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Spatial cumulant models enable spatially informed treatment strategies and analysis of local interactions in cancer systems

Sara Hamis Orcid Logo, Panu Somervuo Orcid Logo, J. Arvid Ågren Orcid Logo, Dagim Shiferaw Tadele Orcid Logo, Juha Kesseli, Jacob G. Scott Orcid Logo, Matti Nykter Orcid Logo, Philip Gerlee Orcid Logo, Dmitri Finkelshtein Orcid Logo, Otso Ovaskainen Orcid Logo

Journal of Mathematical Biology, Volume: 86, Issue: 5

Swansea University Author: Dmitri Finkelshtein Orcid Logo

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Abstract

Theoretical and applied cancer studies that use individual-based models (IBMs) havebeen limited by the lack of a mathematical formulation that enables rigorous analysis of these models. However, spatial cumulant models (SCMs), which have arisenfrom theoretical ecology, describe population dynamics g...

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Published in: Journal of Mathematical Biology
ISSN: 0303-6812 1432-1416
Published: Springer Science and Business Media LLC 2023
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa63090
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Abstract: Theoretical and applied cancer studies that use individual-based models (IBMs) havebeen limited by the lack of a mathematical formulation that enables rigorous analysis of these models. However, spatial cumulant models (SCMs), which have arisenfrom theoretical ecology, describe population dynamics generated by a specific family of IBMs, namely spatio-temporal point processes (STPPs). SCMs are spatiallyresolved population models formulated by a system of differential equations thatapproximate the dynamics of two STPP-generated summary statistics: first-order spatial cumulants (densities), and second-order spatial cumulants (spatial covariances).We exemplify how SCMs can be used in mathematical oncology by modelling theoretical cancer cell populations comprising interacting growth factor-producing and non-producing cells. To formulate model equations, we use computational tools that enable the generation of STPPs, SCMs and mean-field population models (MFPMs) from user-defined model descriptions (Cornell et al. Nat Commun 10:4716, 2019).To calculate and compare STPP, SCM and MFPM-generated summary statistics, we develop an application-agnostic computational pipeline. Our results demonstrate that SCMs can capture STPP-generated population density dynamics, even when 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 inwhich to study cell-cell interactions, and can be used to describe and perturb STPP-generated cell population dynamics. We, therefore, argue that SCMs can be used to increase IBMs’ applicability in cancer research.
Keywords: Individual-based models · Spatio-temporal point processes · Spatialmoments · Cancer eco-evolution · Mathematical oncology
College: Faculty of Science and Engineering
Funders: Open access funding provided by Tampere University including Tampere University Hospital, Tampere University of Applied Sciences (TUNI). SH was funded by Wenner-Gren Stiftelserna/The Wenner-Gren Foundations (WGF2022-0044), the Tampere Institute for Advanced Study (2021-2023) and the Jyväskylv University Visiting Fellow Programme 2021. JAÅ was funded by Wenner-Gren Stiftelserna/The Wenner-Gren Foundations (WGF2018-0083). DST was funded by the Norwegian Research Council (NRC). JGS was funded by the National Institutes of Health (5R37CA244613-02) and the American Cancer Society Research Scholar Grant (RSG-20-096-01). MN was funded by the Academy of Finland Center of Excellence programme (Project No. 312043). OO was funded by the Academy of Finland (Grant No. 309581), the Jane and Aatos Erkko Foundation, the Research Council of Norway through its Centres of Excellence Funding Scheme (223257), and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 856506; ERC-synergy project LIFEPLAN).
Issue: 5