Table A - 1.
A list of the model variables, including the 16 state and 5 input variables, and the model parameters (* indicates subject-specific personalized parameters with respective interquartile range provided).
| Symbol | Definition | Value/Range and Unit |
|---|---|---|
| S1(t), S2(t) | Insulin amount in two-compartment chains for subcutaneous insulin absorption | mU |
| I(t) | Plasma insulin concentration | mU · L−1 |
| x1(t) | Effects of insulin on glucose distribution/transport | min−1 |
| x2(t) | Effects of insulin on glucose disposal | min−1 |
| x3(t) | Effects of insulin on the endogenous glucose production | min−1 |
| Q1(t) | Glucose in the blood stream (accessible compartment) | mmol |
| Q2(t) | Glucose in the peripheral tissue (non-accessible compartment) | mmol |
| Gsub(t) | Subcutaneous glucose concentration | mmol · L−1 |
| D1(t), D2(t) | Glucose amount in the two-compartment chains for regular meal absorption | mmol |
| DH1(t), DH2(t) | Glucose amount in the two-compartment chains for fast-act rescue carbohydrate absorption | mmol |
| E1(t) | Short-term exercise effect | BPM |
| TE(t) | Characteristic time for long term exercise effect | min |
| E2(t) | Long-term exercise effect | – |
| d1(t)/D1(t) | Carbohydrate intake (regular meal) | mg/mmol |
| d2(t)/D2(t) | Carbohydrate intake (fast-acting rescue) | mg/mmol |
| u1(t) | Basal insulin | mU · min−1 |
| u2(t) | Bolus insulin | mU |
| HR(t) | Heart rate | BPM |
| k12 | Transfer rate | 0.066 min−1 |
| ka,1 | Deactivation rate for effect of insulin on glucose distribution/transport | 0.006 min−1 |
| ka,2 | Deactivation rate for effect of insulin on glucose disposal | 0.06 min−1 |
| ka,3 | Deactivation rate for effect of insulin on endogenous glucose production | 0.03 min−1 |
| SIT* = kb,1*/ka,1 | Insulin sensitivities of transport | 25 [21 – 29] × 10−4 min−1 per mU · L−1 |
| SID* = kb,2*/ka,2 | Insulin sensitivities of disposal | 6 [4 – 7] × 10−4 min−1 per mU · L−1 |
| SIE* = kb,3*/ka,3 | Insulin sensitivities of endogenous glucose production | 217 [178 – 254] × 10−4 per mU · L−1 |
| ke* | Insulin elimination rate from plasma | 0.196 [0.175 – 0.218] min−1 |
| VI | Insulin distribution volume | 0.12 (L · kg−1 |
| VG | Glucose distribution volume | 0.16 (L · kg−1 |
| EGP0* | Extrapolated EGP at zero insulin concentration | 0.0277 [0.0235 – 0.0318] mmol · kg−1 · min−1 |
| F01* | Non-insulin-dependent glucose flux | 0.0109 [0.0088 – 0.0131] mmol · kg−1 · min−1 |
| tmax,I* | Time-to-maximum insulin absorption | 69.5 [62.8 – 75.0] min |
| τG | Time constant for bloodstream to the interstitial tissues | 15 min |
| a | Exercise parameter | 0.77 |
| tHR | Exercise parameter | 5 min |
| tin | Exercise parameter | 1 min |
| n | Exercise parameter | 3 |
| tex | Exercise parameter | 200 min |
| c1 | Exercise parameter | 500 min |
| c2 | Exercise parameter | 100 min |
| AG* | Carbohydrate bioavailability | 0.71 [0.67 – 0.76] unitless |
| tmax, G* | Time-of-maximum glucose appearance rate in the bloodstream (regular meal) | 40.4 [37.8 – 43.4] min |
| β* | Exercise-induced insulin-independent glucose uptake rate | 0.78 [0.57 – 1.03] mmol · min−1 |
| α* | Exercise-induced insulin action | 1.79 [1,41 – 2.19] unitless |
| BW | Body weight | kg |
| HRbase | Basal heart rate | BPM |