Mathematical Modeling of Cancerous Tumor Evolution Incorporating Drug Resistance

ABSTRACT

Cancer is a deadly disease characterized by the uncontrolled growth and spread of abnormal cells. Tumors, the masses formed by these abnormal cells, can vary significantly in size, composition, and behavior. Understanding tumor dynamics is crucial for the development of effective treatments. A novel computational model is presented to analyze the evolution of tumor tissue over time, incorporating drug resistance and the convective mass flux of tumor cell movement for a more realistic representation of tumor dynamics. The governing equations are numerically solved using the finite difference method with forward‐time central‐space discretization. The predictive capabilities of the model were evaluated by investigating the impact of drug therapy on cell death and the sensitivity of the model's outcome to initial nutrient and drug concentrations. Key findings revealed that higher initial nutrient concentrations promote tumor growth, highlighting the importance of monitoring and managing nutrient levels in patients. The tumor consumes nutrients at a faster rate than they can diffuse inward, leading to nutrient gradients and potential necrosis in the core. High drug concentrations do not always correlate with increased cell death due to factors such as drug toxicity or resistance development. The relationship between drug concentration and cell death is nonlinear, suggesting that there might be an optimal drug concentration range to maximize efficacy. These insights offer valuable guidance for optimizing drug delivery and designing effective tumor control strategies. This study contributes to a deeper understanding of tumor growth and the development of more effective cancer treatments to improve patient outcomes. In addition, the proposed model serves as a valuable tool for researchers and clinicians to explore different treatment regimens and predict patient responses to therapy.