# 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

where V

_{V}, V

_{1}and V

_{2}are the volumes of the ventricle, vessel 1 and vessel 2 and F

_{V}, F

_{1}and F

_{2}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:

where P

_{v}, P

_{1}, P

_{2}, R

_{v}, R

_{1}and R

_{2}are pressures and resistances of the ventricle, vessel 1 and vessel 2 respectively. To keep flow in one direction through the ventricle, if P

_{v}is less than P

_{1}then F

_{v}is zero and if P

_{2}is less than P

_{v}then F

_{2}is zero. The pressures at P

_{1}and P

_{2}are derived from the definition of compliance:

so we have:

where V

_{1,rest}and V

_{2,rest}are the resting volumes of vessel 1 and vessel 2 respectively and P

_{ext}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.

## Download JSim model project file

## References

Ohm GS. Die galvanische Kette, mathematisch bearbeitet, 1827

## Related Models

- Resistive Element
- Compliant Element
- Single Vessel
- Pressure Driven Single Vessel
- Ventricle Driven Three Vessel

## Key Terms

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## Model History

Get Model history in CVS.Posted by: BEJ

## Acknowledgements

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The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

[This page was last modified 14Mar18, 3:17 pm.]

**Model development and archiving support at
physiome.org provided by the following grants:** NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, NIH/NIBIB BE08407 Software Integration,
JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ,
4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation,
8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer
Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior
support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass
Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973
JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.