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'''Cell-based models''' are [[mathematical model]]s that represent biological [[cell (biology)|cells]] as a discrete entities. Within the field of [[computational biology]] they are often simply called [[Agent-based model|agent-based models]]<ref name=":0" /> of which they are a specific application and they are used for simulating the [[biomechanics]] of multicellular structures such as [[Tissue (biology)|tissue]]s. to study the influence of these behaviors on how tissues are organised in time and space. Their main advantage is the easy integration of cell level processes such as [[cell division]], intracellular processes and [[single-cell variability]] within a cell population.<ref name=Liederkerke2015>{{cite journal | vauthors = Van Liedekerke P, Palm MM, Jagiella N, Drasdo D | title=Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results|journal=Computational Particle Mechanics|date=1 December 2015|volume=2|issue=4|pages=401–444|doi=10.1007/s40571-015-0082-3 | bibcode=2015CPM.....2..401V|doi-access=free}}</ref>
Continuum-based models (PDE-based) models have also been developed – in particular, for cardiomyocytes and neurons. These represent the cells through explicit geometries and take into account spatial distributions of both intracellular and extracellular processes. They capture, depending on the research question and areas, ranges from a few to many thousand cells. In particular, the framework for electrophysiological models of cardiac cells is well-developed and made highly efficient using [[high-performance computing]].<ref>{{cite book | url=https://link.springer.com/book/10.1007/978-3-030-61157-6 | title=Modeling Excitable Tissue | series=Simula SpringerBriefs on Computing |editor=Aslak Tveito |editor2=Kent-Andre Mardal |editor3=Marie E. Rognes | year=2021 | volume=7 | publisher=Springer| doi=10.1007/978-3-030-61157-6 | isbn=978-3-030-61156-9 | s2cid=228872673 }}</ref>
== Model types ==
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=== Off-lattice ===
Off-lattice models allow for continuous movement of cells in space and evolve the system in time according to [[force]] laws governing the mechanical interactions between the individual cells. Examples of off-lattice models are center-based models,<ref>{{cite journal | vauthors = Osborne JM, Fletcher AG, Pitt-Francis JM, Maini PK, Gavaghan DJ | title = Comparing individual-based approaches to modelling the self-organization of multicellular tissues | journal =
based on the [[immersed boundary method]]<ref>{{cite journal | vauthors = Rejniak KA | title = An immersed boundary framework for modelling the growth of individual cells: an application to the early tumour development | journal = Journal of Theoretical Biology | volume = 247 | issue = 1 | pages = 186–204 | date = July 2007 | pmid = 17416390 | doi = 10.1016/j.jtbi.2007.02.019 | bibcode = 2007JThBi.247..186R }}</ref> and the subcellular element
method.<ref>{{cite book | vauthors = Newman TJ | title = Modeling multicellular systems using subcellular elements | journal = Mathematical Biosciences and Engineering | volume = 2 | issue = 3 | pages = 613–24 | date = July 2005 | pmid = 20369943 | doi = 10.1007/978-3-7643-8123-3_10 | series = Mathematics and Biosciences in Interaction | isbn = 978-3-7643-8101-1 }}</ref> They differ mainly in the level of detail with which they represent the
cell shape. As a consequence they vary in their ability to capture different biological mechanisms, the effort needed to extend them from two- to three-dimensional models and also in their computational cost.<ref>{{cite journal | vauthors = Osborne JM, Fletcher AG, Pitt-Francis JM, Maini PK, Gavaghan DJ | title = Comparing individual-based approaches to modelling the self-organization of multicellular tissues | journal =
