Searched for: subject%3A%22models%22
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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), 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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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), 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)
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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Chen, J. (author), Weihs, D. (author), Vermolen, F.J. (author)
Oncolytic virotherapy is known as a new treatment to employ less virulent viruses to specifically target and damage cancer cells. This work presents a cellular automata model of oncolytic virotherapy with an application to pancreatic cancer. The fundamental biomedical processes (like cell proliferation, mutation, apoptosis) are modeled by the...
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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Lopez Pena, L.A. (author), Meulenbroek, B.J. (author), Vermolen, F.J. (author)
Successful microbial enhanced oil recovery depends on several factors like reservoir characteristics and microbial activity. In this work, a pore network is used to study the hydrodynamic evolution over time as a result of the development of a biofilm in the pores. A new microscopic model is proposed for biofilm growth which takes into...
journal article 2019
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Chen, J. (author), Weihs, Daphne (author), Vermolen, F.J. (author)
More than eighty percent of pancreatic cancer involves ductal adenocarcinoma with an abundant desmoplastic extracellular matrix surrounding the solid tumor entity. This aberrant tumor microenvironment facilitates a strong resistance of pancreatic cancer to medication. Although various therapeutic strategies have been reported to be effective...
journal article 2019
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Chen, J. (author), Weihs, Daphne (author), van Dijk, Marcel (author), Vermolen, F.J. (author)
Cell migration plays an essential role in cancer metastasis. In cancer invasion through confined spaces, cells must undergo extensive deformation, which is a capability related to their metastatic potentials. Here, we simulate the deformation of the cell and nucleus during invasion through a dense, physiological microenvironment by developing...
journal article 2018
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Lopez Pena, L.A. (author), Meulenbroek, B.J. (author), Vermolen, F.J. (author)
In this work, we model the biofilm growth at the microscale using a rectangular pore network model in 2D and a cubic network in 3D. For the 2D network, we study the effects of bioclogging on porosity and permeability when we change parameters like the number of nodes in the network, the network size, and the concentration of nutrients at the...
journal article 2018
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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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Chen, J. (author), Weihs, Daphne (author), Vermolen, F.J. (author)
Cell migration, known as an orchestrated movement of cells, is crucially important for wound healing, tumor growth, immune response as well as other biomedical processes. This paper presents a cell-based model to describe cell migration in non-isotropic fibrin networks around pancreatic tumor islets. This migration is determined by the...
journal article 2017
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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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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, 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...
journal article 2016
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Vermolen, F.J. (author)
The paper deals with a compilation of several of our modelling studies on particle methods used for simulation of wound healing and tumor growth processes. The paper serves as an introduction of our modelling approaches to researchers with interest in biological cell-based models that use particle-based modelling approaches. The particles that...
journal article 2015
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Vermolen, F.J. (author), Gefen, A. (author)
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...
journal article 2015
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Vermolen, F.J. (author), Van der Meijden, R.P. (author), Van Es, M. (author), Gefen, A. (author), Weihs, D. (author)
A phenomenological model is formulated to model the early stages of tumor formation. The model is based on a cell-based formalism, where each cell is represented as a circle or sphere in two-and three dimensional simulations, respectively. The model takes into account constituent cells, such as epithelial cells, tumor cells, and T-cells that...
journal article 2015
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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
Searched for: subject%3A%22models%22
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