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Table 1 Comparison of each component of three models

From: Modeling glucose and free fatty acid kinetics in glucose and meal tolerance test

  MOD 1 MOD 2 MOD 3
Glucose kinetics S G G b  − (S G  + S 1 X)G -
Insulin kinetics C x [I(t) − X − I bx ] -
FFA lipolysis \( {l}_0+\frac{l_2}{1+{\left(X/{X}_2\right)}^{A_{lipo}}} \) \( {l}_0+\left[\frac{l_2}{1+{\left(X/{X}_2\right)}^{A_l}}\right] \) \( \frac{V_m^{Lip}}{1+{\left(I\left(t-{t}_{DelayLip}\right)/{K}_{Lip}\right)}^{h_{lip}}} \)
FFA clearance \( {C}_f\left[1+\frac{{\left(X/{K}_{Cl}\right)}^{A_{Cl}}}{1+{\left(X/{K}_{Cl}\right)}^{A_{Cl}}}\right]F \) C f0 F \( {k}_{\mathrm{Re}m}F+\frac{V_m^{\mathrm{Re}m}{I}^{h_{rem}}\left(t-{t}_{Delay\mathrm{R}\mathrm{e}m}\right)}{K_m^{h_{\mathrm{Re}m}}+{\left(I\left(t-{t}_{Delay\mathrm{R}\mathrm{e}m}\right)/{K}_{\mathrm{Re}m}\right)}^{h_{\mathrm{Re}m}}}F \)
  1. G is plasma glucose, F is plasma FFA, I is plasma insulin as model input, X is the insulin action representing the indirect effect of insulin on the regulation of plasma glucose and FFA. The detailed descriptions of parameters are listed in Additional file 1: Table S2. Note that I bx is a fitted parameter that is determined through the action of X on glucose and FFA. Thus, it is not necessarily the same as measured basal insulin, and we have used the subscript bx to emphasize this fact