Modeliranje kretanja deformabilnog tela u fluidu i primena u biomedicinskom inženjeringu

Abstract

Kardiovaskularni sistem je jedan od najvažnijih sistema u ljudskom organizmu. Istraživanja strujanja krvi su klinički veoma značajna zbog mogućnosti poboljšane dijagnostike bolesti, planiranja odgovarajućih preventivnih mera, analize transporta lekova itd. Ove pojave se teško eksperimentalno ispituju i zbog toga u ovoj oblasti numeričke simulacije mogu da doprinesu dobijanju mnogo novih i korisnih informacija. U okviru ovog rada predstavljen je kompletan numerički model koji uspešno simulira trodimenzionalno strujanje krvi kroz krvne sudove u ljudskom organizmu. Ovo je pokazano na nekoliko primera, gde je modelirano strujanje krvi kroz ljudsku aortu, karotidnu i koronarnu arteriju. Takođe, predstavljen je numerički model koji simulira kretanje crvenih krvnih zrnaca i sfernih čestica kroz kompleksne geometrijske domene, kao što su mali krvni sudovi sa stenozom, bifurkacijom, kao i kroz mikrofluidne čipove za separaciju kancer ćelija, ali i kroz realne domene dobijene eksperimentalnim snimanjem protoka krvi kroz posebnu vrstu ribe, tzv. zebra ribu. S obzirom da jedan ovakav softver za naučne simulacije zahteva mnogo računarskih resursa i da izvršavanje jedne simulacije traje dosta dugo, prilikom implementacije numeričke metode posebna pažnja posvećena je tehnikama paralelizacije. Kompjuterski program je razvijan tako da pored rada na standardnim PC računarima, može da se izvršava i na kompjuterskim klasterima sa velikim brojem procesora, kao što su Tesla superkompjuteri, koje proizvodi svetska kompanija NVIDIA. Postignuta su značajna ubrzanja razvijenog softvera, tako da se numeričke simulacije mogu izvršavati za samo nekoliko minuta, naspram par sati koliko je potrebno za izvršavanje iste simulacije na standardnom PC računaru, što omogućava praktično interaktivno praćenje kretanja deformabilnih tela u realnom vremenu. Zbog numeričke metode koja dosta realno oslikava uslove u ljudskom organizmu, velike tačnosti koja je pokazana kroz poređenje sa eksperimentalnim rezultatima i brojnim drugim rešenjima iz literature, kao i zbog brzog izvršavanja na kompjuterskim klasterima, koje je omogućeno paralelizacijom, numerička metoda predstavljena u ovom radu i razvijeni softver imaju veliki potencijal kada je reč o praktičnoj primeni u simulacijama realnih problema u biomedicinskom inženjeringu.

Cardiovascular system is one of the most important systems in human organism. Investigation of blood flow is clinically very relevant due to the possibility of improved diagnostic of diseases, planning of appropriate preventive measures, analisys of drug transport etc. Experimental investigation of these phenomena is difficult and therefore numerical simulation can contribute to the acquisition of manu new and useful information. Within this dissertation a complete numerical model is presented, that is capable of simulating three-dimensional blood flow through the blood vessels in human organism. This is demonstrated on several examples, where blood flow through human aorta, carotid and coronary arteries is modelled. Also, numerical model that simulates solid-fluid interaction is presented and this model is used to simulate motion of red blood cells and spherical particles through complex geometric domains, such as small blood vessels with stenosis and bifurcation, as well as microfluidic chips for cancer cell separation and real domains obtained by experimental recording of blood flow through a specific type of fish, so called zebrafish. This type of software for numerical simulation requires a lot of computer resources and the execution of one simulation lasts quite long. Therefore, during the implementation of the numerical method, special attention was dedicated to parallelisation techniques. The software was developed such that beside execution on standarad PC computer, it is possible to execute the program on computer clusters with large number of processors, such as Tesla supercomputers, that are manufactured by the world known company NVIDIA. Significant speed-ups were obtained and numerical simulation can now be executed in several minutes, instead of several hours, which was the case when the same simulation was executed on standard PC computer. This enables interactive tracking of motion of deformable bodies in real time. Due to the numerical method that describes the conditions in human organism quite realistically, big accuracy of the solutions that was demonstrated through the comparison with experimental results and other results presented in literature and fast program execution on computer clusters that is enabled with parallelisation, the numerical model that is presented in this dissertation and the developed software have a great potential when it comes to practical application in modeling real phenomena in biomedical engineering.