Biomedical subjects

M Zamir

Publications and source records attributed to M Zamir.

At least 19 recordsLinked to original sources

PubMed2001

Fractal dimensions and multifractility in vascular branching.

A definition for the fractal dimension of a vascular tree is proposed based on the hemodynamic function of the tree and in terms of two key branching parameters: the asymmetry ratio of arterial bifurcations and the power law exponent governing the relation between vessel diameter and flow. Data from the cardiovascular system, which generally exhibit considerable scatter in the values of these two parameters, are found to produce the same degree of scatter in the value of the fractal dimension. When this scatter is explored for a multifractal pattern, however, it is found that the required collapse onto a single curve is achieved in terms of the coarse Hölder exponent. Thus, the presence of multifractility is confirmed, and the legitimacy of the defined dimension is affirmed in the sense of the theoretical Hausdorff limit in as much as this limit can be reached with experimental data.

Animals↗

PubMed2001

Smaller, stiffer coronary bypass can moderate or reverse the adverse effects of wave reflections.

The question of whether the mechanical stiffness of a coronary bypass or that of a diseased coronary artery can have a significant effect on the hemodynamics in these vessels is addressed analytically, with emphasis on the effects of wave reflections. The analysis is based on a model of the vessels involved, and the results show the essential hemodynamic effects in each vessel. It is found that in the absence of a bypass graft, wave reflections resulting from a narrowing and stiffening of a diseased coronary artery have the effect of actually aiding the flow in the diseased vessel. In the presence of a bypass graft, however, the effects of wave reflections are reversed and become adverse to flow in both the bypass graft and the diseased coronary artery. A stiffer bypass moderates these effects and is therefore preferable to a more elastic bypass. The adverse effects also depend critically on the relative diameter of the bypass. Here the results indicate that a bypass of smaller diameter than that of the native coronary artery can moderate and even reverse the adverse effects of wave reflections resulting from the presence of the bypass.

Anastomosis, Surgical↗

PubMed2001

Arterial branching within the confines of fractal L-system formalism.

Parametric Lindenmayer systems (L-systems) are formulated to generate branching tree structures that can incorporate the physiological laws of arterial branching. By construction, the generated trees are de facto fractal structures, and with appropriate choice of parameters, they can be made to exhibit some of the branching patterns of arterial trees, particularly those with a preponderant value of the asymmetry ratio. The question of whether arterial trees in general have these fractal characteristics is examined by comparison of pattern with vasculature from the cardiovascular system. The results suggest that parametric L-systems can be used to produce fractal tree structures but not with the variability in branching parameters observed in arterial trees. These parameters include the asymmetry ratio, the area ratio, branch diameters, and branching angles. The key issue is that the source of variability in these parameters is not known and, hence, it cannot be accurately reproduced in a model. L-systems with a random choice of parameters can be made to mimic some of the observed variability, but the legitimacy of that choice is not clear.

Algorithms↗

PubMed1999

On fractal properties of arterial trees.

The question of fractal properties of arterial trees is considered in light of data from the extensive tree structure of the right coronary artery of a human heart. Because of the highly non-uniform structure of this tree, the study focuses on the purely geometrical rather than statistical aspects of fractal properties. The large number of arterial bifurcations comprising the tree were found to have a mixed degree of asymmetry at all levels of the tree, including the depth of the tree where it has been generally supposed that they would be symmetrical. Cross-sectional area ratios of daughter to parent vessels were also found to be highly mixed at all levels, having values both above and below 1.0, rather than consistently above as has been generally supposed in the past. Calculated values of the power law index which describes the theoretical relation between the diameters of the three vessel segments at an arterial bifurcation were found to range far beyond the two values associated with the cube and square laws, and not clearly favoring one or the other. On the whole the tree structure was found to have what we have termed "pseudo-fractal" properties, in the sense that vessels of different calibers displayed the same branching pattern but with a range of values of the branching parameters. The results suggest that a higher degree of fractal character, one in which the branching parameters are constant throughout the tree structure, is unlikely to be attained in non-uniform vascular structures.

