Analytical Basal-State Model of the Glucose, Insulin, and C-Peptide Systems for Type 2 Diabetes
Abstract
1. Introduction
2. Basal-State Model Derivation Methodology
2.1. Foundational Dynamic Model
2.1.1. Glucose System
2.1.2. Insulin System
2.1.3. C-Peptide System
2.2. System of Literal Basal-State Equations
2.3. Methodology for Solving the System of Literal Basal-State Equations
3. Analytical Basal-State Model—Derivation and Result
3.1. Quartic Equation for
3.2. The Full Basal-State Model
3.3. Identifying Physical Basal Solutions
4. Analytical Basal-State Model—Applications and Model Verification
4.1. Basal Values Corresponding to Reported Median T2DM Parameter Values
4.2. Basal Model Parameter Study
4.3. Model Verification
4.4. Misusing the Dynamic Model via Incorrect Basal Values
5. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
ADA | American Diabetes Association |
DM | Diabetes mellitus |
JSPS | Japanese Society for the Promotion of Science |
LADA | Latent autoimmune diabetes of adults |
MODY | Maturity-onset diabetes of the young |
ODE | Ordinary differential equation |
OGTT | Oral glucose tolerance test |
T1DM | Type 1 diabetes mellitus |
T2DM | Type 2 diabetes mellitus |
Appendix A. Physiological Model Parameters
Subsystem | Symbol | Description | Units | Value | Origin | Basal? |
---|---|---|---|---|---|---|
Rate of Appearance | Maximum gastric emptying rate | 1/min | 0.0426 | [18] | No | |
Minimum gastric emptying rate | 1/min | 0.0076 | [18] | No | ||
Intestinal absorption rate | 1/min | 0.0542 | [18] | No | ||
Stomach-grinding rate | 1/min | 0.0465 | [14] | No | ||
f | Intestinal absorption fraction | Unitless | 0.9 | [18] | No | |
b | Gastric-emptying reduction inflection point | Unitless | 0.73 | [18] | No | |
c | Gastric-emptying recovery inflection point | Unitless | 0.1 | [18] | No | |
Gastric-emptying reduction mass rate | 1/mg | 0.00010 | (D2) | No | ||
Gastric-emptying recovery mass rate | 1/mg | 0.00037 | (D3) | No | ||
Glucose Kinetics | Rate parameter | 1/min | 0.066 | [18] | Yes | |
Rate parameter | 1/min | 0.043 | [18] | Yes | ||
Glucose distribution volume | dL/kg | 1.00 | [18] | Yes | ||
Glucose Excretion | Glomerular filtration rate | 1/min | 0.0005 | [18] | Yes | |
Glucose excretion threshold | mg/kg | 339 | [18] | Yes | ||
s | Excretion switch parameter | Unitless | 0 or 1 | (5b) | Yes | |
Endogenous Glucose Production | Extrapolated EGP for zero glucose and insulin | mg/(kg·min) | 3.09 | [14] | Yes | |
Hepatic glucose effectiveness | 1/min | 0.0008 | [18] | Yes | ||
Hepatic insulin sensitivity | 0.0060 | [18] | Yes | |||
Portal insulin sensitivity | 0.0484 | [18] | Yes | |||
Glucose Utilization | Insulin-independent glucose utilization | mg/(kg·min) | 1 | [18] | Yes | |
Michaelis–Menten parameter | mg/(kg·min) | 4.65 | [14] | Yes | ||
Michaelis–Menten parameter | mg/kg | 466.2 | [18] | Yes | ||
Insulin sensitivity to glucose utilization | 0.034 | [18] | No | |||
Risk function parameter | Unitless | 0 | Appendix A | No | ||
Risk function parameter | Unitless | 0 | Appendix A | No | ||
Hypoglycemic threshold | mg/dL | 60 | [17] | No | ||
Insulin Secretion | Delay between glucose and insulin secretion | 1/min | 0.034 | [18] | No | |
Beta-cell responsivity to glucose | /min | 20.30 | [18] | No | ||
Beta-cell responsivity to glucose rate of change | 286.0 | [18] | No | |||
h | Glucose threshold for beta-cell secretion | mg/dL | (D20) | No | ||
Insulin Kinetics | Rate parameter | 1/min | 0.314 | [18] | Yes | |
