Ventricle_three_vessel_loop

Model number
0215

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:

e0

e1
e2

e3

where VV, V1, V2, and V3 are the volumes of the ventricle, vessel 1, vessel 2 and vessel 3 and FV, 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:

e4

e5

e6

e7

where Pv, P1, P2, P3, Rv, 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 Pv is less than P1 then Fv is zero and if P3 is less than Pv then F3 is zero. The pressures at P1, P2 and P3 are derived from the definition of compliance:

e8

so we have:
e9

e10

e11

where V1,rest, V2,rest and V3,rest are the resting volumes of vessel 1, vessel 2, and vessel 3 respectively and Pext 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.

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References
  Ohm GS. Die galvanische Kette, mathematisch bearbeitet, 1827
Key terms
RC Closed Loop Model
Varying Elastance
Ventricle
Resistance
Capacitance
Pressure
Flow
Circ3seg
Cardiovascular System
Hemodynamics
Tutorial
Acknowledgements

Please cite https://www.imagwiki.nibib.nih.gov/physiome in any publication for which this software is used and send one reprint to the address given below:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

Model development and archiving support at https://www.imagwiki.nibib.nih.gov/physiome 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.