PFE I · Homework 3 — Glucose-Insulin Model (OGTT, Diabetes, Metformin)

Scenario presets (from the assignment)

Normal fasting adult: gains = 1, Q_L = 8400 mg/hr, no glucose load. Steady state ≈ 0.81 mg/ml glucose, 0.057 IU/ml insulin.

Patient & test parameters

Type 1 severity κ (insulin production)

Type 2 severity η (insulin sensitivity)

Liver glucose output Q_L (mg/hr)

OGTT glucose dose (g)

Give 1 g oral metformin at t = 0 (halves hepatic glucose output at peak concentration)

Give subcutaneous Humulin injection at t = 0 (adds injected insulin; for a Type 1 patient set κ = 0)

Insulin dose (IU)

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Fasting glucose (mg/ml)

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Fasting insulin (IU/ml)

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Glucose @ 1 hr post-load

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Glucose @ 2 hr post-load

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OGTT interpretation

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Glucose nadir (mg/ml)

OGTT positivity criteria used in the assignment: glucose ≥ 2.0 mg/ml at 1 hr or ≥ 1.4 mg/ml at 2 hr after the 75 g load. Fasting levels are found automatically by pre-running the model to steady state before the test begins (the load is given at t = 0.5 hr).

Pharmacokinetics used (one-compartment oral/subcutaneous models)

Metformin: dose 1 g, V_d = 15 L, k_a = 0.275/hr, k_e = 0.25/hr, F = 0.95. Bateman concentration C(t) = F·D·k_a/[V_d(k_a−k_e)]·(e^−k_et−e^−k_at). Hepatic output is scaled as Q_L(t) = Q_L0·[1 − 0.5·C(t)/C_max,1g].
Humulin: V_d = 30 L, k_a = 1.55/hr, k_e = 0.43/hr, F = 0.65 (peak at ≈1.1 hr, duration ≈5 hr, matching the Lilly data quoted in the assignment). With the course units a 30 IU dose produces a small plasma concentration relative to the model’s fasting insulin of 0.057 IU/ml — raise the dose slider to explore a clear hypoglycemic nadir.