Mathematical modeling and topology optimization in cardiology
| školitel: | doc. Ing. Radek Fučík, Ph.D. |
| e-mail: | zobrazit e-mail |
| typ práce: | dizertační práce |
| zaměření: | MI_MM |
| klíčová slova: | mathematical modeling, numerical methods, optimization, fluid flow, non-Newtonian fluid flow, cardiology |
| popis: | This topic deals with several applications of state-of-the-art mathematical modeling and optimization methods in cardiology in cooperation with Czech (IKEM) and US partners (Children's Healthcenter, UT SouthWestern Medical Center, Dallas). One of the main tasks is to optimize the shape of the idealized Total Cavopulmonary Connection (TCPC) used in cardiac surgery for children with congenital heart defects. TCPC involves the connection of major blood vessels to facilitate blood flow to a single functioning ventricle. The procedure is sensitive to energy losses caused by factors such as turbulent flow, which can lead to complications. Optimizing the shape of the extracardiac conduit to minimize energy loss and tissue stress is critical. The model can also be used for more accurate diagnosis of current state. This is a complex topic in terms of understanding the physical nature of the studied problem, mathematical description and implementation aspects with the possibility to use and improve existing software solutions developed for a long time at the Department of Mathematics of FJFI CTU in Prague. One of the main objectives of the PhD study will be to develop a suitable mathematical model of vascular flow and topology optimization framework, and at the same time to design and implement an efficient numerical method for its solution based on the lattice Boltzmann method. The next step will be the validation of the model in confrontation with measured data from flow MRI and intensive collaboration with experts from the above mentioned departments. Experimental magnetic resonance imaging (MRI) data are available thanks to a long-term collaboration between FNSPE CTU in Prague, IKEM Prague and UTSW, Dallas, Texas. The topic has an interdisciplinary nature and has a good publication potential. It has been also part of several project proposals by the advisor. |
| literatura: | [1] T. Krüger, et al., The lattice Boltzmann method: Principles and Practice. Springer International Publishing, 2017. [2] Z. Guo, S. Chang, Lattice Boltzmann method and its application in engineering. World Scientific, 2013. [3] J. D. Anderson, Computational Fluid Dynamics. McGraw-Hill series in mechanical engineering. McGraw-Hill Professional, 1995. [4] F. M. Rijnberg, et al., Energetics of blood flow in cardiovascular disease. Circulation,137(22), 2018, 2393–2407. [5] S. Boyd, L. Vandenberghe, Convex optimization. Cambridge University Press, 2004. [6] C. Audet a W. Hare. Derivative-free and blackbox optimization. Springer Series in Operations Research and Financial Engineering. Springer International Publishing, Cham, Switzerland, 1.edice, 2017. |
| naposledy změněno: | 06.12.2024 08:05:40 |
za obsah této stránky zodpovídá:
Ľubomíra Dvořáková | naposledy změněno: 12.9.2011