Vascular Circulation Model

A full description of heart and circulation should account for all the various circulations in the body. Different organs have different ciculations, and also not always simply between artery and vene. So, the model shown in the figure is simplified, in fact, as simplified as possible. The left heart chamber pumps blood into the systemic arteries, starting with the aorta, from where it is distributed through the body and collected into (both sides of) the vena cava. The "body" is represented by a single Total Peripheral Resistance (TPR). The right heart chamber pumps blood into the lung arteries; again, both lung capillary systems are represented by a single pulmonary resistance R_P and the back flow by a combined venous return – into the left heart half.

Leg veins have valves as indicated in the figure but in a this simplified model these will be ignored.

As with the Basic Model, the relevant variables are pressures P, volume V and blood flow Q now for each compartment, Left and Right, and compliance C except both microcirculations, where the flow resistances are relevant. But we have a double system, with a doubled pump. Both heart chambers work with a pressure-volume loop as explained in the Basic model but the "lung" pump does so at much lower pressures, ~30 mmHg instead of 120 mmHg.

The equations now are:
- Arterial compliance: ΔP_aL = C_aLΔV_aL and ΔP_aR = C_aRΔV_aR
- Arterial volume change: dV_aL/dt = Q_H,outL − Q_L and dV_aR/dt = Q_H,outR − Q_R
- Microcirculation Resistances: P_aL − P_vL = Q_L×TPR and P_aR − P_vR = Q_R×R_P
- Venous volume changes: dV_vL/dt = Q_L − Q_H,inR and dV_vR/dt = Q_R − Q_H,inL
- Venous compliances: ΔP_vL = C_vLΔV_vL and ΔP_vR = C_vRΔV_vR

Some remarks:
- Again, a computer program is needed to solve for pressures and volumes.
- Both heart halves have their own Stroke Volume SV, but the system itself will fade out any difference. If, for instance, SV_L>SV_R, the systemic pressures will increase and more fill up the right heart half, increasing SV_R. This so-called Frank-Starling mechanism has the effect that both strokes volumes match, but it is not a regulation mechanism of the heart itself, as often misunderstood.

Back to the top of the topic
–