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Guerra A, Belinha J, Salgado C, Monteiro FJ, Natal Jorge R. Computational Insights into the Interplay of Mechanical Forces in Angiogenesis. Biomedicines 2024; 12:1045. [PMID: 38791007 PMCID: PMC11117778 DOI: 10.3390/biomedicines12051045] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2024] [Revised: 04/15/2024] [Accepted: 04/22/2024] [Indexed: 05/26/2024] Open
Abstract
This study employs a meshless computational model to investigate the impacts of compression and traction on angiogenesis, exploring their effects on vascular endothelial growth factor (VEGF) diffusion and subsequent capillary network formation. Three distinct initial domain geometries were defined to simulate variations in endothelial cell sprouting and VEGF release. Compression and traction were applied, and the ensuing effects on VEGF diffusion coefficients were analysed. Compression promoted angiogenesis, increasing capillary network density. The reduction in the VEGF diffusion coefficient under compression altered VEGF concentration, impacting endothelial cell migration patterns. The findings were consistent across diverse simulation scenarios, demonstrating the robust influence of compression on angiogenesis. This computational study enhances our understanding of the intricate interplay between mechanical forces and angiogenesis. Compression emerges as an effective mediator of angiogenesis, influencing VEGF diffusion and vascular pattern. These insights may contribute to innovative therapeutic strategies for angiogenesis-related disorders, fostering tissue regeneration and addressing diseases where angiogenesis is crucial.
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Affiliation(s)
- Ana Guerra
- INEGI—Instituto de Ciência e Inovação em Engenharia Mecânica e Engenharia Industrial, 4200-465 Porto, Portugal
| | - Jorge Belinha
- ISEP—Instituto Superior de Engenharia do Porto, Departamento de Engenharia Mecânica, Politécnico do Porto, Rua Dr. António Bernardino de Almeida, 431, 4249-015 Porto, Portugal;
| | - Christiane Salgado
- i3S—Instituto de Investigação e Inovação em Saúde, Universidade do Porto, 4200-135 Porto, Portugal; (C.S.); (F.J.M.)
- INEB—Instituto de Engenharia Biomédica, Universidade do Porto, 4200-135 Porto, Portugal
| | - Fernando Jorge Monteiro
- i3S—Instituto de Investigação e Inovação em Saúde, Universidade do Porto, 4200-135 Porto, Portugal; (C.S.); (F.J.M.)
- INEB—Instituto de Engenharia Biomédica, Universidade do Porto, 4200-135 Porto, Portugal
| | - Renato Natal Jorge
- LAETA—Laboratório Associado de Energia, Transportes e Aeronáutica, Universidade do Porto, 4200-165 Porto, Portugal;
- FEUP—Faculdade de Engenharia, Departamento de Engenharia Mecânica, Universidade do Porto, 4200-165 Porto, Portugal
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2
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Abu Bakar N, Mydin RBSMN, Yusop N, Matmin J, Ghazalli NF. Understanding the ideal wound healing mechanistic behavior using in silico modelling perspectives: A review. J Tissue Viability 2024; 33:104-115. [PMID: 38092620 DOI: 10.1016/j.jtv.2023.11.001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2023] [Revised: 10/24/2023] [Accepted: 11/03/2023] [Indexed: 03/17/2024]
Abstract
Complexity of the entire body precludes an accurate assessment of the specific contributions of tissues or cells during the healing process, which might be expensive and time consuming. Because of this, controlling the wound's size, depth, and dimensions may be challenging, and there is not yet an efficient and reliable chronic wound model representation. Furthermore, given the inherent challenges associated with conducting non-invasive in vivo investigations, it becomes peremptory to explore alternative methodologies for studying wound healing. In this context, biologically-realistic mathematical and computational models emerge as a valuable framework that can effectively address this need. Therefore, it might improve our approach to understanding the process at its core. This article will examines all facets of wound healing, including the kinds, pathways, and most current developments in wound treatment worldwide, particularly in silico modelling utilizing both mathematical and structure-based modelling techniques. It may be helpful to identify the crucial traits through the feedback loop of computer models and experimental investigations in order to build innovative therapies to cure wounds. Hence the effectiveness of personalised medicine and more targeted therapy in the healing of wounds may be enhanced by this interdisciplinary expertise.
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Affiliation(s)
- Norshamiza Abu Bakar
- School of Dental Sciences, Universiti Sains Malaysia, 16150, Kota Bharu, Kelantan, Malaysia
| | - Rabiatul Basria S M N Mydin
- Department of Biomedical Science, Advanced Medical and Dental Institute, Universiti Sains Malaysia, 13200, Bertam, Kepala Batas, Pulau Pinang, Malaysia
| | - Norhayati Yusop
- Basic and Medical Sciences Department, School of Dental Sciences, Universiti Sains Malaysia, Kubang Kerian, Malaysia
| | - Juan Matmin
- Department of Chemistry, Faculty of Science, Universiti Teknologi Malaysia, 81310, UTM, Johor Bahru, Malaysia
| | - Nur Fatiha Ghazalli
- Basic and Medical Sciences Department, School of Dental Sciences, Universiti Sains Malaysia, Kubang Kerian, Malaysia.
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3
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Ahmed RK, Abdalrahman T, Davies NH, Vermolen F, Franz T. Mathematical model of mechano-sensing and mechanically induced collective motility of cells on planar elastic substrates. Biomech Model Mechanobiol 2023; 22:809-824. [PMID: 36814004 DOI: 10.1007/s10237-022-01682-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2022] [Accepted: 12/28/2022] [Indexed: 02/24/2023]
Abstract
Cells mechanically interact with their environment to sense, for example, topography, elasticity and mechanical cues from other cells. Mechano-sensing has profound effects on cellular behaviour, including motility. The current study aims to develop a mathematical model of cellular mechano-sensing on planar elastic substrates and demonstrate the model's predictive capabilities for the motility of individual cells in a colony. In the model, a cell is assumed to transmit an adhesion force, derived from a dynamic focal adhesion integrin density, that locally deforms a substrate, and to sense substrate deformation originating from neighbouring cells. The substrate deformation from multiple cells is expressed as total strain energy density with a spatially varying gradient. The magnitude and direction of the gradient at the cell location define the cell motion. Cell-substrate friction, partial motion randomness, and cell death and division are included. The substrate deformation by a single cell and the motility of two cells are presented for several substrate elasticities and thicknesses. The collective motility of 25 cells on a uniform substrate mimicking the closure of a circular wound of 200 µm is predicted for deterministic and random motion. Cell motility on substrates with varying elasticity and thickness is explored for four cells and 15 cells, the latter again mimicking wound closure. Wound closure by 45 cells is used to demonstrate the simulation of cell death and division during migration. The mathematical model can adequately simulate the mechanically induced collective cell motility on planar elastic substrates. The model is suitable for extension to other cell and substrates shapes and the inclusion of chemotactic cues, offering the potential to complement in vitro and in vivo studies.
