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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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van Kan, J.J.I.M. (author), Segal, A. (author), Vermolen, Fred (author)Partial differential equations are paramount in mathematical modelling with applications in engineering and science. The book starts with a crash course on partial differential equations in order to familiarize the reader with fundamental properties such as existence, uniqueness and possibly existing maximum principles. The main topic of the...book 2023
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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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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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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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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
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Peng, Q. (author), Vermolen, F.J. (author)In this paper, we extend the model of wound healing by Boon et al. (J Biomech 49(8):1388–1401, 2016). In addition to explaining the model explicitly regarding every component, namely cells, signalling molecules and tissue bundles, we categorized fibroblasts as regular fibroblasts and myofibroblasts. We do so since it is widely documented that...journal article 2020
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Rahrah, M. (author), Vermolen, F.J. (author)Stress and water injection induce deformations and changes in pore pressure in the soil. The interaction between the mechanical deformations and the flow of water induces a change in porosity and permeability, which results in nonlinearity. To investigate this interaction and the impact of mechanical vibrations and pressure pulses on the flow...journal article 2018
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Vermolen, F.J. (author), Segal, A. (author)In finite-element computations, one often needs to calculate integrals of products of powers of monomials over simplexes. In this manuscript, we prove a generalisation of the exact integration formula that was reported and proved for two-dimensional simplexes by Holand & Bell in 1969. We extend the proof to n-dimensional simplexes and to...journal article 2018
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Koppenol, D.C. (author), Vermolen, F.J. (author)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,...journal article 2017
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Koppenol, D.C. (author), Vermolen, F.J. (author), Koppenol-Gonzalez, Gabriela V. (author), Niessen, Frank B. (author), van Zuijlen, Paul P.M. (author), Vuik, Cornelis (author)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...journal article 2016
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Bookholt, F.D. (author), Monsuur, H.N. (author), Gibbs, S. (author), Vermolen, F.J. (author)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)...journal article 2016
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Koppenol, D.C. (author), Vermolen, F.J. (author), Niessen, Frank B. (author), van Zuijlen, Paul P.M. (author), Vuik, Cornelis (author)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...journal article 2016
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Zemskov, S.V. (author), Copuroglu, O. (author), Vermolen, F.J. (author)A mathematical model for the post-damage recovery of carbonated cement is described. The model is based on a two-dimensional initial-boundary value problem for a system of partial differential equations. The study is embedded within the framework of investigating the effect of using lightweight expanded clay aggregate, which is incorporated into...conference paper 2013
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Zemskov, S.V. (author), Copuroglu, O. (author), Vermolen, F.J. (author)A mathematical model for the post-damage recovery of carbonated cement is described. The model is based on a two-dimensional initial-boundary value problem for a system of partial differential equations. The study is embedded within the framework of investigating the effect of using lightweight expanded clay aggregate, which is incorporated into...conference paper 2013
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Vermolen, F.J. (author), Javierre, E. (author)A simplified finite-element model for wound healing is proposed. The model takes into account the sequential steps of dermal regeneration, wound contraction, angiogenesis and wound closure. An innovation in the present study is the combination of the aforementioned partially overlapping processes, which can be used to deliver novel insights into...journal article 2011
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Vermolen, F.J. (author), Segal, A. (author), Gefen, A. (author)We consider the accumulation and formation of lipid droplets in an adipocyte cell. The process incorporates adipose nucleation (adipogenesis) and growth. At later stages, there will be merging of droplets and growth of larger droplets at the expense of the smaller droplets, which will essentially undergo lipolysis. The process is modeled by the...journal article 2011
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- Zemskov, S.V. (author), Jonkers, H.M. (author), Vermolen, F.J. (author) conference paper 2011
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