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

time

glucose plasma concentration at time t

basal (preinjection) plasma glucose concentration

insulin plasma concentration at time t

basal (preinjection) insulin plasma concentration

net rate of (insulin-dependent) glucose uptake by tissues per pM of plasma insulin concentration

net balance of the constant fraction of hepatic glucose output (HGO) and insulin-independent zero-order glucose tissue uptake

apparent distribution volume for glucose

administered intravenous dose of glucose at time 0

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

apparent first-order disappearance rate constant for insulin

maximal rate of second-phase insulin release; at a glycemia equal to G* there corresponds an insulin secretion equal to T_igmax/2

apparent distribution volume for insulin

apparent delay with which the pancreas changes secondary insulin release in response to varying plasma glucose concentrations

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

first-phase insulin concentration increase per mM increase in glucose concentration at time zero due to the injected bolus

glycemia at which the insulin secretion rate is half of its maximum