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Peng Q, Vermolen FJ, Weihs D. Physical confinement and cell proximity increase cell migration rates and invasiveness: A mathematical model of cancer cell invasion through flexible channels. J Mech Behav Biomed Mater 2023; 142:105843. [PMID: 37104897 DOI: 10.1016/j.jmbbm.2023.105843] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2022] [Revised: 03/28/2023] [Accepted: 04/07/2023] [Indexed: 04/29/2023]
Abstract
Cancer cell migration between different body parts is the driving force behind cancer metastasis, which is the main cause of mortality of patients. Migration of cancer cells often proceeds by penetration through narrow cavities in locally stiff, yet flexible tissues. In our previous work, we developed a model for cell geometry evolution during invasion, which we extend here to investigate whether leader and follower (cancer) cells that only interact mechanically can benefit from sequential transmigration through narrow micro-channels and cavities. We consider two cases of cells sequentially migrating through a flexible channel: leader and follower cells being closely adjacent or distant. Using Wilcoxon's signed-rank test on the data collected from Monte Carlo simulations, we conclude that the modelled transmigration speed for the follower cell is significantly larger than for the leader cell when cells are distant, i.e. follower cells transmigrate after the leader has completed the crossing. Furthermore, it appears that there exists an optimum with respect to the width of the channel such that cell moves fastest. On the other hand, in the case of closely adjacent cells, effectively performing collective migration, the leader cell moves 12% faster since the follower cell pushes it. This work shows that mechanical interactions between cells can increase the net transmigration speed of cancer cells, resulting in increased invasiveness. In other words, interaction between cancer cells can accelerate metastatic invasion.
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Affiliation(s)
- Qiyao Peng
- Mathematical Institute, Faculty of Science, Leiden University, Neils Bohrweg 1, 2333 CA, Leiden, The Netherlands.
| | - Fred J Vermolen
- Computational Mathematics Group, Department of Mathematics and Statistics, Faculty of Science, University of Hasselt, 3590 Diepenbeek, Belgium
| | - Daphne Weihs
- Faculty of Biomedical Engineering, Technion-Israel Institute of Technology, 3200003 Haifa, Israel
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2
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A formalism for modelling traction forces and cell shape evolution during cell migration in various biomedical processes. Biomech Model Mechanobiol 2021; 20:1459-1475. [PMID: 33893558 PMCID: PMC8298374 DOI: 10.1007/s10237-021-01456-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2020] [Accepted: 03/31/2021] [Indexed: 01/17/2023]
Abstract
The phenomenological model for cell shape deformation and cell migration Chen (BMM 17:1429–1450, 2018), Vermolen and Gefen (BMM 12:301–323, 2012), is extended with the incorporation of cell traction forces and the evolution of cell equilibrium shapes as a result of cell differentiation. Plastic deformations of the extracellular matrix are modelled using morphoelasticity theory. The resulting partial differential differential equations are solved by the use of the finite element method. The paper treats various biological scenarios that entail cell migration and cell shape evolution. The experimental observations in Mak et al. (LC 13:340–348, 2013), where transmigration of cancer cells through narrow apertures is studied, are reproduced using a Monte Carlo framework.
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Pearce KJ, Nellenbach K, Smith RC, Brown AC, Haider MA. Modeling and Parameter Subset Selection for Fibrin Polymerization Kinetics with Applications to Wound Healing. Bull Math Biol 2021; 83:47. [PMID: 33751272 PMCID: PMC8237246 DOI: 10.1007/s11538-021-00876-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2020] [Accepted: 02/25/2021] [Indexed: 11/29/2022]
Abstract
During the hemostatic phase of wound healing, vascular injury leads to endothelial cell damage, initiation of a coagulation cascade involving platelets, and formation of a fibrin-rich clot. As this cascade culminates, activation of the protease thrombin occurs and soluble fibrinogen is converted into an insoluble polymerized fibrin network. Fibrin polymerization is critical for bleeding cessation and subsequent stages of wound healing. We develop a cooperative enzyme kinetics model for in vitro fibrin matrix polymerization capturing dynamic interactions among fibrinogen, thrombin, fibrin, and intermediate complexes. A tailored parameter subset selection technique is also developed to evaluate parameter identifiability for a representative data curve for fibrin accumulation in a short-duration in vitro polymerization experiment. Our approach is based on systematic analysis of eigenvalues and eigenvectors of the classical information matrix for simulations of accumulating fibrin matrix via optimization based on a least squares objective function. Results demonstrate robustness of our approach in that a significant reduction in objective function cost is achieved relative to a more ad hoc curve-fitting procedure. Capabilities of this approach to integrate non-overlapping subsets of the data to enhance the evaluation of parameter identifiability are also demonstrated. Unidentifiable reaction rate parameters are screened to determine whether individual reactions can be eliminated from the overall system while preserving the low objective cost. These findings demonstrate the high degree of information within a single fibrin accumulation curve, and a tailored model and parameter subset selection approach for improving optimization and reducing model complexity in the context of polymerization experiments.
