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# Archive: Applied Mathematics and Mathematical Medicine and Biology Seminar

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 Alison Marsden (Stanford) 122 Alison Marsden (Stanford) EWG336 Title:Patient-specific modeling for virtual treatment planning in pediatric cardiology

Abstract: Cardiovascular disease is the leading cause of death worldwide, with nearly 1 in 4 deaths caused by heart disease alone. In children, congenital heart disease affects 1 in 100 infants, and is the leading cause of infant mortality in the US. Patient-specific modeling based on medical image data increasingly enables personalized medicine and individualized treatment planning in cardiovascular disease patients, providing key links between the mechanical environment and subsequent disease progression. We will discuss recent methodological advances in cardiovascular simulations, including (1) optimization and uncertainty quantification for surgical planning, and (2) a unified finite element formulation for fluid structure interaction towards fluid solid growth. Clinical application of these methods will be demonstrated in two applications: 1) a novel surgical method for stage one single ventricle palliation, and 2) virtual treatment planning in pediatric patients with peripheral pulmonary stenosis. We will also provide an overview of our open source SimVascular project, which makes our tools available to the scientific community (www.simvascular.org). Finally, we will provide an outlook on recent successes and challenges of translating modeling tools to the clinic. 3/3/2020 8:30:00 PM 3/3/2020 9:30:00 PM Giovanna Guidoboni, University of Missouri 130 Giovanna Guidoboni, University of Missouri EWG336 Title: Physically-based modeling for a virtual laboratory in Science and Engineering: theory and applications

Description: Physically-based models combine fundamental principles of physics, engineering, mathematics and scientific computing to provide qualitative and quantitative assessments of the mechanisms governing the behavior of complex systems. The utilization of physically-based models to study living systems helps disentangle the interaction among coexisting (often competing) factors that is not possible to single out in experimental and clinical studies. Thus, physically-based models can serve as a virtual laboratory where multiple scenarios can be simulated, conjectures can be tested and new hypotheses can be formulated. This talk will present two particular applications of physically-based models. The first application aims at characterizing changes in ocular hemodynamics due to alterations in intraocular pressure (IOP), blood pressure (BP) and vascular autoregulation (AR) of each individual. The knowledge on interacting factors gained via physically-based models can also be used as a guide for the statistical analysis of clinical data for more informative outcomes, as shown by the Singapore Epidemiology of Eye Diseases study, where our theoretical predictions on the interplay between IOP and BP have been confirmed on nearly 10,000 people. The second, more recent, application aims at elucidating the cardiovascular mechanisms giving rise to the ballistocardiogram (BCG). BCG is a signal generated by the repetitive motion of the human body due to sudden ejection of blood into the great vessels with each heartbeat. Main cardiovascular diseases, such as hypertension and congestive heart failure, have been shown to alter the BCG signal, which then yields a great potential for passive, noncontact monitoring of the cardiovascular status (e.g. through sensors positioned under the bed or on an armchair). Our work aims at standardizing BCG measurements in order to achieve a consistent clinical interpretation of the BCG signal across sensing devices. Interestingly, the need to address specific questions arising in the applied sciences calls for the theoretical study of new mathematical problems and computational methods. Examples discussed in this talk include: (i) well-posedness of partial differential equations of mixed parabolic/elliptic type with nonhomogeneous boundary conditions utilized to describe the perfusion of deformable tissues; and the (ii) energy-preserving numerical algorithms based on operator splitting to simulate multiscale problems. 12/3/2019 8:30:00 PM 12/3/2019 9:30:00 PM Shawn Walker, Louisiana State University 124 Shawn Walker, Louisiana State University EWG336 Title: The Uniaxially Constrained Q-tensor Model for Nematic Liquid Crystals

Abstract: We consider the one-constant Landau-de Gennes (LdG) model for nematic liquid crystals with traceless tensor field Q as the order parameter that seeks to minimize a Dirichlet energy plus a double well potential that confines the eigenvalues of Q (examples/applications will be described). Moreover, we constrain Q to be uniaxial, which involves a rank-1 constraint. Building on similarities with the one-constant Ericksen energy, we propose a structure-preserving finite element method for the computation of equilibrium configurations. We prove stability and consistency of the method without regularization, and $\Gamma$-convergence of the discrete energies towards the continuous one as the mesh size goes to zero. We also give a monotone gradient flow scheme to find minimizers. We illustrate the method's capabilities with several numerical simulations in two and three dimensions including non-orientable line fields. In addition, we do a direct comparison between the standard LdG model, and the uniaxially constrained model. 11/19/2019 8:30:00 PM 11/19/2019 9:30:00 PM Daniela Egas, EPFL 127 Daniela Egas, EPFL EWG336 Title: Topology and neuroscience

Abstract: I will broadly present some of the applications of topology and topological data analysis to neuroscience through an exploration of the collaboration between the applied topology group at EPFL and the Blue Brain Project. In particular, I will describe how we are using topology to further understand brain architectures, learning and neuroimaging techniques. 11/18/2019 8:30:00 PM 11/18/2019 9:30:00 PM