November 19, 2024, 1:00-2:00pm
Speaker: Dr. Elena Louca (The Cyprus Institute)
Title: Mixed boundary value problems for slow viscous flows: new transform methods and applications
Abstract: Motivated by microfluidics applications, where it is necessary to manipulate viscous fluids at small scales, we present a new transform method for solving mixed boundary value problems for biharmonic fields arising therein. The new method provides a unified general approach to finding quasi-analytical solutions to a variety of technologically important problems of slow viscous flows and leads to fast and accurate schemes for evaluating the solutions. The key ingredient of the method lies in the analysis of the so-called global relation, which couples integral transforms of the known boundary data with those of the unknown boundary values.
In this talk, we analyze viscous flow problems in polygonal and circular geometries and present recent advancements that extend the methodology to non-circular and non-convex geometries. To illustrate the power and versatility of our approach, we solve and numerically implement a number of mixed boundary value problems.
November 12, 2024, 1:00-2:00pm
Speaker: Dilmini Warnakulasooriya
(PhD student, GSU)
Title: Mechanisms of EADs in hypertrophic mouse ventricular myocytes: Insights from a mathematical model
Abstract: Compensated cardiac hypertrophy is considered as an adaptive response of the myocytes to increased workload and develops at early stages of heart failure. Experimentally, cardiac hypertrophy is induced by the procedure called transverse aortic constriction (TAC) during the first week after surgery. It is believed that during the early stage of hypertrophy the heart increases its function without adverse effects. To investigate cardiac hypertrophy, we developed a new comprehensive compartmentalized mathematical model of hypertrophic mouse ventricular myocytes that described the cell geometry, cardiac action potentials, [Ca2+]i transients, and β1- and β2-adrenergic signaling systems. Simulation results obtained with the hypertrophic cell model were compared to those from the control ventricular myocyte model. Our model simulations revealed the prolongation of the action potential, increased [Ca2+]i transients, and generation of pro-arrhythmic events called early afterdepolarizations (EADs) in hypertrophic myocytes as compared to control myocytes. We also demonstrated an important role of the late Na+ current INaL, the T-type Ca2+ current ICaT, the L-type Ca2+ current ICaL, and the slow component of the fast Na+ current INa in the hypertrophic cells in generation of EADs at relatively slow pacing rate (less than 1 Hz) and upon application of 1 μM of β-adrenergic agonist isoproterenol.
October 29, 2024, 1:00-2:00pm
Speaker: Sima Moshafi (PhD student, GSU)
Title: Understanding fouling mechanisms in pleated membrane filters: A simplified model
Abstract: Pleated membrane filters play a crucial role in diverse industries, offering enhanced filtration efficiency due to their increased surface area-to-volume ratio compared to flat filters. However, their performance is often compromised by fouling mechanisms, particularly cake formation, which can significantly impede flow and increase operational costs. This study introduces a mathematical model to explore these dynamics in a pleated filter cartridge, segmented into six key regions. By leveraging Darcy’s law, the Stokes equations, and an advection-diffusion-reaction model, we analyze how particle accumulation impacts fluid flow and particle transport through the filter. Through scaling and asymptotic analysis, we simplify the system to reveal critical insights into the interplay between filter geometry and fouling. Our findings underscore the importance of pleat design in managing cake formation and optimizing filtration performance, providing guidelines for enhancing filter efficiency across applications such as water purification, healthcare, and the food industry.
October 22, 2024, 1:00-2:00pm
Speaker: Somiya Rauf (PhD student, GSU)
Title: Immunogenic cell death: the key to unlocking the potential of combined immuno- and radiation therapy in cancer
Abstract: In cancer treatment, immunogenic cell death (ICD) triggered by irradiation or chemotherapy promotes the release of tumor-associated antigens, changes the tumor microenvironment, and activates the anti-tumor immune system response. Here, we develop a mathematical model to determine the role of ICD in combined, macrophage-based immunotherapy and radiotherapy, focusing on the SIRPα-CD47 pathway. The model is calibrated using tumor growth in preclinical murine models of SIRPα perturbation, with and without local irradiation. The model first dis- covers that radiotherapy invokes minimal ICD in tumors in wild-type mice, and that ICD depends on radiation dose and tumor size in SIRPα-deficient mice. ICD levels are highest in SIRPα-deficient mice, followed by injection of SIRPα-deficient macrophages in wild-type mice, then treatments of anti-SIRPα, anti-CD47, and finally CD47 knockout. The control group shows the lowest ICD. Analysis of the phagocytosis parameter reveals that SIRPα-deficient mice exhibit the highest phagocytic activity, resembling M1 phenotype, followed by CD47-knockout and SIRPα-deficient macrophage injections, anti-SIRPα, anti-CD47, while wild-type macrophages show no phagocytosis activity, indicative of an M2-like phenotype. Moreover, the model predicts the abscopal effect of the combined radio- and macrophage-based immuno- therapy. Using this calibrated model, we predict the treatment efficacy given radiation doses, macrophage phagocytosis capacity, and ICD strength, for various tumor sizes. The results highlight the critical role of ICD in capitulating the efficacy of the combined radio- and immuno-therapies and offer a new framework to better conceptualize and design optimal cancer treatment strategies.