PubMed Health⌕ Search

Biomedical subjects

R Holenstein

Publications and source records attributed to R Holenstein.

5 recordsLinked to original sources
PubMed1990

Parametric analysis of flow in the intramyocardial circulation.

A simple mathematical model of the intramyocardial circulation has been utilized to provide a better understanding of coronary blood flow. The model includes three myocardial layers, each characterized by a three-parameter windkessel with one capacitance and two resistances. The effects of the beating heart are taken into account by means of an intramyocardial pump and the possible collapse of the vessels by an elevated backpressure. The three basic parameters that govern the flow are a normalized time constant, tau, the total resistance, Rt, and a parameter, alpha, which specifies the resistance distribution in the intramyocardial circulation. Both the normal beating heart and prolonged diastole have been investigated analytically as well as numerically. It is shown that each of these parameters has its own special significance. Calculated pressure-flow relationships and zero-flow pressures for the case of prolonged diastole show a high sensitivity to tau and alpha.

Animals↗
PubMed1988

Reverse flow in the major infrarenal vessels--a capacitive phenomenon.

The arterial blood flow waveform is shown to change abruptly when passing from the thoracic aorta into the abdominal aorta in humans. Although this change has been accurately predicted by numerical solution of complicated pulse propagation equations, this paper demonstrates the ability of a simple lumped parameter model to explain this change in the waveforms using easily understood physical terms. The model correctly predicts changes in flow waveform under conditions of exercise and peripheral vascular disease. This analysis is useful in understanding abdominal artery physiology and explains the basis for clinical ultrasound Doppler examination of the legs.

Aorta, Abdominal↗
PubMed1984

On the propagation of a wave front in viscoelastic arteries.

In formulating a mathematical model of the arterial system, the one-dimensional flow approximation yields realistic pressure and flow pulses in the proximal as well as in the distal regions of a simulated arterial conduit, provided that the viscoelastic damping induced by the vessel wall is properly taken into account. Models which are based on a purely elastic formulation of the arterial wall properties are known to produce shocklike transitions in the propagating pulses which are not observed in man under physiological conditions. The viscoelastic damping characteristics are such that they are expected to reduce the tendency of shock formation in the model. In order to analyze this phenomenon, the propagation of first and second-order pressure waves is calculated with the aid of a wave front expansion, and criteria for the formation of shocks are derived. The application of the results to the human arterial system show that shock waves are not to be expected under normal conditions, while in case of a pathologically increased pressure rise at the root of the aorta, shocklike transitions may develop in the periphery. In particular, it is shown that second-order waves never lead to shock formation in finite time for the class of initial conditions and mechanical wave guides which are of interest in the mammalian circulation.

Arteries↗
PubMed1980

A viscoelastic model for use in predicting arterial pulse waves.

In nonlinear mathematical models of the arterial circulation, the viscoelasticity of the vessel walls has generally been neglected or only taken into account in a highly approximate manner. A new method is proposed to simulate the nonlinear viscoelastic properties of the wall material with the aid of a convolution integral of the creep function and the pressure history. With this simulation it is possible to properly describe the measured characteristics of arterial viscoelasticity. Moreover, it is utilized in a mathematical model of arterial pulse propagation to study the influence of the internal wall friction on the shape, amplitude and mean value of pressure and flow pulses. The corresponding predictions are in much better agreement with in-vivo measurements, especially for the distal part of the circulation, than those obtained without viscoelasticity.

Animals↗