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Affiliation(s)
- Riham K Ahmed
- Division of Biomedical Engineering, Department of Human Biology, Biomedical Engineering Research Centre, University of Cape Town, Observatory, South Africa.
| | - Tamer Abdalrahman
- Division of Biomedical Engineering, Department of Human Biology, Biomedical Engineering Research Centre, University of Cape Town, Observatory, South Africa
- Computational Mechanobiology, Julius Wolff Institute for Biomechanics and Musculoskeletal Regeneration, Charité Universitätsmedizin, Berlin, Germany
| | - Neil H Davies
- Cardiovascular Research Unit, Chris Barnard Division of Cardiothoracic Surgery, MRC IUCHRU, University of Cape Town, Observatory, South Africa
| | - Fred Vermolen
- Computational Mathematics Group, Department of Mathematics and Statistics, University of Hasselt, Diepenbeek, Belgium
| | - Thomas Franz
- Division of Biomedical Engineering, Department of Human Biology, Biomedical Engineering Research Centre, University of Cape Town, Observatory, South Africa
- Bioengineering Science Research Group, Faculty of Engineering and Physical Sciences, University of Southampton, Southampton, UK
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4
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Egberts G, Vermolen F, van Zuijlen P. Stability of a two-dimensional biomorphoelastic model for post-burn contraction. J Math Biol 2023; 86:59. [PMID: 36964257 PMCID: PMC10038978 DOI: 10.1007/s00285-023-01893-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2022] [Revised: 02/24/2023] [Accepted: 02/27/2023] [Indexed: 03/26/2023]
Abstract
We consider the stability analysis of a two-dimensional model for post-burn contraction. The model is based on morphoelasticity for permanent deformations and combined with a chemical-biological model that incorporates cellular densities, collagen density, and the concentration of chemoattractants. We formulate stability conditions depending on the decay rate of signaling molecules for both the continuous partial differential equations-based problem and the (semi-)discrete representation. We analyze the difference and convergence between the resulting spatial eigenvalues from the continuous and semi-discrete problems.
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Affiliation(s)
- Ginger Egberts
- Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands.
- Research Group Computational Mathematics (CMAT), Department of Mathematics and Statistics, University of Hasselt, Hasselt, Belgium.
| | - Fred Vermolen
- Research Group Computational Mathematics (CMAT), University of Hasselt, Hasselt, Belgium
- Data Science Institute (DSI), University of Hasselt, Hasselt, Belgium
| | - Paul van Zuijlen
- Burn Centre and Department of Plastic, Reconstructive and Hand Surgery, Red Cross Hospital, Beverwijk, The Netherlands
- Department of Plastic, Reconstructive and Hand Surgery, Amsterdam UMC, location VUmc, Amsterdam Movement Sciences, Amsterdam, The Netherlands
- Pediatric Surgical Centre, Emma Children's Hospital, Amsterdam UMC, location AMC and VUmc, Amsterdam, The Netherlands
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5
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Guo Y, Mofrad MRK, Tepole AB. On modeling the multiscale mechanobiology of soft tissues: Challenges and progress. BIOPHYSICS REVIEWS 2022; 3:031303. [PMID: 38505274 PMCID: PMC10903412 DOI: 10.1063/5.0085025] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2022] [Accepted: 07/12/2022] [Indexed: 03/21/2024]
Abstract
Tissues grow and remodel in response to mechanical cues, extracellular and intracellular signals experienced through various biological events, from the developing embryo to disease and aging. The macroscale response of soft tissues is typically nonlinear, viscoelastic anisotropic, and often emerges from the hierarchical structure of tissues, primarily their biopolymer fiber networks at the microscale. The adaptation to mechanical cues is likewise a multiscale phenomenon. Cell mechanobiology, the ability of cells to transform mechanical inputs into chemical signaling inside the cell, and subsequent regulation of cellular behavior through intra- and inter-cellular signaling networks, is the key coupling at the microscale between the mechanical cues and the mechanical adaptation seen macroscopically. To fully understand mechanics of tissues in growth and remodeling as observed at the tissue level, multiscale models of tissue mechanobiology are essential. In this review, we summarize the state-of-the art modeling tools of soft tissues at both scales, the tissue level response, and the cell scale mechanobiology models. To help the interested reader become more familiar with these modeling frameworks, we also show representative examples. Our aim here is to bring together scientists from different disciplines and enable the future leap in multiscale modeling of tissue mechanobiology.
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Affiliation(s)
- Yifan Guo
- School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| | - Mohammad R. K. Mofrad
- Departments of Bioengineering and Mechanical Engineering, University of California Berkeley, Berkeley, California 94720, USA
| | - Adrian Buganza Tepole
- School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907, USA
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Merino-Casallo F, Gomez-Benito MJ, Martinez-Cantin R, Garcia-Aznar JM. A mechanistic protrusive-based model for 3D cell migration. Eur J Cell Biol 2022; 101:151255. [PMID: 35843121 DOI: 10.1016/j.ejcb.2022.151255] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2022] [Revised: 06/15/2022] [Accepted: 07/01/2022] [Indexed: 11/17/2022] Open
Abstract
Cell migration is essential for a variety of biological processes, such as embryogenesis, wound healing, and the immune response. After more than a century of research-mainly on flat surfaces-, there are still many unknowns about cell motility. In particular, regarding how cells migrate within 3D matrices, which more accurately replicate in vivo conditions. We present a novel in silico model of 3D mesenchymal cell migration regulated by the chemical and mechanical profile of the surrounding environment. This in silico model considers cell's adhesive and nuclear phenotypes, the effects of the steric hindrance of the matrix, and cells ability to degradate the ECM. These factors are crucial when investigating the increasing difficulty that migrating cells find to squeeze their nuclei through dense matrices, which may act as physical barriers. Our results agree with previous in vitro observations where fibroblasts cultured in collagen-based hydrogels did not durotax toward regions with higher collagen concentrations. Instead, they exhibited an adurotactic behavior, following a more random trajectory. Overall, cell's migratory response in 3D domains depends on its phenotype, and the properties of the surrounding environment, that is, 3D cell motion is strongly dependent on the context.
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Affiliation(s)
- Francisco Merino-Casallo
- Multiscale in Mechanical and Biological Engineering (M2BE), Aragon Institute of Engineering Research (I3A), Zaragoza 50018, Spain; Department of Mechanical Engineering, Universidad de Zaragoza, Zaragoza 50009, Spain
| | - Maria Jose Gomez-Benito
- Multiscale in Mechanical and Biological Engineering (M2BE), Aragon Institute of Engineering Research (I3A), Zaragoza 50018, Spain; Department of Mechanical Engineering, Universidad de Zaragoza, Zaragoza 50009, Spain
| | - Ruben Martinez-Cantin
- Robotics, Perception and Real Time Group (RoPeRT), Aragon Institute of Engineering Research (I3A), Zaragoza 50018, Spain; Department of Computer Science and System Engineering, Universidad de Zaragoza, Zaragoza 50009, Spain
| | - Jose Manuel Garcia-Aznar
- Multiscale in Mechanical and Biological Engineering (M2BE), Aragon Institute of Engineering Research (I3A), Zaragoza 50018, Spain; Department of Mechanical Engineering, Universidad de Zaragoza, Zaragoza 50009, Spain.
