Biomedical subjects
Publications and source records attributed to M Zamir.
The branching angles and relative diameters of blood vessels in 51 arterial bifurcations in the retina of a normal human eye were measured. In eight other bifurcations, only the total branching angles were measured. The results are compared with theoretical predictions in an attempt to understand the physiological principles governing branching in the cardiovascular system.
The results of optimality studies of the branching angles of arterial bifurcations are extended to nonsymmetrical bifurcations. Predicted nonsymmetrical bifurcations are found to be not unlike those observed in the cardiovascular system.
What mathematical or physiological principles govern the radii of blood vessels in the cardiovascular system and by what mechanisms are those principles implemented? This question is studied in the contexts of fluid dynamics and physiology of the cardiovascular system, and a possible answer is examined in the light of empirical data.
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A new optimality principle for the branching angles of blood vessels in the cardiovascular system is proposed: the principle of minimum drag. The results are examined in the light of general observations and compared with those obtained from the principles of minimum work and minimum volume. It is shown that in some aspects the new principle is equally consistent with observations, and, in other aspects, it is perhaps more plausible than the other two principles.
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An analytical iterative scheme is presented for computing the local characteristics of pressure and flow waves as they progress along a tree structure and become modified by wave reflections. Results are obtained to illustrate the phenomenon of pressure peaking under two different sets of circumstances. In the first case, the propagation of a single harmonic wave along a simple tree is considered, where wave reflections modify the amplitude of the pressure wave as it travels. In the second case, the propagation of a composite wave along a tree with multiple branches is considered, where wave reflections modify the shape of the wave as it travels and cause it to peak. The results demonstrate unambiguously that the root cause of this phenomenon is wave reflections caused by stepwise decreases in admittance, as has been previously suggested, rather than due to nonlinear interactions, as has also been previously suggested. It is shown clearly that even when wave reflections combine linearly, they lead to considerable peaking in the pressure waveform.
The compression of blood vessels by surrounding tissue is an important problem in hemodynamics, most prominently in studies relating to the heart. In this study we consider a long tube of elliptic cross section as an idealization of the geometry of a compressed blood vessel. An exact solution of the governing equations for pulsatile flow in a tube of elliptic cross section involves Mathieu functions which are considerably more difficult to evaluate than the Bessel functions in the case of a circular cross section. Results for the velocity field, flow rate and wall shear stress are obtained for different values of the pulsation frequency and ellipticity, with emphasis on how the effects of frequency and ellipticity combine to determine the flow characteristics. It is found that in general the effects of ellipticity are minor when frequency is low but become highly significant as the frequency increases. More specifically, the velocity profile along the major axis of the elliptic cross section develops sharp double peaks; the flow rate is reduced in approximately the same proportion as in the case of circular cross section; and the point of maximum shear on the tube wall migrates away from the minor axis where it is located in steady flow.
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The vascular beds of 42 human hearts were examined to determine the underlying morpho-functional arrangement of the coronary arteries. The hearts were obtained at autopsy from cases where the immediate cause of death was not related to cardiovascular disease. It was found that while the course and size of individual vessels vary considerably from heart to heart, there is an underlying pattern in the functional arrangement of the vessels. On the basis of this pattern, a new functional classification of coronary arteries is proposed, together with a related concept of intrinsic "zones" of the myocardium. It is concluded that a deficiency in coronary blood supply in ischemic heart disease would be more accurately described in terms of the affected zones of the myocardium rather than the affected vessels. It is the effect of stenosis, not the stenosis per se, which must be assessed and documented ultimately. A chart is proposed to facilitate that documentation.