Method and device for estimating blood glucose control ability

Abstract

To estimate a parameter related to glucose homeostasis by a simple calculation.SOLUTION: The blood glucose control ability K is estimated using the total amount of glucose F administered to a subject and the blood glucose variation G of the subject to whom the total amount of glucose was administered, based on the equation F=K G, which defines blood glucose. The glucose control ability K is estimated as a vector consisting of the P, I, and D components in PID control.SELECTED DRAWING: Figure 16

Description

[Technical field]

[0001] The present invention relates to the estimation of parameters related to glucose homeostasis. [Background technology]

[0002] Homeostasis is a fundamental concept for understanding the control mechanisms of physiological functions in biological systems, and elucidating its principles is one of the major goals in biology. Blood glucose level is one of the variables that maintain homeostasis. The main regulators of glucose are insulin and glucose itself, and various mathematical models and parameters have been developed to represent homeostasis.

[0003] Homeostatic regulation mechanisms in physiology have been described by applying engineering control system analysis. The most well-known concept is the feedback system, and various mathematical models have been developed to represent the feedback linking glucose and insulin. A representative one is the βIG model, which can represent the well-known relationship between insulin secretion and insulin sensitivity, called the hyperbolic law. This law indicates that as insulin sensitivity decreases, insulin secretion increases to maintain glucose homeostasis, resulting in a compensatory shift along a hyperbola representing insulin sensitivity and secretory capacity. Therefore, the disposition index (DI), defined as the product of insulin sensitivity and insulin secretion, has been used as an index of glucose homeostasis.

[0004] As an application of engineering control system analysis, research is being conducted to link the concept of proportional-integral-derivative (PID) control with the pattern of insulin secretion (Non-Patent Document 1). It has been reported that insulin secretion has three phases, which can be interpreted as the proportional (P), integral (I), and derivative (D) components in PID control.

[0005] In these models, the focus is mainly on the control of insulin secretion and insulin sensitivity, but insulin clearance and glucose effectiveness (blood glucose-induced blood glucose lowering effect) also play important roles in maintaining glucose homeostasis. The present inventors proposed the concept of DI / cle, an index that incorporates insulin clearance in addition to insulin sensitivity and insulin secretion, and showed that in healthy individuals, insulin secretion, insulin sensitivity, and insulin clearance are distributed on a hyperbolic surface representing DI / cle (Non-Patent Document 2). However, even if DI / cle is constant, the dynamics of blood glucose levels may differ. Considering that blood glucose levels are not always stable and are constantly subject to external and internal disturbances, it is essential to understand glucose homeostasis by creating an index that can express blood glucose dynamics and a mathematical formula that links blood glucose regulation parameters and blood glucose dynamics. Furthermore, the relationship between glucose effectiveness and DI / cle in maintaining glucose homeostasis remains unclear. Furthermore, because the molecular mechanisms of insulin clearance and glucose effectiveness are still not fully understood, methods are needed that allow researchers without expertise in mathematical modeling to easily estimate these parameters without complex numerical calculations.

[0006] Disruption of glucose homeostasis leads to diabetes and various complications. Disruption of glucose homeostasis is characterized in part by high blood glucose levels, which can be estimated from fasting blood glucose (FBG) and plasma glucose concentrations at 120 min in an oral glucose tolerance test (OGTT). In addition to glucose concentration, glucose fluctuations contribute to the development and prognosis of complications. Research by the inventors and others has revealed that there are three different components underlying the indices related to blood glucose levels: concentration, fluctuation, and autocorrelation, each of which is independently associated with complications. However, most of these studies have only been correlation analyses, and it remains unclear how these three components are related to the parameters underlying glucose homeostasis. In order to more accurately infer abnormalities in parameters underlying glycemic control from glucose dynamics, it is necessary to clarify the mathematical equations connecting glucose dynamics and parameters related to glucose regulation.

[0007] On the other hand, the establishment of a method for "simple" and "accurate" estimation of lifestyle-related diseases and diabetes is a major public health issue, and several blood glucose monitoring methods are known. A representative example is a continuous blood glucose monitoring device. A continuous blood glucose monitoring device continuously measures blood glucose fluctuations without blood sampling by continuously measuring the glucose concentration in subcutaneous interstitial fluid using a thin sensor inserted subcutaneously. Patent Document 1 and Patent Document 2 disclose a method for estimating abnormalities using information obtained by a continuous blood glucose monitoring device, but a method for determining abnormalities based on blood glucose fluctuations has not necessarily been established. In addition, it has not been clarified how blood glucose fluctuations are defined.

[0008] The clamp test consists of a hyperglycemic clamp test, which measures blood glucose, insulin, and C-peptide concentrations when glucose is administered, and a hyperinsulinemic-euglycemic clamp test, which measures blood glucose, insulin, and C-peptide concentrations when glucose and insulin are administered. The clamp test was developed as a method capable of analytically calculating insulin clearance and insulin sensitivity (Non-Patent Document 3). In this specification, the term "clamp test" basically means a test that combines a hyperglycemic clamp and a hyperinsulinemic-euglycemic clamp, and in the embodiment described later, this clamp test is called a hyperglycemic and a hyperinsulinemic-euglycemic clamp. The clamp test is accurate, but requires analysis using a mathematical model.

[0009] It would be advantageous to estimate parameters related to glucose homeostasis using information obtained from existing techniques such as clamp testing and continuous glucose monitoring devices. [Prior art documents] [Patent documents]

[0010] [Patent Document 1] US11,385,237 [Patent Document 2] US2020 / 0205742 [Non-patent literature]

[0011] [Non-Patent Document 1] Watson, EM, Chappell, MJ, Ducrozet, F., Poucher, SM & Yates, JWT A new general glucose homeostatic model using a proportional-integral-derivative controller. Comput. Methods Programs Biomed. 102, 119-129 (2011). [Non-Patent Document 2] Sugimoto H, Hironaka KI, Yamada T, Sakaguchi K, Ogawa W, Kuroda S. DI / cle, a Measure Consisting of Insulin Sensitivity, Secretion, and Clearance, Captures Diabetic States. J Clin Endocrinol Metab. 2023 Jul 5:dgad392. doi: 10.1210 / clinem / dgad392. Epub ahead of print. PMID: 37406246. [Non-Patent Document 3] DeFronzo, RA, Tobin, JD & Andres, R. Glucose clamp technique: a method for quantifying insulin secretion and resistance. Am. J. Physiol. 237, E214-23 (1979). DISCLOSURE OF THEINVENTION [Problem to be solved by the invention]

[0012] An object of the present invention is to estimate parameters related to glucose homeostasis by simple calculations. [Means for solving the problem]

[0013] The first technical means disclosed in the present specification is The formula for defining blood glucose is calculated by using the total amount of glucose administered to the subject, F, and the blood glucose fluctuation, G, of the subject to which the total amount of glucose was administered. TIFF2025043453000002.tif7169 is used to estimate the blood glucose control ability K, which is estimated as a vector consisting of P, I, and D components in PID control. A method for estimating blood glucose control ability.

[0014] The first technical means can be provided as a computer program for causing a computer to execute the above-mentioned method for estimating blood glucose control ability.

[0015] The first technical measure is: A memory and a processor, The memory stores a formula that defines the relationship between the total amount of glucose administered to the subject F, the blood glucose fluctuation G of the subject to which the total amount of glucose was administered, and the blood glucose control ability K. TIFF2025043453000003.tif7169 is stored, The processor estimates the blood glucose control ability K by using the input total glucose amount F and blood glucose fluctuation G and the above formula, and the blood glucose control ability K is estimated as a vector consisting of P components, I components, and D components in PID control. It may be provided as a blood glucose control ability estimation device.