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Mathematical model and computational scheme for multi-phase modeling of cellular population and microenvironmental dynamics in soft tissue. PLoS One 2021; 16:e0260108. [PMID: 34788347 PMCID: PMC8598064 DOI: 10.1371/journal.pone.0260108] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2021] [Accepted: 11/02/2021] [Indexed: 01/21/2023] Open
Abstract
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.
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8
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Guerra A, Belinha J, Mangir N, MacNeil S, Natal Jorge R. Simulation of the process of angiogenesis: Quantification and assessment of vascular patterning in the chicken chorioallantoic membrane. Comput Biol Med 2021; 136:104647. [PMID: 34274599 DOI: 10.1016/j.compbiomed.2021.104647] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2021] [Revised: 06/22/2021] [Accepted: 07/08/2021] [Indexed: 12/26/2022]
Abstract
Angiogenesis, the formation of new blood vessels from pre-existing ones, begins during embryonic development and continues throughout life. Sprouting angiogenesis is a well-defined process, being mainly influenced by vascular endothelial growth factor (VEGF). In this study, we propose a meshless-based model capable of mimicking the angiogenic response to several VEGF concentrations. In this model, endothelial cells migrate according to a diffusion-reaction equation, following the VEGF gradient concentration. The chick chorioallantoic membrane (CAM) assay was used to model the branching process and to validate the obtained numerical results. To analyse the angiogenic response, the total vessel number and the total vessel length presented in the CAM images and in the simulations for all the VEGF concentrations tested were quantified. In both the CAM assay and simulation, the treatments with VEGF increased the total vessel number and the total vessel length. The obtained quantitative results were very similar between the two methodologies used. The proposed model accurately simulates the capillary network pattern concerning its structure and morphology, for the lowest VEGF concentration tested. For the highest VEGF concentration, the capillary network predicted by the model was less accurate when compared to the one presented in the CAM assay but this may be explained by changes in blood vessel width at higher VEGF concentrations. This remains to be tested.
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Affiliation(s)
- Ana Guerra
- Institute of Science and Innovation in Mechanical and Industrial Engineering (INEGI), Rua Dr. Roberto Frias, 400, 4200-465, Porto, Portugal.
| | - Jorge Belinha
- School of Engineering, Polytechnic of Porto (ISEP), Mechanical Engineering Department, Rua Dr. António Bernardino de Almeida, 431, 4249-015, Porto, Portugal.
| | - Naside Mangir
- Kroto Research Institute, Department of Material Science and Engineering, University of Sheffield, North Campus, Broad Lane, Sheffield, S3 7HQ, UK; Hacettepe University School of Medicine, Department of Urology, Sihhiye, 06100, Ankara, Turkey.
| | - Sheila MacNeil
- Kroto Research Institute, Department of Material Science and Engineering, University of Sheffield, North Campus, Broad Lane, Sheffield, S3 7HQ, UK.
| | - Renato Natal Jorge
- Associated Laboratory for Energy, Transports and Aeronautics (LAETA - INEGI), Rua Dr. Roberto Frias, 400, 4200-465, Porto, Portugal; Faculty of Engineering of the University of Porto (FEUP), Mechanical Engineering Department, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal.
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9
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Menon SN, Flegg JA. Mathematical Modeling Can Advance Wound Healing Research. Adv Wound Care (New Rochelle) 2021; 10:328-344. [PMID: 32634070 PMCID: PMC8082733 DOI: 10.1089/wound.2019.1132] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2019] [Accepted: 06/26/2020] [Indexed: 12/27/2022] Open
Abstract
Significance: For over 30 years, there has been sustained interest in the development of mathematical models for investigating the complex mechanisms underlying each stage of the wound healing process. Despite the immense associated challenges, such models have helped usher in a paradigm shift in wound healing research. Recent Advances: In this article, we review contributions in the field that span epidermal, dermal, and corneal wound healing, and treatments of nonhealing wounds. The recent influence of mathematical models on biological experiments is detailed, with a focus on wound healing assays and fibroblast-populated collagen lattices. Critical Issues: We provide an overview of the field of mathematical modeling of wound healing, highlighting key advances made in recent decades, and discuss how such models have contributed to the development of improved treatment strategies and/or an enhanced understanding of the tightly regulated steps that comprise the healing process. Future Directions: We detail some of the open problems in the field that could be addressed through a combination of theoretical and/or experimental approaches. To move the field forward, we need to have a common language between scientists to facilitate cross-collaboration, which we hope this review can support by highlighting progress to date.
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Affiliation(s)
| | - Jennifer A. Flegg
- School of Mathematics and Statistics, University of Melbourne, Melbourne, Australia
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10
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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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Guerra A, Belinha J, Natal Jorge R. A preliminary study of endothelial cell migration during angiogenesis using a meshless method approach. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2020; 36:e3393. [PMID: 32783379 DOI: 10.1002/cnm.3393] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2020] [Revised: 08/03/2020] [Accepted: 08/07/2020] [Indexed: 06/11/2023]
Abstract
Angiogenesis, the development of new blood capillaries, is crucial for the wound healing process. This biological process allows the proper blood supply to the tissue, essential for cell proliferation and viability. Several biological factors modulate angiogenesis, however the vascular endothelial growth factor (VEGF) is the main one. Given the complexity of angiogenesis, in the last years, computational modelling aroused the interest of scientists since it allows to model this process with different, more economic and faster methodologies, comparatively to experimental approaches. In this work, a mathematical model motivated by the analysis of the effect of VEGF diffusion gradient in endothelial cell migration is presented. This is the process that allows capillary formation and it is essential for angiogenesis. The proposed mathematical model is combined with the Radial Point Interpolation Method, being the area discretized considering an unorganized nodal cloud and a background mesh of integration points, without predefined relations. The nodal connectivity was achieved using the "influence-domain" approach. The interpolation functions were constructed using the Radial Point Interpolators techniques. This method combines a radial basis functions with a polynomial functions to obtain the approximation. This preliminary work does not account for the whole complexity of cell and tissue biology, and numerical results are presented for an idealised two-dimensional setting. Nevertheless, the developed RPIM software is a valid numerical tool that can be adjusted to biological problems and may also be able to complement the biological and medical subjects.
