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# Zinemanas1994_CoronaryCirc

A lumped parameter model of the coronary circulation. A resistive-compliant network is used to simulate the following circulatory compartments: epicardial arteries, large coronary arteries, small coronary arteries, coronary capillaries, small coronary veins, large coronary veins, and epicardial veins.

Model number: 0128

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## Description

 Myocardial mechanics, perfusion and across-capillary mass transport are functionally related.
The effects of these interacting phenomena on the performance of the left ventricle (LV) are
investigated here. The effect of fluid balance on the diastolic and systolic intramyocardial
pressures (IMP) and the interstitial and myocardial volumes as well as the global ventricular
mechanics are of particular interest. The LV is approximated by a cylindrical geometry,
containing blood vessels imbedded in the interstitial fluid and a fibrous matrix with active
and passive elements. The coronary circulation is described by pressure dependent
resistance-capacitance analog elements. Fluid and mass transport are calculated assuming an
ideal semipermeable capillary wall and the lymphatic drainage depends linearly on the IMP.
Changes in lymphatic flow are used to simulate edema formation, and its effects on myocardial
mechanics and coronary flow. The empty beating and isovolumic contracting hearts are studied
under constant coronary perfusion pressures. The model successfully predicts the corresponding
changes of the coronary flow, the IMP, the LV pressure and the ventricular compliance.
The simulated effects of a transient contractile dysfunction on the dynamics of fluid
transport and coronary flow are in agreement with experimental data.



## Equations

$\large F_{IN} = \frac {P_{AOP}-P_{EA}}{R_{IN}}$

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

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

$\large F_{SA} = \frac {P_{SA}-P_{CAP}}{R_{SA}}$

$\large F_{CAP} = \frac {P_{CAP}-P_{SV}}{R_{CAP}}$

$\large F_{SV} = \frac {P_{SV}-P_{LV}}{R_{SV}}$

$\large F_{LV} = \frac {P_{LV}-P_{EV}}{R_{LV}}$

$\large F_{EV} = \frac {P_{EV}-P_{RA}}{R_{EV}}$

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

$\large P_{LA} = \frac {V_{LA}}{C_{LA}}+P_{ISF}$

$\large P_{SA} = \frac {V_{SA}}{C_{SA}}+P_{ISF}$

$\large P_{CAP} = \frac {V_{CAP}}{C_{CAP}}+P_{ISF}$

$\large P_{SV} = \frac {V_{SV}}{C_{SV}}+P_{ISF}$

$\large P_{LV} = \frac {V_{LV}}{C_{LV}}+P_{ISF}$

$\large P_{EV} = \frac {V_{EV}}{C_{EV}}+P_{ISF}$

$\large \frac{dV_{EA}}{dt} = F_{IN} - F_{EA}$

$\large \frac{dV_{LA}}{dt} = F_{EA} - F_{LA}$

$\large \frac{dV_{SA}}{dt} = F_{LA} - F_{SA}$

$\large \frac{dV_{CAP}}{dt} = F_{SA} - F_{CAP}$

$\large \frac{dV_{SV}}{dt} = F_{CAP} - F_{SV}$

$\large \frac{dV_{LV}}{dt} = F_{SV} - F_{LV}$

$\large \frac{dV_{EV}}{dt} = F_{LV} - F_{EV}$

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

 Zinemanas D, Beyar R, Sideman S. Relating mechanics, blood flow and mass transport in the
cardiac muscle. Int. J. Heat Mass Transfer. 37(suppl. 1) 191-205, 1994.

Ohm GS. Die galvanische Kette mathematisch bearbeitet, 1827



## Key Terms

coronaries, coronary, circulation, intramyocardial pressure, cardiovascular system, circulatory networks, Zinemanas, epicardial, endocardial, lumped parameter, Publication

## 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.