[0016] In one embodiment, the glycemic control ability K is It is specified as TIFF2025043453000004.tif33169, Where: TIFF2025043453000005.tif14169 is the P component, TIFF2025043453000006.tif14169 is the I component, TIFF2025043453000007.tif14169 is the D component, k Glub is the blood sugar lowering effect (glucose effectiveness), k Sen is insulin sensitivity, k Sb is basal insulin secretion, k Sp is the potentiation factor of insulin secretion, kSf is the first-phase insulin secretion, 1-k r is hepatic insulin clearance, k Ic is peripheral insulin clearance, It is.

[0017] In one embodiment, the blood glucose fluctuation G is the area under the curve obtained from the blood glucose waveform, the degree of distortion in the time direction, and the fluctuation range. In one embodiment, the blood glucose fluctuation G is a three-dimensional vector having an equation corresponding to the area under the curve, the degree of distortion in the time direction, and the fluctuation range. It is specified by TIFF2025043453000008.tif26169, G is the blood glucose level obtained by the continuous glucose monitoring device, G b is the fasting blood glucose level, G max is the maximum blood glucose value obtained by the continuous blood glucose monitoring device, G min is the minimum blood glucose value obtained by the continuous blood glucose monitoring device.

[0018] The second technical means disclosed in the present specification is A clamp test consisting of a hyperglycemic clamp test for measuring blood glucose, insulin, and C-peptide concentrations when glucose is administered, and a hyperinsulinemic euglycemic clamp test for measuring blood glucose, insulin, and C-peptide concentrations when glucose and insulin are administered was performed, and the following equation was obtained: Based on TIFF2025043453000009.tif34169 k Sb is basal insulin secretion, k Sp is the potentiation factor of insulin secretion, k Sf is the first-phase insulin secretion, 1-k r is hepatic insulin clearance, k Ic is peripheral insulin clearance, k Cc C-peptide clearance, A method for estimating blood glucose control ability, comprising: Where: C is the C-peptide concentration obtained in the clamp study, G is the blood glucose level obtained in the clamp test, I is the insulin concentration obtained in the clamp study, f is the insulin dose, Each subscript is a time in the clamp test. 0 is the start of the measurement, t1 is the first few minutes after glucose administration t2, t3, and t4 are the times when blood glucose levels reached a steady state in the hyperglycemic clamp test. t5 and t6 are the times when the insulin concentration reached a steady state in the hyperinsulinemic clamp test.

[0019] The second technical means can be provided as a computer program for causing a computer to execute the above-mentioned method for estimating glycemic control ability. The second technical means may be provided as a blood glucose control ability estimation device including a memory and a processor.

[0020] The third technical means disclosed in the present specification is: A clamp test consisting of a hyperglycemic clamp test for measuring blood glucose, insulin, and C-peptide concentrations when glucose is administered, and a hyperinsulinemic euglycemic clamp test for measuring blood glucose, insulin, and C-peptide concentrations when glucose and insulin are administered was performed, and the following equation was obtained: Based on TIFF2025043453000010.tif41169, k Glub is the blood sugar lowering effect (glucose effectiveness), k Sen is insulin sensitivity, k GluG , k GluQ is the glucose exchange rate parameter between the intravascular and extravascular compartments, A method for estimating blood glucose control ability, comprising: Where: G g is the steady-state plasma glucose level in the hyperglycemic clamp test, G i is the plasma glucose level at steady state during hyperinsulinemic clamp test, I g is the steady-state serum insulin level in the hyperglycemic clamp study, I i is the steady-state serum insulin level in the hyperinsulinemic clamp test, f Gg is the glucose dose at which blood glucose reaches a stable steady state in the hyperglycemic clamp test, f Gi is the glucose dose at which blood glucose reaches a stable steady state in the hyperinsulinemic clamp test, F G0-Gt1 is the total amount of glucose administered during the first t1 minute of the hyperglycemic clamp test, G is the blood glucose level obtained in the clamp test, I is the insulin concentration obtained in the clamp study, Each subscript is a time in the clamp test. 0 is the start of the measurement, t1 is the first few minutes after glucose administration.

[0021] A third technical means can be provided as a computer program for causing a computer to execute the above-mentioned method for estimating blood glucose control ability. The third technical means may be provided as a blood glucose control ability estimation device including a memory and a processor. Effect of the Invention

[0022] The present invention can estimate parameters related to glucose homeostasis with a low computational load. In the first technical means, glucose tolerance can be estimated "conveniently" and "accurately" from a continuous blood glucose monitoring device. In the second and third technical means, blood glucose control ability can be estimated with a low computational load from a clamp test. [Brief description of the drawings]

[0023] [Figure 1] Glucose is the input, and insulin and C-peptide are the outputs, and the results of analytical estimation of insulin secretion and clearance are shown. [Diagram 2] The input is insulin and the output is glucose, and the results of analytical estimation of insulin sensitivity and glucose effectiveness are shown. [Diagram 3] The results of simultaneous numerical estimation of glucose, insulin, and C-peptide are shown. [Figure 4] The correlation between each index (parameter) is shown. [Diagram 5] The derivation of the equation that links the combination of each parameter and blood glucose dynamics will be explained. [Figure 6] We will explain the classification of blood glucose fluctuation patterns after OGTT and glucose tolerance in each classification. [Figure 7] This paper explains the changes in parameters related to blood glucose control observed in the early stages of impaired glucose tolerance and the resulting changes in blood glucose dynamics. [Figure 8]The insulin / glucose ratio and C-peptide / glucose ratio are shown. Initial secretion and the need for additional secretion are indicated. [Figure 9] A comparison of one-compartment and two-compartment models is shown. [Figure 10] The results are shown taking into account the time change in insulin clearance and the time delay in insulin secretion. [Figure 11] The values ​​of glucose effectiveness and insulin sensitivity estimated using other models are shown. [Figure 12] The parameters related to glucose effectiveness and insulin sensitivity derived by numerical calculation are shown. [Figure 13] The distribution of numerical and analytical solutions is shown. [Figure 14] 4 shows blood glucose fluctuations with various sugar administration patterns. [Figure 15] The relationship between blood glucose and glucose effectiveness, insulin sensitivity, and insulin clearance is shown. [Figure 16] FIG. 1 is a block diagram showing a first technical means for estimating blood glucose control ability. [Figure 17] FIG. 13 is a block diagram showing a second technical means and a third technical means for estimating blood glucose control ability. [Figure 18] FIG. 2 is a diagram illustrating a clamp test according to the present embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0024] [A] Disclosure of the Present Invention This embodiment discloses (1) analytically estimating insulin secretion, insulin sensitivity, insulin clearance, and glucose effectiveness from clamp tests (a hyperglycemic and a hyperinsulinemic-euglycemic clam), (2) evaluating the difference between analytically estimated parameters and numerically estimated parameters, and (3) deriving a relational equation between parameters related to glucose homeostasis and glucose dynamics.

[0025] We have presented a formula for estimating the parameters related to glucose homeostasis using only four arithmetic operations. These parameters are It was shown that this can be summarized by the formula TIFF2025043453000011.tif7169, where F is the total amount of glucose administered, K is the combination of parameters, which is a three-dimensional vector consisting of the P, I, and D components of the PID control, and G is a three-dimensional vector consisting of the area under the curve, the fluctuation, and the degree of distortion.

[0026] The parameters of glycemic control by insulin and glucose estimated by the approximate analytical method correlated well with the parameters estimated numerically. These parameters of glycemic dynamics were The formula was summarized as TIFF2025043453000012.tif7169. Here, F is the total amount of glucose administered, K is a three-dimensional vector consisting of the proportional (P), integral (I), and derivative (D) components in the Proportional-Integral-Differential (PID) control that is composed of these parameters, and G is a three-dimensional vector consisting of the area under the blood glucose curve, the fluctuation range, and the degree of distortion in the time direction. The above formula specifies the law that connects these parameters and glucose dynamics. It is expected that the basic mechanism of glucose homeostasis will be examined in more detail starting from this law, and at the same time, since F and G are easily measurable and K can be estimated from this law, it is expected that the breakdown of homeostasis will be easily detected.

