Sep 23, 2014
Charles University in Prague, Faculty of Mathematics and Physics, Prague, Czech Republic Stenotic heart valve diseases are among the leading causes of death worldwide. A stenosis in the cardiovascular system is a reduction in cross-sectional area of a structure across which blood flows due to the plack or other incapabillities. Interventional and surgical treatments have provided improvements in survival, cardiac function, and functional capacity. Still, accurate and precise assessment of stenosis severity is required in order to appropriately decide whether and what type of treatment is warranted for a given lesion. Current approaches to interpreting non-invasive data are still incapable of ascertaining hemodynamic stenosis severity. Various methods have been used to evaluate stenoses by either anatomic or physiologic criteria. In this work, we develop an improved approach to determination of blood energy dissipation and pressure differences across cardiovascular stenoses, which can be applied to non-invasive diagnostic modalities. Even if we consider incompressible newtonian fluid in rigid wall, the problem is quite challenging. We will start with the flow in different geometries of the stenotic vessels to obtain the reference velocity field and pressure drop across the stenosis and compute corresponding dissipation. Finally, we discuss two approaches to obtain pressure from the measured velocity.
MOdelling REvisited + MOdel REduction Modeling, analysis and computing in nonlinear PDEs. September 21-26, 2014, Chateau Liblice, Czech Republic. Recently developed implicit constitutive theory allows one to describe nonlinear response of complex materials in complicated processes and to model phenomena in both fluid and solid mechanics that have hitherto remained unexplained. The theory also provides a thermodynamically consistent framework for technologically important but so far only ad hoc engineering models without sound footing. The overall goal of the project is to develop accurate, efficient and robust numerical methods that allow one to perform large-scale simulations for the models arising from the new theoretical framework. A natural part of the goal is rigorous mathematical analysis of the models. The nonstandard structure of constitutive relations arising from the new framework requires the reconsideration of many existing approaches in the mathematical theory of partial differential equations and the development of new ones. In particular, basic notions such as the concept of the solution and its well-posedness need to be reconsidered. Further, the complexity of the constitutive relations calls for rigorous investigation on model reduction - the identification of simplified models that capture the chosen (practically relevant) information about the behaviour of the system and disregard irrelevant information. Reliable numerical simulations require the derivation of sharp a posteriori error estimates to control all possible sources of errors, including rarely studied but important algebraic errors. We believe that in solving difficult problems in mathematical modelling the individual aspects discussed above - physics, mathematical analysis and numerical analysis - are so closely interrelated that no breakthrough can be achieved without emphasising the holistic approach as the main principle. Our vision is to follow this principle: the entire process of modelling of complex materials will be revisited in an innovative manner.
Professional recording and live streaming, delivered globally.
Presentations on similar topic, category or speaker