. Author manuscript; available in PMC: 2013 May 2.

Published in final edited form as: Cell Mol Bioeng. 2011 Mar 8;4(2):281–301. doi: 10.1007/s12195-011-0162-2

TABLE 4.

Model input functions^*.

Time (min)	Input functions
t ≤ 15	Q = Q₀, C_I = C_I,0, C_a,GLC = C_a,GLC,0, C_a,LAC = C_a,LAC,0
t ≤ 15	C_a,GLR = C_a,GLR,0, C_a,FA = C_a,FA,0, C_a,TG = C_a,TG,0
t > 15	Q = Q₀ ·(1 + 7.76 · (1 − e⁻⁽^t^−15)/20.54) − 7.68 · (1 − e⁻⁽^t^−15)/36.48))
	C_I = C_I,0 + 65.1 · (1 − e⁻⁽^t^−15)/10)
	C_a,GLC = C_a,GLC,0 · (1 − 0.177 · (t − 15)^5.26/(22.82^5.26 + (t − 15)^5.26) + 0.421 · (1 − e⁻⁽^t^−15)/350.3))
	C_a,LAC = C_a,LAC,0 · (1 + 0.389 · (t − 15)^7.05/(18.88^7.05 + (t − 15)^7.05))
	C_a,GLR = C_a,GLR,0 · (0.41 + 0.59e⁻⁽^t^−15)/10.38)
	C_a,FA = C_a,FA,0 · (0.11 + 0.89e⁻⁽^t^−15)/17.22)
	C_a,TG = C_a,TG,0 · (1 − 0.0015 · (t − 15))

Parameters for the input functions were optimally estimated based on the data from the human in vivo study.^8,9,19 Q: Blood flow to the adipose tissue; C_I: Insulin concentration in the interstitial fluid; C_a,GLC, C_a,LAC, C_a,GLR, C_a,FA, C_a,TG: Arterial concentrations of glucose, lactate, glycerol, FA and TG; C_a_,i,₀: Initial arterial concentration of chemical species i as shown in Table 1. Time courses of these input functions are shown in Fig. 2.