Models for the Study of Whole-Body Glucose Kinetics: A Mathematical Synthesis

Table 1

Mathematical notation.

𝐷,𝐷^∗	Dose of total and labelled glucose, respectively, injected into primary pool (mmol)
𝐹𝑖𝑗	Flow of total glucose to pool i from pool 𝑗; 𝐹𝑖0 represents external flow of glucose into pool 𝑖 and 𝐹0𝑖 flow of glucose from pool 𝑖 out of the system (mmol/min)
𝜙	Constant rate of labelled glucose infusion into primary pool (mmol/min)
𝐺,𝐺^∗	Total and labelled glucose concentration, respectively, in primary pool (mmol/mL)
𝐼,𝐼^′	Plasma and remote insulin concentrations, respectively (pmol)
𝑘𝑖𝑗	Relative rate constant for flow from pool 𝑖 from pool 𝑗 (per min)
𝑄𝑖	Quantity of total glucose in pool 𝑖 (mmol)
𝑞𝑖	Quantity of labelled glucose in pool 𝑖 (mmol)
𝑠𝑖	Enrichment (or specific activity) of pool 𝑖 (mmol labelled glucose/mmol total glucose)
𝑡	Time since isotope first administered (min)
𝑉𝑖	Volume of pool 𝑖; 𝑉1 represents primary (plasma) pool volume (mL)