This model simulates a closed loop resistor-capacitor network driven by a pressure generator (Pv). Volumes flow through a varying-elastance pressure generator component (simulating a contracting ventricle) and three compliant vessels in series.

Description

This model simulates a closed loop resistor-capacitor network driven by a pressure generator (Pv). Volumes flow through a varying-elastance pressure generator component (simulating a contracting ventricle) and three compliant vessels in series. The simulated ventricle has two one-way valves: one at either opening, but only one (Rv) offers resitance.

Equations

The governing equations are:

where V_V, V₁, V₂, and V₃ are the volumes of the ventricle, vessel 1, vessel 2 and vessel 3 and F_V, F₁, F₂ and F₃ are the volumetric flow rates in the ventricle, vessel 1, 2, and 3. The volumetric flows are determined from the fluid analog of Ohm's law:

where P_v, P₁, P₂, P₃, R_v, R₁, R₂ and R₃ are pressures and resistances of the ventricle, vessel 1, 2, and 3 respectively. To keep flow in one direction through the ventricle, if P_v is less than P₁ then F_v is zero and if P₃ is less than P_v then F₃ is zero. The pressures at P₁, P₂ and P₃ are derived from the definition of compliance:

so we have:

where V_1,rest, V_2,rest and V_3,rest are the resting volumes of vessel 1, vessel 2, and vessel 3 respectively and P_ext is the external pressure of the system. The volumes of vessel 1, vessel 2, and 3 are not allowed to become negative in these equations as enforced by condition statements given in the JSim code.

The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.