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Affiliation(s)
- Katherine J Pearce
- Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC, 27695-8205, USA
| | - Kimberly Nellenbach
- Joint Department of Biomedical Engineering, North Carolina State University and The University of North Carolina at Chapel Hill, Raleigh, NC, 27695, USA
| | - Ralph C Smith
- Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC, 27695-8205, USA
| | - Ashley C Brown
- Joint Department of Biomedical Engineering, North Carolina State University and The University of North Carolina at Chapel Hill, Raleigh, NC, 27695, USA
| | - Mansoor A Haider
- Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC, 27695-8205, USA.
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Chen J, Weihs D, Van Dijk M, Vermolen FJ. A phenomenological model for cell and nucleus deformation during cancer metastasis. Biomech Model Mechanobiol 2018; 17:1429-1450. [PMID: 29845458 PMCID: PMC6154301 DOI: 10.1007/s10237-018-1036-5] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2018] [Accepted: 05/21/2018] [Indexed: 12/21/2022]
Abstract
Cell migration plays an essential role in cancer metastasis. In cancer invasion through confined spaces, cells must undergo extensive deformation, which is a capability related to their metastatic potentials. Here, we simulate the deformation of the cell and nucleus during invasion through a dense, physiological microenvironment by developing a phenomenological computational model. In our work, cells are attracted by a generic emitting source (e.g., a chemokine or stiffness signal), which is treated by using Green’s Fundamental solutions. We use an IMEX integration method where the linear parts and the nonlinear parts are treated by using an Euler backward scheme and an Euler forward method, respectively. We develop the numerical model for an obstacle-induced deformation in 2D or/and 3D. Considering the uncertainty in cell mobility, stochastic processes are incorporated and uncertainties in the input variables are evaluated using Monte Carlo simulations. This quantitative study aims at estimating the likelihood for invasion and the length of the time interval in which the cell invades the tissue through an obstacle. Subsequently, the two-dimensional cell deformation model is applied to simplified cancer metastasis processes to serve as a model for in vivo or in vitro biomedical experiments.
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Affiliation(s)
- Jiao Chen
- Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands.
| | - Daphne Weihs
- Faculty of Biomedical Engineering, Technion-Israel Institute of Technology, 3200003, Haifa, Israel
| | - Marcel Van Dijk
- Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands
| | - Fred J Vermolen
- Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands
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5
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Three-dimensional simulation of obstacle-mediated chemotaxis. Biomech Model Mechanobiol 2018; 17:1243-1268. [DOI: 10.1007/s10237-018-1023-x] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2017] [Accepted: 04/25/2018] [Indexed: 01/07/2023]
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6
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The role of nuclear mechanics in cell deformation under creeping flows. J Theor Biol 2017; 432:25-32. [DOI: 10.1016/j.jtbi.2017.07.028] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2017] [Revised: 07/24/2017] [Accepted: 07/30/2017] [Indexed: 11/19/2022]
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Chen J, Weihs D, Vermolen FJ. A model for cell migration in non-isotropic fibrin networks with an application to pancreatic tumor islets. Biomech Model Mechanobiol 2017; 17:367-386. [PMID: 28993948 PMCID: PMC5845079 DOI: 10.1007/s10237-017-0966-7] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2017] [Accepted: 09/21/2017] [Indexed: 11/23/2022]
Abstract
Cell migration, known as an orchestrated movement of cells, is crucially important for wound healing, tumor growth, immune response as well as other biomedical processes. This paper presents a cell-based model to describe cell migration in non-isotropic fibrin networks around pancreatic tumor islets. This migration is determined by the mechanical strain energy density as well as cytokines-driven chemotaxis. Cell displacement is modeled by solving a large system of ordinary stochastic differential equations where the stochastic parts result from random walk. The stochastic differential equations are solved by the use of the classical Euler–Maruyama method. In this paper, the influence of anisotropic stromal extracellular matrix in pancreatic tumor islets on T-lymphocytes migration in different immune systems is investigated. As a result, tumor peripheral stromal extracellular matrix impedes the immune response of T-lymphocytes through changing direction of their migration.
