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# Ventricle_Driven_Two_Vessel

This model simulates a closed loop resistor-capacitor circulatory network driven by a pressure generator (PV).

Model number: 0222

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## 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 two 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:

$\large \frac{dV_v}{dt} = F_2 - F_v$
$\large \frac{dV_1}{dt} = F_v - F_1$
$\large \frac{dV_2}{dt} = F_1 - F_2$

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

$\large F_v = \frac{P_v - P_1}{Rv}$
$\large F_1 = \frac{P_1 - P_2}{R1}$
$\large F_2 = \frac{P_2 - P_v}{R2}$

where Pv, P1, P2, Rv, R1 and R2 are pressures and resistances of the ventricle, vessel 1 and vessel 2 respectively. To keep flow in one direction through the ventricle, if Pv is less than P1 then Fv is zero and if P2 is less than Pv then F2 is zero. The pressures at P1 and P2 are derived from the definition of compliance:

$\large C = \frac{V-V_{rest}}{P-P_{ext}}$

so we have:

$\large P_1 = \frac{V_1 - V_1_{rest}}{C_1} + P_{ext}$
$\large P_2 = \frac{V_2 - V_2_{rest}}{C_2} + P_{ext}$

where V1,rest and V2,rest are the resting volumes of vessel 1 and vessel 2 respectively and Pext is the external pressure of the system. The volumes of vessel 1 and vessel 2 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 also 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.

## References

Ohm GS. Die galvanische Kette, mathematisch bearbeitet, 1827



## Key Terms

Ventricle, Driven, Two, Vessel, Loop, resistor-capacitor, pressure, flow, Circ2Seg, Tutorial, Cardiovascular system, Hemodynamics

## Model History

Get Model history in CVS.

Posted by: BEJ

## Acknowledgements

Please cite www.physiome.org in any publication for which this software is used and send an email with the citation and, if possible, a PDF file of the paper to: staff@physiome.org.
Or send a copy to:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.