A stochastic hierarchical model for low grade glioma evolution.

Area of Science:

• Mathematical Biology
• Computational Oncology
• Biophysics

Background:

• Low-grade gliomas can progress to high-grade gliomas.
• Understanding the mechanisms of glioma evolution is crucial for effective treatment.

Purpose of the Study:

• To develop a stochastic hierarchical model for glioma evolution.
• To investigate the relationship between microscopic cell dynamics and macroscopic tumor progression.
• To analyze factors influencing the transition from low-grade to high-grade gliomas.

Main Methods:

• Describing cell motion using a piecewise diffusion Markov process (PDifMP).
• Deriving transition probability density using the generalized Fokker-Planck equation.
• Developing a macroscopic model via parabolic limit and Hilbert expansions.
• Performing numerical tests to study tumor progression.

Main Results:

• The model links microscopic jump rates to macroscopic diffusion coefficients.
• Numerical tests reveal the role of local characteristics and PDifMP generator in tumor progression.
• Insights into how microscopic variations influence glioma cell diffusion and malignancy onset.

Conclusions:

• The proposed stochastic hierarchical model provides a framework for studying glioma evolution.
• Understanding the interplay between microscopic and macroscopic scales is key to predicting glioma progression.
• This model can inform strategies for targeting glioma malignancy transition.