// MODEL NUMBER: 0128
// MODEL NAME: Zinemanas1994_CoronaryCirc
// SHORT DESCRIPTION: 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.
JSim v1.1 import nsrunit; unit conversion on;
math CoronCirc_Zinemanas { realDomain t sec; t.min=0; t.max=5.0; t.delta=0.01;
/* SUBSCRIPTS:
ea = epicard art, la = large art, sa = small art, cap = capillary
sv = small veins, lv = large veins, ev = epicard veins, isf = interstitial fluid, ra = right atrium*/
real /* PARAMETERS: Resistances, R, and Compliances, C */ Rin = 0.001 s*mmHg/ml,
Rea = 4.2 s*mmHg/ml, Rla = 5.4 s*mmHg/ml,Rsa = 5.4 s*mmHg/ml, Rcap = 4.8 s*mmHg/ml,
Rsv = 4.2 s*mmHg/ml, Rlv = 3 s*mmHg/ml, Rev = 2.4 s*mmHg/ml, Rtot = Rin+Rea+Rla+Rsa+Rcap+Rsv+Rlv+Rev,
Cea = 0.08 ml/mmHg, Cla = 0.07 ml/mmHg, Csa = 0.8 ml/mmHg, Ccap = 0.25 ml/mmHg,
Csv = 0.5 ml/mmHg, Clv = 9 ml/mmHg, Cev = 0.65 ml/mmHg;
/* INPUTS */ extern real Paop(t) mmHg, Pisf (t); real Fin(t) ml/s, HR = 1 s^-1, Pra = 5 mmHg;
real /* STATE VARIABLES DEFINED: Segment Pressures, Flows and Volumes */
Pea(t) mmHg, Pla(t) mmHg,Psa(t) mmHg, Pcap(t) mmHg, Psv(t) mmHg, Plv(t) mmHg, Pev(t) mmHg,
Fea(t) ml/s, Fla(t) ml/s,Fsa(t) ml/s, Fcap(t) ml/s, Fsv(t) ml/s, Flv(t) ml/s, Fev(t) ml/s,
Vea(t) ml, Vla(t) ml, Vsa(t) ml, Vcap(t) ml, Vsv(t) ml, Vlv(t) ml, Vev(t) ml;
/* INITIAL CONDns */ when(t=t.min) {
Vea = 6.98; Vla = 5.48; Vsa = 4.28; Vcap = 7.70; Vsv = 7.3; Vlv = 7.2; Vev = 4.87; }
/* EQUATIONS */ Fin = (Paop-Pea)/Rin;
Fea = (Pea-Pla)/Rea; Fla = (Pla-Psa)/Rla; Fsa = (Psa-Pcap)/Rsa; Fcap = (Pcap-Psv)/Rcap;
Pea = (Vea/Cea); Pla = (Vla/Cla)+Pisf; Psa = (Vsa/Csa)+Pisf; Pcap = (Vcap/Ccap)+Pisf;
Vea:t = Fin-Fea; Vla:t = Fea-Fla; Vsa:t = Fla-Fsa; Vcap:t = Fsa-Fcap;
Fsv = (Psv-Plv)/Rsv; Flv = (Plv-Pev)/Rlv; Fev = (Pev-Pra)/Rev;
Psv = (Vsv/Csv)+Pisf; Plv = (Vlv/Clv)+Pisf; Pev = (Vev/Cev);
Vsv:t = Fcap-Fsv; Vlv:t = Fsv-Flv; Vev:t = Flv-Fev;
}
/* NOTES:
1. FUNCTION GENERATORS:
FOR PRESSURE, Paop(t) set fgen1 to 20*sin(2*pi*1*t +0.38) +100.
For ISF Pressure, Pisf(t) fgen2 to a half sine with Amp= 60 mmHg, e.g. Start=0; Duration-0.5;
Amp = 60; offset = 0; phase = 0; period = 1; Time to repeat =1.
2. If the interstitial fluid pressure is set too high negative volumes will appear in the large and
small veins compartments. The resistances downstream of these compartments are small, and the
compartment chamber pressures are low. Therefore, if the external pressures exceed the chamber
pressures over the course of the heart cycle, transmural pressures will be negative overall,
pushing more and more blood out of these compartments.
3. A more realistic pressure-volume curve that produces larger and larger negative pressures with very
small volumes would ensure that no negative volumes arose; however, with high interstitial fluid
pressure, endocardial venous volumes would remain collapsed, and these volumes would not be tunable.
-MNeal See Notes Tab for further points. JBB
DETAILED 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.
SHORTCOMINGS/GENERAL COMMENTS:
KEY WORDS: coronaries, coronary, circulation, intramyocardial pressure, cardiovascular system,
circulatory networks, Zinemanas, epicardial, endocardial, lumped parameter, Publication
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
REVISION HISTORY:
Original Author : Max Neal Date: jan/05
Revised by: JBB Data:29dec05 : for format
Revised by: Date:18may11 : Update comment format
COPYRIGHT AND REQUEST FOR ACKNOWLEDGMENT OF USE:
Copyright (C) 1999-2011 University of Washington. From the National Simulation Resource,
Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.
Academic use is unrestricted. Software may be copied so long as this copyright notice is included.
This software was developed with support from NIH grant HL073598.
Please cite this grant 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.
*/