The simplest off-lattice model, the center-based model, depicts cells as spheres and models their mechanical interactions using pairwise potentials.<ref>{{cite journal | vauthors = Meineke FA, Potten CS, Loeffler M | title = Cell migration and organization in the intestinal crypt using a lattice-free model | journal = Cell Proliferation | volume = 34 | issue = 4 | pages = 253–266 | date = August 2001 | pmid = 11529883 | pmc = 6495866 | doi = 10.1046/j.0960-7722.2001.00216.x }}</ref><ref>{{cite journal | vauthors = Drasdo D, Höhme S | title = A single-cell-based model of tumor growth in vitro: monolayers and spheroids | journal = Physical Biology | volume = 2 | issue = 3 | pages = 133–147 | date = July 2005 | pmid = 16224119 | doi = 10.1088/1478-3975/2/3/001 | bibcode = 2005PhBio...2..133D | s2cid = 24191020 }}</ref> It is easily extended to a large number of cells in both 2D and 3D.<ref>{{cite journal | vauthors = Galle J, Aust G, Schaller G, Beyer T, Drasdo D | title = Individual cell-based models of the spatial-temporal organization of multicellular systems--achievements and limitations | journal = Cytometry. Part A | volume = 69 | issue = 7 | pages = 704–710 | date = July 2006 | pmid = 16807896 | doi = 10.1002/cyto.a.20287 | doi-access = free }}</ref>
==== Vertex ====
Vertex-based models are a subset of off-lattice models.<ref name=":0">{{cite journal | vauthors = Metzcar J, Wang Y, Heiland R, Macklin P | title = A Review of Cell-Based Computational Modeling in Cancer Biology | journal = JCO Clinical Cancer Informatics | volume = 3 | issue = 3 | pages = 1–13 | date = February 2019 | pmid = 30715927 | pmc = 6584763 | doi = 10.1200/CCI.18.00069 }}</ref> They track the cell membrane as a set of polygonal points and update the position of each vertex according to tensions in the cell membrane resulting from cell-cell adhesion forces and cell elasticity.<ref>{{cite journal | vauthors = Fletcher AG, Osterfield M, Baker RE, Shvartsman SY | title = Vertex models of epithelial morphogenesis | journal = Biophysical Journal | volume = 106 | issue = 11 | pages = 2291–2304 | date = June 2014 | pmid = 24896108 | pmc = 4052277 | doi = 10.1016/j.bpj.2013.11.4498 | bibcode = 2014BpJ...106.2291F }}</ref> They are more difficult to implement and also more costly to run.
As cells move past one another during a simulation, regular updates of the polygonal edge connections are necessary.<ref>{{cite journal | vauthors = Fletcher AG, Osborne JM, Maini PK, Gavaghan DJ | title = Implementing vertex dynamics models of cell populations in biology within a consistent computational framework | journal = Progress in Biophysics and Molecular Biology | volume = 113 | issue = 2 | pages = 299–326 | date = November 2013 | pmid = 24120733 | doi = 10.1016/j.pbiomolbio.2013.09.003 | url = https://ora.ox.ac.uk/objects/uuid:ff94a74e-ef93-4ac2-ab61-1e08795e67b8 }}</ref>
== Applications ==
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!Speedup
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|Agents.jl<ref>{{Cite journal | vauthors = Datseris G, Vahdati AR, DuBois TC |date=2022-01-05 |title=Agents.jl: a performant and feature-full agent-based modeling software of minimal code complexity |url=http://journals.sagepub.com/doi/10.1177/00375497211068820 |journal=
|Center/agent-based
|2D,3D
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|GPU
