A theoretical investigation of low frequency diameter oscillations of muscular arteries
| Autor: | H. Achak, Nikolaos Stergiopulos, Alexander Rachev, J.-J. Meister |
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| Rok vydání: | 1994 |
| Předmět: |
Materials science
Dynamical systems theory Differential equation Quantitative Biology::Tissues and Organs Physics::Medical Physics Biomedical Engineering Low frequency Instability Muscle Smooth Vascular Control theory Reference Values Oscillometry Active component medicine Shear stress Arterial wall Nonlinear Oscillations Mechanical instability Bifurcation Physics Steady state Nonlinear stability Models Cardiovascular Arteries Mechanics Biomechanical Phenomena Nonlinear system medicine.anatomical_structure Nonlinear Dynamics Calcium Vascular Resistance Stress Mechanical Artery |
| Zdroj: | Annals of Biomedical Engineering. 22:253-263 |
| ISSN: | 1573-9686 0090-6964 |
| DOI: | 10.1007/bf02368232 |
| Popis: | Spontaneous low frequency diameter oscillations have been observed in vivo in some muscular arteries. The aim of this paper is to propose a possible mechanism for their appearance. A lumped parameter mathematical model for the mechanical response of an artery perfused with constant flow is proposed, which takes into account the active behavior of the vascular smooth muscle. The system of governing equations is reduced into two nonlinear autonomous differential equations for the arterial circumferential stretch ratio, and the concentration of calcium ions, Ca2+, within the smooth muscle cells. Factors controlling the muscular tone are taken into account by assuming that the rate of change of Ca2+ depends on arterial pressure and on shear stress acting on the endothelium. Using the theory of dynamical systems, it was found that the stationary solution of the set of governing equations may become unstable and a periodic solution arises, yielding self-sustained diameter oscillations. It is found that a necessary condition for the appearance of diameter oscillations is the existence of a negative slope of the steady state pressure-diameter relationship, a phenomenon known to exist in arterioles. A numerical parametric study was performed and bifurcation diagrams were obtained for a typical muscular artery. Results show that low frequency diameter oscillations develop when the magnitude of the perfused inflow, the distal resistance, as well as the length of the artery are within a range of critical values. |
| Databáze: | OpenAIRE |
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