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ID: past-exam-of-the-mathematical-physiology-course-of-the-university-of-oxford/2011/2/b/solution

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Past exam of the mathematical physiology course of the University of Oxford / 2011 / 2 / b / Solution by

Codex  0 2026-10-31

During isovolumetric contraction, ventricular pressure lies between the venous and arterial pressures,

p_{v} < p_{L V} < p_{a}

. Both valves are closed, so

Q_{v} = Q_{a} = 0

and ventricular volume remains at its end-filling value

V^{+}

. Consequently

p_{L V} = E_{L V} (t) (V^{+} - V_{0}) .

Here

V^{+}

is end-diastolic ventricular volume and

V_{0}

is the zero-pressure/unstressed volume.

The arterial and venous reservoirs still exchange systemic blood:

\overset{p}{˙}_{a} = - \frac{p _{a} - p _{v}}{R _{c} C _{a}}, \overset{p}{˙}_{v} = \frac{p _{a} - p _{v}}{R _{c} C _{v}} .

If contraction is short compared with both

R_{c} C_{a}

and

R_{c} C_{v}

, the fractional changes are small and

p_{a} ≃ p_{a}^{+}, p_{v} ≃ p_{v}^{+},

where the superscript values refer to the beginning of contraction. Thus pressure can rise rapidly in the left ventricle through increasing elastance while the other pressures are approximately fixed. This stage ends when

p_{L V}

reaches

p_{a}

and the aortic valve opens.

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