A Population Balance Model of Cell Cycle-Specific Tumor Growth

Chemotherapeutics are often treated as having a lumped tumor effect; however, the growth state and exposure for individual cancer cells ultimately determines the response of the tumor to treatment. A multi-staged, age structured cell population balance equation (PBE) capable of cell-cycle tracking was formulated to account for this limitation. The method of orthogonal collocation on finite elements was used to decompose the original partial differential and algebraic equation formulation into a system of nonlinear ODEs with a renewal algebraic equation for age zero cells. The model was then adapted to include growth inhibitory effects and drug induced apoptosis specific to the S-phase for the testing of two theoretical drugs in adjuvant therapy. Simulations evaluated the delivery of apoptotic drug alone, or both drugs in combination. Increases in overall tumor reduction resulted from the adjuvant therapy, typical of results observed experimentally. Additional refinement is necessary regarding transition, division, and apoptotic intensity function construction prior to clinical application, but this model represents a feasible structure for describing distributed tumor progression with incorporated drug effect.