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Egberts, G. (author), Vermolen, F.J. (author), van Zuijlen, Paul (author)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...journal article 2023
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Vuik, Cornelis (author), Vermolen, F.J. (author), van Gijzen, M.B. (author), Vuik, Thea (author)In this book we discuss several numerical methods for solving ordinary differential equations. We emphasize the aspects that play an important role in practical problems. We confine ourselves to ordinary differential equations with the exception of the last chapter in which we discuss the heat equation, a parabolic partial differential equation....book 2023
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Lu, Jenny (author), Vermolen, F.J. (author)In this paper a Spatial Markov Chain Cellular Automata model for the spread of viruses is proposed. The model is based on a graph with connected nodes, where the nodes represent individuals and the connections between the nodes denote the relations between humans. In this way, a graph is connected where the probability of infectious spread...book chapter 2023
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Peng, Q. (author), Vermolen, F.J. (author), Weihs, D. (author)Cancer cell migration between different body parts is the driving force behind cancer metastasis, which causes mortality of patients. Migration of cancer cells often proceeds by penetration through narrow cavities in possibly stiff tissues. In our previous work [12], a model for the evolution of cell geometry is developed, and in the current...book chapter 2023
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Egberts, G. (author), Vermolen, F.J. (author), van Zuijlen, Paul (author)Severe burn injuries often lead to skin contraction, leading to stresses in and around the damaged skin region. If this contraction leads to impaired joint mobility, one speaks of contracture. To optimize treatment, a mathematical model, that is based on finite element methods, is developed. Since the finite element-based simulation of skin...journal article 2023
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Vermolen, F.J. (author), Bakker, D.R. (author), Vuik, Cornelis (author)The discretisation of the Laplacian results into the well-known Laplace matrix. In the case of a one dimensional problem, an explicit formula for its inverse is derived on the basis of fundamental solutions (Green’s functions) for general boundary conditions. For a linear reaction–diffusion equation, approximations of the inverse are given.journal article 2022
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Peng, Q. (author), Vermolen, F.J. (author)We consider a mathematical model for skin contraction, which is based on solving a momentum balance under the assumptions of isotropy, homogeneity, Hooke's Law, infinitesimal strain theory and point forces exerted by cells. However, point forces, described by Dirac Delta distributions lead to a singular solution, which in many cases may cause...journal article 2022
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Egberts, G. (author), Schaaphok, Marianne (author), Vermolen, F.J. (author), Zuijlen, Paul van (author)Burn injuries can decrease the quality of life of a patient tremendously, because of esthetic reasons and because of contractions that result from them. In severe case, skin contraction takes place at such a large extent that joint mobility of a patient is significantly inhibited. In these cases, one refers to a contracture. In order to...journal article 2022
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Egberts, G. (author), Desmoulière, Alexis (author), Vermolen, F.J. (author), van Zuijlen, Paul (author)We consider a two-dimensional biomorphoelastic model describing post-burn scar contraction. This model describes skin displacement and the development of the effective Eulerian strain in the tissue. Besides these mechanical components, signaling molecules, fibroblasts, myofibroblasts, and collagen also play a significant role in the model. We...journal article 2022
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Peng, Q. (author), Vermolen, F.J. (author)Deep dermal wounds induce skin contraction as a result of the traction forcing exerted by (myo)fibroblasts on their immediate environment. These (myo)fibroblasts are skin cells that are responsible for the regeneration of collagen that is necessary for the integrity of skin We consider several mathematical issues regarding models that...journal article 2022
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Peng, Q. (author), Gorter, W.S. (author), Vermolen, F.J. (author)Plastic (permanent) deformations were earlier, modeled by a phenomenological model in Peng and Vermolen (Biomech Model Mechanobiol 19(6):2525–2551, 2020). In this manusctipt, we consider a more physics-based formulation that is based on morphoelasticity. We firstly introduce the morphoelasticity approach and investigate the impact of various...journal article 2022
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van Zuijlen, Paul P.M. (author), Korkmaz, Halil Ibrahim (author), Sheraton, Vivek M. (author), Haanstra, Tsjitske M. (author), Pijpe, Anouk (author), de Vries, Annebeth (author), van der Vlies, Cornelis H. (author), Bosma, Eelke (author), de Jong, Evelien (author), Middelkoop, Esther (author), Vermolen, F.J. (author), Sloot, Peter M.A. (author)Health care is undergoing a profound technological and digital transformation and has become increasingly complex. It is important for burns professionals and researchers to adapt to these developments which may require new ways of thinking and subsequent new strategies. As Einstein has put it: "We must learn to see the world anew." The...journal article 2022
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Peng, Q. (author), Vermolen, F.J. (author)Skin contraction is an important biophysical process that takes place during and after recovery of deep tissue injury. This process is mainly caused by fibroblasts (skin cells) and myofibroblasts (differentiated fibroblasts which exert larger pulling forces and produce larger amounts of collagen) that both exert pulling forces on the...journal article 2022
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Egberts, G. (author), Vermolen, F.J. (author), van Zuijlen, Paul (author)We consider a one-dimensional morphoelastic model describing post-burn scar contraction. Contraction can lead to a limited range of motion (contracture). Reported prevalence of burn scar contractures are 58.6% at 3–6 weeks and 20.9% at 12 months post-reconstructive surgery after burns. This model describes the displacement of the dermal layer...journal article 2021
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Peng, Q. (author), Vermolen, F.J. (author), Weihs, D. (author)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...journal article 2021
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Egberts, G. (author), Vermolen, F.J. (author), van Zuijlen, Paul (author)To deal with permanent deformations and residual stresses, we consider a morphoelastic model for the scar formation as the result of wound healing after a skin trauma. Next to the mechanical components such as strain and displacements, the model accounts for biological constituents such as the concentration of signaling molecules, the...journal article 2021
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Peng, Q. (author), Vermolen, F.J. (author)</p><p class="MsoNormal">We consider several mathematical issues regarding models that simulate forces exerted by cells. Since the size of cells is much smaller than the size of the domain of computation, one often considers point forces, modelled by Dirac Delta distributions on boundary segments of cells. In the current paper, we treat...report 2020
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Peng, Q. (author), Vermolen, F.J. (author)Deep tissue injury is often followed by contraction of the scar tissue. This contraction occurs as a result of pulling forces that are exerted by fibroblasts (skin cells). We consider a cell-based approach to simulate the contraction behavior of the skin. Since the cells are much smaller than the wound region, we model cellular forces by...conference paper 2020
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Rahrah, M. (author), Vermolen, F.J. (author)Poroelasticity theory can be used to analyse the coupled interaction between fluid flow and porous media (matrix) deformation. The classical theory of linear poroelasticity captures this coupling by combining Terzaghi’s effective stress with a linear continuity equation. Linear poroelasticity is a good model for very small deformations;...journal article 2020
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Rahrah, M. (author), Lopez Pena, L.A. (author), Vermolen, F.J. (author), Meulenbroek, B.J. (author)Water injection in the aquifer induces deformations in the soil. These mechanical deformations give rise to a change in porosity and permeability, which results in non-linearity of the mathematical problem. Assuming that the deformations are very small, the model provided by Biot’s theory of linear poroelasticity is used to determine the...journal article 2020