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Affiliation(s)
- Ana Guerra
- Institute of Science and Innovation in Mechanical and Industrial Engineering (INEGI), Porto, Portugal
| | - Jorge Belinha
- School of Engineering, Polytechnic of Porto (ISEP), Mechanical Engineering Department, Porto, Portugal
| | - Renato Natal Jorge
- LAETA, INEGI, Porto, Portugal
- Mechanical Engineering Department, University of Porto (FEUP), Porto, Portugal
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12
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Guerra A, Belinha J, Mangir N, MacNeil S, Natal Jorge R. Sprouting Angiogenesis: A Numerical Approach with Experimental Validation. Ann Biomed Eng 2020; 49:871-884. [PMID: 32974754 DOI: 10.1007/s10439-020-02622-w] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2020] [Accepted: 09/14/2020] [Indexed: 12/13/2022]
Abstract
A functional vascular network is essential to the correct wound healing. In sprouting angiogenesis, vascular endothelial growth factor (VEGF) regulates the formation of new capillaries from pre-existing vessels. This is a very complex process and mathematical formulation permits to study angiogenesis using less time-consuming, reproducible and cheaper methodologies. This study aimed to mimic the chemoattractant effect of VEGF in stimulating sprouting angiogenesis. We developed a numerical model in which endothelial cells migrate according to a diffusion-reaction equation for VEGF. A chick chorioallantoic membrane (CAM) bioassay was used to obtain some important parameters to implement in the model and also to validate the numerical results. We verified that endothelial cells migrate following the highest VEGF concentration. We compared the parameters-total branching number, total vessel length and branching angle-that were obtained in the in silico and the in vivo methodologies and similar results were achieved (p-value smaller than 0.5; n = 6). For the difference between the total capillary volume fractions assessed using both methodologies values smaller than 15% were obtained. In this study we simulated, for the first time, the capillary network obtained during the CAM assay with a realistic morphology and structure.
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Affiliation(s)
- Ana Guerra
- Institute of Science and Innovation in Mechanical and Industrial Engineering (INEGI), Rua Dr. Roberto Frias, 400, 4200-465, Porto, Portugal
| | - Jorge Belinha
- Mechanical Engineering Department, School of Engineering, Polytechnic of Porto (ISEP), Rua Dr. António Bernardino de Almeida, 431, 4249-015, Porto, Portugal
| | - Naside Mangir
- Kroto Research Institute, Department of Material Science and Engineering, University of Sheffield, North Campus, Broad Lane, Sheffield, S3 7HQ, UK.,Department of Urology, Royal Hallamshire Hospital, Glossop Rd, Sheffield, S10 2JF, UK
| | - Sheila MacNeil
- Kroto Research Institute, Department of Material Science and Engineering, University of Sheffield, North Campus, Broad Lane, Sheffield, S3 7HQ, UK
| | - Renato Natal Jorge
- Associated Laboratory for Energy, Transports and Aeronautics (LAETA - INEGI), Rua Dr. Roberto Frias, 400, 4200-465, Porto, Portugal. .,Mechanical Engineering Department, Faculty of Engineering of the University of Porto (FEUP), Rua Dr. Roberto Frias, 4200-465, Porto, Portugal.
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13
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Wang Y, Guerrero-Juarez CF, Qiu Y, Du H, Chen W, Figueroa S, Plikus MV, Nie Q. A multiscale hybrid mathematical model of epidermal-dermal interactions during skin wound healing. Exp Dermatol 2020; 28:493-502. [PMID: 30801791 DOI: 10.1111/exd.13909] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2018] [Accepted: 02/13/2019] [Indexed: 12/18/2022]
Abstract
Following injury, skin activates a complex wound healing programme. While cellular and signalling mechanisms of wound repair have been extensively studied, the principles of epidermal-dermal interactions and their effects on wound healing outcomes are only partially understood. To gain new insight into the effects of epidermal-dermal interactions, we developed a multiscale, hybrid mathematical model of skin wound healing. The model takes into consideration interactions between epidermis and dermis across the basement membrane via diffusible signals, defined as activator and inhibitor. Simulations revealed that epidermal-dermal interactions are critical for proper extracellular matrix deposition in the dermis, suggesting these signals may influence how wound scars form. Our model makes several theoretical predictions. First, basal levels of epidermal activator and inhibitor help to maintain dermis in a steady state, whereas their absence results in a raised, scar-like dermal phenotype. Second, wound-triggered increase in activator and inhibitor production by basal epidermal cells, coupled with fast re-epithelialization kinetics, reduces dermal scar size. Third, high-density fibrin clot leads to a raised, hypertrophic scar phenotype, whereas low-density fibrin clot leads to a hypotrophic phenotype. Fourth, shallow wounds, compared to deep wounds, result in overall reduced scarring. Taken together, our model predicts the important role of signalling across dermal-epidermal interface and the effect of fibrin clot density and wound geometry on scar formation. This hybrid modelling approach may be also applicable to other complex tissue systems, enabling the simulation of dynamic processes, otherwise computationally prohibitive with fully discrete models due to a large number of variables.
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Affiliation(s)
- Yangyang Wang
- NSF-Simons Center for Multiscale Cell Fate Research, University of California, Irvine, Irvine, California.,Center for Complex Biological Systems, University of California, Irvine, Irvine, California.,Department of Mathematics, University of California, Irvine, Irvine, California
| | - Christian F Guerrero-Juarez
- NSF-Simons Center for Multiscale Cell Fate Research, University of California, Irvine, Irvine, California.,Center for Complex Biological Systems, University of California, Irvine, Irvine, California.,Department of Mathematics, University of California, Irvine, Irvine, California.,Sue and Bill Gross Stem Cell Research Center, University of California, Irvine, Irvine, California.,Department of Developmental and Cell Biology, University of California, Irvine, Irvine, California
| | - Yuchi Qiu
- NSF-Simons Center for Multiscale Cell Fate Research, University of California, Irvine, Irvine, California.,Center for Complex Biological Systems, University of California, Irvine, Irvine, California.,Department of Mathematics, University of California, Irvine, Irvine, California
| | - Huijing Du
- Department of Mathematics, University of Nebraska-Lincoln, Lincoln, Nebraska
| | - Weitao Chen
- Department of Mathematics, University of California, Riverside, Riverside, California
| | - Seth Figueroa
- NSF-Simons Center for Multiscale Cell Fate Research, University of California, Irvine, Irvine, California.,Center for Complex Biological Systems, University of California, Irvine, Irvine, California.,Department of Mathematics, University of California, Irvine, Irvine, California
| | - Maksim V Plikus
- NSF-Simons Center for Multiscale Cell Fate Research, University of California, Irvine, Irvine, California.,Center for Complex Biological Systems, University of California, Irvine, Irvine, California.,Sue and Bill Gross Stem Cell Research Center, University of California, Irvine, Irvine, California.,Department of Developmental and Cell Biology, University of California, Irvine, Irvine, California
| | - Qing Nie
- NSF-Simons Center for Multiscale Cell Fate Research, University of California, Irvine, Irvine, California.,Center for Complex Biological Systems, University of California, Irvine, Irvine, California.,Department of Mathematics, University of California, Irvine, Irvine, California.,Department of Developmental and Cell Biology, University of California, Irvine, Irvine, California
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14
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Mohamadi S, Norooznezhad AH, Mostafaei S, Nikbakht M, Nassiri S, Safar H, Moghaddam KA, Ghavamzadeh A, Kazemnejad A. A randomized controlled trial of effectiveness of platelet-rich plasma gel and regular dressing on wound healing time in pilonidal sinus surgery: Role of different affecting factors. Biomed J 2019; 42:403-410. [PMID: 31948604 PMCID: PMC6963006 DOI: 10.1016/j.bj.2019.05.002] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2017] [Revised: 09/02/2018] [Accepted: 05/02/2019] [Indexed: 12/16/2022] Open
Abstract
Background The aim of this study was to assess the possible association between different factors such as age, sex, antibiotic consumption duration, angiogenesis and pain and “acceleration of wound healing” in pilonidal sinus patients after treating with platelet-rich plasma (PRP). Methods In this clinical trial, 110 patients were randomly divided into treatment arm and control group. After surgery, control group underwent classic wound dressing and the treatment arm experienced PRP gel therapy. Before achieving complete healing, wound incisional biopsy was performed in order to evaluate angiogenesis. During the study, other data such as pain and antibiotic consumption duration were also collected. Wound healing time of pilonidal sinus disease was analyzed using Extended and Stratify Cox model. Data were analyzed using R and STATA software. p<0.05 were considered statistically significant. Results The average wound volume was calculated 41.9 ± 8.01 cc in the controls and 42.35 ± 10.81 in the treatment arm group. The mean of healing time was 8.7 ± 1.18, 4.8 ± 0.87 weeks for control and treatment arm, respectively. There was a significant and strong negative association between healing time and wound volume (p<0.01). Moreover, a significant negative association was found between pain duration and angiogenesis (p<0.001), a strong positive significant association was found between healing time of the treatment arms (p<0.01), and the rate of wound healing for participants treated with PRP gel was 37.2 times more than that of controls. Conclusion Authors hope for these finding to help the future researches to more thoroughly focus on the mentioned factors in order to find a suitable strategy for wound healing using PRP.
