This "biodigital twin" mirrors a patient's cardiovascular response to a beta-blocker style drug. A one-compartment pharmacokinetic (PK) model tracks plasma drug concentration, and a Hill-equation pharmacodynamic (PD) model converts that concentration into a heart-rate-lowering effect — the same class of math used in real clinical dosing simulators.
dC/dt = -ke·C (first-order elimination)
E(C) = Emax·C / (C50 + C) (Hill eqn, n=1)
HRbase = 70 + 0.9·load
HR = HRbase·(1 - E(C))
CO = HR · SV / 1000 (SV = stroke volume, mL)
- Administer Dose: injects a bolus, raising C instantly by Dose/Vd (Vd = 40 L volume of distribution).
- Dose Size: sets the mg delivered by the next bolus.
- Exercise / Stress Load: raises baseline metabolic demand and heart rate before drug effect is applied.
- Time Scale: how many simulated minutes elapse per real second.
- Metabolism Phenotype: sets the elimination rate constant ke (slow/normal/fast metabolizer), changing the drug's half-life — the core idea of a personalized digital twin: identical dose, different response.
Clinics use this exact approach — calibrating a per-patient PK/PD twin from real vitals — to rehearse dosing strategies safely before they ever reach the patient.