 Three-compartment ventricular circulation model

ID: three-compartment-ventricular-circulation-model

Q_{a}, Q_{v}, Q_{c}

C_{a} \overset{p}{˙}_{a} = Q_{a} - Q_{c}

C_{v} \overset{p}{˙}_{v} = Q_{c} - Q_{v}

, and

d (p_{L V} / E_{L V}) / d t = Q_{v} - Q_{a}

. Ideal one-way valves give

Q_{a} = [p_{L V} - p_{a}]_{+} / R_{a}

Q_{v} = [p_{v} - p_{L V}]_{+} / R_{v}

; systemic resistance gives

Q_{c} = (p_{a} - p_{v}) / R_{c}

. Summing the three equations verifies total mass conservation for incompressible blood.

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