[0027] The estimation of the parameters related to glucose homeostasis according to this embodiment is performed by a computer (including an input unit, an output unit, a processor, a memory, etc.). The memory stores a program and a calculation formula for estimating a predetermined parameter based on predetermined input data, and the processor estimates and outputs the parameter using the input data and the calculation formula. In one aspect, the computer is a portable or wearable computer and can be attached to the subject. The first technical means, the second technical means, and the third technical means according to this embodiment are described below.

[0028] [A-1] First technical means The first technical means disclosed in the present specification is The formula for defining blood glucose is calculated by using the total amount of glucose administered to the subject, F, and the blood glucose fluctuation, G, of the subject to which the total amount of glucose was administered. TIFF2025043453000013.tif7169 is used to estimate the blood glucose control ability K, which is estimated as a vector consisting of P, I, and D components in PID control. A method for estimating blood glucose control ability. In one embodiment, the total amount of glucose administered to a subject F and the blood glucose fluctuation G of the subject are obtained based on at least three types of glucose loading patterns.

[0029] In one embodiment, the glycemic control ability K is It is specified as TIFF2025043453000014.tif33169, Where: TIFF2025043453000015.tif14169 is the P component, TIFF2025043453000016.tif14169 is the I component, TIFF2025043453000017.tif14169 is the D component, k Glub is the blood sugar lowering effect (glucose effectiveness), k Sen is insulin sensitivity, k Sb is basal insulin secretion, k Sp is the potentiation factor of insulin secretion, k Sf is the first-phase insulin secretion, 1-k r is hepatic insulin clearance, k Ic is peripheral insulin clearance, It is.

[0030] In one embodiment, the blood glucose fluctuation G is the area under the curve obtained from the blood glucose waveform, the degree of distortion in the time direction, and the fluctuation range. In one embodiment, the blood glucose fluctuation G is a three-dimensional vector having an equation corresponding to the area under the curve, the degree of distortion in the time direction, and the fluctuation range. It is specified by TIFF2025043453000018.tif26169, G is the blood glucose level obtained by the continuous glucose monitoring device, G b is the fasting blood glucose level, G max is the maximum blood glucose value obtained by the continuous blood glucose monitoring device, G min is the minimum blood glucose value obtained by the continuous blood glucose monitoring device.

[0031] The first technical means can be provided as a computer program for causing a computer to execute the above-mentioned method for estimating blood glucose control ability (glucose tolerance). As shown in FIG. 16, the blood glucose control ability (glucose tolerance) estimation device according to this embodiment (first technical means) includes: A memory and a processor, The memory stores a formula that defines the relationship between the total amount of glucose administered to the subject F, the blood glucose fluctuation G of the subject to which the total amount of glucose was administered, and the blood glucose control ability K. TIFF2025043453000019.tif7169 is stored, The processor estimates blood glucose control ability K using the input total glucose amount F and blood glucose fluctuation G and the above formula, and the blood glucose control ability K is estimated as a vector consisting of P components, I components, and D components in PID control. In one embodiment, the total amount of glucose administered to a subject F and the blood glucose fluctuation G of the subject are obtained based on at least three types of glucose loading patterns. For example, subjects would simply consume 100g, 125g, and 150g of sugar for breakfast for three days and measure their blood glucose levels using a continuous glucose monitoring device.

[0032] [A-2] Second technical means, third technical means The second and third technical means disclosed in this specification estimate the blood glucose control ability using information from a clamp test consisting of a hyperglycemic clamp test that measures blood glucose, insulin, and C-peptide concentrations when glucose is administered, and a hyperinsulinemic euglycemic clamp test that measures blood glucose, insulin, and C-peptide concentrations when glucose and insulin are administered. In terms of the mathematical model, it is important to know the values ​​when blood glucose and insulin are stable and approximately in a steady state, and how much insulin increases in the first few minutes at the moment glucose is administered, and the clamp test measures values ​​that change rapidly from the steady state values ​​in this way. In the second and third technical means, a predetermined parameter is estimated based on the values ​​when blood glucose and insulin are approximately in a steady state during the clamp test and the changes immediately after glucose is administered, and the specific times of each are exemplified in FIG. 17. As one embodiment, the following times are considered as candidates. The second and third technical means can be implemented in the same device (see FIG. 17).

[0033] The second technical means disclosed in the present specification is a compound represented by the following formula: Based on TIFF2025043453000020.tif34169, k Sb is basal insulin secretion, k Sp is the potentiation factor of insulin secretion, k Sf is the first-phase insulin secretion, 1-k r is hepatic insulin clearance, k Ic is peripheral insulin clearance, k CcC-peptide clearance, A method for estimating blood glucose control ability, comprising: Where: C is the C-peptide concentration obtained in the clamp study, G is the blood glucose level obtained in the clamp test, I is the insulin concentration obtained in the clamp study, f is the insulin dose, Each subscript is a time in the clamp test. 0 is the start of the measurement. t1 is the first few minutes after glucose administration; t2, t3, and t4 are the times when blood glucose levels reached a steady state in the hyperglycemic clamp test. t5 and t6 are the times when the insulin concentration reached a steady state in the hyperinsulinemic clamp test.

[0034] In one embodiment, t1=5 min, t2, t3, t4=60 min, 75 min, 90 min, t5, t6=190 min, 220 min. That is, the following formula: Based on TIFF2025043453000021.tif35169, each parameter k Sb ,k Sp ,K Sf ,1-k r ,K Ic ,k Cc is estimated. In one embodiment, the clamp test consists of a hyperglycemic clamp test (first 100 minutes) and a hyperinsulinemic euglycemic clamp test (second 120 minutes) (see FIG. 18). The duration and times of the clamp test are merely examples.

[0035] The third technical means disclosed in the present specification is a compound represented by the following formula: Based on TIFF2025043453000022.tif41169, k Glub is the blood sugar lowering effect (glucose effectiveness), k Sen is insulin sensitivity, k GluG , k GluQ is the glucose exchange rate parameter between the intravascular and extravascular compartments, A method for estimating blood glucose control ability, comprising: Where: G g is the steady-state plasma glucose level in the hyperglycemic clamp test, G i is the plasma glucose level at steady state during hyperinsulinemic clamp test, I g is the steady-state serum insulin level in the hyperglycemic clamp study, I i is the steady-state serum insulin level in the hyperinsulinemic clamp test, f Gg is the glucose dose at which blood glucose reaches a stable steady state in the hyperglycemic clamp test, f Gi is the glucose dose at which blood glucose reaches a stable steady state in the hyperinsulinemic clamp test, F G0-Gt1 is the total amount of glucose administered during the first t1 minute of the hyperglycemic clamp test, G is the blood glucose level obtained in the clamp test, I is the insulin concentration obtained in the clamp study, Each subscript is a time in the clamp test. 0 is the start of the measurement, t1 is the first few minutes after glucose administration.

[0036] In one embodiment, t1=5 minutes. That is, the following formula: Based on TIFF2025043453000023.tif42169, each parameter k Glub ,K Sen ,k GluG / k GluQ Estimate. Where: F G0-G5 is the total amount of glucose administered during the first 5 minutes of the hyperglycemic clamp test. In one embodiment, the clamp test consists of a hyperglycemic clamp test (first 100 minutes) and a hyperinsulinemic euglycemic clamp test (second 120 minutes). The duration and times of the clamp test are merely examples.

[0037] The second and third technical means can be provided as a computer program for causing a computer to execute the method for estimating blood glucose control ability. As shown in FIG. 17, the blood glucose control ability estimating device according to the present embodiment (second and third technical means) comprises: The present invention includes a memory and a processor, and the processor receives clamp test information as an input and calculates k using the above formula. Sb , k Sp , k Sf , 1-k r , k Ic , K Cc , K Glub , K Sen , K GluG / k GluQ Estimate.

[0038] [A-3] Formulas on which the first to third technical means are based The calculation formulas used in the first, second and third technical means are derived based on the following calculation formulas that define a mathematical model. TIFF2025043453000024.tif36169G: Blood glucose concentration Q: Extravascular glucose concentration X: Extravascular insulin concentration I: Blood insulin concentration C: Blood C-peptide concentration. All the subscripted k's are parameters related to the ability to control blood sugar.

