Using Green’s Functions to Model Electrokinetic Flow in Tumor Cells for Tumor Treating Fields (TTF) Therapy

Tumor treating fields (TTF) therapy has recently emerged as a viable treatment for Glioblastoma Multiforme (GBM). This therapy uses frequency specific alternating current (AC) applied electrical fields to interfere with cell division by disrupting mitosis through prevention of tubulin polymerization. This treatment, however, remains unpredictable and a comprehensive mechanistic understanding of its effects on cells has yet to be achieved. The mathematical model presented here studies electroosmotic flows inside a single tumor cell during different cell cycle phases. Idealized descriptions of the cell geometries are employed with the electrokinetic hydrodynamics (EKHD) approach to obtain electroosmotic velocity profiles within the tumor cell under the influence of direct current (DC, limiting case) and AC electrical fields. The governing equations were solved both analytically, using Green’s Function approaches, as well as numerically. Various physiochemical and geometrical parameters were identified and varied to study their effects on the flow profiles, and it was found that the ratio between the electrical and viscous contributions to the flow had the largest impact on the profiles.