A Fokker-Planck Framework for Parameter Estimation and Sensitivity Analysis in Colon Cancer

Area of Science:

• Computational Biology
• Immunology
• Mathematical Oncology

Background:

• Colon cancer dynamics involve complex biological processes with inherent randomness.
• Accurate parameter estimation and uncertainty quantification are crucial for effective treatment strategies.
• Existing models may not fully capture the stochastic nature of tumor-immune interactions.

Purpose of the Study:

• To develop a novel stochastic framework for parameter estimation and uncertainty quantification in colon cancer-induced immune response.
• To model the inherent randomness in colon cancer dynamics using a stochastic process.
• To identify key parameters for therapeutic intervention through sensitivity analysis.

Main Methods:

• A stochastic framework based on the Fokker-Planck equation was developed to model the probability density function evolution.
• An optimization problem was formulated using individual patient data with inherent randomness.
• Sensitivity analysis was performed on the estimated parameters to identify critical control points.

Main Results:

• The framework successfully estimated unknown parameters related to individual tumor characteristics.
• Sensitivity analysis identified key parameters influencing the tumor-immune system dynamics.
• The study provides insights into parameters that require control for effective treatment.

Conclusions:

• The developed stochastic framework offers a robust method for parameter estimation and uncertainty quantification in colon cancer research.
• This approach can inform the development of personalized treatment strategies by identifying critical therapeutic targets.
• The findings highlight the importance of considering stochasticity in modeling tumor-immune interactions for improved clinical outcomes.