[0039] [B] Estimation of insulin secretion and insulin clearance from a hyperglycemic and a hyperinsulinemic-euglycemic clamp study using an analytically computable method To explain the estimation of insulin secretion and insulin clearance, first consider the following simple formula: TIFF2025043453000025.tif16169, where k Sb is basal insulin secretion, 1-k r is hepatic insulin clearance, k Ic is peripheral insulin clearance, k Cc C-peptide clearance, f I is the insulin infused.

[0040] At steady state in the hyperglycemic clamp study, these equations can be approximated as follows: TIFF2025043453000026.tif26169In the hyperglycemic clamp test, blood glucose levels at 0, 60, 75, and 90 minutes were almost constant and were approximately steady, but the values ​​increased over time (Figure 8A, Figure 8B). In addition, insulin and C-peptide concentrations were high during the first few minutes of the hyperglycemic clamp test (Figure 8C, Figure 8D).

[0041] Therefore, the above formula is modified as follows: TIFF2025043453000027.tif16169, where k Sb is basal insulin secretion, k Spis the potentiation factor of insulin secretion, k Sf is the first-phase insulin secretion, k r is hepatic insulin clearance, k Ic is peripheral insulin clearance, k Cc C-peptide clearance, f I is the insulin infused. G b is the fasting blood glucose level (basal steady-state value), Parameter k Sb , k Sp , k Sf has shown that insulin secretion has three components (basal, early and booster insulin secretion), which can be considered as proportional-integral-derivative (PID) control (Non-Patent Document 1).

[0042] It is important to note that for an infinite time, blood glucose level is G b If higher than k Sp (GG b )t may be finite, a biologically impossible phenomenon. However, k calculated from 60–75 min during the hyperglycemic clamp Sp and k calculated from 75–90 min during the hyperglycemic clamp Sp were almost the same (Fig. 8E). This approximation is considered reasonable for the hyperglycemic clamp test in this study. Furthermore, k Sp (GG b )t can be derived from another equation. Considering that blood glucose levels quickly reach steady-state blood glucose levels during the hyperglycemic clamp, kSp ∫(GG b )dt is k Sp (GG b )t.

[0043] We considered estimating the parameters of equations (5) and (6) using an analytically calculable method. By approximating the first derivative of 0 during the clamp test as 0, equations (5) and (6) can be written as follows: TIFF2025043453000028.tif16169The time (minutes) in the clamp test (hyperglycemic and hyperinsulinemic-euglycemic clamp) is shown. k r k Sb G0=k Ic I0, k Sb G=k Cc By approximating C, equations (5) and (6) can be written as follows: TIFF2025043453000029.tif16169For the first 5 minutes of the clamp test, equations (9) and (10) can be approximated as follows: TIFF2025043453000030.tif26169By approximating the second and first derivatives of the blood glucose level from 60 to 90 minutes during the clamp study as zero, equation (6) can be written as: TIFF2025043453000031.tif8169From 60 to 90 minutes during the clamp test, equation (13) is approximated as follows: TIFF2025043453000032.tif15169From 190 minutes to 220 minutes during the clamp test, the first derivative was set to 0, k r K Sp (GG b )t=0, equation (5) can be written as: TIFF2025043453000033.tif15169

[0044] Equations (7), (8), (15), and (16) can be rearranged as follows: TIFF2025043453000034.tif22169Therefore, the parameters in equations (5) and (6) are estimated as follows: TIFF2025043453000035.tif35169

[0045] [C] Estimation of insulin secretion and insulin clearance from other models Next, equations (5) and (6) were compared with other models. The kinetics of C-peptide is described by a two-compartment model (Van Cauter, E., Mestrez, F., Sturis, J. & Polonsky, KS Estimation of insulin secretion rates from C-peptide levels. Comparison of individual and standard kinetic parameters for C-peptide clearance. Diabetes 41, 368-377 (1992).) as follows: TIFF2025043453000036.tif16169, where C and Y denote the concentrations of C-peptide in the accessible and inaccessible compartments, respectively. The parameter k CY ,k YC are the rate parameters describing the exchange kinetics of C-peptide. The second derivative is approximated as zero, and k Sb G=k Cc Approximating C, k Sf is calculated as follows: Similarly, k is calculated from the two-compartment model more than from the one-compartment model. r is small, k Cc ,k Sb ,k Sp is large (Table 1). [Table 1] Table 1 compares the equations for C-peptide kinetics estimated using the one-compartment model and the two-compartment model.

[0046] To compare the fitness of these models, we simulated serum C-peptide using these parameters (Figure 9A, B). CY ,k YC Since the parameters cannot be estimated due to their structural non-identifiability, these parameters are estimated from individual characteristics, which is a widely used method. Notably, the fluctuations of insulin are the same in both models. The serum C-peptide simulated by the 1-compartment model showed a better fit compared to the serum C-peptide simulated by the 2-compartment model (Figure 9A, B). Notably, the 2-compartment model should be better at fitting because of the larger number of parameters. However, the method using the approximation used in this study obtained a worse fit. The parameters estimated by the 1-compartment model and the 2-compartment model were significantly correlated, although the values ​​were different (Figure 9C). Here, considering the results that the 1-compartment model can reproduce the serum C-peptide concentration well, can estimate the magnitude relationship of the above parameters, and is simple and structurally identifiable, the 1-compartment model was used in this study.

[0047] The two-compartment model in this study also Cc can be estimated. k estimated from clamp test Cc and k estimated from previous studies CcThe correlation between insulin secretion rates and C-peptide clearance is relatively low (Figure 9D). In a previous study (Van Cauter, E., Mestrez, F., Sturis, J. & Polonsky, KS Estimation of insulin secretion rates from C-peptide levels. Comparison of individual and standard kinetic parameters for C-peptide clearance. Diabetes 41, 368-377 (1992)), the k values ​​estimated from the actual values ​​were Cc and k estimated from individual characteristics Cc The correlation between k and k is also low. Cc It is considered more accurate to estimate

[0048] Next, we investigated the time-dependent changes in insulin clearance. Although simulated serum insulin tended to be lower, simulated serum C-peptide was not lower when blood glucose levels were high, especially compared to serum C-peptide measured in NGT and IGT (Figure 10A). This may be due to reduced insulin clearance and increased insulin concentrations in hyperglycemic states. This result is consistent with previous studies showing that insulin clearance is suppressed during OGTT in NGT and IGT individuals, but the suppression was minimal in T2DM6. Although it is unclear whether insulin clearance is reduced by glucose or insulin, as both glucose and insulin are elevated during OGTT, the results of this study showed that there is at least a glucose-induced reduction in insulin clearance. For simplicity, we did not consider this time-dependent change in insulin clearance. Of note, the C-peptide / glucose ratio did not change significantly from the 0-min time point during the hyperinsulinemic-euglycemic clamp (Figure 10C).

[0049] We then investigated the time delay in insulin secretion. By approximating the second derivative in the hyperglycemic clamp test to zero, equations (5) and (6) can be written as follows: At 90 minutes into the clamp study, equations (5) and (6) can be written as follows: TIFF2025043453000040.tif28169

[0050] By approximating TIFF2025043453000041.tif10169, equations (21), (22), (23), and (24) can be written as: TIFF2025043453000042.tif16169The larger the time delay in insulin secretion, the smaller the right-hand side of these equations can be expected to be. The value was not significantly different from 0 (Figure 10C). Although it is still possible that there is a time delay in insulin secretion, the time delay in insulin secretion is not significant in the data examined in this study for intervals of 10 min or more. Of note, previous studies have shown that the length of the past period during which plasma glucose levels affect current insulin secretion is approximately 14.9 min, which also indicates that the effect of the time delay in insulin secretion is likely small in the current data examined for intervals of 5 to 15 min or more.

