! APMonitor Modeling Language ! http://www.apmonitor.com ! ! Model source: ! A. Roy and R.S. Parker. “Dynamic Modeling of Free Fatty ! Acids, Glucose, and Insulin: An Extended Minimal Model,” ! Diabetes Technology and Therapeutics 8(6), 617-626, 2006. ! Model human Parameters p1 = 0.068 ! 1/min p2 = 0.037 ! 1/min p3 = 0.000012 ! 1/min p4 = 1.3 ! mL/(min * micro-U) p5 = 0.000568 ! 1/mL p6 = 0.00006 ! 1/(min * micro-mol) p7 = 0.03 ! 1/min p8 = 4.5 ! mL/(min * micro-U) k1 = 0.02 ! 1/min k2 = 0.03 ! 1/min pF2 = 0.17 ! 1/min pF3 = 0.00001 ! 1/min n = 0.142 ! 1/min VolG = 117 ! dL VolF = 11.7 ! L ! basal parameters for Type-I diabetic Ib = 0 ! Insulin (micro-U/mL) Xb = 0 ! Remote insulin (micro-U/mL) Gb = 98 ! Blood Glucose (mg/dL) Yb = 0 ! Insulin for Lipogenesis (micro-U/mL) Fb = 380 ! Plasma Free Fatty Acid (micro-mol/L) Zb = 380 ! Remote Free Fatty Acid (micro-mol/L) ! insulin infusion rate u1 = 3 ! micro-U/min ! glucose uptake rate u2 = 300 ! mg/min ! external lipid infusion u3 = 0 ! mg/min End Parameters Intermediates p9 = 0.00021 * exp(-0.0055*G) ! dL/(min*mg) End Intermediates Variables I = Ib X = Xb G = Gb Y = Yb F = Fb Z = Zb End Variables Equations ! Insulin dynamics $I = -n*I + p5*u1 ! Remote insulin compartment dynamics $X = -p2*X + p3*I ! Glucose dynamics $G = -p1*G - p4*X*G + p6*G*Z + p1*Gb - p6*Gb*Zb + u2/VolG ! Insulin dynamics for lipogenesis $Y = -pF2*Y + pF3*I ! Plasma Free Fatty Acid (FFA) dynamics $F = -p7*(F-Fb) - p8*Y*F + p9 * (F*G-Fb*Gb) + u3/VolF ! Remote FFA dynamics $Z = -k2*(Z-Zb) + k1*(F-Fb) End Equations End Model