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Affiliation(s)
- Jiao Chen
- Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands.
| | - Daphne Weihs
- Faculty of Biomedical Engineering, Technion-Israel Institute of Technology, 3200003, Haifa, Israel
| | - Fred J Vermolen
- Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands
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Weihs D, Gefen A, Vermolen FJ. Review on experiment-based two- and three-dimensional models for wound healing. Interface Focus 2016; 6:20160038. [PMID: 27708762 DOI: 10.1098/rsfs.2016.0038] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
Traumatic and chronic wounds are a considerable medical challenge that affects many populations and their treatment is a monetary and time-consuming burden in an ageing society to the medical systems. Because wounds are very common and their treatment is so costly, approaches to reveal the responses of a specific wound type to different medical procedures and treatments could accelerate healing and reduce patient suffering. The effects of treatments can be forecast using mathematical modelling that has the predictive power to quantify the effects of induced changes to the wound-healing process. Wound healing involves a diverse and complex combination of biophysical and biomechanical processes. We review a wide variety of contemporary approaches of mathematical modelling of gap closure and wound-healing-related processes, such as angiogenesis. We provide examples of the understanding and insights that may be garnered using those models, and how those relate to experimental evidence. Mathematical modelling-based simulations can provide an important visualization tool that can be used for illustrational purposes for physicians, patients and researchers.
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Affiliation(s)
- Daphne Weihs
- Faculty of Biomedical Engineering , Technion-Israel Institute of Technology , Haifa 3200003 , Israel
| | - Amit Gefen
- Department of Biomedical Engineering, Faculty of Engineering , Tel Aviv University , Tel Aviv 6997801 , Israel
| | - Fred J Vermolen
- Department of Applied Mathematics , Delft University of Technology , Delft , The Netherlands
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Gefen A, Weihs D. Mechanical cytoprotection: A review of cytoskeleton-protection approaches for cells. J Biomech 2016; 49:1321-1329. [DOI: 10.1016/j.jbiomech.2015.10.030] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2015] [Revised: 10/20/2015] [Accepted: 10/21/2015] [Indexed: 12/28/2022]
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Bookholt FD, Monsuur HN, Gibbs S, Vermolen FJ. Mathematical modelling of angiogenesis using continuous cell-based models. Biomech Model Mechanobiol 2016; 15:1577-1600. [PMID: 27037954 PMCID: PMC5106520 DOI: 10.1007/s10237-016-0784-3] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2015] [Accepted: 03/15/2016] [Indexed: 11/25/2022]
Abstract
In this work, we develop a mathematical formalism based on a 3D in vitro model that is used to simulate the early stages of angiogenesis. The model treats cells as individual entities that are migrating as a result of chemotaxis and durotaxis. The phenotypes used here are endothelial cells that can be distinguished into stalk and tip (leading) cells. The model takes into account the dynamic interaction and interchange between both phenotypes. Next to the cells, the model takes into account several proteins such as vascular endothelial growth factor, delta-like ligand 4, urokinase plasminogen activator and matrix metalloproteinase, which are computed through the solution of a system of reaction–diffusion equations. The method used in the present study is classified into the hybrid approaches. The present study, implemented in three spatial dimensions, demonstrates the feasibility of the approach that is qualitatively confirmed by experimental results.
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Affiliation(s)
- F D Bookholt
- Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands
| | - H N Monsuur
- Department of Dermatology (VUmc), VU University Medical Center, MOVE Research Institute Amsterdam, Amsterdam, The Netherlands
| | - S Gibbs
- Department of Dermatology (VUmc), VU University Medical Center, MOVE Research Institute Amsterdam, Amsterdam, The Netherlands
- Department of Oral Cell Biology, Academic Centre for Dentistry Amsterdam (ACTA), University of Amsterdam and VU University Amsterdam, MOVE Research Institute Amsterdam, Amsterdam, The Netherlands
| | - F J Vermolen
- Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands.
