Mathematical modelling of time-related blood velocity changes in human aorta

Abstract

Background. The paper deals with original blood velocity measurements in the human aorta, by Accuvix 30 measurement system, based on the Doppler effect. The results were processed by three different methods. First method, The first method is rel ated to the image of the laminar blood flow in the aorta. The time interval between two heart beats is defined for the blood flow velocity to be analyzed. A mathematical model is offered for the analysis of blood flow velocity data: the differential equation of the process, its solution, and the initial conditions. Second method. Also, deviations of the blood flow velocity are analyzed considering the main consistent pattern. A set of data describing actu al deviations ofblood flow velocity values from the theoretical trend established during the first processing of the measurement results is formed for this purpose. Analysis ofthese blood velocity fluctuations has revealed that the density function of the Fourier spectrum is modelled by the noise 1/fα where the index α = 0.722 is determined from actual measurements. Third method. Finally, upon assessing the blood velocity values, the Reynolds number of the blood flow is found, which is very far from the critical value Re = 2300. The blood velocity values should be 2.5–3 times higher for the features of a turbulent blood flow to manifesto Conclueions, To harmonize the laminar blood flow nature and the low Reynolds number with the low blood velocity fluctuations, the suggestion is made that this discrepancy may be caused by the superposition of laminar and turbulent flows at the micro level.

Išvados. Norint suderinti laminarinį kraujo srauto pobūdį ir mažą Reynoldso skaičitį bei negausini kraujo greičiu fliuktuacijų pobūdį, iškelta mintis, kad mikroskopiniame lygyje neatitikimą galėjo lemti laminarinio bei turbulentinio srautu superpozicijos.