Differential properties of Van der Pol — Duffing mathematical model of cerebrovascular haemodynamics based on clinical measurements

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

Parshin, D.V.^1 ; Ufimtseva, I.V.^1,2 ; Cherevko, A.A.^1,2 ; Khe, A.K.^1,2 ; Orlov, K.Yu.^3 ; Krivoshapkin, A.L.^3 ; Chupakhin, A.P.^1,2

Lavrentyev Institute of Hydrodynamics of the Siberian Branch, Russian Academy of Sciences, Lavrentyev av 15, Novosibirsk

630090, Russia^1

Novosibirsk State University, Pirogova st 2, Novosibirsk

630090, Russia^2

E. N. Meshalkin Research Institute of Circulation Pathology, Rechkunovskaya st 15, Novosibirsk

630055, Russia^3

关键词: Arterial aneurysms;    Cerebral circulation;    Cerebral vessels;    Clinical measurements;    Differential properties;    Method of identifications;    Van der Pol-Duffing equation;    Vascular pathology;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/722/1/012030/pdf
DOI  :  10.1088/1742-6596/722/1/012030

来源: IOP

【 摘 要 】

The present paper discusses the method of identification (diseased/healthy) human cerebral vessels by using of mathematical model. Human cerebral circulation as a single tuned circuit, which consists of blood flow, elastic vessels and elastic brain gel tissue is under consideration. Non linear Van der Pol-Duffing equation is assumed as mathematical model of cerebrovascular circulation. Hypothesis of vascular pathology existence in some position of blood vessel, based on mathematical model properties for this position is formulated. Good reliability of hypothesis is proved statistically for 7 patients with arterial aneurysms.