Biomathematics
Department of Mathematics and Statistics
Texas Tech University
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biomath
2019
fall
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In this work, we study the effect of drug distribution on tumor cell death whenthe drug is internally injected in the tumorous tissue. We derive a full 3-dimensionalinhomogeneous – anisotropic diffusion model. To capture the anisotropic nature of thediffusion process in the model, we use an MRI data of a 35-year old patient diagnosedwith Glioblastoma multiform(GBM) which is the most common and most aggressiveprimary brain tumor. After preprocessing the data with a medical image processingsoftware, we employ finite element method in parallel setting to numerically simulatethe full model and produce dose-response curves. Finally we illustrate the apoptosis(cell death) fractions in the tumorous region over the course of the simulation. Sincethe model is built directly on the top of a patient-specific data, we hope that thisstudy will make a contribution to the individualized cancer treatment efforts from acomputational bio-mechanics viewpoint.
We investigate the clustering dynamics of a network of inhibitory interneurons, where each neuron is connected to some set of its neighbors. We use phase model analysis to study the existence and stability of cluster solutions. In particular,we describe cluster solutions which exist for any type of oscillator, coupling and connectivity. We derive conditions for the stability of these solutions in the case where each neuron is coupled to its two nearest neighbors on each side. We apply our analysis to show that changing the connection weights in the network can change the stability of solutions in the inhibitory network. Numerical simulations of the full network model confirm and supplement our theoretical analysis. Our results support the hypothesis that cluster solutions may be related to the formation of neural assemblies.