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Affiliation(s)
- Saeed Mohamadi
- Hematology, Oncology and Stem Cell Transplantation Research Center, Tehran University of Medical Sciences, Tehran, Iran
| | - Amir Hossein Norooznezhad
- Regenerative Medicine Research Center, Kermanshah University of Medical Sciences, Kermanshah, Iran; Medical Biology Research Center, Health Technology Institute, Kermanshah University of Medical Sciences, Kermanshah, Iran
| | - Shayan Mostafaei
- Medical Biology Research Center, Health Technology Institute, Kermanshah University of Medical Sciences, Kermanshah, Iran; Epidemiology and Biostatistics Unit, Rheumatology Research Center, Tehran University of Medical Sciences, Tehran, Iran
| | - Mohsen Nikbakht
- Hematology, Oncology and Stem Cell Transplantation Research Center, Tehran University of Medical Sciences, Tehran, Iran
| | - Shirzad Nassiri
- Surgery Ward, Shariati Hospital, Tehran University of Medical Sciences, Tehran, Iran
| | - Hiva Safar
- Pathology Ward, Shariati Hospital, Tehran University of Medical Sciences, Tehran, Iran
| | - Kamran Ali Moghaddam
- Hematology, Oncology and Stem Cell Transplantation Research Center, Tehran University of Medical Sciences, Tehran, Iran
| | - Ardeshir Ghavamzadeh
- Hematology, Oncology and Stem Cell Transplantation Research Center, Tehran University of Medical Sciences, Tehran, Iran
| | - Anoshirvan Kazemnejad
- Department of Biostatistics, Faculty of Medical Sciences, Tarbiat Modares University, Tehran, Iran.
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15
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Blacklow SO, Li J, Freedman BR, Zeidi M, Chen C, Mooney DJ. Bioinspired mechanically active adhesive dressings to accelerate wound closure. SCIENCE ADVANCES 2019; 5:eaaw3963. [PMID: 31355332 PMCID: PMC6656537 DOI: 10.1126/sciadv.aaw3963] [Citation(s) in RCA: 226] [Impact Index Per Article: 45.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2018] [Accepted: 06/20/2019] [Indexed: 05/21/2023]
Abstract
Inspired by embryonic wound closure, we present mechanically active dressings to accelerate wound healing. Conventional dressings passively aid healing by maintaining moisture at wound sites. Recent developments have focused on drug and cell delivery to drive a healing process, but these methods are often complicated by drug side effects, sophisticated fabrication, and high cost. Here, we present novel active adhesive dressings consisting of thermoresponsive tough adhesive hydrogels that combine high stretchability, toughness, tissue adhesion, and antimicrobial function. They adhere strongly to the skin and actively contract wounds, in response to exposure to the skin temperature. In vitro and in vivo studies demonstrate their efficacy in accelerating and supporting skin wound healing. Finite element models validate and refine the wound contraction process enabled by these active adhesive dressings. This mechanobiological approach opens new avenues for wound management and may find broad utility in applications ranging from regenerative medicine to soft robotics.
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Affiliation(s)
- S. O. Blacklow
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
- Wyss Institute for Biologically Inspired Engineering, Harvard University, Cambridge, MA 02138, USA
- School of Medicine, University of California, San Francisco, San Francisco, CA 94143, USA
- Department of Bioengineering, University of California, Berkeley, Berkeley, CA 94720, USA
| | - J. Li
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
- Wyss Institute for Biologically Inspired Engineering, Harvard University, Cambridge, MA 02138, USA
- Department of Mechanical Engineering, McGill University, Montreal, QC H3A 0G4, Canada
- Department of Biomedical Engineering, McGill University, Montreal, QC H3A 0G4, Canada
| | - B. R. Freedman
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
- Wyss Institute for Biologically Inspired Engineering, Harvard University, Cambridge, MA 02138, USA
| | - M. Zeidi
- Department of Mechanical Engineering, McGill University, Montreal, QC H3A 0G4, Canada
| | - C. Chen
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
- Wyss Institute for Biologically Inspired Engineering, Harvard University, Cambridge, MA 02138, USA
| | - D. J. Mooney
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
- Wyss Institute for Biologically Inspired Engineering, Harvard University, Cambridge, MA 02138, USA
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16
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Guerra A, Belinha J, Jorge RN. Modelling skin wound healing angiogenesis: A review. J Theor Biol 2018; 459:1-17. [PMID: 30240579 DOI: 10.1016/j.jtbi.2018.09.020] [Citation(s) in RCA: 56] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2017] [Revised: 09/14/2018] [Accepted: 09/18/2018] [Indexed: 12/22/2022]
Abstract
The occurrence of wounds is a main health concern in Western society due to their high frequency and treatment cost. During wound healing, the formation of a functional blood vessel network through angiogenesis is an essential process. Angiogenesis allows the reestablishment of the normal blood flow, the sufficient exchange of oxygen and nutrients and the removal of metabolic waste, necessary for cell proliferation and viability. Mathematical and computational models provide new tools to improve the healing process. In fact, over the last thirty years, in silico models have been continuously formulated to describe the effect of several biological and mechanical factors in angiogenesis during wound healing. Additionally, with different levels of complexity, these models allow coupling the human skin structure, to distinct cell types and growth factors, to study extracellular matrix composition and to understand its deformation. This paper discusses how in silico models, which are more economical and less time-consuming comparatively to laboratory methodologies, can help test new strategies to promote/optimize angiogenesis. The continuum, cell-based and hybrid mathematical models of wound healing angiogenesis are reviewed in the present paper, in order to identify possible improvements. Accordingly, the development of higher dimension models incorporating multiscale analysis at molecular, cellular and tissue level remains a challenge that future models should consider.
