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Table 3 Definition of the symbols in the discrete Single Delay Model

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
Gb [mM] basal (preinjection) plasma glucose concentration
I(t) [pM] insulin plasma concentration at time t
Ib [pM] basal (preinjection) insulin plasma concentration
KxgI [min-1 pM-1] net rate of (insulin-dependent) glucose uptake by tissues per pM of plasma insulin concentration
Tgh [mmol min-1 kgBW-1] net balance of the constant fraction of hepatic glucose output (HGO) and insulin-independent zero-order glucose tissue uptake
Vg [L kgBW-1] apparent distribution volume for glucose
Dg [mmol kgBW-1] administered intravenous dose of glucose at time 0
GΔ [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
Kxi [min-1] apparent first-order disappearance rate constant for insulin
Tigmax [pmol min-1kgBW-1] maximal rate of second-phase insulin release; at a glycemia equal to G* there corresponds an insulin secretion equal to Tigmax/2
Vi [L kgBW-1] apparent distribution volume for insulin
τg [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
IΔG [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