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# Pulmonary_Circulation_Olansen_et_al_2000

A model of pulmonary circulation based on Olansen et al. (2000) and Lu et al. (2001). A model of pulmonary circulation in which a right ventricle input pressure pulse drives blood flow through vascular components.

Model number: 0181

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## Description

This is a model of pulmonary circulation based on Olansen et al.
(2000) and Lu et al. (2001). A right ventricle input pressure
pulse drives blood flow through the following vascular components:
proximal pulmonary artery, distal pulmonary artery, pulmonary
arterioles, pumonary capillaries and pulmonary veins. All of
these compartments are modeled as windkessels, with single
resistance and compliance parameters. The proximal and distal
pulmonary artery segments are also characterized with inertance
parameters.
Parameter values for distal pulmonary inertance and radial
flow resistance were not provided in Lu et al. (2001)



Figure: Schematic representation of Pulmonary circulation model.

## Equations

$\large P_{PAP1} = \frac {R_{PUV}\cdot V_{PAP} + C_{TPAP}\cdot P_{RV}\cdot R_{TPAP} - R_{PUV}\cdot R_{TPAP}\cdot C_{TPAP}\cdot F_{PAP}}{C_{TPAP}\cdot(R_{TPAP}+R_{PUV})}$

$\large P_{PAP2} = \frac{V_{PAP} - C_{TPAP}\cdot R_{TPAP}\cdot F_{PAP}}{C_{TPAP}}$

$\large P_{PAP} = \{{P_{PAP1} \text if P_{RV}>P_{PAP1} \atop P_{PAP2} \text if P_{RV}\leq P_{PAP1}}$

$\large P_{PAD} = \frac{V_{PAD}}{C_{TPAD}}$

$\large P_{PA} = \frac{V_{PA}}{C_{PA}}$

$\large P_{PC} = \frac{V_{PC}}{C_{PC}}$

$\large P_{PV} = \frac{V_{PV}}{C_{PV}}$

$\large F_{RV} = \{{\frac{P_{RV}-P_{PAP}}{R_{PUV}}\text if P_{RV}>P_{PAP1} \atop 0 \text if P_{RV}\leq P_{PAP1}}$

$\large F_{PS} = \frac{P_{PA}-P_{PV}}{R_{PS}}$

$\large F_{PA} = \frac{P_{PA}-P_{PC}}{R_{PA}}$

$\large F_{PC} = \frac{P_{PC}-P_{PV}}{R_{PC}}$

$\large F_{PV} = \frac{P_{PV}-P_{LA}}{R_{PV}}$

$\large F_{TPAD} = F_{PAP}-F_{PAD}$

$\large F_{TPAP} = F_{RV}-F_{PAP}$

$\large F_{TPA} = F_{PAD}-F_{PS}-F_{PA}$

$\large F_{TPC} = F_{PA}-F_{PC}$

$\large F_{TPV} = F_{PC}+F_{PS}-F_{PV}$

$\large \frac {dV_{PAP}}{dt} = F_{TPAP}$

$\large \frac {dV_{PAD}}{dt} = F_{TPAD}$

$\large \frac {dV_{PA}}{dt} = F_{TPA}$

$\large \frac {dV_{PC}}{dt} = F_{TPC}$

$\large \frac {dV_{PV}}{dt} = F_{TPV}$

$\large \frac {dF_{PAP}}{dt} = \frac {P_{PAP}-P_{PAD}-F_{PAP}\cdot R_{PAP}}{L_{PAP}}$

$\large \frac {dF_{PAD}}{dt} = \frac {P_{PAD}-P_{PA}-F_{PAD}\cdot R_{PAD}}{L_{PAD}}$

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.

## References

Lu K, Clark JW, Ghorbel FH, Ware DL, Bidani A. A human cardiopulmonary system model
applied to the analysis of the Valsalva maneuver.  Am J Physiol Heart Circ Physiol.
281: H2661-H2679, 2001.

Olansen JB, Clark JW, Khoury D, Ghorbel F, Bidani A. A closed-loop
model of the canine cardiovascular system that includes ventricular
interaction. Computers and Biomedical Research. 33: 260-295, 2000.

Ohm GS. Die galvanische Kette mathematisch bearbeitet, 1827



## Related Models

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## Key Terms

Cardiovascular system, circulatory networks, pulmonary circulation, lumped parameter, Olansen, pulmonary arteries, pulmonary capillaries, pulmonary veins, pulmonary shunt, pulmonary blood flow

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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.

[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.