I use the Computer Graphics Laboratory facilities for many pharmacokinetic, pharmacodynamic, diffusion, and optimal control simulations. We are currently involved in two major areas of research: 1) optimal control theory applied to dosing drugs that exhibit tolerance and 2) the mapping of the GTN-induced cGMP tolerance kinetics (both development and recovery space). We have selected different pharmacokinetic/pharmacodynamic (PK/PD) models for tolerance and simulated these models. We have also run optimal simulations/calculations. The optimal surfaces describing an optimal dosing regimen for some given objective function can best be described by 2-D and 3-D plots. This work is done using the interactive graphics workstations in CGL. Now we are adding another mathematical model to the array of tolerance models. This model is still being developed and is based upon experimental work with LLC-PK1 cells and GTN. We have obtained some experimental results regarding the kinetic development of tolerance in this cell line. We are actively mathematically modeling this kinetic process and are doing simulations too. CGL resources allow us to do both the simulations and graphical mapping of our experimental data, as well as visual comparisions to the theoretically generated kinetic space.
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