Mathematical modeling of pulse wave propagation along human aorta

Abstract

Background: Physical characteristics of pulse waves, which are generated by the heart contractions and propagated along the arteries, are used in medicine for diagnostics of the blood circulation system and blood supply to the organs and tissues. At the sites with significant wave reflections the high local pressure oscillations appear that may lead to damage of the endothelium, development of atherosclerotic plaques and aortic aneurysm. Therefore, elaboration of a detailed biophysical model of the individual aorta based on tomography and determination of the dangerous sites with high wave reflections are important for medical diagnostics. Objectives: The aim of the work is to study the regularities of the pulse wave propagation and reflection along the aorta and to propose new methods for early diagnosis of disorders in the blood circulation system. Materials and methods: The measurement data on diameters and lengths of segments of aorta and its branches conducted on 5 corpses have been used. Calculations of the wave conduction and reflection coefficients are based on the linear theory of pulse waves developed by J. Lighthill. Results: It is shown that from the biophysical point of view, the aorta is an optimal waveguide, which provides almost zero local reflections of the pulse waves. Most of the branches possess negative reflection, which accelerates the blood flow and decreases the load on the heart due to the suction effect. The calculated values of the branching coefficients and pulse waves speeds correspond to the data of the previous experimental measurements. It is shown that most of the branches have an optimal Murray coefficient close to one. It implies, aorta also provides the optimal volumetric blood flow over the period of cardiac contraction with minimal energy expenses. Conclusions: Human aorta and its branches possess optimal biophysical properties, which ensure the blood flow with minimal energy consumption. Aorta as an optimal waveguide provides pulse wave propagation with almost without reflection. The proposed method of estimation of the biophysical properties of aorta as a waveguide can be useful for medical diagnostics, allowing early identification of the regions which are dangerous in terms of the progressive development of vascular pathologies in the individual geometry of the patient's vasculature.