Biophysical Simulation & Nonlinear Diffusion Modeling
Developed advanced mathematical simulations of oxygen and volatile anesthetic (isoflurane) diffusion from the vasculature to surrounding cellular structures. This involved engineering a nonlinear diffusion model of the neurovascular unit to analyze anesthetic delivery kinetics. The computational workflow required applying linear regression and complex parameter optimization to fit real-world in vivo data to Gaussian distributions. These custom biophysical models were rigorously validated against experimental data to test hypotheses regarding hypoxia-induced neural activity and delivery kinetics, culminating in first-author scientific publication.