International Conference on Spectral and High Order Methods
12th - 16th July 2021 | Vienna, Austria
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Please note that all times are shown in the time zone of the conference. The current conference time is: 8th Dec 2022, 11:34:10pm CET
MS 32: High Order Methods in Medical Applications
High order numerical methods have been proven to play a critical role in
various applications in science. Among those areas of applications, the medical applications must
be the most important and significant areas because they are directly related to human lives. Due
to high order accuracy, high order methods can serve as a superior analyzer for simulation of
biological phenomena and for medical judgment. In this mini-symposium, we plan to bring
together researchers in developing high order methods for the applications in medical sciences
and provide opportunities for them to share their recent progress and to discuss further
development. The subjects that this mini-symposium covers include discontinuous Galerkin
methods in neuroscience, spectral methods in vascular research, the combination of deep
learning approach and high order methods, high order methods in medical imaging,
multidimensional simulation and patient-specific electric flow map in cardiac electrophysiology.
12:00pm - 12:30pm
Conservative cut-cell discretization methods for brain source analysis
WWU Münster, Germany
Brain source analysis is an important tool in brain research. It is used for example during operation planing for epilepsy patients. Given EEG (electroencephalography) and MEG (magnetoencephalography) measurements the goal is to reconstruct the brain activity, i.e. the electric potential in the brain. This poses an inverse problem, but its accuracy strongly depends on the quality of the forward simulation, in particular the head model. We discuss how discontinuous Galerkin (dG) methods and cut-cell techniques can increase robustness of the forward problem and simplify the overall workflow.
12:30pm - 1:00pm
High Order Polygonal Staggered Discontinuous Galerkin Methods
1Yonsei University, Korea, Republic of (South Korea); 2Chinse University of Hong Kong
In this talk, we present a high order polygonal staggered discontinuous Galerkin method. The method can be flexibly applied to general grids such as highly distorted grids and the polygonal grids. In addition, the method allows non-matching grids on the interface. Some applications will be discussed such as Darcy-Forchheimer and Stokes problem, Darcy flows in fractured porous media, and the pseudostress formulation of Stokes problem.
1:00pm - 1:30pm
High-order time map for the electric flow in the heart and brain
1Yonsei University, Korea, Republic of Korea; 2POSTECH, Korea, Republic of Korea
A modern concept of time sees time as a sequence of events. Without a series of events, there is no time. An application of this idea to heart and brain’s electric flow propagation yields a scalar map, called time map, which has also been known as excitation time map or arrival time map. This time map provides the time when the applied current is above the threshold by diffusion in PDEs for the cell or a cell group, depending on the scale. Thus, a PDE is decomposed into ODEs and a time map. One important application of the time map is to compute the potential of the electric flow by computing its velocity and acceleration field. However, the time map is fundamentally a record of independent pointwise events and does not guarantee continuity nor differentiability with respect to its neighbors. This talk explains how to construct at least a second differentiable time map to derive a potential for the flow and how it can be used for fast 3D computations and spacetime analysis of flow patterns in the heart and brain.
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