[0051] [D] Estimation of hypoglycemic effect and insulin sensitivity from a hyperglycemic and a hyperinsulinemic-euglycemic clamp test using an analytically computable method To explain the estimation of glucose effectiveness and insulin sensitivity, first consider the following simple formula: TIFF2025043453000043.tif9169, where k Glub is the blood sugar lowering effect (glucose effectiveness), k Senis insulin sensitivity, f G is the glucose administered (infused glucose), It is.

[0052] At steady state in the clamp test, equation (29) can be rearranged as follows: TIFF2025043453000044.tif27169, where G g is the steady-state plasma glucose level in the hyperglycemic clamp test, G i is the plasma glucose level at steady state during hyperinsulinemic clamp test, I g is the steady-state serum insulin level in the hyperglycemic clamp study, I i is the steady-state serum insulin level in the hyperinsulinemic clamp test, f Gg is the glucose dose at which blood glucose reaches a stable steady state in the hyperglycemic clamp test, f Gi is the glucose dose at which blood glucose reaches a stable steady state in the hyperinsulinemic clamp test, It is.

[0053] Even if there is a time delay in the action of insulin, if the steady state in the clamp experiment is long enough, k Glu and k Sen The k in NGT is the same. Glu The average value of is −0.05 (Figure 11A), which is biologically impossible. We next investigated a model with a first-order approximation near the equilibrium point. TIFF2025043453000045.tif10169

[0054] At steady state in the clamp test, equation (32) can be rearranged as follows: TIFF2025043453000046.tif28169k in NGTGlu The average value of was positive (Figure 11B). Based on these results, we adopted equation (32) in the following analysis.

[0055] To determine the extent to which Equation (32) produces error when blood glucose levels fluctuate, the first 5 minutes of a hyperglycemic clamp test were characterized as follows. TIFF2025043453000047.tif14169The difference between the right side of equation (35) and the left side of equation (35) was significantly different from 0 (Figure 11C). Therefore, we attempted to modify this model.

[0056] Since glucose kinetics was described as a two-compartment model (Cobelli, C., Caumo, A. & Omenetto, M. Minimal model SG overestimation and SI underestimation: improved accuracy by a Bayesian two-compartment model. Am. J. Physiol. 277, E481-8 (1999)), we modified equation (32) as follows: TIFF2025043453000048.tif14169, where G and Q denote the concentrations of glucose in the accessible and inaccessible compartments, respectively. The parameter k GluG ,k GluQ are the rate parameters describing glucose exchange kinetics. At steady state during the clamp study, k Glub ,k Sen They can be estimated by equations (33) and (34), respectively. During the first 5 min of the hyperglycemic clamp test, equations (36) and (37) can be transformed as follows: Since Q5 is greater than Q0 and the right hand side of equation (38) is positive, this two-compartment model (equations (36) and (37)) will correct the error observed in the first 5 min in the one-compartment model (equation (32)). By approximating the second derivative as zero, equation (37) can be approximated as follows: TIFF2025043453000050.tif14169

[0057] In summary, the parameter k Glub ,k Sen ,k GluG / k GluQ is estimated as follows: TIFF2025043453000051.tif40169, where F G0-G5 is the total amount of glucose administered during the first 5 minutes of the hyperglycemic clamp test. Thus, k estimated from the clamp test GluG / k GluQ are compared with values ​​estimated in existing research (Cobelli, C., Caumo, A. & Omenetto, M. Minimal model SG overestimation and SI underestimation: improved accuracy by a Bayesian two-compartment model. Am. J. Physiol. 277, E481-8 (1999)).

[0058] [E] Derivation of equations relating to parameters related to blood glucose level and glucose homeostasis This supplementary text details how equations relating blood glucose levels to parameters related to glucose homeostasis were derived in this study. The equations were derived based on the following equation: TIFF2025043453000052.tif29169By integrating these equations from 0 to infinity, we can transform them into the following: TIFF2025043453000053.tif26169Here, F is the total amount of glucose administered. Equations (47) and (48) can be transformed as follows: TIFF2025043453000054.tif11169If blood glucose level rises once and does not rise again, equation (49) can be transformed as follows: TIFF2025043453000055.tif8169, where TIFF2025043453000056.tif68169

[0059] [F] Experimental Method (Subjects and Measurement Items) In this experiment, a previously reported data set was analyzed (Non-Patent Document 2, Ohashi, K. et al. Glucose Homeostatic Law: Insulin Clearance Predicts the Progression of Glucose Intolerance in Humans. PLoS One 10, e0143880 (2015)). Glucose was administered intravenously for 15 minutes to maintain plasma glucose levels at 200 mg / dL, followed by a hyperglycemic clamp with varying amounts of glucose. Insulin was administered intravenously 10 minutes after the end of the hyperglycemic clamp, and a hyperinsulinemic-euglycemic clamp was performed to target fasting plasma glucose levels at 90 mg / dL or in NGT and IGT with fasting plasma glucose levels below 90 mg / dL. These clamp analyses and 75-g oral glucose tolerance tests (OGTTs) were performed within 10 days. 50 NGT patients, 18 IGT patients, and 53 T2DM patients were used for parameter estimation. Missing values ​​were imputed using the K nearest neighbor method (k = 2).

[0060] [G] Results: Estimation of insulin secretion and insulin clearance First, we attempted to clarify how insulin responds to glucose fluctuations and to analytically estimate insulin secretion and insulin clearance. In this study, we analyzed a previously published dataset (Ohashi, K. et al. Glucose Homeostatic Law: Insulin Clearance Predicts the Progression of Glucose Intolerance in Humans. PLoS One 10, e0143880 (2015)) in which 47 subjects with normal glucose tolerance (NGT), 16 subjects with impaired glucose tolerance (IGT), and 49 subjects with type 2 diabetes mellitus (T2DM) were subjected to clamp tests (a hyperglycemic and a hyperinsulinemic-euglycemic clamp).

[0061] Following previous studies and their suitability to our dataset, we adopted the following equations here to represent the concentrations of insulin (I) and C-peptide (C) (section [B], Figures 8, 9, and 10, Table 1): TIFF2025043453000057.tif15169, where k Sb is basal insulin secretion, k Sp is the potentiation factor of insulin secretion, k Sf is the first-phase insulin secretion, 1-k r is hepatic insulin clearance, k Ic is peripheral insulin clearance, k CcC-peptide clearance, f I is the insulin infused.

[0062] Each parameter was analytically estimated using the following equation (Section [B]): TIFF2025043453000058.tif34169 Subscripts indicate times (min) during clamp studies (a hyperglycemic and a hyperinsulinemic-euglycemic clamp).

[0063] The simulated time courses and normalized residuals of insulin and C-peptide using these parameters showed sufficient accuracy (Figure 1A and 1B). Sb ,k Sp ,k Sf ) was significantly decreased in T2DM compared with NGT, and peripheral insulin clearance (k Ic ) was significantly decreased in IGT and T2DM compared with NGT, which is consistent with previous studies. These results suggest that insulin secretion and peripheral insulin clearance are involved in impaired glucose tolerance.

[0064] [G] Results: Estimation of glucose effectiveness and insulin sensitivity Next, we attempted to clarify how plasma glucose responds to fluctuations in serum insulin and to analytically estimate glucose effectiveness and insulin sensitivity. Following previous studies and the good fit to our dataset, we used the following equation to describe the concentration of blood glucose (G) (section [D], Figure 11): TIFF2025043453000059.tif15169G,Q represent the glucose concentrations in the accessible and non-accessible compartments. k GluG ,k GluQ is the glucose exchange rate parameter between the intravascular and extravascular compartments, k Glub is the blood sugar lowering effect (glucose effectiveness), k Sen is insulin sensitivity, It is.

