Using non-linear analogue of Nyquist diagrams for analysis of the equation describing the hemodynamics in blood vessels near pathologies

All-Russian conference on Nonlinear Waves: Theory and New Applications

Cherevko, A.A.^1,2 ; Bord, E.E.^2 ; Khe, A.K.^1,2 ; Panarin, V.A.^3 ; Orlov, K.J.^3 ; Chupakhin, A.P.^1,2

Lavrentyev Institute of Hydrodynamics of the Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia^1

Novosibirsk State University, Novosibirsk, Russia^2

Meshalkin Research Institute of Blood Circulation Pathology, Novosibirsk, Russia^3

关键词: Arterial aneurysms;    Arteriovenous malformation;    Blood flow parameters;    Generalized models;    Hemodynamic parameters;    Properties of solutions;    Vascular pathology;    Vascular system;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/722/1/012005/pdf
DOI  :  10.1088/1742-6596/722/1/012005

来源: IOP

【 摘 要 】

This article considers method of describing the behaviour of hemodynamic parameters near vascular pathologies. We study the influence of arterial aneurysms and arteriovenous malformations on the vascular system. The proposed method involves using generalized model of Van der Pol-Duffing to find out the characteristic behaviour of blood flow parameters. These parameters are blood velocity and pressure in the vessel. The velocity and pressure are obtained during the neurosurgery measurements. It is noted that substituting velocity on the right side of the equation gives good pressure approximation. Thus, the model reproduces clinical data well enough. In regard to the right side of the equation, it means external impact on the system. The harmonic functions with various frequencies and amplitudes are substituted on the right side of the equation to investigate its properties. Besides, variation of the right side parameters provides additional information about pressure. Non-linear analogue of Nyquist diagrams is used to find out how the properties of solution depend on the parameter values. We have analysed 60 cases with aneurysms and 14 cases with arteriovenous malformations. It is shown that the diagrams are divided into classes. Also, the classes are replaced by another one in the definite order with increasing of the right side amplitude.