Non-local parabolic and hyperbolic models for cell polarisation in heterogeneous cancer cell populations

TY - JOUR

T1 - Non-local parabolic and hyperbolic models for cell polarisation in heterogeneous cancer cell populations

AU - Bitsouni, Vasiliki

AU - Eftimie, Raluca

N1 - VB acknowledges support from an Engineering and Physical Sciences Research Council (UK) grant number EP/L504932/1. RE was partially supported by an Engineering and Physical Sciences Research Council (UK) grant number EP/K033689/1.

PY - 2018/10/1

Y1 - 2018/10/1

N2 - Tumours consist of heterogeneous populations of cells. The subpopulations can have different features, including cell motility, proliferation and metastatic potential. The interactions between clonal sub-populations are complex, from stable coexistence to dominant behaviours. The cell-cell interactions, i.e., attraction, repulsion and alignment, processes critical in cancer invasion and metastasis, can be influenced by the mutation of cancer cells. In this study, we develop a mathematical model describing cancer cell invasion and movement for two polarised cancer cell populations with different levels of mutation. We consider a system of non-local hyperbolic equations that incorporate cell-cell interactions in the speed and the turning behaviour of cancer cells, and take a formal parabolic limit to transform this model into a non-local parabolic model. We then investigate the possibility of aggregations to form, and perform numerical simulations for both hyperbolic and parabolic models, comparing the patterns obtained for these models.

AB - Tumours consist of heterogeneous populations of cells. The subpopulations can have different features, including cell motility, proliferation and metastatic potential. The interactions between clonal sub-populations are complex, from stable coexistence to dominant behaviours. The cell-cell interactions, i.e., attraction, repulsion and alignment, processes critical in cancer invasion and metastasis, can be influenced by the mutation of cancer cells. In this study, we develop a mathematical model describing cancer cell invasion and movement for two polarised cancer cell populations with different levels of mutation. We consider a system of non-local hyperbolic equations that incorporate cell-cell interactions in the speed and the turning behaviour of cancer cells, and take a formal parabolic limit to transform this model into a non-local parabolic model. We then investigate the possibility of aggregations to form, and perform numerical simulations for both hyperbolic and parabolic models, comparing the patterns obtained for these models.

KW - Aggregation patterns

KW - Alignment

KW - Cancer cells

KW - Cell–cell interactions

KW - Non-local hyperbolic model

KW - Parabolic limit

U2 - 10.1007/s11538-018-0477-4

DO - 10.1007/s11538-018-0477-4

M3 - Article

C2 - 30136211

SN - 0092-8240

VL - 80

SP - 2600

EP - 2632

JO - Bulletin of Mathematical Biology

JF - Bulletin of Mathematical Biology

IS - 10

ER -