Summary
The effect of pressure-dependent changes in vascular volume, resistance and capacitance in the coronary micro-circulation, has been studied by a distributed mathematical model of the coronary micro-vasculature in the left ventricular wall. The model does not include regulation of coronary blood flow and is evaluated only for the fully dilated coronary vasculature. The left ventricular wall was thought to consist of eight parallel layers, each of them with an arteriolar, capillary and venular compartment. The resistance of each vessel was thought to depend on the inverse of squared volume, according to Poiseuille's Law for tubes with constant length. Tissue pressure has been assumed to be equal to left ventricular cavity pressure at the endocardium and to decrease linearly to atmospheric level at the epicardium. The pressure-volume relation of the vessel compartments were assumed to be sigmoidal. There is a rest volume at transmural pressure zero and ΔV/ΔP decreases with increasing transmural pressure. Simulation of experimental protocols described by other authors yielded results which were similar to the experimental outcomes, illustrated by: (1) a parallel shift to the flow axis of the pressure-flow curves due to cardiac arrest (2) steady-state endo/epi ratio of flow as a function of heart rate. It is concluded that interpretation of transients in coronary flow and/or pressure by models containing fixed resistance and capacitance may seriously underestimate intramyocardial capacitative effects and characteristic time constants for pressure-induced resistance changes.
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References
Archie JP (1975) Intramyocardial pressure: effect of preload on transmural distribution of systolic coronary blood flow. Am J Cardiol 35:904–911
Arts MGJ (1978) A mathematical model of the dynamics of the left ventricle and the coronary circulation. Ph.D. Thesis, State University of Limburg, Maastricht, The Netherlands.
Arts T, Reneman RS, Veenstra PC (1979) A model of the mechanics of the left ventricle. Am Biomed Eng 7:299–318
Arts T, Reneman RS (1985) Interaction between intramyocardial pressure and myocardial circulation. J Biomech Eng 107:51–56
Bache RJ, Cobb FR (1977) Effect of maximal coronary vasodilation on transmural myocardial perfusion during tachycardia in the awake dog. Circ Res 41:648–653
Beyar R, Sideman S (1987) Time-dependent coronary blood flow distribution in left ventricular wall. Am J Physiol 252:H417-H433
Borg TK, Caulfield JB (1981) The collagen matrix of the heart. Fed Proc 40:2037–2041
Bruinsma P, Arts T, Spaan JAE (1985) Coronary pressure-flow characteristics in relation to the distensibility of the microvessels. Med Biol Eng and Comp 23 suppl II:1325–1326
Buckberg GD, Eixler DE, Archie JP, Henney RP, Hoffman JIE (1975) Variable effects of heart rate on phasic and regional left ventricular muscle blood flow in anaesthetized dogs. Cardiovasc Res 9:1–11
Canty JM, Klocke FJ, Mates RE (1985) Pressure and tone dependence of coronary diastolic input impedance and capacitance. Am J Physiol 248:H700-H711
Crystal GJ, Downey HF, Bashour FA (1981) Small vessel and total coronary blood volume during intracoronary adenosine. Am J Physiol 241:H194-H201
Dole WP, Alexander GM, Campbell AB, Hixson EL, Bishop VS (1984) Interpretation and physiological significance of diastolic coronary artery pressure-flow relationships in the canine coronary bed. Circ Res 55:215–226
Domenech RJ, Goich J (1976) Effect of heart rate on regional coronary blood flow. Cardiovasc Res 10:224–231
Domenech RJ (1978) Regional diastolic coronary blood flow during diastolic ventricular hypertension. Cardiovasc Res 12:639–645
Downey JM, Kirk ES (1975) Inhibition of coronary blood flow by a vascular waterfall mechanism. Circ Res 36:753–760
Downey HF, Bashour FA, Boatwright RB, Parker PE, Kechejian SJ (1975) Uniformity of transmural perfusion in anesthetized dogs with maximal dilated coronary circulations. Circ Res 37:111–117
Feigl EO (1983) Coronary physiology. Physiol Rev 63:1–205
Gregg DE, Green HD, Wiggers CJ (1935) Phasic variations in peripheral coronary resistance and their determinants. Am J Physiol 112:362–373
Gregg DE, Green HD (1940) Registration and interpretation of normal phasic inflow into a left coronary artery by an improved differential manometric method. Am J Physiol 130:114–125
Heineman FW, Grayson J (1985) Transmural distribution of intramyocardial pressure measured by micropipette technique. Am J Physiol 249:H1216–1223
Hoffman JIE (1981) Why is myocardial ischaemia so commonly subendocardial? Clin Sci 61:657–662
Kajiya F, Tsujioka K, Goto M, Wada Y, Chen X-L, Nakai M, Tadaoka S, Hiramatsu O, Ogasawara Y, Mito K, Tomonaga G (1986) Functional characteristics of intramyocardial capacitance vessels during diastoles in the dog. Circ Res 58:476–485
Klocke FJ, Mates RE, Canty jr JM, Ellis AK (1985) Coronary pressure-flow relationships: controversial issues and probable implications. Circ Res 56:310–323
Lee J, Chambers DE, Akizuki S, Downey JM (1984) The role of vascular capacitance in the coronary arteries. Circ Res 55:751–762
Myers WW, Honig CR (1964) Number and distribution of capillaries as determinants of myocardial oxygen tension. Am J Physiol 207:653–660
Smaje LA, Fraser PA, Clough G (1980) The distensibility of single capillaries and vessels in the cat mesentery. Microvasc Res 20:358–370
Spaan JAE, Breuls NPW, Laird JD (1981) Diastolic-systolic coronary flow differences are caused by intramyocardial pump action in the anesthetized dog. Circ Res 49:584–593
Spaan JAE, Breuls NPW, Laird JD (1981) Forward coronary flow normally seen in systole is the result of both forward and concealed back flow. Basic Res Cardiol 76:582–586
Spaan JAE (1985) Coronary diastolic pressure-flow relation and zero flow pressure explained on the basis of intramyocardial compliance. Circ Res 56:293–309
Spaan JAE, Bruinsma P, Vergroesen I, Dankelman J, Stassen HG (1987) Distensibility of microvasculature and its consequence on coronary arterial and venous flow. In: Sideman S, Beyar R (eds) Activation, metabolism and perfusion of the heart. Martinus Nijhoff Publishers, pp 389–407
Spaan JAE, Dankelman J (in press) Prediction of dynamic transcapillary pressure difference in the coronary circulation. In: Sideman S, Beyar R (eds) Analysis and simulation of the cardiac systemischemia. CRC Press, Inc
Weiss HR, Winbury MM (1974) Nitroglycerin and chromonar on small-vessel blood content of ventricular walls. Am J Physiol 220:838–843
Wiederhielm CA (1965) Distensibility characteristics of small bloodvessels. Fed Proc 24:1075–1084
Wüsten B, Buss DD, Deist H, Schaper W (1977) Dilatory capacity of the coronary circulation and its correlation to the arterial vasculature in the canine left ventricle. Basic Res Cardiol 72:636–650
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Supported by grants from the Foundation for Medical Research Medigon (grant 13-22-63) and Biophysics (grant 810-406-014).
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Bruinsma, P., Arts, T., Dankelman, J. et al. Model of the coronary circulation based on pressure dependence of coronary resistance and compliance. Basic Res Cardiol 83, 510–524 (1988). https://doi.org/10.1007/BF01906680
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DOI: https://doi.org/10.1007/BF01906680