[0065] The values ​​of each parameter were analytically estimated using the following equation (section [C]): TIFF2025043453000060.tif42169, where G g is the steady-state plasma glucose level in the hyperglycemic clamp test, G i is the plasma glucose level at steady state during hyperinsulinemic clamp test, I g is the steady-state serum insulin level in the hyperglycemic clamp study, I i is the steady-state serum insulin level in the hyperinsulinemic clamp test, f Gg is the glucose dose at which blood glucose reaches a stable steady state in the hyperglycemic clamp test, f Gi is the glucose dose at which blood glucose reaches a stable steady state in the hyperinsulinemic clamp test, F G0-G5 is the total amount of glucose administered during the first 5 min of the hyperglycemic clamp test, It is.

[0066] k GluQThe value of was fixed at 0.0885, which is the population mean reported in a previous study (Cobelli, C., Caumo, A. & Omenetto, M. Minimal model SG overestimation and SI underestimation: improved accuracy by a Bayesian two-compartment model. American Journal of Physiology-Endocrinology and Metabolism 277, E481-E488 (1999)). The simulated time courses and normalized residuals of plasma glucose using these parameters showed a satisfactory behavior (Figure 2A). Glub , k GluG / k GluQ , k Sen was significantly decreased in IGT or T2DM compared with NGT, suggesting that the two types of hypoglycemic effects and insulin sensitivity are associated with impaired glucose tolerance.

[0067] [H] Results: Comparison of analytically and numerically estimated parameters In analytically estimating the parameters, several approximations were applied (sections [B] and [C]). The time delay of insulin action was not considered. To examine the bias due to these approximations, we compared the analytically estimated parameters with the numerically estimated parameters using the following equations: TIFF2025043453000061.tif36169Here, X indicates the concentration of insulin in the remote compartment.

[0068] Figure 3 shows the simultaneous numerical estimation of glucose, insulin and C-peptide, Figure 12 shows the numerically derived parameters for hypoglycemic action and insulin sensitivity, and Figure 13 shows the distribution of the numerical and analytical solutions. The simulated waveforms and normalized residuals of plasma glucose, serum insulin and C-peptide showed satisfactory behavior (Figures 3A and 3B). GluQ and k SenX There was no significant difference between NGT, IGT, and T2DM (Figure 12). Analytical insulin secretion (k Sb ,k Sp ,k Sf ) tends to be larger than the numerical solution, and the blood glucose lowering effect (k Glub ,k GluG / k GluQ ) tended to be small (Fig. 3C, S6). In addition, the numerically calculated hepatic insulin clearance (1-k r ) had a large variance (Figure 13), and in some people, hepatic insulin clearance was nearly zero, suggesting poor convergence of the numerical solution. Based on these results, analytically estimated parameters were used in the following analysis, taking into account the ease with which analytically estimated parameters can estimate magnitude relationships, and the poor convergence of the numerical solution parameters.

[0069] In this study, we analytically estimated insulin secretion, insulin sensitivity, insulin clearance, and hypoglycemic effect from clamp tests (a hyperglycemic and a hyperinsulinemic-euglycemic clamp), and evaluated the difference between analytically estimated parameters and numerically estimated parameters (Figure 3). The clamp test was developed as a method to analytically calculate insulin clearance and insulin sensitivity. In this study, we analytically calculated all major parameters related to glucose homeostasis and compared them with parameters calculated numerically. Although the analytical solution tends to overestimate insulin secretion and underestimate hypoglycemic effect, it was suggested that there is a significant correlation between the two values. It is thought that an analytical solution that can be easily calculated is useful for comparing the magnitude relationship of each parameter.

[0070] [I] Results: Relationships of parameters related to glucose homeostasis A correlation network was constructed to examine the relationships between parameters (Figure 4). Here, relationships with an absolute value of Spearman's correlation coefficient of 0.3 or more were linked. When examining all subjects, no combination of parameters with strong negative correlations was found (Figure 4, gray), but when examining NGT, IGT and T2DM subjects separately, negative correlations were found for some combinations (Figure 4, green, red and blue). Please note that the figures attached to this specification are in grayscale due to patent drawing restrictions, but the original figures are in color.

[0071] It has been reported that in NGT, insulin secretion increases in response to decreased insulin sensitivity, maintaining normal glucose homeostasis. Sen and k Sf A negative correlation was observed between low insulin sensitivity (k Sen ) is mainly responsible for early insulin secretion (k Sf ) and basal insulin secretion (k Sb ) and extra insulin secretion (k Sp) is not dependent on the k Sf and k GluG / k GluQ showed a negative correlation, and early insulin secretion (k Sf ) has a blood sugar lowering effect (k GluG / k GluQ It was also suggested that this could compensate for the decline in

[0072] In IGT, there were more negatively correlated combinations than in NGT. Sen and k Sf The correlation between k is weak. Sen k Sb and k Sp It showed a negative correlation with Sf and k GluG / k GluQ A negative correlation of was also observed in the IGT. Sb k GluG / k GluQ , k Glub ,k Ic was negatively correlated with

[0073] In T2DM, there are fewer negative correlation combinations compared to IGT, and k Sen and insulin secretion (k Sp ,k Sp ,k Sf ) was not observed. GluG / k GluQ k Sb and k Sp and negative correlation, k Glub k Sp A negative correlation was observed.

[0074] Taken together, these results suggest that maintaining glucose homeostasis involves not only insulin secretion and insulin sensitivity, but also hypoglycemic action and insulin clearance, and that which abilities are interrelated depends on the degree of glucose tolerance.

[0075] Furthermore, when the relationship between each parameter was examined, it was found that insulin secretion, insulin sensitivity, insulin clearance, and hypoglycemic action are all mutually related to maintain glucose homeostasis, and which ability is particularly related depends on the degree of glucose tolerance (Figure 4). It has been reported that NGT is maintained by increasing insulin secretion in response to a decrease in insulin sensitivity. This study shows that in NGT, the decrease in insulin sensitivity is mainly compensated for by early insulin secretion, in IGT, it is mainly compensated for by basal insulin secretion and additional insulin secretion, and in T2DM, there is almost no change in insulin secretion in response to a decrease in insulin sensitivity. Furthermore, two types of hypoglycemic action (k Glub and k GluG / k GluQ ) was also negatively correlated with insulin secretion in NGT, IGT, and T2DM. In addition, peripheral insulin clearance and hepatic insulin clearance were also negatively correlated with hypoglycemic effect or insulin secretion. Considering that insulin sensitivity and insulin secretion complement each other, it is necessary to evaluate both to evaluate glucose tolerance, and the product of the two, DI, is used to evaluate glucose tolerance. This study suggests that it is important to consider an index that integrates hypoglycemic effect and insulin clearance when evaluating glucose tolerance.

[0076] [J] Results: Relationship between blood glucose levels and parameters related to glucose homeostasis To investigate the relationship between blood glucose levels and parameters related to glucose homeostasis, a combination of parameters was calculated. As an index of glucose handling, the disposition index (DI), defined as the product of insulin sensitivity and insulin secretion, is used, so we first examined the DI. Since there are three types of insulin secretion, there are three definitions of DI: TIFF2025043453000062.tif20169However, because insulin clearance and hypoglycemic action are also involved in glucose homeostasis, we tried to add insulin clearance and hypoglycemic action to DI. Blood glucose level and each parameter are expressed by the following formula (Section [E]): TIFF2025043453000063.tif7169, where F is the total amount of glucose administered, K is TIFF2025043453000064.tif33169G is The file is TIFF2025043453000065.tif26169.

[0077] k Glub and k Sb Since it has a blood sugar lowering effect according to blood sugar level, TIFF2025043453000066.tif14169 can be considered as the P component in PID control. This component is DI / cleb k Sp has a blood sugar lowering effect according to the difference between blood sugar level and fasting blood sugar level, TIFF2025043453000067.tif14169 can be considered as the I component of PID control. This component is DI / clep k Sf Since has a blood sugar lowering effect according to the differential value of blood sugar level, TIFF2025043453000068.tif14169 can be considered as the D component of PID control. This component is called DI / clef It was defined as follows.

