Estimating intratumoral heterogeneity from spatiotemporal data

Area of Science:

• Mathematical Biology
• Computational Neuroscience
• Oncology

Background:

• Glioblastoma multiforme (GBM) is an aggressive brain cancer characterized by significant cellular heterogeneity.
• Understanding GBM's migration and proliferation is crucial for effective treatment strategies.
• Existing models often simplify GBM as a homogeneous population, potentially limiting predictive accuracy.

Purpose of the Study:

• To develop and validate a novel mathematical model for glioblastoma multiforme (GBM) incorporating cell phenotype heterogeneity.
• To investigate the recovery of probability distributions for diffusion (D) and proliferation ([Formula: see text]) parameters using inverse problem methods.
• To compare the predicted efficacy of chemotherapy on heterogeneous GBM populations versus homogeneous models.

Main Methods:

• Utilized a random differential equation framework based on the reaction-diffusion equation to model GBM.
• Employed the Prohorov metric to perform the inverse problem, aiming to recover probability distributions of diffusion and proliferation parameters.
• Tested model performance with noisy synthetic data and simulated chemotherapy treatment effects.

Main Results:

• Successfully demonstrated the ability to recover probability distributions of diffusion (D) and proliferation ([Formula: see text]) from synthetic data.
• The inverse problem was solvable even with noisy data, indicating model robustness.
• Predictions for chemotherapy effects differed between heterogeneous and homogeneous GBM models, highlighting the impact of cell diversity.

Conclusions:

• Modeling glioblastoma multiforme (GBM) with heterogeneous cell phenotypes using random differential equations is feasible and provides valuable insights.
• The developed inverse problem approach can effectively recover key biological parameters governing GBM.
• Accounting for cellular heterogeneity in GBM models is essential for more accurate predictions of treatment response, particularly for chemotherapy.