Coupled SDE-ODE Modeling of Tumor-Immune Dynamics to Infer Biomarker Release

Area of Science:

• Oncology
• Immunology
• Mathematical Biology

Background:

• Tumor-immune interactions are critical for cancer progression and treatment outcomes.
• Monitoring early-stage or residual cancer relies on noisy biomarkers like circulating tumor DNA (ctDNA).
• Current methods struggle to accurately infer tumor burden from low-concentration biomarker signals.

Purpose of the Study:

• To develop a robust mathematical framework linking tumor-immune dynamics to biomarker release.
• To provide a mechanistically interpretable and mathematically tractable method for inferring tumor burden from noisy biomarker data.
• To analyze how tumor heterogeneity, immune pressure, and noise structure affect biomarker detectability.

Main Methods:

• Developed a coupled deterministic-stochastic framework integrating a Lotka-Volterra predator-prey model for tumor-immune dynamics.
• Modeled biomarker production using stochastic differential equations with both square-root and multiplicative noise.
• Derived analytical expressions for biomarker trajectories and first-passage statistics, including mean detection times.

Main Results:

• Demonstrated how tumor heterogeneity, immune pressure, and noise characteristics jointly influence biomarker emergence and detectability.
• Showcased the framework's ability to infer tumor burden from noisy biomarker signals across various concentration regimes.
• Provided insights into the dynamics of biomarker release driven by immune-mediated apoptosis and necrosis.

Conclusions:

• The developed framework offers a foundation for improved tumor burden inference from noisy biomarker signals.
• Understanding the interplay of tumor biology, immune response, and stochasticity is key for accurate cancer monitoring.
• This approach enhances the interpretability and tractability of biomarker-based cancer detection and management.