Spatial cumulant models for mathematical cancer research

Abstract: Spatial cumulant models (SCMs) are spatially resolved population models, formulated by differential equations, that describe population dynamics generated by spatio-temporal point processes (STPPs). Specifically, SCMs approximate the dynamics of two STPP-generated summary statistics: first-order spatial cumulants (densities), and second-order spatial cumulants (spatial covariances).

In this talk, I’ll exemplify how SCMs can be used in mathematical oncology by modelling theoretical cancer cell populations comprising interacting subclones. Our results demonstrate that SCMs can capture STPP-generated population density dynamics, even when mean-field population models (MFPMs) fail to do so. From both MFPM and SCM equations, we derive treatment-induced death rates required to achieve non-growing cell populations. When testing these treatment strategies in STPP-generated cell populations, our results demonstrate that SCM-informed strategies outperform MFPM-informed strategies in terms of inhibiting population growths. We thus demonstrate that SCMs provide a new framework in which to study cell-cell interactions and treatments that take cell-cell interactions into account.

Joint work with: Panu Somervuo; J. Arvid Ågren; Dagim S. Tadele; Juha Kesseli; Jacob G. Scott; Matti Nykter; Philip Gerlee; Dmitri Finkelshtein; Otso Ovaskainen.

machine learningprobabilitystatistics theory

Audience: researchers in the discipline

( paper )

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Gothenburg statistics seminar

Series comments: Gothenburg statistics seminar is open to the interested public, everybody is welcome. It usually takes place in MVL14 (http://maps.chalmers.se/#05137ad7-4d34-45e2-9d14-7f970517e2b60, see specific talk). Speakers are asked to prepare material for 35 minutes excluding questions from the audience.

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