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Affiliation(s)
- Ana Guerra
- INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, Porto 4200-465, Portugal.
| | - Jorge Belinha
- ISEP, School of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, Porto 4200-072, Portugal.
| | - Renato Natal Jorge
- INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, Porto 4200-465, Portugal.
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17
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Merino-Casallo F, Gomez-Benito MJ, Juste-Lanas Y, Martinez-Cantin R, Garcia-Aznar JM. Integration of in vitro and in silico Models Using Bayesian Optimization With an Application to Stochastic Modeling of Mesenchymal 3D Cell Migration. Front Physiol 2018; 9:1246. [PMID: 30271351 PMCID: PMC6142046 DOI: 10.3389/fphys.2018.01246] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2018] [Accepted: 08/17/2018] [Indexed: 11/13/2022] Open
Abstract
Cellular migration plays a crucial role in many aspects of life and development. In this paper, we propose a computational model of 3D migration that is solved by means of the tau-leaping algorithm and whose parameters have been calibrated using Bayesian optimization. Our main focus is two-fold: to optimize the numerical performance of the mechano-chemical model as well as to automate the calibration process of in silico models using Bayesian optimization. The presented mechano-chemical model allows us to simulate the stochastic behavior of our chemically reacting system in combination with mechanical constraints due to the surrounding collagen-based matrix. This numerical model has been used to simulate fibroblast migration. Moreover, we have performed in vitro analysis of migrating fibroblasts embedded in 3D collagen-based fibrous matrices (2 mg/ml). These in vitro experiments have been performed with the main objective of calibrating our model. Nine model parameters have been calibrated testing 300 different parametrizations using a completely automatic approach. Two competing evaluation metrics based on the Bhattacharyya coefficient have been defined in order to fit the model parameters. These metrics evaluate how accurately the in silico model is replicating in vitro measurements regarding the two main variables quantified in the experimental data (number of protrusions and the length of the longest protrusion). The selection of an optimal parametrization is based on the balance between the defined evaluation metrics. Results show how the calibrated model is able to predict the main features observed in the in vitro experiments.
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Affiliation(s)
- Francisco Merino-Casallo
- Multiscale in Mechanical and Biological Engineering, Department of Mechanical Engineering, Aragón Institute of Engineering Research, Universidad de Zaragoza, Zaragoza, Spain
| | - Maria J Gomez-Benito
- Multiscale in Mechanical and Biological Engineering, Department of Mechanical Engineering, Aragón Institute of Engineering Research, Universidad de Zaragoza, Zaragoza, Spain
| | - Yago Juste-Lanas
- Multiscale in Mechanical and Biological Engineering, Department of Mechanical Engineering, Aragón Institute of Engineering Research, Universidad de Zaragoza, Zaragoza, Spain
| | - Ruben Martinez-Cantin
- Centro Universitario de la Defensa, Zaragoza, Spain.,SigOpt, Inc., San Francisco, CA, United States
| | - Jose M Garcia-Aznar
- Multiscale in Mechanical and Biological Engineering, Department of Mechanical Engineering, Aragón Institute of Engineering Research, Universidad de Zaragoza, Zaragoza, Spain
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18
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Weinstein N, Mendoza L, Gitler I, Klapp J. A Network Model to Explore the Effect of the Micro-environment on Endothelial Cell Behavior during Angiogenesis. Front Physiol 2017; 8:960. [PMID: 29230182 PMCID: PMC5711888 DOI: 10.3389/fphys.2017.00960] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2017] [Accepted: 11/10/2017] [Indexed: 01/07/2023] Open
Abstract
Angiogenesis is an important adaptation mechanism of the blood vessels to the changing requirements of the body during development, aging, and wound healing. Angiogenesis allows existing blood vessels to form new connections or to reabsorb existing ones. Blood vessels are composed of a layer of endothelial cells (ECs) covered by one or more layers of mural cells (smooth muscle cells or pericytes). We constructed a computational Boolean model of the molecular regulatory network involved in the control of angiogenesis. Our model includes the ANG/TIE, HIF, AMPK/mTOR, VEGF, IGF, FGF, PLCγ/Calcium, PI3K/AKT, NO, NOTCH, and WNT signaling pathways, as well as the mechanosensory components of the cytoskeleton. The dynamical behavior of our model recovers the patterns of molecular activation observed in Phalanx, Tip, and Stalk ECs. Furthermore, our model is able to describe the modulation of EC behavior due to extracellular micro-environments, as well as the effect due to loss- and gain-of-function mutations. These properties make our model a suitable platform for the understanding of the molecular mechanisms underlying some pathologies. For example, it is possible to follow the changes in the activation patterns caused by mutations that promote Tip EC behavior and inhibit Phalanx EC behavior, that lead to the conditions associated with retinal vascular disorders and tumor vascularization. Moreover, the model describes how mutations that promote Phalanx EC behavior are associated with the development of arteriovenous and venous malformations. These results suggest that the network model that we propose has the potential to be used in the study of how the modulation of the EC extracellular micro-environment may improve the outcome of vascular disease treatments.
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Affiliation(s)
- Nathan Weinstein
- ABACUS-Laboratorio de Matemáticas Aplicadas y Cómputo de Alto Rendimiento, Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados CINVESTAV-IPN, Mexico City, Mexico
| | - Luis Mendoza
- CompBioLab, Departamento de Biología Molecular y Biotecnología, Instituto de Investigaciones Biomédicas, Universidad Nacional Autónoma de México, Mexico City, Mexico
| | - Isidoro Gitler
- ABACUS-Laboratorio de Matemáticas Aplicadas y Cómputo de Alto Rendimiento, Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados CINVESTAV-IPN, Mexico City, Mexico
| | - Jaime Klapp
- ABACUS-Laboratorio de Matemáticas Aplicadas y Cómputo de Alto Rendimiento, Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados CINVESTAV-IPN, Mexico City, Mexico
- Departamento de Física, Instituto Nacional de Investigaciones Nucleares, Mexico City, Mexico
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19
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Koppenol DC, Vermolen FJ. Biomedical implications from a morphoelastic continuum model for the simulation of contracture formation in skin grafts that cover excised burns. Biomech Model Mechanobiol 2017; 16:1187-1206. [PMID: 28181018 PMCID: PMC5511621 DOI: 10.1007/s10237-017-0881-y] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2016] [Accepted: 01/25/2017] [Indexed: 12/20/2022]
Abstract
A continuum hypothesis-based model is developed for the simulation of the (long term) contraction of skin grafts that cover excised burns in order to obtain suggestions regarding the ideal length of splinting therapy and when to start with this therapy such that the therapy is effective optimally. Tissue is modeled as an isotropic, heterogeneous, morphoelastic solid. With respect to the constituents of the tissue, we selected the following constituents as primary model components: fibroblasts, myofibroblasts, collagen molecules, and a generic signaling molecule. Good agreement is demonstrated with respect to the evolution over time of the surface area of unmeshed skin grafts that cover excised burns between outcomes of computer simulations obtained in this study and scar assessment data gathered previously in a clinical study. Based on the simulation results, we suggest that the optimal point in time to start with splinting therapy is directly after placement of the skin graft on its recipient bed. Furthermore, we suggest that it is desirable to continue with splinting therapy until the concentration of the signaling molecules in the grafted area has become negligible such that the formation of contractures can be prevented. We conclude this study with a presentation of some alternative ideas on how to diminish the degree of contracture formation that are not based on a mechanical intervention, and a discussion about how the presented model can be adjusted.