Arteries↗

PubMed1998

Mechanics of blood supply to the heart: wave reflection effects in a right coronary artery.

Mechanics of blood flow in the coronary circulation have in the past been based largely on models in which the detailed architecture of the coronary network is not included because of lack of data: properties of individual vessels do not appear individually in the model but are represented collectively by the elements of a single electric circuit. Recent data from the human heart make it possible, for the first time, to examine the dynamics of flow in the coronary network based on detailed, measured vascular architecture. In particular, admittance values along the full course of the right coronary artery are computed based on actual lengths and diameters of the many thousands of branches which make up the distribution system of this vessel. The results indicate that effects of wave reflections on this flow are far more significant than those generally suspected to occur in coronary blood flow and that they are actually the reverse of the well known wave reflection effects in the aorta.

Animals↗

PubMed1996

Tree structure and branching characteristics of the right coronary artery in a right-dominant human heart.

The hierarchic branching tree structure of the right coronary artery in a right-dominant human heart is examined in terms of detailed measurements of lengths and diameters of the individual vessel segments comprising the structure. The results show that, while the right coronary artery in this heart does not supply a large portion of the posterior left ventricular wall, it nevertheless serves the left side of the heart to a greater extent than it does the right side in terms of the number and volume of vessel segments involved. The results show further that on the right side of this heart the right coronary artery exhibits clear features of a "distributing' vessel, but these features change abruptly as the vessel reaches the small region of the posterior left ventricular wall which it serves.

Anthropometry↗

PubMed1995

Mechanics of wave reflections in a coronary bypass loop model: the possibility of partial flow cut-off.

Local hemodynamics in a bypass loop model with dimensions typical of those in the human coronary circulation are studied, particularly with regards to the effects of wave reflections. While in a single vessel of such dimensions and a single source of wave reflections the effects would be insignificant, in a bypass loop the combination of a narrowed vessel with a converging junction and several reflection sites may produce wave reflections with significant effects on the pressure and flow distributions within the vessels forming the loop. Calculations to test this possibility were performed, based on D'Alembert's solutions of the wave equation and with a proposed matching scheme to deal with the converging junction. The results indicate that there are very large wave reflection effects at a frequency of 10 Hz, smaller but significant effects at 5 Hz, and some insignificant effects at 1 Hz. The results also indicate that partial flow cut-off may occur within the loop under some singular circumstances, whereby certain harmonic components of the incident wave are totally reflected. In the clinical setting these effects would detract from the efficiency of the bypass as a conduit, to a degree dependent on the degree of occlusion of the bypassed vessel. The choice of a larger diameter for the bypass appears to diminish this dependence and is thus on the whole favorable despite the contribution it makes to impedance mismatch at the junction.

Biomechanical Phenomena↗

PubMed1993

Reflection coefficients in pulsatile flow through converging junctions and the pressure distribution in a simple loop.

Analytical expressions for the reflection coefficients in pulsatile flow through converging junctions are derived by two independent methods and are used to study the effects of wave reflections on the pressure distribution in a simple vascular loop. A simulated physiological situation is used as an example in which the loop is formed by the combination of a bypass and a bypassed vessel, the relative diameter of the latter being varied in order to simulate a narrowing. The results demonstrate how, in the case of a converging junction, the effects of wave reflections on the pressure distribution in one vessel depend on conditions within the vessel itself as well as in the other. The new reflection coefficients take into account this interdependence of flow in the two vessels forming a converging junction, and are shown to be consistent with reflection coefficients commonly used in diverging junctions.

Aorta, Abdominal↗

PubMed1993

Velocity profiles and phasic flow patterns in the non-stenotic human left anterior descending coronary artery during cardiac surgery.