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Mousavi SJ, Hamdy Doweidar M. Three-dimensional numerical model of cell morphology during migration in multi-signaling substrates. PLoS One 2015; 10:e0122094. [PMID: 25822332 PMCID: PMC4379188 DOI: 10.1371/journal.pone.0122094] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2014] [Accepted: 02/21/2015] [Indexed: 12/19/2022] Open
Abstract
Cell Migration associated with cell shape changes are of central importance in many biological processes ranging from morphogenesis to metastatic cancer cells. Cell movement is a result of cyclic changes of cell morphology due to effective forces on cell body, leading to periodic fluctuations of the cell length and cell membrane area. It is well-known that the cell can be guided by different effective stimuli such as mechanotaxis, thermotaxis, chemotaxis and/or electrotaxis. Regulation of intracellular mechanics and cell's physical interaction with its substrate rely on control of cell shape during cell migration. In this notion, it is essential to understand how each natural or external stimulus may affect the cell behavior. Therefore, a three-dimensional (3D) computational model is here developed to analyze a free mode of cell shape changes during migration in a multi-signaling micro-environment. This model is based on previous models that are presented by the same authors to study cell migration with a constant spherical cell shape in a multi-signaling substrates and mechanotaxis effect on cell morphology. Using the finite element discrete methodology, the cell is represented by a group of finite elements. The cell motion is modeled by equilibrium of effective forces on cell body such as traction, protrusion, electrostatic and drag forces, where the cell traction force is a function of the cell internal deformations. To study cell behavior in the presence of different stimuli, the model has been employed in different numerical cases. Our findings, which are qualitatively consistent with well-known related experimental observations, indicate that adding a new stimulus to the cell substrate pushes the cell to migrate more directionally in more elongated form towards the more effective stimuli. For instance, the presence of thermotaxis, chemotaxis and electrotaxis can further move the cell centroid towards the corresponding stimulus, respectively, diminishing the mechanotaxis effect. Besides, the stronger stimulus imposes a greater cell elongation and more cell membrane area. The present model not only provides new insights into cell morphology in a multi-signaling micro-environment but also enables us to investigate in more precise way the cell migration in the presence of different stimuli.
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Affiliation(s)
- Seyed Jamaleddin Mousavi
- Group of Structural Mechanics and Materials Modeling (GEMM), Aragón Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza, Spain
- Mechanical Engineering Department, School of Engineering and Architecture (EINA), University of Zaragoza, Zaragoza, Spain
- Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), Zaragoza, Spain
| | - Mohamed Hamdy Doweidar
- Group of Structural Mechanics and Materials Modeling (GEMM), Aragón Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza, Spain
- Mechanical Engineering Department, School of Engineering and Architecture (EINA), University of Zaragoza, Zaragoza, Spain
- Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), Zaragoza, Spain
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12
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Semi-stochastic cell-level computational modelling of cellular forces: application to contractures in burns and cyclic loading. Biomech Model Mechanobiol 2015; 14:1181-95. [PMID: 25776519 DOI: 10.1007/s10237-015-0664-2] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2014] [Accepted: 02/28/2015] [Indexed: 10/23/2022]
Abstract
A phenomenological model is formulated to model cellular forces on extracellular material. The model is capable of modelling both expansion and contractile forces. This work is based on the assumption of linear elasticity, which allows a superposition argument to arrive at fundamental expressions for cellular forces. It is also shown how the cellular forces can be implemented using different strategies, as well as an extension to cellular point sources. Illustrations are given for modelling a (permanent) contraction (e.g. a contracture) of burns and for cyclic loading by the cells.
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Towards a Mathematical Formalism for Semi-stochastic Cell-Level Computational Modeling of Tumor Initiation. Ann Biomed Eng 2015; 43:1680-94. [PMID: 25670322 PMCID: PMC4495267 DOI: 10.1007/s10439-015-1271-1] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2014] [Accepted: 01/30/2015] [Indexed: 10/27/2022]
Abstract
A phenomenological model is formulated to model the early stages of tumor formation. The model is based on a cell-based formalism, where each cell is represented as a circle or sphere in two-and three dimensional simulations, respectively. The model takes into account constituent cells, such as epithelial cells, tumor cells, and T-cells that chase the tumor cells and engulf them. Fundamental biological processes such as random walk, haptotaxis/chemotaxis, contact mechanics, cell proliferation and death, as well as secretion of chemokines are taken into account. The developed formalism is based on the representation of partial differential equations in terms of fundamental solutions, as well as on stochastic processes and stochastic differential equations. We also take into account the likelihood of seeding of tumors. The model shows the initiation of tumors and allows to study a quantification of the impact of various subprocesses and possibly even of various treatments.
