Integrating Mathematical Modeling and Oncology: An Improvised Collocation Approach for Prediction of Chemotherapy...

Area of Science:

• Oncology
• Mathematical Biology
• Computational Science

Background:

• Cancer treatment response prediction is challenging due to complex spatio-temporal dynamics.
• Mathematical modeling offers a systematic approach to simulate tumor behavior under chemotherapy.
• Understanding these dynamics is crucial for evaluating therapeutic strategies.

Purpose of the Study:

• To develop and analyze a reaction-diffusion model for malignant tumor dynamics during chemotherapy.
• To implement a robust numerical scheme for simulating tumor growth and drug effects.
• To evaluate the accuracy and efficiency of the proposed computational method.

Main Methods:

• A reaction-diffusion model was employed to represent tumor-drug interactions.
• The Crank-Nicolson scheme discretized temporal derivatives, and an improvised cubic B-spline collocation method handled spatial derivatives.
• Nonlinearities were managed using the Rubin-Graves method, ensuring matrix diagonal dominance and consistent boundary conditions.
• Fourier spectral analysis was used for stability evaluation.

Main Results:

• Numerical simulations demonstrated the scheme's effectiveness under various treatment parameters.
• The computed solutions showed high accuracy and good agreement with existing literature.
• The method proved to be computationally efficient and easy to implement.

Conclusions:

• The proposed numerical approach provides an accurate and efficient method for simulating malignant tumor dynamics under chemotherapy.
• This reliable computational tool can aid in evaluating treatment outcomes and optimizing therapeutic strategies.
• The study highlights the potential of mathematical modeling in advancing cancer research and personalized medicine.