Mathematical model and computational scheme for multi-phase modeling of cellular population and microenvironmental dynamics in soft tissue.

In this paper we introduce a system of partial differential equations that is capable of modeling a variety of dynamic processes in soft tissue cellular populations and their microenvironments. The model is designed to be general enough to simulate such processes as tissue regeneration, tumor growth...

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Autores principales:	Gregory Baramidze, Victoria Baramidze, Ying Xu
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/b2e8e3d4997945ffb3813378af5c1c42
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spelling	oai:doaj.org-article:b2e8e3d4997945ffb3813378af5c1c422021-12-02T20:12:53ZMathematical model and computational scheme for multi-phase modeling of cellular population and microenvironmental dynamics in soft tissue.1932-620310.1371/journal.pone.0260108https://doaj.org/article/b2e8e3d4997945ffb3813378af5c1c422021-01-01T00:00:00Zhttps://doi.org/10.1371/journal.pone.0260108https://doaj.org/toc/1932-6203In this paper we introduce a system of partial differential equations that is capable of modeling a variety of dynamic processes in soft tissue cellular populations and their microenvironments. The model is designed to be general enough to simulate such processes as tissue regeneration, tumor growth, immune response, and many more. It also has built-in flexibility to include multiple chemical fields and/or sub-populations of cells, interstitial fluid and/or extracellular matrix. The model is derived from the conservation laws for mass and linear momentum and therefore can be classified as a continuum multi-phase model. A careful choice of state variables provides stability in solving the system of discretized equations defining advective flux terms. A concept of deviation from normal allows us to use simplified constitutive relations for stresses. We also present an algorithm for computing numerical approximations to the solutions of the system and discuss properties of these approximations. We demonstrate several examples of applications of the model. Numerical simulations show a significant potential of the model for simulating a variety of processes in soft tissues.Gregory BaramidzeVictoria BaramidzeYing XuPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 16, Iss 11, p e0260108 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Gregory Baramidze Victoria Baramidze Ying Xu Mathematical model and computational scheme for multi-phase modeling of cellular population and microenvironmental dynamics in soft tissue.
description	In this paper we introduce a system of partial differential equations that is capable of modeling a variety of dynamic processes in soft tissue cellular populations and their microenvironments. The model is designed to be general enough to simulate such processes as tissue regeneration, tumor growth, immune response, and many more. It also has built-in flexibility to include multiple chemical fields and/or sub-populations of cells, interstitial fluid and/or extracellular matrix. The model is derived from the conservation laws for mass and linear momentum and therefore can be classified as a continuum multi-phase model. A careful choice of state variables provides stability in solving the system of discretized equations defining advective flux terms. A concept of deviation from normal allows us to use simplified constitutive relations for stresses. We also present an algorithm for computing numerical approximations to the solutions of the system and discuss properties of these approximations. We demonstrate several examples of applications of the model. Numerical simulations show a significant potential of the model for simulating a variety of processes in soft tissues.
format	article
author	Gregory Baramidze Victoria Baramidze Ying Xu
author_facet	Gregory Baramidze Victoria Baramidze Ying Xu
author_sort	Gregory Baramidze
title	Mathematical model and computational scheme for multi-phase modeling of cellular population and microenvironmental dynamics in soft tissue.
title_short	Mathematical model and computational scheme for multi-phase modeling of cellular population and microenvironmental dynamics in soft tissue.
title_full	Mathematical model and computational scheme for multi-phase modeling of cellular population and microenvironmental dynamics in soft tissue.
title_fullStr	Mathematical model and computational scheme for multi-phase modeling of cellular population and microenvironmental dynamics in soft tissue.
title_full_unstemmed	Mathematical model and computational scheme for multi-phase modeling of cellular population and microenvironmental dynamics in soft tissue.
title_sort	mathematical model and computational scheme for multi-phase modeling of cellular population and microenvironmental dynamics in soft tissue.
publisher	Public Library of Science (PLoS)
publishDate	2021
url	https://doaj.org/article/b2e8e3d4997945ffb3813378af5c1c42
work_keys_str_mv	AT gregorybaramidze mathematicalmodelandcomputationalschemeformultiphasemodelingofcellularpopulationandmicroenvironmentaldynamicsinsofttissue AT victoriabaramidze mathematicalmodelandcomputationalschemeformultiphasemodelingofcellularpopulationandmicroenvironmentaldynamicsinsofttissue AT yingxu mathematicalmodelandcomputationalschemeformultiphasemodelingofcellularpopulationandmicroenvironmentaldynamicsinsofttissue
_version_	1718374844799647744

Mathematical model and computational scheme for multi-phase modeling of cellular population and microenvironmental dynamics in soft tissue.

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