OBJECTIVE: The aim was to investigate the phasic characteristics of normal human left coronary artery flow and velocity profiles across the vessel. METHODS: The phasic characteristics of flow in the human left anterior descending coronary artery, the centreline flow velocities, and the velocity profiles were measured in 10 patients during corrective surgery for atrial septal defect after closure of the defect. None of these patients had any detectable coronary artery stenosis or left ventricular hypertrophy. Measurements were made with a 20 MHz 80 channel pulsed Doppler velocimeter. RESULTS: The velocity waveform displayed a diastolic-predominant pattern with a systolic to diastolic velocity ratio of 0.29(SD 0.17). Reverse flow was observed in early systole in five patients and in mid to late systole in six patients. The values of peak Reynolds number, unsteadiness parameter, and pulsatility index were 504(198), 2.5(0.6), and 5.9(4.4) respectively. The velocity profiles during diastole showed considerable variability in shape, ranging from symmetrical to skewed to M shaped patterns. The peak wall shear rate was 765(250) s-1 on the epicardial wall of the vessel and 712(301) s-1 on the myocardial wall; the difference was not statistically significant. CONCLUSIONS: The velocity waveform displayed a diastolic-predominant pattern. Considerable variability in shape of the velocity profile was found and was perhaps due to the time evolution of the velocity profile within the diastolic time period.

Adolescent↗

PubMed1992

Relation between diameter and flow in major branches of the arch of the aorta.

In the analysis of arterial branching the classical "cube law' has provided a working model for the relation between the diameter of a blood vessel and the flow which the vessel carries on a long-term basis. The law has shown good agreement with biological data, but questions remain regarding its applicability to all levels of the arterial tree. The present study tests the hypothesis that the cube law may not be valid in the first few generations of the arterial tree, where vessel capacitance and gross anatomy may play important roles. Biological data have shown some support for this hypothesis in the past but the heterogeneity characteristic of past data has not allowed a conclusive test so far. We present new data which have been obtained from the same location on the arterial tree and in sufficient number to make this test possible for the first time. Also, while past tests have been based primarily on correlation of the measured data with an assumed power law, we show here that this can be misleading. The present data allow a simpler test which does not involve correlation and which leads to more direct conclusions. For the vessels surveyed, the results show unequivocally that the relation between diameter and flow is governed by a 'square law' rather than the classical cube law. Coupled with past findings this suggests that the square law may apply at the first few levels of the arterial tree, while the cube law continues from there to perhaps the precapillary levels.

Adult↗

PubMed1992

'Hemorrhagic' and microvascular phenomena within the arterial wall.

OBJECTIVE: To study microvasculature and hemorrhage within the arterial wall. DESIGN: Human autopsy specimens of the arch of the aorta, the carotid, brachiocephalic, subclavian and coronary arteries perfused with liquid casting material and maintained at physiological pressure until the material had set. MAIN RESULTS: Evidence of dense microvasculature and other phenomena which have the morphological appearance of 'hemorrhage' within the arterial wall, coupled with calcified matter and other impressions made on the cast by atherosclerotic plaques. CONCLUSIONS: The findings lend support to suggestions in the literature that neovascularization may play a role in the pathogenesis of coronary atherosclerosis and its sequelae, that hemorrhage into the intima may be due to rupture of capillaries which are derived from the coronary lumen, and that an increase in microvasculature occurs in the immediate vicinity of localized atherosclerotic lesions.

Coronary Artery Disease↗

PubMed1992

[Vascular radiology and physics of fluids].

In the cardiovascular system, morphology and functionality are closely related. The observation that atherosclerotic lesions appear with different incidence in the various sites and prefer bifurcations, suggested that vascular architecture might be an important pathogenic factor. Vascular geometry deals with the evaluation of the "form" element from a theoretical point of a view, pointing out the angles and diameters which can make the arterial system physiologically more efficient. The key element of the system is the bifurcation: depending on whether bifurcations are considered as a single entity or as a whole, either "local" or "global" geometry is employed. The morphology of the bifurcation directly affects blood flow patterns, influencing both blood flow velocity and wall shear stress. Experimental studies evidenced that high blood flow velocities and low wall shear stress have, respectively, a preventive or favorable role in atheroma development. By observing these altered flow sites, the areas which are most likely to develop atherosclerotic damage have been detected in the various bifurcations; the areas correspond to angiographic and autoptic findings. Based on their experience, the authors discuss the contribution that the different imaging techniques can give to the study of vascular geometry.

