(157e) Integral-Spectral Methods with Healthcare Applications: Cancerous Tumor Treatment, Hemodialysis, and Kidney Malfunction- Some Exciting Opportunities

Authors: 
Arce, P. E., Tennessee Technological University
Allred, A. N., Tennessee Technological University
Liu, Y. W., Tennessee Technological University
Sanders, J. R., Tennessee Technological University
Problems in healthcare (HC) applications often have complicated model equations which typically consist of linear aspects (transport-based) and non-linear aspects (kinetics or generation based). The equations are challenging to solve using traditional methods used in engineering. Integral-spectral methods (ISM) are a combination of integral equations and linear-operator methods and they are uniquely suited for decoupling the linear and non-linear aspects of these problems. The selected applications represent various levels of increasing mathematical complexity in the solving of the partial differential equations models using ISM. For instance, cancer tumor treatment via hyperthermia consists of a second-order, non-homogeneous partial differential equation with constant coefficients. The complexity increases when the problem of dialysis is introduced as variable coefficients (by way of a non-uniform hydrodynamic velocity) are now present, and these variable coefficients become even more complex when we study the electrokinetic-hydrodynamics in kidney malfunction. During the presentation, an overview of the mathematical-computational aspects of ISM will be presented and selected illustrated with applications to the HC examples mentioned above.