PFE I · Homework 1 — Blood Pressure (Windkessel) Model

Scenario presets (from the assignment)

Baseline course parameters. Adjust the compliance slider to reproduce Exercise 3: find C_sa giving ≈120/80 mmHg.

Model parameters

Heart rate (beats/min)

Systemic compliance C_sa (L/mmHg)

Systemic resistance R_s (mmHg/(L/min))

Peak aortic flow Q_max (L/min)

Systole fraction T_S/T

Initial pressure P_sa(0) (mmHg)

Heart block (Exercise: ventricle stops at 1.8 s, resumes at 7.8 s — Q_Ao=0 for 0.03–0.13 min)

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Blood pressure (sys/dia, mmHg)

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Pulse pressure (mmHg)

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Cardiac output (L/min)

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Stroke volume (mL)

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Mean arterial pressure

What the assignment explores

Arteriosclerosis = stiffening of the large arteries → decrease C_sa. Systolic pressure rises and diastolic falls (widened pulse pressure) because a stiff reservoir can no longer store systolic volume and recoil during diastole.
Arteriolosclerosis = narrowing of the arterioles → increase R_s. Both systolic and diastolic rise together (≈150/105) since the same cardiac output must cross a higher resistance.
Obesity: heart rate and Q_max increase to perfuse extra tissue → hypertension with elevated cardiac output.
Exercise: R_s halves (muscle vasodilation) while heart rate and Q_max roughly double → CO doubles with little change in pressure.
Heart block: when beats stop, pressure decays exponentially with time constant R_sC_sa; recovery after resumption takes several beats, explaining syncope.