Modeliranje biofizike srčanog mišića

master's thesis

• Title (english): Modeling of cardiac muscle biophysics
• Author: Vinko Dragušica
• Mentor: Andrej Novak (mentor)
• Committee member: Andrej Novak (predsjednik povjerenstva)
• Committee member: Matko Glunčić (član povjerenstva)
• Committee member: Vedran Đerek (član povjerenstva)
• Committee member: Danko Radić (član povjerenstva)
• Committee member: Nenad Pavin (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2024-02-23, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

U radu je predstavljen princip rada srčanog mišića, pojam elektrokardiograma i akcijskog potencijala. Matematički je izveden dvodomenski model te potom i jednodomenski model kao aproksimacija dvodomenskog. Zatim je pokazan algoritam Strangove podjele kojim se modeli mogu numerički riješiti te je izvedena varijacijska/slaba formulacija jednadžbi. Prikazani su dobiveni rezultati za pravokutnu domenu s reparametriziranim FitzHugh-Nagumo modelom, Nobleovim modelom i Beeler-Reuter modelom. Rezultati modela na domeni presjeka srca uspoređeni su s literaturom. Na jednakoj domeni modelirana je lokalna ishemija srca te su prezentirana rješenja takvog modela. Uspoređena su rješenja jednodomenskog i dvodomenskog modela i pokazano je rješenje dvodomenskog modela na trodimenzionalnoj domeni lijeve klijetke.

Abstract (english)

This thesis presents the physiology of the heart muscle, the concept of the electrocardiogram, and action potential. The bidomain model and subsequently the mo nodomain model, as an approximation of the bidomain model, are mathematically derived. Then, the Strang operator splitting scheme, which is used to solve the models numerically, is shown, and the variational/weak form of the equations is derived. The results obtained for the rectangular domain with the reparameterized FitzHugh-Nagumo model, the Noble model, and the Beeler-Reuter model are presented. The results of the model on the heart cross-section domain are compared with the literature. Local ischemia was added to the same domain, and solutions for such a model are presented. The solutions of the monodomain and bidomain models are compared, and the solutions of the bidomain model on the three-dimensional domain of the left ventricle are shown.

• Keywords: srce; dvodomenski model; jednodomenski model; metoda konačnih elemenata; FEniCSx; dolfinx
• Keywords (english): heart; bidomain model; monodomain model; finite element method; FEniCSx; dolfinx
• Language: croatian
• URN:NBN: urn:nbn:hr:217:765379
• Study programme: Title: The University Integrated Undergraduate and Graduate Programme in Physics; Research Physics; specializations in: Research Physics; Course: Research Physics; Study programme type: university; Study level: integrated undergraduate and graduate; Academic / professional title: sveučilišni magistar fizike (sveučilišni magistar fizike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Embargoed access; Embargo expiration date: 2024-07-23
• Created on: 2024-04-05 12:17:34