Modeliranje vremenskog dosega širenja lijeka kod stentova koji otpuštaju lijekove

master's thesis

• Author: Petra Ćutek
• Mentor: Josip Tambača (mentor)
• Committee member: Josip Tambača (predsjednik povjerenstva)
• Committee member: Boris Muha (član povjerenstva)
• Committee member: Ana Prlić (član povjerenstva)
• Committee member: Matko Ljulj (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2025-03-03, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics; Applied Mathematics and Mathematical Modeling

Abstract

U ovom diplomskom radu matematičkim modelom opisujemo otpuštanje lijeka iz premaza stenta koji otpušta lijekove u arterijsku stijenku. U početku opisujemo ulogu stentova koji otpuštaju lijekove. Potom izvodimo matematički model koji opisuje otpuštanje lijeka iz premaza stenta u arterijsku stijenku u dvije prostorne dimenzije. Također izvodimo slabu formulaciju te zadaće, kao i pojednostavljenja modela linearizacijom i smanjenjem prostorne domene na samo jednu dimenziju. Zatim diskretiziramo... More vremensku i prostornu domenu te uvodimo Newtonovu metodu za rješavanje nelinearnog člana zadaće polaznog modela. Naposljetku definiramo parametre modela, kojeg zatim rješavamo pomoću alata FreeFEM++ te uspoređujemo rješenja polaznog modela s rješenjima pojednostavljenja modela. Za kraj analiziramo utjecaje određenih parametara na rješenja modela. Less

Abstract (english)

In this Master Thesis, we describe drug release from the coating of drug-eluting stents using a mathematical model. We start by elaborating on the role drug-eluting stents (DES) have in medicine, after which we formulate a mathematical model that describes drug release from the coating of DES into the arterial wall using only two dimensions for the spatial variable. We also derive the weak formulation of the problem, as well as simplify the model through linearization and by reducing the... More spatial domain to only one dimension. Then, we discretize the time and the space domain, and introduce Newthon's method for solving nonlinear part of the equation. Finally, we define the parameters of the model, solve it using the FreeFEM++ tool, and compare the results of the model with those of the simplified models. Lastly, we analyze the influence of certain parameters on the numerical solutions. Less

• Keywords: stent; otpuštanje lijeka; numerička simulacija; metoda konačnih elemenata
• Keywords (english): stent; drug release; numerical simulations; finite element method
• Language: croatian
• URN:NBN: urn:nbn:hr:217:190208
• Study programme: Title: Applied Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: sveučilišni magistar matematike (sveučilišni magistar matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2025-02-10 19:58:52