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|Chaste<ref>{{cite journal | vauthors = Pitt-Francis J, Bernabeu MO, Cooper J, Garny A, Momtahan L, Osborne J, Pathmanathan P, Rodriguez B, Whiteley JP, Gavaghan DJ | display-authors = 6 | title = Chaste: using agile programming techniques to develop computational biology software | journal = Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences | volume = 366 | issue = 1878 | pages = 3111–3136 | date = September 2008 | pmid = 18565813 | doi = 10.1016/j.cpc.2009.07.019 | url = http://eprints.maths.ox.ac.uk/846 | access-date = 2019-02-01 | author16-link = Sarah L. Waters | archive-url = https://web.archive.org/web/20151120234903/http://eprints.maths.ox.ac.uk/846/ | archive-date = 2015-11-20 }}</ref><ref>{{cite journal | vauthors = Mirams GR, Arthurs CJ, Bernabeu MO, Bordas R, Cooper J, Corrias A, Davit Y, Dunn SJ, Fletcher AG, Harvey DG, Marsh ME, Osborne JM, Pathmanathan P, Pitt-Francis J, Southern J, Zemzemi N, Gavaghan DJ | display-authors = 6 | title = Chaste: an open source C++ library for computational physiology and biology | journal =
|Center/agent-based, on-/off-lattice, cellular automata, vertex-based, immersed boundary
|2D, 3D
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|[[OpenMP]]
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|EdgeBased<ref>{{Cite journal | vauthors = Brown PJ, Green JE, Binder BJ, Osborne JM
|Off-lattice, ODE solvers
|2D
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|IAS (Interacting Active Surfaces)<ref>{{Cite journal | vauthors = Torres-Sánchez A, Winter MK, Salbreux G |date=2022-03-22 |title=Interacting active surfaces: a model for three-dimensional cell aggregates | journal = bioRxiv |pages=2022.03.21.484343 |doi=10.1101/2022.03.21.484343|s2cid=247631653 }}</ref>
|[[Finite element method|FEM]], ODE solvers
|3D
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|[[CUDA]], [[Graphics processing unit|GPU]]
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|Minimal Cell<ref>{{cite journal | vauthors = Thornburg ZR, Bianchi DM, Brier TA, Gilbert BR, Earnest TM, Melo MC, Safronova N, Sáenz JP, Cook AT, Wise KS, Hutchison CA, Smith HO, Glass JI, Luthey-Schulten Z | display-authors = 6 | title = Fundamental behaviors emerge from simulations of a living minimal cell | language = English | journal = Cell | volume = 185 | issue = 2 | pages = 345–360.e28 | date = January 2022 | pmid = 35063075 | doi = 10.1016/j.cell.2021.12.025 | s2cid = 246065847 }}</ref>
|ODE solvers, stochastic PDE solvers
|3D
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|PhysiCell<ref>{{cite journal | vauthors = Ghaffarizadeh A, Heiland R, Friedman SH, Mumenthaler SM, Macklin P | title = PhysiCell: An open source physics-based cell simulator for 3-D multicellular systems | journal =
|Center/agent-based, ODE
|3D
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|Timothy<ref>{{Cite journal | vauthors = Cytowski M, Szymanska Z |date=September 2014 |title=Large-Scale Parallel Simulations of 3D Cell Colony Dynamics |journal=Computing in Science & Engineering |volume=16 |issue=5 |pages=86–95 |doi=10.1109/MCSE.2014.2 |bibcode=2014CSE....16e..86C |s2cid=427712 |issn=1558-366X}}</ref>
|Center/agent-based
|3D
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|VirtualLeaf<ref>{{cite
|Off-lattice
|2D
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|yalla<ref>{{cite journal | vauthors = Germann P, Marin-Riera M, Sharpe J | title = ya||a: GPU-Powered Spheroid Models for Mesenchyme and Epithelium | language = English | journal = Cell Systems | volume = 8 | issue = 3 | pages = 261–266.e3 | date = March 2019 | pmid = 30904379 | doi = 10.1016/j.cels.2019.02.007 | s2cid = 85497718 }}</ref>
|Center/agent-based
|3D
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|Tyssue<ref>{{Cite journal | vauthors = Theis S, Suzanne M, Gay G |date=2021-06-07 |title=Tyssue: an epithelium simulation library |url=https://joss.theoj.org/papers/10.21105/joss.02973 |journal=Journal of Open Source Software |language=en |volume=6 |issue=62 |pages=2973 |doi=10.21105/joss.02973 |bibcode=2021JOSS....6.2973T |s2cid=235965728 |issn=2475-9066}}</ref>
|Vertex-based
|2D, 3D
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