Geodesic
Interaction between crowding and growth in tumours with stem cells: Conceptual mathematical modelling
Luca Meacci1 ; Mario Primicerio2
1 Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Av. Trab. São Carlense 400, São Carlos (SP), 13566-590 Brazil
2 Dipartimento di Matematica “U. Dini”, Università degli Studi di Firenze, Viale Morgagni, 67/a- 50134 Firenze (FI), Italy
Mathematical modelling of natural phenomena, Tome 18 (2023), article no. 15.

Voir la notice de l'article provenant de la source EDP Sciences

This research paper proposes and discusses a conceptual modelling of both growth of tumours in presence of immortal multipotent cancer stem cells (CSCs) and of several lineages of differentiated tumour cells (CCs). The replication of CSCs is assumed symmetric or asymmetric with a prescribed mean ratio and mitosis and apoptosis are taken into account for the CCs aging. Replication can be hindered by the local crowding of the cells in the vicinity of the mother cell. The model is implemented in the framework of 3D cellular automata (CA) whose dynamics is governed by stochastic rules. Some simulations are displayed showing the growth of a tumour and the fractions of different lineages and age classes of CCs. Then, an approach that considers the same dynamics of aging, replication, and apoptosis, but with the aim to study the time evolution of the fractions of the different lineages and age classes of cells averaged over the total volume is presented. The dynamics is governed by a system of ordinary differential equations (ODEs), hence by deterministic rules. Numerical simulations of the solution of this system show qualitative similarity with the CA results, although the crowding effect is no longer a local effect, but also averaged over the total volume. The Appendix provides the proof of the mathematical well-poscdness of this model in a general framework.
DOI : 10.1051/mmnp/2023011

Luca Meacci 1 ; Mario Primicerio 2

1 Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Av. Trab. São Carlense 400, São Carlos (SP), 13566-590 Brazil
2 Dipartimento di Matematica “U. Dini”, Università degli Studi di Firenze, Viale Morgagni, 67/a- 50134 Firenze (FI), Italy 
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Luca Meacci; Mario Primicerio. Interaction between crowding and growth in tumours with stem cells: Conceptual mathematical modelling. Mathematical modelling of natural phenomena, Tome 18 (2023), article  no. 15. doi : 10.1051/mmnp/2023011. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/2023011/

[1] A. Anderson, M.A.J. Chaplain and K. Rejniak, Single-cell-based models in biology and medicine. Springer Science Business Media (2007).

[2] E.C. Anderson, C. Hessman, T.G. Levin, M.M. Monroe, M.H. Wong The role of colorectal cancer stem cells in metastatic disease and therapeutic response Cancers 2011 319 339

[3] E. Beretta, V. Capasso, N. Morozova Mathematical modelling of cancer stem cells population behavior Math. Modell. Natur. Phenomena 2012 279 305

[4] E. Beretta, N. Morozova, V. Capasso and A. Harel-Bellan, Some results on the population behavior of cancer stem cells. In New Challenges for Cancer Systems Biomedicine. Springer (2012), pp. 145–172.

[5] R. Betteridge, M.R. Owen, H.M. Byrne, T. Alarcón, P.K. Maini The impact of cell crowding and active cell movement on vascular tumour growth Netw. Heterogene. Media 2006 515

[6] A. Boondirek, W. Triampo, N. Nuttavut A review of cellular automata models of tumor growth Int. Math. Forum 2010 3023 3029

[7] I. Borsi, A. Fasano, M. Primicerio, T. Hillen Mathematical properties of a non-local integro-PDE model for cancer stem cells Math. Med. Biol 2015 59 75

[8] R.W. Cho, M.F. Clarke Recent advances in cancer stem cells Curr. Opin. Genetics Dev 2008 48 53

[9] M.F. Clarke, M. Fuller Stem cells and cancer: two faces of eve Cell 2006 1111 1115

[10] H. Clevers The cancer stem cell: premises, promises and challenges Nat. Med 2011 313 319

[11] G. De Vries, T. Hillen, M. Lewis, J. Müller and B. Schönfisch, A course in mathematical biology: quantitative modeling with mathematical and computational methods. SIAM (2006).

[12] H. Enderling, A.R. Anderson, M.A. Chaplain, A. Beheshti, L. Hlatky, P. Hahnfeldt Paradoxical dependencies of tumor dormancy and progression on basic cell kinetics Cancer Res 2009 8814 8821

[13] H. Enderling, P. Hahnfeldt Cancer stem cells in solid tumors: Is ‘evading apoptosis a hallmark of cancer Progr. Biophys. Molec. Biol 2011 391 399

[14] A. Fasano, A. Mancini, M. Primicerio Tumours with cancer stem cells: a PDE model Math. Biosci 2016 76 80

[15] F. Forouzannia, H. Enderling, M. Kohandel Mathematical modeling of the effects of tumor heterogeneity on the efficiency of radiation treatment schedule Bull. Math. Biol 2018 283 293

[16] R. Ganguly, I. Puri Mathematical model for the cancer stem cell hypothesis Cell Proliferat 2006 3 14

[17] X. Gao, J.T. McDonald, L. Hlatky and H. Enderling, Cell-cell interactions in solid tumors - the role of cancer stem cells. In New Challenges for Cancer Systems Biomedicine (Springer, 2012), pp. 191–204

[18] K.V. Gurova, A.V. Gudkov Paradoxical role of apoptosis in tumor progression J. Cell. Biochem 2003 128 137

