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Archive : Applied Mathematics and Mathematical Medicine and Biology Seminar

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Dr Ashutosh Khandha, Delaware Rehabilitation Institute, UD Dr Ashutosh Khandha, Delaware Rehabilitation Institute, UD Ewing 336Title: Knee biomechanical and biochemical variables early after anterior cruciate ligament reconstruction - mathematical modeling and experimentation. <br></br> <p>Abstract: Premature knee osteoarthritis (OA) after anterior cruciate ligament reconstruction (ACLR) is a growing concern in a young population. 30 % of subjects with ACLR have radiographic knee OA 5 years after surgery. Using experimental gait analysis and electromyography-informed mathematical neuromusculoskeletal modeling, we have seen that those with OA at 5 years can show inter-limb differences in “biomechanical” knee gait variables (joint loading and kinematics) as early as 6 months after surgery. Also, quantitative magnetic resonance imaging (qMRI) has the potential to detect “biochemical” OA related changes in the knee cartilage, earlier than radiographs. High values of cartilage T2 relaxation time, a qMRI time constant, can indicate early OA onset changes (collagen matrix degradation). Currently, it is not known whether both inter-limb differences in knee gait variables as well as cartilage T2 values are present as early as 3 months after ACLR. As the first step of a longitudinal study, we investigated these biomechanical and biochemical variables in 15 subjects, at both 3 and 6 months after ACLR. The overall goal of the study is to evaluate the changes in these variables over time (up to 2 years after ACLR) and to evaluate how soon can OA related changes be detected. The sooner the detection, the greater the potential for intervention to delay OA progression. </p>11/15/2017 7:30:00 PM11/15/2017 8:30:00 PMFalse
Andrew Bernoff, Mathematics, Harvey MuddAndrew Bernoff, Mathematics, Harvey MuddEWG 336Title: Energy driven pattern formation in thin fluid layers: The good, the bad and the beautiful <br></br> Abstract: A wide variety of physical and biological systems can be described as continuum limits of interacting particles. Many of these problems are gradient flows and their dynamics are governed by a monotonically decreasing interaction energy that is often non-local in nature. We show how to exploit these energies numerically, analytically, and asymptotically to characterize the observed behavior. We describe three such systems. In the first, a Langmuir layer, line tension (the two-dimensional analog of surface tension) drives the fluid domains to become circular and the rate of relaxation to these circular domains can be used to deduce the magnitude of the line tension forces. In the second, a Hele-Shaw problem, vexing changes in topology are observed. The third system models the formation of the convoluted fingered domains observed experimentally in ferrofluids for which pattern formation is driven by line tension and dipole-dipole repulsion. We show that noise in this system plays an unexpected but essential role and deduce an algorithm for extracting the dipole strength using only a shape's perimeter and morphology.10/18/2017 6:30:00 PM10/18/2017 7:20:00 PMFalse
Dr Hacene Boukari, Physics and Engineering, Delaware State UniversityDr Hacene Boukari, Physics and Engineering, Delaware State UniversityEwing 336Title: Measuring and Modeling Diffusional Processes in Biological Systems <br></br> <p>Abstract: Most biological processes occur and evolve in crowded macromolecular environments such as cells. They often involve diverse biomacromolecules that interact with each other within the host environment. However, our understanding of these interactions is commonly derived from studies in buffered solutions. My laboratory has focused on the development and application of fluorescence-based techniques to assess the effects of crowding on the translational and rotational diffusions of fluorescent nanoprobes. In particular, we have combined fluorescence fluctuation spectroscopy, fluorescence anisotropy, and time-lapse fluorescence confocal microscopy to measure the diffusion of simple fluorophores or fluorescent proteins embedded in polymeric systems and cells. In this talk, I will describe the results of studies of 1) movements (or not) of HIV-virions embedded in raw human cervical mucus, 2) interactions of GFP proteins in live-cells, and 3), if time allows, rotation/translation of nanoprobes in concentrated ficoll solutions. Challenging is modeling the data in order to determine or assess the dependence of relevant biophysical parameters (e.g. translational and rotational diffusion coefficients, binding constants, viscoelastic coefficients) on the dynamic environment. I will discuss our approach which is based on the relevant lengthscales of the processes, and describe our results. </p>10/4/2017 6:30:00 PM10/4/2017 7:30:00 PMFalse
Vu Dinh, Mathematical Sciences, UDVu Dinh, Mathematical Sciences, UDEWG 336Title: Consistency and convergence of phylogenetic regularization <br></br> <p>Abstract: Phylogenetics, the inference of evolutionary trees from molecular sequence data such as DNA, is an important enterprise enabling an evolutionary understanding of biological systems. The set of phylogenetic trees forms a space with discrete (graph structure) and continuous (branch lengths) components, and is modeled by a (non-differentiable) cubical complex. The resulting lack of manifold structure poses a problem to the uses of standard statistical methods on tree spaces. </p> <p>In this talk, I will discuss my recent work on regularized estimator for tree reconstruction, which uses the squared geodesic distance on tree space as an L2-type penalty. This estimator incorporates information about the species tree to enhance the accuracy and stability of individual gene trees estimation. Through the construction of this estimator, the talk aims to outline the main challenges in building a mathematical foundation for statistical analyses on tree spaces. </p>9/27/2017 6:30:00 PM9/27/2017 7:20:00 PMFalse

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