Analysis of pig’s coronary arterial blood flow with detailed anatomical data

Blood flow to perfuse the muscle cells of the heart is distributed by the capillary blood vessels via the coronary arterial tree. Because the branching pattern and vascular geometry of the coronary vessels in the ventricles and atria are nonuniform, the flow in all of the coronary capillary blood vessels is not the same. This nonuniformity of perfusion has obvious physiological meaning, and must depend on the anatomy and branching pattern of the arterial tree. In this study, the statistical distribution of blood pressure, blood flow, and blood volume in all branches of the coronary arterial tree is determined based on the anatomical branching pattern of the coronary arterial tree and the statistical data on the lengths and diameters of the blood vessels. Spatial nonuniformity of the flow field is represented by dispersions of various quantities (SD/mean) that are determined as functions of the order numbers of the blood vessels. In the determination, we used a new, complete set of statistical data on the branching pattern and vascular geometry of the coronary arterial trees. We wrote hemodynamic equations for flow in every vessel and every node of a circuit, and solved them numerically. The results of two circuits are compared: oneasymmetric model satisfies all anatomical data (including the meanconnectivity matrix) and the other, asymmetric model, satisfies all mean anatomical data except the connectivity matrix. It was found that the mean longitudinal pressure drop profile as functions of the vessel order numbers are similar in both models, but the asymmetric model yields interesting dispersion profiles of blood pressure and blood flow. Mathematical modeling of the anatomy and hemodynamics is illustrated with discussions on its accuracy.

[1]  G. Schmid-Schönbein,et al.  A theory of blood flow in skeletal muscle. , 1988, Journal of biomechanical engineering.

[2]  Y C Fung,et al.  Analysis of blood flow in cat's lung with detailed anatomical and elasticity data. , 1983, Journal of applied physiology: respiratory, environmental and exercise physiology.

[3]  Jos A. E. Spaan,et al.  Coronary Blood Flow , 1991, Developments in Cardiovascular Medicine.

[4]  C. Gans,et al.  Biomechanics: Motion, Flow, Stress, and Growth , 1990 .

[5]  S. Nellis,et al.  Modeling study on the distribution of flow and volume in the microcirculation of cat mesentery , 2006, Annals of Biomedical Engineering.

[6]  M. Marcus,et al.  Redistribution of coronary microvascular resistance produced by dipyridamole. , 1989, The American journal of physiology.

[7]  A. Popel,et al.  A Model of Pressure and Flow Distribution in Branching Networks. , 1980, Journal of applied mechanics.

[8]  T. A. Bronikowski,et al.  A hemodynamic model representation of the dog lung. , 1991, Journal of applied physiology.

[9]  I I Chen,et al.  A mathematical representation for vessel network. , 1982, Journal of theoretical biology.

[10]  E. Chang,et al.  Phorbol ester inhibition of chicken intestinal brush-border sodium-proton exchange. , 1991, The American journal of physiology.

[11]  E. vanBavel,et al.  Branching patterns in the porcine coronary arterial tree. Estimation of flow heterogeneity. , 1992, Circulation research.

[12]  J. Hoffman,et al.  Heterogeneity of myocardial blood flow , 1995, Basic Research in Cardiology.

[13]  B. Zweifach,et al.  Network analysis of microcirculation of cat mesentery. , 1974, Microvascular research.

[14]  M. Marcus,et al.  Microvascular distribution of coronary vascular resistance in beating left ventricle. , 1986, The American journal of physiology.

[15]  M. Marcus,et al.  Coronary microvascular resistance in hypertensive cats. , 1991, Circulation research.

[16]  W. Kubler,et al.  Pressure Measurements in the Terminal Vascular Bed of the Epimyocardium of Rats and Cats , 1981, Circulation research.

[17]  G S Kassab,et al.  Topology and dimensions of pig coronary capillary network. , 1994, The American journal of physiology.

[18]  G S Kassab,et al.  Coronary arterial tree remodeling in right ventricular hypertrophy. , 1993, The American journal of physiology.

[19]  I I Chen A mathematical representation for vessel networks II. , 1983, Journal of theoretical biology.

[20]  A. Pries,et al.  Blood flow in microvascular networks. Experiments and simulation. , 1990, Circulation research.

[21]  J H Halsey,et al.  Pressure Distribution in the Pial Arterial System of Rats Based on Morphometric Data and Mathematical Models , 1987, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

[22]  S. Nellis,et al.  Measurement of phasic velocities in vessels of intact freely beating hearts. , 1991, The American journal of physiology.

[23]  Jos A. E. Spaan,et al.  Coronary Blood Flow , 1991, Developments in Cardiovascular Medicine.

[24]  J. Gross,et al.  Network model of pulsatile hemodynamics in the microcirculation of the rabbit omentum. , 1974, The American journal of physiology.

[25]  J. Bassingthwaighte,et al.  Fractal Nature of Regional Myocardial Blood Flow Heterogeneity , 1989, Circulation research.

[26]  M Intaglietta,et al.  Blood pressure, flow, and elastic properties in microvessels of cat omentum. , 1971, The American journal of physiology.

[27]  J I Hoffman,et al.  Pressure-flow relations in coronary circulation. , 1990, Physiological reviews.

[28]  G S Kassab,et al.  Morphometry of pig coronary arterial trees. , 1993, The American journal of physiology.

[29]  G S Kassab,et al.  Morphometry of pig coronary venous system. , 1994, The American journal of physiology.

[30]  B. Fenton,et al.  Microcirculatory model relating geometrical variation to changes in pressure and flow rate , 1981, Annals of Biomedical Engineering.