parameter of the conventional linear infusion rate.

3. The system for optimizing the insulin infusion rate in an artificial pancreas according to claim 1, characterized in that, In step S3, the insulin infusion rate is improved by controlling the gain parameter. The optimization method is as follows: Improve control gain parameters The following constraints must be satisfied: in, Representing variables initial value, Indicates the precision coefficient. The physical meaning is that the settling time of a non-smooth infusion rate is no greater than the minimum gain parameter of a conventional linear infusion rate. The physical meaning of is the maximum gain parameter where the energy consumed by the non-smooth infusion rate is no more than that of the conventional linear infusion rate.

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