On a Mathematical Model Describing Chemotherapeutic Drug Treatment for Tumor Cells

TL;DR

This paper develops and analyzes a mathematical model of tumor-immune-drug interactions, demonstrating the effects of different chemotherapeutic scheduling strategies on tumor suppression and normal tissue preservation.

Contribution

It extends existing models by incorporating Allee effects and provides rigorous mathematical analysis along with simulation-based insights into treatment scheduling.

Findings

Pulsed treatment effectively suppresses tumor growth.

Frequent, gentle pulses preserve normal tissue better.

Model predicts rapid tumor invasion without treatment.

Abstract

In this paper, we study a semilinear parabolic PDE system which describes the interaction of normal cells, tumor cells, immune cells, with a chemotherapeutic drug. The model extends the previous model with incorporating strong Allee affects in the normal-tissue and tumor dynamics. Under mild assumptions, we establish global-in-time existence and uniqueness of nonnegative weak solutions and derive L-infinity bounds for all time. We then investigate spatiotemporal dynamics of the model and therapy scheduling using an implicit Crank Nicolson Backward Euler (CNBE) scheme. Simulations in a heterogeneous two-dimensional space-dimensional tissue region with three tumor peaks indicate rapid tumor invasion without treatment and significant tumor suppression under pulsed chemotherapeutic treatment. Moreover, in a fixed total dose delivered within the treatment cycle, while keeping each injection duration fixed, concentrated pulses produce stronger early knock-down of tumor density, while more frequent but gentler pulses achieve comparable control of the tumor invasive front while better preserving normal tissue over a four-week period.