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Affiliation(s)
- Daniël C Koppenol
- 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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20
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Koppenol DC, Vermolen FJ, Koppenol-Gonzalez GV, Niessen FB, van Zuijlen PPM, Vuik K. A mathematical model for the simulation of the contraction of burns. J Math Biol 2016; 75:1-31. [PMID: 27826736 PMCID: PMC5486856 DOI: 10.1007/s00285-016-1075-4] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2016] [Revised: 08/04/2016] [Indexed: 12/31/2022]
Abstract
A continuum hypothesis-based model is developed for the simulation of the contraction of burns in order to gain new insights into which elements of the healing response might have a substantial influence on this process. Tissue is modeled as a neo-Hookean solid. Furthermore, (myo)fibroblasts, collagen molecules, and a generic signaling molecule are selected as model components. An overview of the custom-made numerical algorithm is presented. Subsequently, good agreement is demonstrated with respect to variability in the evolution of the surface area of burns over time between the outcomes of computer simulations and measurements obtained in an experimental study. In the model this variability is caused by varying the values for some of its parameters simultaneously. A factorial design combined with a regression analysis are used to quantify the individual contributions of these parameter value variations to the dispersion in the surface area of healing burns. The analysis shows that almost all variability in the surface area can be explained by variability in the value for the myofibroblast apoptosis rate and, to a lesser extent, the value for the collagen molecule secretion rate. This suggests that most of the variability in the evolution of the surface area of burns over time in the experimental study might be attributed to variability in these two rates. Finally, a probabilistic analysis is used in order to investigate in more detail the effect of variability in the values for the two rates on the healing process. Results of this analysis are presented and discussed.
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Affiliation(s)
- Daniël C Koppenol
- 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
| | | | - Frank B Niessen
- Department of Plastic, Reconstructive and Hand Surgery, MOVE Research Institute, VU University Medical Centre, Amsterdam, The Netherlands
| | - Paul P M van Zuijlen
- Department of Plastic, Reconstructive and Hand Surgery, MOVE Research Institute, VU University Medical Centre, Amsterdam, The Netherlands.,Burn Centre, Red Cross Hospital, Beverwijk, The Netherlands.,Department of Plastic, Reconstructive and Hand Surgery, Red Cross Hospital, Beverwijk, The Netherlands
| | - Kees Vuik
- Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands
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21
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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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22
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Koppenol DC, Vermolen FJ, Niessen FB, van Zuijlen PPM, Vuik K. A biomechanical mathematical model for the collagen bundle distribution-dependent contraction and subsequent retraction of healing dermal wounds. Biomech Model Mechanobiol 2016; 16:345-361. [PMID: 27581323 PMCID: PMC5285442 DOI: 10.1007/s10237-016-0821-2] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2016] [Accepted: 08/19/2016] [Indexed: 12/05/2022]
Abstract
A continuum hypothesis-based, biomechanical model is presented for the simulation of the collagen bundle distribution-dependent contraction and subsequent retraction of healing dermal wounds that cover a large surface area. Since wound contraction mainly takes place in the dermal layer of the skin, solely a portion of this layer is included explicitly into the model. This portion of dermal layer is modeled as a heterogeneous, orthotropic continuous solid with bulk mechanical properties that are locally dependent on both the local concentration and the local geometrical arrangement of the collagen bundles. With respect to the dynamic regulation of the geometrical arrangement of the collagen bundles, it is assumed that a portion of the collagen molecules are deposited and reoriented in the direction of movement of (myo)fibroblasts. The remainder of the newly secreted collagen molecules are deposited by ratio in the direction of the present collagen bundles. Simulation results show that the distribution of the collagen bundles influences the evolution over time of both the shape of the wounded area and the degree of overall contraction of the wounded area. Interestingly, these effects are solely a consequence of alterations in the initial overall distribution of the collagen bundles, and not a consequence of alterations in the evolution over time of the different cell densities and concentrations of the modeled constituents. In accordance with experimental observations, simulation results show furthermore that ultimately the majority of the collagen molecules ends up permanently oriented toward the center of the wound and in the plane that runs parallel to the surface of the skin.
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Affiliation(s)
- Daniël C Koppenol
- 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
| | - Frank B Niessen
- Department of Plastic, Reconstructive and Hand Surgery, MOVE Research Institute, VU University Medical Centre, Amsterdam, The Netherlands
| | - Paul P M van Zuijlen
- Department of Plastic, Reconstructive and Hand Surgery, MOVE Research Institute, VU University Medical Centre, Amsterdam, The Netherlands.,Burn Centre, Red Cross Hospital, Beverwijk, The Netherlands.,Department of Plastic, Reconstructive and Hand Surgery, Red Cross Hospital, Beverwijk, The Netherlands
| | - Kees Vuik
- Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands
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23
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A mathematical model for the simulation of the formation and the subsequent regression of hypertrophic scar tissue after dermal wounding. Biomech Model Mechanobiol 2016; 16:15-32. [PMID: 27229739 PMCID: PMC5285433 DOI: 10.1007/s10237-016-0799-9] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2015] [Accepted: 05/11/2016] [Indexed: 01/13/2023]
Abstract
A continuum hypothesis-based model is presented for the simulation of the formation and the subsequent regression of hypertrophic scar tissue after dermal wounding. Solely the dermal layer of the skin is modeled explicitly and it is modeled as a heterogeneous, isotropic and compressible neo-Hookean solid. With respect to the constituents of the dermal layer, the following components are selected as primary model components: fibroblasts, myofibroblasts, a generic signaling molecule and collagen molecules. A good match with respect to the evolution of the thickness of the dermal layer of scars between the outcomes of simulations and clinical measurements on hypertrophic scars at different time points after injury in human subjects is demonstrated. Interestingly, the comparison between the outcomes of the simulations and the clinical measurements demonstrates that a relatively high apoptosis rate of myofibroblasts results in scar tissue that behaves more like normal scar tissue with respect to the evolution of the thickness of the tissue over time, while a relatively low apoptosis rate results in scar tissue that behaves like hypertrophic scar tissue with respect to the evolution of the thickness of the tissue over time. Our ultimate goal is to construct models with which the properties of newly generated tissues that form during wound healing can be predicted with a high degree of certainty. The development of the presented model is considered by us as a step toward their construction.
