From: A discrete Single Delay Model for the Intra-Venous Glucose Tolerance Test
Symbol | Units | Definition |
---|---|---|
t | [min] | time |
G(t) | [mM] | glucose plasma concentration at time t |
G_{b} | [mM] | basal (preinjection) plasma glucose concentration |
I(t) | [pM] | insulin plasma concentration at time t |
I_{b} | [pM] | basal (preinjection) insulin plasma concentration |
K_{xgI} | [min^{-1} pM^{-1}] | net rate of (insulin-dependent) glucose uptake by tissues per pM of plasma insulin concentration |
T_{gh} | [mmol min^{-1} kgBW^{-1}] | net balance of the constant fraction of hepatic glucose output (HGO) and insulin-independent zero-order glucose tissue uptake |
V_{g} | [L kgBW^{-1}] | apparent distribution volume for glucose |
D_{g} | [mmol kgBW^{-1}] | administered intravenous dose of glucose at time 0 |
G_{Δ} | [mM] | theoretical increase in plasma glucose concentration over basal glucose concentration at time zero, after the instantaneous administration and distribution of the I.V. glucose bolus |
K_{xi} | [min^{-1}] | apparent first-order disappearance rate constant for insulin |
T_{igmax} | [pmol min^{-1}kgBW^{-1}] | maximal rate of second-phase insulin release; at a glycemia equal to G* there corresponds an insulin secretion equal to T_{igmax}/2 |
V_{i} | [L kgBW^{-1}] | apparent distribution volume for insulin |
τ_{g} | [min] | apparent delay with which the pancreas changes secondary insulin release in response to varying plasma glucose concentrations |
γ | [#] | progressivity with which the pancreas reacts to circulating glucose concentrations. If γ were zero, the pancreas would not react to circulating glucose; if γ were 1, the pancreas would respond according to a Michaelis-Menten dynamics, with G* mM as the glucose concentration of half-maximal insulin secretion; if γ were greater than 1, the pancreas would respond according to a sigmoidal function, more and more sharply increasing as γ grows larger and larger |
I_{ΔG} | [pM mM^{-1}] | first-phase insulin concentration increase per mM increase in glucose concentration at time zero due to the injected bolus |
G* | [mM] | glycemia at which the insulin secretion rate is half of its maximum |