Modeliranje strujanja krvi u arterijskom stablu s viskoelastičnom stijenkom

Korade, Ivan (2017) Modeliranje strujanja krvi u arterijskom stablu s viskoelastičnom stijenkom. = Modeling of blood flow in an arterial tree with viscoelastic wall. Doctoral thesis , Sveučilište u Zagrebu, Fakultet strojarstva i brodogradnje, UNSPECIFIED. Mentor: Virag, Zdravko.

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Abstract (Croatian)

U današnjoj medicini sve više raste potreba za korištenjem matematičkog modeliranja strujanja krvi u cirkulacijskom sustavu radi boljeg razumijevanja nastanka kardiovaskularnih bolesti te pri planiranju operativnih zahvata. Ovdje je definiran jednodimenzijski matematički model pulsirajućeg strujanja krvi u velikim arterijama s viskoelastičnom stijenkom (Kelvin- Voight model), čija elastičnost može zavisiti od tlaka. Mikrocirkulacija je modelirana rubnim uvjetima pomoću Windkessel modela. Za rješavanje jednodimenzijskog modela razvijena je nova verzija numeričke metode karakteristika. Točnost metode provjerena je u četiri slučaja s poznatim rješenjem te na skupu referentnih testova korištenih u literaturi. Pokazano je da je metoda drugog reda točnosti i bezuvjetno stabilna. Razvijeni računalni program primjenjen je za analizu fenomena u arterijskom stablu. Kod analize promjene strmine tlačnog vala s udaljavanjem od srca kroz variranje parametara u modelu arterijskog stabla, zaključeno je da povećanju strmine doprinosi zavisnost brzine zvuka od tlaka. Kod objašnjenja pojave incizure u profilu tlaka, nakon zatvaranja aortnog zalistka, zaključeno je da viskoznost stijenke doprinosi nastanku i povećanju incizure u tlaku. Kod ocjene mogućnosti mjerenja parametara u viskoelastičnom modelu arterijske stijenke ispitano je šest metoda. Zaključeno je da frekvencijska metoda, s mjerenjima tlaka i površine poprečnog presjeka, daje najbolje rezultate u određivanju parametara arterijske stijenke i da je najmanje osjetljiva na unesenu pogrešku mjerenja.

Abstract

In today's medicine, there is a growing need for the use of mathematical modeling of blood flow in the circulatory system for a better understanding of cardiovascular diseases and for the planning of surgeries. Here is defined the one-dimensional mathematical model of the pulsatile blood flow in large arteries with viscoelastic wall properties (Kelvin-Voight model), where the elasticity can depend on pressure. The microcirculation is modelled by boundary conditions using the Windkessel model. To solve the one-dimensional model, a new version of numerical method of characteristics is developed. The accuracy of the method was tested on four cases with known solutions and a set of reference tests used in literature. It is shown that the method is the second order accurate and unconditionally stable. An in-house developed computer program was used to analyse the phenomenon in the arterial tree. When analysing changes in the slope of the pressure wave with increasing distances from the heart through the variation of parameters in the model of the arterial tree, it was concluded that the dependence of the speed of sound on the pressure contributes to increasing the pressure wave slope. In the explanations of the appearance of incisures in the pressure wave profile after the closure of the aortic valve, it is concluded that the wall viscosity contributes to the formation and increase of incisures in the pressure wave. In the assessment of the possibilities for the measurement of parameters in the model of a viscoelastic arterial wall six numerical schemes were tested. It was concluded that the frequency method, with measurements of the pressure and the cross-sectional area, gives the best results in the determination of the parameters of the arterial wall and that it is the least sensitive to the entered measurement error.

Item Type: Thesis (Doctoral thesis)
Uncontrolled Keywords: metoda karakteristika; Kelvin-Voigt model; Windkessel model; promjena strmine tlačnog vala; incizura u profilu tlaka; određivanje parametara arterijske stijenke
Keywords (Croatian): method of characteristics; Kelvin-Voigt model; Windkessel model; changes in the slope of the pressure wave; incisure in the pressure wave profile; determination of the parameters of the arterial wall
Subjects: TECHNICAL SCIENCE > Mechanical Engineering
Divisions: 500 Department of Energy, Power Engineering and Environment > 520 Chair of Fluid Mechanics
Date Deposited: 17 Mar 2017 10:02
Last Modified: 17 Mar 2017 10:02
URI: http://repozitorij.fsb.hr/id/eprint/7575

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