[19] M. Hadjicharalambous, P.A. Wijeratne, V. Vavourakis From tumour perfusion to drug delivery and clinical translation of in silico cancer models Methods 2021 82 93

[20] T. Hillen, H. Enderling, P. Hahnfeldt The tumor growth paradox and immune system-mediated selection for cancer stem cells Bull. Math. Biol 2013 161 184

[21] B.J. Huntly, D.G. Gilliland Summing up cancer stem cells Nature 2005 1169 1170

[22] M. Marzagalli, F. Fontana, M. Raimondi, P. Limonta Cancer stem cells - key players in tumor relapse Cancers 2021 376

[23] L. Meacci, D. De Oliveira Medeiros, G. Buscaglia, M. Primicerio O paradoxo do crescimento tumoral atraves de um modelo 3d de automatos celulares com celulas- tronco cancerígenas CQD-Revista Eletronica Paulista de Matematica 2019 132 146

[24] L. Meacci, M. Primicerio Mathematical models for tumours with cancer stem cells Comput. Appl. Math 2018 6544 6559

[25] L. Meacci, M. Primicerio, G.C. Buscaglia Growth of tumours with stem cells: The effect of crowding and ageing of cells Physica A 2021 125841

[26] J. Metzcar, Y. Wang, R. Heiland, P. Macklin A review of cell-based computational modeling in cancer biology JCO Clin. Cancer Inf 2019 1 13

[27] F. Michor Mathematical models of cancer stem cells J. Clin. Oncol 2008 2854 2861

[28] R. Molina-Peña, M.M. Álvarez A simple mathematical model based on the cancer stem cell hypothesis suggests kinetic commonalities in solid tumor growth PloS One 2012 e26233

[29] R. Molina-Peña, J.C. Tudon-Martinez, O. Aquines-Gutiérrez A mathematical model of average dynamics in a stem cell hierarchy suggests the combinatorial targeting of cancer stem cells and progenitor cells as a potential strategy against tumor growth Cancers 2020 2590

[30] Á. Monteagudo, J. Santos Studying the capability of different cancer hallmarks to initiate tumor growth using a cellular automaton simulation. Application in a cancer stem cell context Biosystems 2014 46 58

[31] Á. Monteagudo, J. Santos Treatment analysis in a cancer stem cell context using a tumor growth model based on cellular automata PloS ONE 2015 e0132306

[32] T. Nunes, D. Hamdan, C. Leboeuf, M. El Bouchtaoui, G. Gapihan, T.T. Nguyen, S. Meles, E. Angeli, P. Ratajczak, H. Lu Targeting cancer stem cells to overcome chemoresistance Int. J. Molec. Sci 2018 4036

[33] J. Poleszczuk, H. Enderling A high-performance cellular automaton model of tumor growth with dynamically growing domains Appl. Math 2014 144

[34] M. Prieto-Vila, R.-U. Takahashi, W. Usuba, I. Kohama, T. Ochiya Drug resistance driven by cancer stem cells and their niche Int. J. Mol. Sci 2017 2574

[35] T. Reya, S.J. Morrison, M.F. Clarke, I.L. Weissman Stem cells, cancer, and cancer stem cells Nature 2001 105 111

[36] A. Rivaz, M. Azizian, M. Soltani Various mathematical models of tumor growth with reference to cancer stem cells: a review Iran. J. Sci. Technol. Trans. A 2019 687 700

[37] M.W. Schmitt, M.J. Prindle, L.A. Loeb Implications of genetic heterogeneity in cancer Ann. New York Acad. Sci 2012 110

[38] A. Shyntar, A. Patel, M. Rhodes, H. Enderling, T. Hillen The tumor invasion paradox in cancer stem cell-driven solid tumors Bull. Mathemat. Biol 2022 1 24

[39] H.R. Thieme, Vol. 12 of Mathematics in population biology. Princeton University Press (2018).

[40] C. Tomasetti, L. Li, B. Vogelstein Stem cell divisions, somatic mutations, cancer etiology, and cancer prevention Science 2017 1330 1334

[41] C. Tomasetti, B. Vogelstein, G. Parmigiani Half or more of the somatic mutations in cancers of self-renewing tissues originate prior to tumor initiation Proc. Natl. Acad. Sci 2013 1999 2004

[42] J.E. Visvader, G.J. Lindeman Cancer stem cells in solid tumours: accumulating evidence and unresolved questions Nat. Rev. Cancer 2008 755 768

[43] S.L. Weekes, B. Barker, S. Bober, K. Cisneros, J. Cline, A. Thompson, L. Hlatky, P. Hahnfeldt, H. Enderling A multicompartment mathematical model of cancer stem cell-driven tumor growth dynamics Bull. Math. Biol 2014 1762 1782

[44] L.D. Weiss, N.L. Komarova, I.A. Rodriguez-Brenes Mathematical modeling of normal and cancer stem cells Curr. Stem Cell Rep 2017 232 239

[45] L.D. Weiss, P. Van Den Driessche, J.S. Lowengrub, D. Wodarz, N.L. Komarova Effect of feedback regulation on stem cell fractions in tissues and tumors: understanding chemoresistance in cancer J. Theor. Biol 2021 110499

[46] D. Wodarz, N. Komarova Can loss of apoptosis protect against cancer? Trends Genet 2007 232 237

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