Angiography↗

PubMed1991

Origin of the brachiocephalic trunk, left carotid, and left subclavian arteries from the arch of the human aorta.

We measured branching angles of the brachiocephalic trunk, left carotid, and left subclavian arteries at their points of origin from the arch in 117 human specimens. We compared the measured angles with theoretical values commonly used in the study of arterial branching, and examined possible correlations with age and with the presence of atherosclerotic lesions. The results may be useful in the modelling and analysis of hemodynamic factors in the pathogenesis of vascular disease at these junctions and may be of some interest in clinical angiography. The junctions are important gateways for blood supply to the head and upper limbs and often are involved with lesions that affect blood supply to the brain.

Adolescent↗

PubMed1990

Continuum analysis of common branching patterns in the human arch of the aorta.

A model is proposed for describing common variations in the arrangement of branches on the arch of the human aorta, and the model is used to analyze data from 123 human arches. The analysis allows the observed variations to fall freely along a continuous spectrum, rather than be confined to discrete categories as is commonly done at present. The results thus describe these variations in a more natural way and throw some new light on their likely source.

Aorta, Thoracic↗

PubMed1988

Roots and calibers of the human coronary arteries.

The anatomical structure of the coronary-aortic junctions in humans is studied by using corrosion casts of the coronary network. A model is proposed for the specification of these junctions in terms of vessel diameters and branching angles, and the model is used to produce morphological data on these junctions which hitherto have not been available. This anatomical model correlates poorly with the accepted theoretical model of arterial bifurcations in the cardiovascular system. The results suggest that the structure of the coronary-aortic junctions is very different from the structure of typical arterial bifurcations and, by implication, that the flow conditions under which they function are very different. A good understanding of these junctions is important in coronary bypass surgery, where the coronary-aortic junctions are emulated by creating a new anastomosis for the graft at the base of the ascending aorta, and in coronary artery disease, where atherosclerotic lesions occur not far from the coronary-aortic junctions.

Aorta↗

PubMed1988

Network analysis of an arterial tree.

The arterial tree of a Sprague-Dawley rat was casted and carefully mapped with the aim of comparing its network characteristics with those suggested by the classical model of an arterial tree. It is shown that if the tree is to be measured accurately, the concept of 'whole vessels' on which the classical model is based must be abandoned since such vessels do not actually exist in the network, nor can they be accurately defined. The concept of 'vessel segments' is proposed instead and its use is demonstrated. A total of 1313 vessel segments in the arterial tree of the rat are mapped and divided into well defined 'levels'. The length and diameter of each segment are measured and the distribution and averages of these at different levels are presented as indicators of the branching characteristics of the tree.

Animals↗

PubMed1988

Distributing and delivering vessels of the human heart.

The branching characteristics of the right coronary artery, acute marginal, posterior descending, left anterior descending, circumflex, and obtuse marginal arteries are compared with those of diagonal branches, left and right ventricular branches, septal, and higher-order branches, to test a newly proposed functional classification of the coronary arteries in which the first group rank as distributing vessels and the second as delivering vessels. According to this classification, the function of the first type is merely to convey blood to the borders of myocardial zones, while the function of the second is to implement the actual delivery of blood into these zones. This functional difference is important in the hemodynamic analysis of coronary heart disease, as it provides an assessment of the role of a vessel within the coronary network and hence an assessment of the functional importance of that vessel in a particular heart. Measurements from casts of human coronary arteries are used to examine the relevant characteristics of these vessels and hence to test the basis of this classification.

Arteries↗

PubMed1987

Morphometric analysis of the distributing vessels of the kidney.

Branching angles and branch diameters of the distributing vessels in the renal networks of rats were measured and the results are compared with data reported previously from the coronary network of the same species. Comparison is also made with what is known to be optimum on theoretical grounds to determine to what extent the branching characteristics of the renal network are governed by considerations of optimality, and to what extent they are affected by other considerations, relating particularly to the role that the network plays in the blood processing function of the kidney.

Animals↗