[0078] Therefore, K can be considered as a three-dimensional vector consisting of the P, I, and D components of the PID control. G is the area under the curve of blood glucose level (∫(GG b )dt), the degree of distortion in the time direction (distortion) (∫(GG b )tdt), variability (G max-G min ), which conceptually correspond to the three previously reported components of glucose dynamics, namely, value, autocorrelation, and fluctuation range, respectively.

[0079] Figure 5 explains the derivation of the equation that links the combination of each parameter and blood glucose dynamics. b ,Di p ,D.I. f was decreased (Fig. 5A), whereas DI / cleb and D.I. / clep was comparable in NGT and IGT (Fig. 5B), whereas DI b and D.I. p When insulin is decreased, DI is increased due to decreased insulin clearance or increased hypoglycemic effect. / cleb and D.I. / clep This suggests that the k Glub and k Ic But, k Sb This is consistent with the results showing a negative correlation with (Figure 4).

[0080] DI is generally expressed as a hyperbola with insulin sensitivity and insulin secretion as its coordinate axes, and the stabilization points on the curve vary from person to person. We attempted to evaluate individual differences by expressing the equation TIFF2025043453000069.tif7169 geometrically (Figure 5C-F). From this equation, if F and G are measured, it can be calculated that K is somewhere on the plane shown in Figure 5C. As glucose tolerance progresses, it is thought that the area under the curve of blood glucose levels and the fluctuation of blood glucose levels will increase, so the length of G will become longer and the plane on which K exists is expected to be near 0 (Figure 5C). G and K were calculated based on the data from the OGTT and clamp test (Figure 5D, 5E). Incidentally, G needs to be calculated from blood glucose levels between steady states, but since there is no data, G calculated from OGTT is shown for reference. In particular, K is scattered in three-dimensional space among NGT, IGT, and T2DM, and principal component analysis showed that the contribution rates of each component were diverse depending on the individual, with 0.42, 0.32, and 0.26 for NGT. In addition, the contribution rate of the first component in T2DM was greater than that in NGT and IGT (Figure 5F). Taken together, these results indicate that there are individual differences not only in insulin sensitivity and insulin secretion but also in each component of K, and that this diversity tends to decrease in T2DM.

[0081] Figure 14 shows blood glucose fluctuations for various glucose administration patterns. It is noteworthy that since K is a three-dimensional vector, as shown in Figure 14, each component of K can be uniquely identified by simply measuring the total glucose administration amount and the glucose dynamics after administration of three or more types of glucose. Therefore, it is believed that K can be calculated only from the blood glucose waveform.

[0082] To examine the relationship between blood glucose levels and parameters related to glucose homeostasis, We proposed the formula TIFF2025043453000070.tif7169. Here, F is the administered glucose, K is a combination of parameters, and is a three-dimensional vector consisting of the P, I, and D components of PID control, and G is a three-dimensional vector consisting of the area under the blood glucose curve, fluctuation, and the degree of distortion in the time direction (Figure 5). Research by the inventors and others has shown that glucose dynamics has three elements: concentration, fluctuation range, and autocorrelation, and each is independently associated with complications. The three components of G conceptually correspond to these three components. In addition, the inventors and others proposed the concept of DI / cle, which is an index that incorporates insulin clearance in addition to insulin sensitivity and insulin secretion (Non-Patent Document 2). K is an index that extends the concept of DI / cle to three dimensions. If the components of K are well correlated and can be compressed to one dimension, there is no need to calculate each component of K individually. However, since the values ​​of each element of K vary from person to person and K could not be compressed into one dimension, it is necessary to consider a three-dimensional vector like K, rather than a one-dimensional index like DI / cle. Based on these results, we propose the following law regarding glucose homeostasis: (1) The parameters responsible for glucose dynamics and its regulation are TIFF2025043453000071.tif7169, and (2) individual differences exist within the range in which this formula is satisfied. Using this law as a starting point, it is expected that the fundamental mechanisms of glucose homeostasis can be examined in more detail. At the same time, since F and G can be easily measured by continuous glucose monitoring and K can be estimated from this law, it is thought that disruptions in homeostasis can be easily detected.

[0083] [K] Results: Relationship between plasma glucose levels during OGTT and parameters related to glucose homeostasis To further understand the relationship between blood glucose levels and parameters related to glucose homeostasis, we investigated the relationship between plasma glucose waveforms during OGTT and parameters. Hierarchical clustering analysis was performed based on plasma glucose levels during OGTT. Figure 6 shows the classification of blood glucose fluctuation patterns after OGTT and glucose tolerance in each classification. Silhouette analysis showed that the optimal number of clusters was 4 (Figure 6A, the dotted line). Cluster 1 and Cluster 3 can be interpreted as an incessant increase curve type and a biphasic curve type, respectively (Figure 6C). Cluster 1 was k SP ,k Sf ,k Ic ,K Glub ,k GluG / k GluQ ,k Sen Cluster 4 has low k SP ,k Sf ,k GluG / k GluQ ,k Sen The biphasic curve type is interpreted as good glucose tolerance, while the increasing curve type is interpreted as impaired glucose tolerance. Sp ,k Sf ,k Ic ,k Glub ,k Sen is high, but the difference between cluster 3 and cluster 4 is k GluG / k GluQ It was suggested that the blood glucose lowering effect may be a factor determining whether the curve type is monophasic or biphasic.

[0084] [L] Results: How does blood glucose variability change when NGT progresses to IGT? Figure 7 shows the changes in parameters related to glycemic control observed in the early stage of impaired glucose tolerance and the resulting changes in blood glucose dynamics, and Figure 15 shows the relationship between blood glucose and hypoglycemic action, insulin sensitivity, and insulin clearance. To investigate how the changes in parameters related to glucose homeostasis observed during the transition from NGT to IGT affect glucose dynamics, glucose and insulin were simulated (Figure 7A). For the simulation, the mathematical model used for the analytical calculations in Figures 1 and 2 was used, and the parameters were the average values ​​observed in NGT. Here, k GluG / k GluQ ,k Sen ,k Ic Since these parameters were significantly different between NGT and IGT, we investigated how glucose dynamics would change if these parameters were changed from the average values ​​of NGT to the average values ​​of IGT.

[0085] k GluG / k GluQ As decreases, G variability was particularly increased (Fig. 7B). Sen and k Ic As decreases, G AUC and G Distortion was particularly increased (Fig. 7B). GluG / k GluQ ,k Sen ,k Ic If simultaneously decreasing, G AUC ,G Variability ,G Distortion (Fig. 7B). These results suggest that K GluG / k GluQ ,k Sen ,k Ic If vary independently, k GluG / k GluQ and G Variability are well correlated, and k Sen and k Ic is G AUC and G Distortion should correlate well with K GluG / k GluQ ,k Sen ,k IcWhen these three glucose dynamics properties change simultaneously, K GluG / k GluQ ,k Sen ,k Ic Correlated in the same way as K GluG / k GluQ ,k Sen ,k Ic In IGT, K GluG / k GluQ ,k Sen ,k Ic As expected from the simultaneous decrease in K (Fig. 1 and Fig. 2), these three glucose dynamics characteristics GluG / k GluQ ,k Sen ,k Ic All of them correlate well (Figure 15), and K GluG / k GluQ ,k Sen ,k Ic It was suggested that these three features of glucose dynamics could not be estimated separately.

[0086] We clarified that the magnitude relationship of parameters can be analytically estimated from the clamp test, how each parameter relates to maintain glucose homeostasis, and how these parameters relate to glucose dynamics. This equation is a starting point for elucidating the basic mechanism of glucose homeostasis, and at the same time, because it makes it possible to estimate parameters related to glucose homeostasis from glucose dynamics alone, it may also be a starting point for clinical research into the diagnosis of impaired glucose tolerance.

Claims

1. The formula for defining blood glucose is calculated by using the total amount of glucose administered to the subject, F, and the blood glucose fluctuation, G, of the subject to which the total amount of glucose was administered. The blood glucose control ability K is estimated using the above formula, and the blood glucose control ability K is estimated as a vector consisting of P, I, and D components in PID control. Method for estimating blood glucose control ability.

