Table 2.

Definition of the symbols used in the discrete Single Delay Model

Symbol	Units	Definition
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-1 kgBW-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