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Challenges in the Modeling of Wound Healing Mechanisms in Soft Biological Tissues. Ann Biomed Eng 2014; 43:1654-65. [DOI: 10.1007/s10439-014-1200-8] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2014] [Accepted: 11/19/2014] [Indexed: 02/03/2023]
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Abstract
Cell morphology plays a critical role in many biological processes, such as cell migration, tissue development, wound healing and tumor growth. Recent investigations demonstrate that, among other stimuli, cells adapt their shapes according to their substrate stiffness. Until now, the development of this process has not been clear. Therefore, in this work, a new three-dimensional (3D) computational model for cell morphology has been developed. This model is based on a previous cell migration model presented by the same authors. The new model considers that during cell-substrate interaction, cell shape is governed by internal cell deformation, which leads to an accurate prediction of the cell shape according to the mechanical characteristic of its surrounding micro-environment. To study this phenomenon, the model has been applied to different numerical cases. The obtained results, which are qualitatively consistent with well-known related experimental works, indicate that cell morphology not only depends on substrate stiffness but also on the substrate boundary conditions. A cell located within an unconstrained soft substrate (several kPa) with uniform stiffness is unable to adhere to its substrate or to send out pseudopodia. When the substrate stiffness increases to tens of kPa (intermediate and rigid substrates), the cell can adequately adhere to its substrate. Subsequently, as the traction forces exerted by the cell increase, the cell elongates and its shape changes. Within very stiff (hard) substrates, the cell cannot penetrate into its substrate or send out pseudopodia. On the other hand, a cell is found to be more elongated within substrates with a constrained surface. However, this elongation decreases when the cell approaches it. It can be concluded that the higher the net traction force, the greater the cell elongation, the larger the cell membrane area, and the less random the cell alignment.
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Affiliation(s)
- Seyed Jamaleddin Mousavi
- Group of Structural Mechanics and Materials Modelling (GEMM), Aragón Institute of Engineering Research (I3A), University of Zaragoza, Spain. Mechanical Engineering Department, School of Engineering and Architecture (EINA), University of Zaragoza, Spain. Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), Spain
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Mousavi SJ, Doblaré M, Doweidar MH. Computational modelling of multi-cell migration in a multi-signalling substrate. Phys Biol 2014; 11:026002. [PMID: 24632566 DOI: 10.1088/1478-3975/11/2/026002] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
Cell migration is a vital process in many biological phenomena ranging from wound healing to tissue regeneration. Over the past few years, it has been proven that in addition to cell-cell and cell-substrate mechanical interactions (mechanotaxis), cells can be driven by thermal, chemical and/or electrical stimuli. A numerical model was recently presented by the authors to analyse single cell migration in a multi-signalling substrate. That work is here extended to include multi-cell migration due to cell-cell interaction in a multi-signalling substrate under different conditions. This model is based on balancing the forces that act on the cell population in the presence of different guiding cues. Several numerical experiments are presented to illustrate the effect of different stimuli on the trajectory and final location of the cell population within a 3D heterogeneous multi-signalling substrate. Our findings indicate that although multi-cell migration is relatively similar to single cell migration in some aspects, the associated behaviour is very different. For instance, cell-cell interaction may delay single cell migration towards effective cues while increasing the magnitude of the average net cell traction force as well as the local velocity. Besides, the random movement of a cell within a cell population is slightly greater than that of single cell migration. Moreover, higher electrical field strength causes the cell slug to flatten near the cathode. On the other hand, as with single cell migration, the existence of electrotaxis dominates mechanotaxis, moving the cells to the cathode or anode pole located at the free surface. The numerical results here obtained are qualitatively consistent with related experimental works.
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Affiliation(s)
- Seyed Jamaleddin Mousavi
- Group of Structural Mechanics and Materials Modelling (GEMM), Aragón Institute of Engineering Research (I3A), University of Zaragoza, Spain. Mechanical Engineering Department, School of Engineering and Architecture (EINA), University of Zaragoza, Spain. Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), Spain
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Semi-stochastic cell-level computational modeling of the immune system response to bacterial infections and the effects of antibiotics. Biomech Model Mechanobiol 2013; 13:713-34. [DOI: 10.1007/s10237-013-0529-5] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2013] [Accepted: 09/11/2013] [Indexed: 10/26/2022]
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18
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A semi-stochastic cell-based model for in vitro infected ‘wound’ healing through motility reduction: A simulation study. J Theor Biol 2013; 318:68-80. [DOI: 10.1016/j.jtbi.2012.11.007] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2012] [Revised: 10/05/2012] [Accepted: 11/02/2012] [Indexed: 01/06/2023]
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Vermolen FJ, Gefen A. Wound Healing: Multi-Scale Modeling. MULTISCALE COMPUTER MODELING IN BIOMECHANICS AND BIOMEDICAL ENGINEERING 2013. [DOI: 10.1007/8415_2012_156] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/12/2023]
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