Archive : Applied Mathematics and Mathematical Medicine and Biology Seminar

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Richard Braun and Tobin Driscoll, Dept of Mathematical Sciences132Richard Braun and Tobin Driscoll, Dept of Mathematical Sciences336 Ewing Hall and on Zoom<p><strong>Mode:</strong> In-person and <a href="https://udel.zoom.us/j/98758622578%E2%80%8B" title="Join meeting">Zoom​</a><br><strong>Title:</strong> Fitting Models of Tear Film Thinning to Fluorsescence Data II: Extracted Data and Computed Results<br><strong>Abstract:</strong> We briefly review the methods and algorithms used to extract data from fluorescence movies of healthy eyes and to fit math models to that data (presented Sept 10th). We then show summary results for the pooled results for the population of subjects consisting of 467 instances of TBU, as well as results for individual subjects (26 to 50 instances per subject). The results represent a new baseline for understanding tear film dynamics in healthy subjects. A variety of approaches for understanding the results will be discussed, but we also aim to discuss additional approaches with the participants. In that sense, this seminar will be both discussion and seminar, and a bit like a workshop.<br></p>9/17/2021 2:10:00 PM9/17/2021 2:55:00 PM
Richard Braun, Dept of Mathematical Sciences131Richard Braun, Dept of Mathematical Sciences336 Ewing Hall and on Zoom<p>​<strong>Mode:</strong> In-person and <a href="https://udel.zoom.us/j/98758622578%E2%80%8B" title="Join meeting">Zoom​</a><br><strong>Title:</strong> Fitting Models of Tear Film Thinning to Fluorsescence Data: Models and Algorithms​<br><strong>Abstract:</strong> The tear film is a thin fluid multilayer left on the surface of the eye after a blink. A good tear film is essential for the health and proper function of the eye, yet millions of people have a condition called dry eye disease that inhibits sight and may lead to inflammation and ocular surface damage. There is a dearth of data about how the tear film fails, of called tear break up, or TBU. This is true in both healthy eyes and those with DED. We discuss methods to extract data from video of healthy eyes, and to estimate corresponding parameters in mathematical models for TBU. We then describe methods to automatically extract data from the videos via a deep learning approach, and to then fit simple models to the extracted data. The method has the potential to provide far more data, and more quantitative data, than has been previously available. We hope that it will provide baseline data for TBU in healthy subjects. The level of the presentation will be more like a colloquium than a detailed seminar, that is, accessible to a general technical audience.​<br></p>9/10/2021 2:10:00 PM9/10/2021 2:55:00 PM
Alison Marsden (Stanford)122Alison Marsden (Stanford)EWG336 Title:Patient-specific modeling for virtual treatment planning in pediatric cardiology <br><br> 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 PM3/3/2020 9:30:00 PM
Giovanna Guidoboni, University of Missouri130Giovanna Guidoboni, University of MissouriEWG336Title: Physically-based modeling for a virtual laboratory in Science and Engineering: theory and applications<br><br> 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 PM12/3/2019 9:30:00 PM

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