In:
Journal of Mathematical Biology, Springer Science and Business Media LLC, Vol. 86, No. 1 ( 2023-01)
Abstract:
Cancer progression can be described by continuous-time Markov chains whose state space grows exponentially in the number of somatic mutations. The age of a tumor at diagnosis is typically unknown. Therefore, the quantity of interest is the time-marginal distribution over all possible genotypes of tumors, defined as the transient distribution integrated over an exponentially distributed observation time. It can be obtained as the solution of a large linear system. However, the sheer size of this system renders classical solvers infeasible. We consider Markov chains whose transition rates are separable functions, allowing for an efficient low-rank tensor representation of the linear system’s operator. Thus we can reduce the computational complexity from exponential to linear. We derive a convergent iterative method using low-rank formats whose result satisfies the normalization constraint of a distribution. We also perform numerical experiments illustrating that the marginal distribution is well approximated with low rank.
Type of Medium:
Online Resource
ISSN:
0303-6812
,
1432-1416
DOI:
10.1007/s00285-022-01846-9
Language:
English
Publisher:
Springer Science and Business Media LLC
Publication Date:
2023
detail.hit.zdb_id:
1421292-4
SSG:
12
