A tutorial review of mathematical techniques for quantifying tumor heterogeneity

Area of Science:

• Computational biology
• Mathematical modeling
• Precision medicine

Background:

• Intra-tumor and inter-patient heterogeneity pose significant challenges for developing accurate mathematical models in precision medicine diagnostics.
• Quantifying and inferring these sources of variation from patient data is crucial for advancing personalized treatments.

Purpose of the Study:

• To review and compare various mathematical techniques for inferring and quantifying intra-tumor and inter-patient heterogeneity.
• To provide a practical tutorial for mathematical modelers using simulated data and open-source code.

Main Methods:

• Review of established and emerging techniques: virtual populations, nonlinear mixed effects modeling, non-parametric estimation, Bayesian techniques, and machine learning.
• Simulation of virtual patient populations to generate datasets for method application.
• Comparative analysis of the strengths and weaknesses of four selected techniques (nonlinear mixed effects modeling, non-parametric estimation, Bayesian techniques, machine learning) applied to simulated data.

Main Results:

• The study highlights the distinct advantages and limitations of each mathematical technique when applied to simulated heterogeneous tumor data.
• Code and simulated datasets are provided to facilitate reproducible research and serve as a learning resource.

Conclusions:

• The reviewed mathematical techniques offer valuable tools for addressing tumor and patient heterogeneity in precision medicine.
• This work serves as a guide for modelers, promoting the development of more robust diagnostic and therapeutic strategies.