## Apps.DiabeticGlucose History

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This is a collection of mathematical models that predict the blood glucose levels of a type-I diabetic. These models have been used in research for blood glucose control. The objective is to predict the relationship between insulin injection and blood glucose levels. With a sufficiently accurate mathematical model of a patient, the correct insulin injection rate could be prescribed. By automating the sensing of blood glucose and the injection of insulin, this system would serve as an artificial pancreas. The following mathematical models are composed of differential and algebraic equations.

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# 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

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### Model #1

### Model #2

## Blood Glucose Response of an Insulin Dependent Patient

### Model #1

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 #2

S. M. Lynch and B. W. Bequette, Estimation based Model Predictive Control of Blood Glucose in Type I Diabetes: A Simulation Study, Proc. 27th IEEE Northeast Bioengineering Conference, IEEE, 2001.

and

S. M. Lynch and B. W. Bequette, Model Predictive Control of Blood Glucose in type I Diabetics using Subcutaneous Glucose Measurements, Proc. ACC, Anchorage, AK, 2002.