2. The blood glucose control ability K is It is defined as Where: is the P component, is the I component, is the D component, k Glub is the blood sugar lowering effect (glucose effectiveness), k Sen is insulin sensitivity, k Sb is basal insulin secretion, k Sp is the potentiation factor of insulin secretion, k Sf is the first-phase insulin secretion, 1-k r is hepatic insulin clearance, k Ic is peripheral insulin clearance, That is, The method for estimating blood glucose control ability according to claim 1 .

3. The blood glucose fluctuation G is the area under the curve obtained from the blood glucose waveform, the degree of distortion in the time direction, and the fluctuation range. The method for estimating blood glucose control ability according to claim 1 .

4. The blood glucose fluctuation G is a three-dimensional vector consisting of an equation corresponding to the area under the curve, the degree of distortion in the time direction, and the fluctuation range. It is stipulated by G is the blood glucose level obtained by the continuous glucose monitoring device, G b is the fasting blood glucose level, G max is the maximum blood glucose value obtained by the continuous blood glucose monitoring device, G min is the minimum blood glucose value obtained by the continuous blood glucose monitoring device, The method for estimating blood glucose control ability according to claim 3 .

5. The method for estimating blood glucose control ability according to claim 1 , wherein the total amount F of glucose administered to the subject and the blood glucose fluctuation G of the subject are obtained based on at least three types of glucose loading patterns.

6. A computer program for causing a computer to execute the method for estimating blood glucose control capability according to any one of claims 1 to 5.

7. A memory and a processor, The memory stores a formula that defines the relationship between the total amount of glucose administered to the subject F, the blood glucose fluctuation G of the subject to which the total amount of glucose was administered, and the blood glucose control ability K. is stored, The processor estimates the blood glucose control ability K by using the input total glucose amount F and blood glucose fluctuation G and the above formula, and the blood glucose control ability K is estimated as a vector consisting of P components, I components, and D components in PID control. Blood glucose control ability estimation device.

8. The blood glucose control ability K is It is defined as Where: is the P component, is the I component, is the D component, k Glub is the blood sugar lowering effect (glucose effectiveness), k Sen is insulin sensitivity, k Sb is basal insulin secretion, k Sp is the potentiation factor of insulin secretion, k Sf is the first-phase insulin secretion, 1-k r is hepatic insulin clearance, k Ic is peripheral insulin clearance, That is, The blood sugar control ability estimating device according to claim 7 .

9. A clamp test consisting of a hyperglycemic clamp test for measuring blood glucose, insulin, and C-peptide concentrations when glucose is administered, and a hyperinsulinemic euglycemic clamp test for measuring blood glucose, insulin, and C-peptide concentrations when glucose and insulin are administered was performed, and the following equation was obtained: Based on k Sb is basal insulin secretion, k Sp is the potentiation factor of insulin secretion, k Sf is the first-phase insulin secretion, 1-k r is hepatic insulin clearance, k Ic is peripheral insulin clearance, k Cc C-peptide clearance, A method for estimating blood glucose control ability. Where: C is the C-peptide concentration obtained in the clamp study, G is the blood glucose level obtained in the clamp test, I is the insulin concentration obtained in the clamp study, f is the insulin dose, Each subscript is a time in the clamp test. 0 is the start of the measurement, t1 is the first few minutes after glucose administration; t2, t3, and t4 are the times when blood glucose levels reached a steady state in the hyperglycemic clamp test. t5 and t6 are the times when the insulin concentration reached a steady state in the hyperinsulinemic clamp test.

10. A computer program for causing a computer to execute the method for estimating blood glucose control ability according to claim 9.

11. A memory and a processor, A device for estimating glycemic control ability using information from a clamp test consisting of a hyperglycemic clamp test for measuring blood glucose, insulin, and C-peptide concentrations when glucose is administered, and a hyperinsulinemic euglycemic clamp test for measuring blood glucose, insulin, and C-peptide concentrations when glucose and insulin are administered, The memory stores the following formula: In the above formula, k Sb is basal insulin secretion, k Sp is the potentiation factor of insulin secretion, k Sf is first-phase insulin secretion, 1-k r is hepatic insulin clearance, k Ic is peripheral insulin clearance, k Cc is C-peptide clearance, C is the C-peptide concentration obtained in the clamp study, G is the blood glucose level obtained in the clamp test, I is the insulin concentration obtained in the clamp study, f is the insulin dose, Each subscript is a time in the clamp test. 0 is the start of the measurement, t1 is the first few minutes after glucose administration; t2, t3, and t4 are the times when blood glucose levels reached a steady state in the hyperglycemic clamp test. t5 and t6 are the times when the insulin concentration reaches a steady state in the hyperinsulinaemic clamp test. The processor receives clamp test information as input and calculates k using the above formula. Sb , k Sp , k Sf , 1-k r , k Ic k Cc Estimate Blood glucose control ability estimation device.

12. A clamp test consisting of a hyperglycemic clamp test for measuring blood glucose, insulin, and C-peptide concentrations when glucose is administered, and a hyperinsulinemic euglycemic clamp test for measuring blood glucose, insulin, and C-peptide concentrations when glucose and insulin are administered was performed, and the following equation was obtained: Based on k Glub is the blood sugar lowering effect (glucose effectiveness), k Sen is insulin sensitivity, k GluG ,k GluQ is the glucose exchange rate parameter between the intravascular and extravascular compartments, A method for estimating blood glucose control ability. Where: G g is the steady-state plasma glucose level in the hyperglycemic clamp test, G i is the plasma glucose level at steady state during hyperinsulinemic clamp test, I g is the steady-state serum insulin level in the hyperglycemic clamp study, I i is the steady-state serum insulin level in the hyperinsulinemic clamp test, f Gg is the glucose dose at which blood glucose reaches a stable steady state in the hyperglycemic clamp test, f Gi is the glucose dose at which blood glucose reaches a stable steady state in the hyperinsulinemic clamp test, F G0-Gt1 is the total amount of glucose administered during the first t1 minute of the hyperglycemic clamp test, G is the blood glucose level obtained in the clamp test; I is the insulin concentration obtained in the clamp study; Each subscript is a time in the clamp test. 0 is the start of the measurement, t1 is the first few minutes after glucose administration.

13. A computer program for causing a computer to execute the method for estimating blood glucose control capability according to claim 12.

14. A memory and a processor, A device for estimating glycemic control ability using information from a clamp test consisting of a hyperglycemic clamp test for measuring blood glucose, insulin, and C-peptide concentrations when glucose is administered, and a hyperinsulinemic euglycemic clamp test for measuring blood glucose, insulin, and C-peptide concentrations when glucose and insulin are administered, The memory stores the following formula: In the above formula, k Glub is the blood sugar lowering effect (glucose effectiveness), k Sen is insulin sensitivity, k GluG ,k GluQ is the glucose exchange rate parameter between the intravascular and extravascular compartments, G g is the steady-state plasma glucose level in the hyperglycemic clamp test, G i is the plasma glucose level at steady state during hyperinsulinemic clamp test, I g is the steady-state serum insulin level in the hyperglycemic clamp study, I i is the steady-state serum insulin level in the hyperinsulinemic clamp test, f Gg is the glucose dose at which blood glucose reaches a stable steady state in the hyperglycemic clamp test, f Gi is the glucose dose at which blood glucose reaches a stable steady state in the hyperinsulinemic clamp test, F G0-Gt1 is the total amount of glucose administered during the first t1 minute of the hyperglycemic clamp test, G is the blood glucose level obtained in the clamp test; I is the insulin concentration obtained in the clamp study; Each subscript is a time in the clamp test. 0 is the start of the measurement, t1 is the first few minutes after glucose administration, The processor receives clamp test information as input and calculates k using the above formula. Glub , k Sen , k GluG / k GluQ , to estimate Blood glucose control ability estimation device.

Images