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24
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Flegg JA, Menon SN, Maini PK, McElwain DLS. On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process. Front Physiol 2015; 6:262. [PMID: 26483695 PMCID: PMC4588694 DOI: 10.3389/fphys.2015.00262] [Citation(s) in RCA: 41] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2015] [Accepted: 09/04/2015] [Indexed: 11/13/2022] Open
Abstract
Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e., capillary sprout growth, has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made toward the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration.
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Affiliation(s)
- Jennifer A Flegg
- School of Mathematical Sciences, Monash University Melbourne, VIC, Australia
| | | | - Philip K Maini
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford Oxford, UK
| | - D L Sean McElwain
- Institute of Health and Biomedical Innovation and School of Mathematical Sciences, Queensland University of Technology Brisbane, QLD, Australia
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25
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A morphoelastic model for dermal wound closure. Biomech Model Mechanobiol 2015; 15:663-81. [DOI: 10.1007/s10237-015-0716-7] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2015] [Accepted: 08/01/2015] [Indexed: 02/08/2023]
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26
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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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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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Buganza Tepole A, Kuhl E. Computational modeling of chemo-bio-mechanical coupling: a systems-biology approach toward wound healing. Comput Methods Biomech Biomed Engin 2014; 19:13-30. [DOI: 10.1080/10255842.2014.980821] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Cooper RL, Segal RA, Diegelmann RF, Reynolds AM. Modeling the effects of systemic mediators on the inflammatory phase of wound healing. J Theor Biol 2014; 367:86-99. [PMID: 25446708 DOI: 10.1016/j.jtbi.2014.11.008] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2014] [Revised: 10/08/2014] [Accepted: 11/08/2014] [Indexed: 01/13/2023]
Abstract
The normal wound healing response is characterized by a progression from clot formation, to an inflammatory phase, to a repair phase, and finally, to remodeling. In many chronic wounds there is an extended inflammatory phase that stops this progression. In order to understand the inflammatory phase in more detail, we developed an ordinary differential equation model that accounts for two systemic mediators that are known to modulate this phase, estrogen (a protective hormone during wound healing) and cortisol (a hormone elevated after trauma that slows healing). This model describes the interactions in the wound between wound debris, pathogens, neutrophils and macrophages and the modulation of these interactions by estrogen and cortisol. A collection of parameter sets, which qualitatively match published data on the dynamics of wound healing, was chosen using Latin Hypercube Sampling. This collection of parameter sets represents normal healing in the population as a whole better than one single parameter set. Including the effects of estrogen and cortisol is a necessary step to creating a patient specific model that accounts for gender and trauma. Utilization of math modeling techniques to better understand the wound healing inflammatory phase could lead to new therapeutic strategies for the treatment of chronic wounds. This inflammatory phase model will later become the inflammatory subsystem of our full wound healing model, which includes fibroblast activity, collagen accumulation and remodeling.
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Affiliation(s)
- Racheal L Cooper
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014, USA; The VCU Johnson Center, Virginia Commonwealth University Medical Center, Richmond, VA 23298-0614, USA
| | - Rebecca A Segal
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014, USA; Center for the Study of Biological Complexity, Virginia Commonwealth University, Richmond, VA 23284-2030, USA; The VCU Johnson Center, Virginia Commonwealth University Medical Center, Richmond, VA 23298-0614, USA
| | - Robert F Diegelmann
- The VCU Johnson Center, Virginia Commonwealth University Medical Center, Richmond, VA 23298-0614, USA; Department of Biochemistry & Molecular Biology, Virginia Commonwealth University Medical Center, Richmond, VA 23298-0614, USA
| | - Angela M Reynolds
- Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014, USA; The VCU Johnson Center, Virginia Commonwealth University Medical Center, Richmond, VA 23298-0614, USA.
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Valero C, Javierre E, García-Aznar JM, Gómez-Benito MJ. Nonlinear finite element simulations of injuries with free boundaries: application to surgical wounds. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2014; 30:616-633. [PMID: 24443355 PMCID: PMC4531308 DOI: 10.1002/cnm.2621] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2013] [Revised: 11/12/2013] [Accepted: 11/20/2013] [Indexed: 06/03/2023]
Abstract
Wound healing is a process driven by biochemical and mechanical variables in which a new tissue is synthesised to recover original tissue functionality. Wound morphology plays a crucial role in this process, as the skin behaviour is not uniform along different directions. In this work, we simulate the contraction of surgical wounds, which can be characterised as elongated and deep wounds. Because of the regularity of this morphology, we approximate the evolution of the wound through its cross section, adopting a plane strain hypothesis. This simplification reduces the complexity of the computational problem; while allows for a thorough analysis of the role of wound depth in the healing process, an aspect of medical and computational relevance that has not yet been addressed. To reproduce wound contraction, we consider the role of fibroblasts, myofibroblasts, collagen and a generic growth factor. The contraction phenomenon is driven by cell-generated forces. We postulate that these forces are adjusted to the mechanical environment of the tissue where cells are embedded through a mechanosensing and mechanotransduction mechanism. To solve the nonlinear problem, we use the finite element method (FEM) and an updated Lagrangian approach to represent the change in the geometry. To elucidate the role of wound depth and width on the contraction pattern and evolution of the involved species, we analyse different wound geometries with the same wound area. We find that deeper wounds contract less and reach a maximum contraction rate earlier than superficial wounds.
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Affiliation(s)
- C. Valero
- Multiscale in Mechanical and Biological Engineering (M2BE), Aragón Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza, Spain
| | - E. Javierre
- Centro Universitario de la Defensa, Academia General Militar, Zaragoza, Spain
| | - J. M. García-Aznar
- Multiscale in Mechanical and Biological Engineering (M2BE), Aragón Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza, Spain
| | - M. J. Gómez-Benito
- Multiscale in Mechanical and Biological Engineering (M2BE), Aragón Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza, 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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Scianna M, Bell C, Preziosi L. A review of mathematical models for the formation of vascular networks. J Theor Biol 2013; 333:174-209. [DOI: 10.1016/j.jtbi.2013.04.037] [Citation(s) in RCA: 108] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2012] [Revised: 02/15/2013] [Accepted: 04/30/2013] [Indexed: 02/08/2023]
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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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34
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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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35
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A phenomenological model for chemico-mechanically induced cell shape changes during migration and cell-cell contacts. Biomech Model Mechanobiol 2012; 12:301-23. [PMID: 22623108 DOI: 10.1007/s10237-012-0400-0] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2011] [Accepted: 04/26/2012] [Indexed: 12/27/2022]
Abstract
A phenomenological model for the evolution of shape transition of cells is considered. These transitions are determined by the emission of growth-factors, as well as mechanical interaction if cells are subjected to hard impingement. The originality of this model necessitates a formal treatment of the mathematical model, as well as the presentation of elementary cases in order to illustrate the consistence of the model. We will also show some small-scale relevant applications.
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