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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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DOI (Published version): 10.1007/s00285-023-01903-x

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
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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. 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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).</funders><projectreference/><lastEdited>2023-05-18T14:58:48.2402431</lastEdited><Created>2023-04-05T18:58:01.4968505</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Mathematics and Computer Science - Mathematics</level></path><authors><author><firstname>Sara</firstname><surname>Hamis</surname><orcid>0000-0002-1105-8078</orcid><order>1</order></author><author><firstname>Panu</firstname><surname>Somervuo</surname><orcid>0000-0003-3121-4047</orcid><order>2</order></author><author><firstname>J. 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spelling v2 63090 2023-04-05 Spatial cumulant models enable spatially informed treatment strategies and analysis of local interactions in cancer systems 4dc251ebcd7a89a15b71c846cd0ddaaf 0000-0001-7136-9399 Dmitri Finkelshtein Dmitri Finkelshtein true false 2023-04-05 SMA 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. Journal Article Journal of Mathematical Biology 86 5 Springer Science and Business Media LLC 0303-6812 1432-1416 Individual-based models · Spatio-temporal point processes · Spatialmoments · Cancer eco-evolution · Mathematical oncology 1 5 2023 2023-05-01 10.1007/s00285-023-01903-x http://dx.doi.org/10.1007/s00285-023-01903-x COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University Another institution paid the OA fee 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). 2023-05-18T14:58:48.2402431 2023-04-05T18:58:01.4968505 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Sara Hamis 0000-0002-1105-8078 1 Panu Somervuo 0000-0003-3121-4047 2 J. Arvid Ågren 0000-0003-3619-556x 3 Dagim Shiferaw Tadele 0000-0001-8319-678x 4 Juha Kesseli 5 Jacob G. Scott 0000-0003-2971-7673 6 Matti Nykter 0000-0001-6956-2843 7 Philip Gerlee 0000-0001-8503-0177 8 Dmitri Finkelshtein 0000-0001-7136-9399 9 Otso Ovaskainen 0000-0001-9750-4421 10 63090__27060__f5e5985a563b496fb180cba007dc9468.pdf 63090.pdf 2023-04-17T09:57:43.2714003 Output 2820919 application/pdf Version of Record true This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. true eng http://creativecommons.org/licenses/by/4.0/
title Spatial cumulant models enable spatially informed treatment strategies and analysis of local interactions in cancer systems
spellingShingle Spatial cumulant models enable spatially informed treatment strategies and analysis of local interactions in cancer systems
Dmitri Finkelshtein
title_short Spatial cumulant models enable spatially informed treatment strategies and analysis of local interactions in cancer systems
title_full Spatial cumulant models enable spatially informed treatment strategies and analysis of local interactions in cancer systems
title_fullStr Spatial cumulant models enable spatially informed treatment strategies and analysis of local interactions in cancer systems
title_full_unstemmed Spatial cumulant models enable spatially informed treatment strategies and analysis of local interactions in cancer systems
title_sort Spatial cumulant models enable spatially informed treatment strategies and analysis of local interactions in cancer systems
author_id_str_mv 4dc251ebcd7a89a15b71c846cd0ddaaf
author_id_fullname_str_mv 4dc251ebcd7a89a15b71c846cd0ddaaf_***_Dmitri Finkelshtein
author Dmitri Finkelshtein
author2 Sara Hamis
Panu Somervuo
J. Arvid Ågren
Dagim Shiferaw Tadele
Juha Kesseli
Jacob G. Scott
Matti Nykter
Philip Gerlee
Dmitri Finkelshtein
Otso Ovaskainen
format Journal article
container_title Journal of Mathematical Biology
container_volume 86
container_issue 5
publishDate 2023
institution Swansea University
issn 0303-6812
1432-1416
doi_str_mv 10.1007/s00285-023-01903-x
publisher Springer Science and Business Media LLC
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
url http://dx.doi.org/10.1007/s00285-023-01903-x
document_store_str 1
active_str 0
description 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.
published_date 2023-05-01T14:58:46Z
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