Rate parameter | 1/min | 0.268 | [18] | Yes | ||
Rate parameter | 1/min | 0.443 | [18] | Yes | ||
Rate parameter | 1/min | 0.260 | [18] | Yes | ||
Rate parameter | 1/min | 0.017 | [18] | Yes | ||
Glucose control on HE | dL/mg | 0.005 | [18] | Yes | ||
Extrapolated HE for zero glucose | Unitless | 1.16 | [14] † | Yes | ||
Insulin distribution volume | L/kg | 0.041 | [18] | Yes | ||
Insulin-action delay rate | 1/min | 0.0075 | [18] | No | ||
Rate of insulin action on glucose utilization | 1/min | 0.058 | [18] | No | ||
C-Peptide Kinetics | Rate parameter | 1/min | 0.062 | [23] | Yes | |
Rate parameter | 1/min | 0.051 | [23] | Yes | ||
Rate parameter | 1/min | 0.053 | [23] | Yes | ||
C-peptide distribution volume | L | 4.18 | [23] | Yes | ||
Basal plasma C-peptide concentration | pmol/L | 950 | [18] † | Yes |
Appendix B. Dynamic Model Solver and Oral Glucose Consumption
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k | (mg/dL) | (mg/(kg·min)) | (unitless) | (pmol/L) | ||
---|---|---|---|---|---|---|
1 | + | + | 586.92 | 61.58 | ||
1 | + | − | 140.03 | 2.32 | 0.46 | 62.95 |
1 | − | + | 1669.25 | 5.58 | ||
1 | − | − | 6.54 | 10.19 | ||
2 | + | + | 1669.25 | 5.58 | ||
2 | + | − | 586.92 | 61.58 | ||
2 | − | + | 140.03 | 2.32 | 0.46 | 62.95 |
2 | − | − | 6.54 | 10.19 | ||
3 | + | + | 1669.25 | 5.58 | ||
3 | + | − | 140.03 | 2.32 | 0.46 | 62.95 |
3 | − | + | 586.92 | 61.58 | ||
3 | − | − | 6.54 | 10.19 |
System | Symbol | Basal Quantity Description | Unit | Value |
---|---|---|---|---|
Glucose | Plasma-glucose concentration | mg/dL | 140.03 | |
Plasma-glucose mass | mg/kg | 140.03 | ||
Endogenous glucose-production rate | mg/(kg·min) | 2.32 | ||
Glucose-excretion rate | mg/(kg·min) | 0 | ||
Tissue-glucose mass | mg/kg | 184.30 | ||
Insulin-dependent utilization rate | mg/(kg·min) | 1.32 | ||
Insulin-independent utilization rate | mg/(kg·min) | 1 | ||
Insulin | Insulin-secretion rate | pmol/min | 246.20 | |
Hepatic-extraction ratio | unitless | 0.46 | ||
Hepatic-extraction parameter | 1/min | 0.27 | ||
Plasma-insulin mass | pmol/kg | 2.58 | ||
Liver-insulin mass | pmol/kg | 5.84 | ||
Extravascular-insulin mass | pmol/kg | 39.47 | ||
Plasma-insulin concentration | pmol/L | 62.95 | ||
Anticipated insulin signal | pmol/L | 62.95 | ||
Delayed insulin signal | pmol/L | 62.95 | ||
C-Peptide | Peripheral C-peptide concentration | pmol/L | 987.25 |
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Chichester, C.C.; Yamakuchi, M.; Takenouchi, K.; Hashiguchi, T.; Maywar, D.N. Analytical Basal-State Model of the Glucose, Insulin, and C-Peptide Systems for Type 2 Diabetes. Bioengineering 2025, 12, 553. https://doi.org/10.3390/bioengineering12050553
Chichester CC, Yamakuchi M, Takenouchi K, Hashiguchi T, Maywar DN. Analytical Basal-State Model of the Glucose, Insulin, and C-Peptide Systems for Type 2 Diabetes. Bioengineering. 2025; 12(5):553. https://doi.org/10.3390/bioengineering12050553
Chicago/Turabian StyleChichester, Ched C., Munekazu Yamakuchi, Kazunori Takenouchi, Teruto Hashiguchi, and Drew N. Maywar. 2025. "Analytical Basal-State Model of the Glucose, Insulin, and C-Peptide Systems for Type 2 Diabetes" Bioengineering 12, no. 5: 553. https://doi.org/10.3390/bioengineering12050553
APA StyleChichester, C. C., Yamakuchi, M., Takenouchi, K., Hashiguchi, T., & Maywar, D. N. (2025). Analytical Basal-State Model of the Glucose, Insulin, and C-Peptide Systems for Type 2 Diabetes. Bioengineering, 12(5), 553. https://doi.org/10.3390/bioengineering12050553