Low-rank tensor methods for Markov chains with applications to tumor progression models

Area of Science:

• Computational biology
• Cancer genomics
• Mathematical oncology

Background:

• Cancer progression is modeled using continuous-time Markov chains.
• Tumor genotype state space grows exponentially with somatic mutations.
• Tumor age at diagnosis is often unknown, necessitating time-marginal distributions.

Purpose of the Study:

• To develop a computationally feasible method for calculating time-marginal genotype distributions.
• To address the infeasibility of classical solvers for large linear systems in cancer modeling.
• To enable efficient analysis of tumor evolution dynamics.

Main Methods:

• Utilized separable functions in Markov chain transition rates for low-rank tensor representation.
• Developed a convergent iterative method based on low-rank formats.
• Applied numerical experiments to validate the approximation accuracy.

Main Results:

• Reduced computational complexity from exponential to linear.
• Achieved efficient low-rank tensor representation of the linear system operator.
• Demonstrated that the marginal distribution is well approximated by low-rank formats.

Conclusions:

• The proposed low-rank tensor method offers a computationally efficient solution for cancer progression modeling.
• This approach overcomes the limitations of classical solvers for large-scale cancer genotype analysis.
• Enables accurate approximation of time-marginal tumor genotype distributions.