# Analysis of coronary circulation under ischaemic conditions

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## Abstract

Coronary flow patterns and pressure/flow relationships in coronary vessels with arterial stenoses are examined by using a model that combines the flow in the epicardial arterial tree with the intramyocardial perfusion. By using appropriate resistive elements, the model allows for the autoregulation of the vascular bed and for the development of coronary collaterals. Arterial flow predictions are compared to canine data. Coronary stenosis is simulated by a local pressure drop caused by a combination of viscous and inertial forces; stenosis with a constant cross-sectional area is compared to a dynamic stenosis in which the cross-sectional area is a function of the instantaneous transmural pressure. Simulation results predict that the normal phasic flow patterns in the epicardial arteries are unaffected up to 73% reduction in cross-sectional area, while the average flow remains unchanged up to 90% area reduction. At the critical level of 90% rigid stenosis, the autoregulation is saturated and the phasic nature of the arterial flow is severely damped. Dynamic stenoses demonstrate hysteresis loops of the instantaneous pressure/flow relationship. Theoretical predictions of local and global values are in excellent agreement with experimental measurements, indicating that the proposed approach can be used to realistically describe the coronary flow in the ischemic heart.

## Keywords

Autoregulation Collaterals Compliance Coronary circulation Coronary stenosis Dynamic stenosis Ischaemia Mathematical model Resistance## References

- Bove, A. A., Santamore, W. P., andCarey, R. A. (1983): ‘Reduced myocardial blood flow resulting from dynamic changes in coronary artery stenosis’,
*Int. J. Cardiol.*,**4**, pp. 301–313CrossRefGoogle Scholar - Brown, B. G., Bolson, E. L., andDodge, H. T. (1984): ‘Dynamic mechanisms in human coronary stenosis’,
*Circ.*,**70**, pp. 917–922Google Scholar - Cassanova, R. A., andGiddens, D. P. (1978): ‘Disorder distal to modeled stenoses in steady and pulsatile flow’,
*J. Biomech.*,**11**, pp. 441–453CrossRefGoogle Scholar - Chilian, W. M., Layane, S. M., Klausner, E. C., Eastham, C. L., andMarcus, M. L. (1989): ‘Redistribution of coronary microvascular resistance produced by dipyridamole’,
*Amer. J. Physiol.*,**256**, pp. H383-H390Google Scholar - Costantino, M. L., Fumero, R., and Inzoli, F. (1985): ‘Coronary flow dynamics in the presence of stenoses.’ XIV CCMBE and VII ICMP, Espoo, FinlandGoogle Scholar
- Eng, C., Jentzer, J., andKirk, E. S. (1982): ‘The effect of the coronary capacitance on the interpretation of diastolic pressure-flow relationships’,
*Circ. Res.*,**50**, pp. 334–341Google Scholar - Fujita, M., Sasayama, S., Ohno, A., Yamanishi, K., andHirai, T. (1987): ‘Functional significance of coronary collateral perfusion in preserving myocardial integrity’,
*Clin. Cardiol.*,**10**, pp. 394–398CrossRefGoogle Scholar - Fung, Y. C. (1981): ‘Biomechanics: mechanical properties of living tissues’, (Springer Verlag, New York)Google Scholar
- Gould, K. L. (1978): ‘Pressure flow characteristics of coronary stenosis in unsedated dogs at rest and during coronary vasodilation’,
*Circ. Res.*,**43**, pp. 242–253Google Scholar - Gould, K. L. (1985): ‘Quantification of coronary artery stenosis
*in vivo*’,*Circ. Res.*,**57**, pp. 341–353Google Scholar - Kajiya, F., Tsujioka, K., Goto, M., Wada, Y., Chen, X., Maki, M., Tadaoka, O., Hiramatsu, Y., Ogasawara, K., Mito, K., andTomonaga, G. (1986): ‘Functional characteristics of intramyocardial capacitance vessels during diastole in the dog,’
*Circ. Res.*,**58**, pp. 476–485Google Scholar - Klocke, F. J., andEllis, A. K. (1980): ‘Control of coronary blood flow’,
*Ann. Rev. Med.*,**31**, pp. 489–508CrossRefGoogle Scholar - Levine, D. C. (1974): ‘Pathways and functional significance of the coronary collateral circulation’,
*Circ.*,**50**, pp. 831–837Google Scholar - Manor, D., Sideman, S., Dinnar, U., andBeyar, R. (1993): ‘Analysis of the flow in the coronary epicardial arterial tree and intramyocardial circulation’,
*Med. Biol Eng. Comput.*Google Scholar - Marcus, M. L. (1983): ‘The coronary circulation in health and disease’, (McGraw-Hill, New York)Google Scholar
- Mates, R. E., Gupta, R. L., Bell, A. C., andKlocke, F. J. (1978): ‘Fluid dynamics of coronary artery stenosis’,
*Circ. Res.*,**42**, pp. 152–162Google Scholar - Rooz, E., Wiesner, T. F., andNerem, R. M. (1985): ‘Epicardial coronary blood flow including the presence of stenoses and aorto-coronary bypasses—I Model and numerical method’,
*J. Biomech. Eng.*,**107**, pp. 361–367CrossRefGoogle Scholar - Seeley, B. D., andYoung, D. F. (1976): ‘Effect of geometry on pressure losses across models of arterial stenoses’,
*J. Biomech.*,**9**, pp. 439–448CrossRefGoogle Scholar - Spaan, J. A. E. (1985): ‘Coronary diastolic pressure flow relation and zero flow pressure explained on the basis of intramyocardial compliance’,
*Circ. Res.*,**56**, pp. 293–309Google Scholar - Vergroesen, I. (1987): ‘Local regulation of coronary flow.’ Doctoral dissertation, University of AmsterdamGoogle Scholar
- Wang, J., Tie, B., Welkowitz, W., Kotis, J., andSemmlow, J. (1989): ‘Incremental network analogue model of the coronary artery’,
*Med. Biol. Eng. Comput.*,**27**, pp. 416–422CrossRefGoogle Scholar - Wyatt, D., Lee, J., andDowney, J. M. (1982): ‘Determination of coronary collateral flow by a load line analysis’,
*Circ. Res.*,**50**, pp. 663–670Google Scholar - Young, D. F., Cholvin, N. R., Kirkeeide, R. L., andRoth, A. C. (1977): ‘Hemodynamics of arterial stenoses at elevated flow rates’,
*Circ. Res.*,**41**, pp. 99–107.Google Scholar - Young, D. F., Cholvin, N. R., andRoth, A. C. (1975): ‘Pressure drop across artificially induced stenoses in the femoral arteries of dogs’,
*Circ. Res.*,**36**, pp. 735–743Google Scholar