1,720,952 research outputs found
Comparison between a phenomenological approach and a morphoelasticity approach regarding the displacement of extracellular matrix
Full text linkPlastic (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 input variables on the output parameters by sensitivity analysis. A comparison of both model formulations shows that both models give similar computational results. Furthermore, we carry out Monte Carlo simulations of the skin contraction model containing the morphoelasticity approach. Most statistical correlations from the two models are similar, however, the impact of the collagen density on the severeness of contraction is larger for the morphoelasticity model than for the phenomenological model.Numerical Analysi
A formalism for modelling traction forces and cell shape evolution during cell migration in various biomedical processes
No full textThe 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.</p
Agent-based modelling and parameter sensitivity analysis with a finite-element method for skin contraction
No full textIn 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 myofibroblasts play a significant role during wound healing and skin contraction and that they are the main phenotype of cells that is responsible for the permanent deformations. Furthermore, we carried out some sensitivity tests of the model by modifying certain parameter values, and we observe that the model shows some consistency with several biological phenomena. Using Monte Carlo simulations, we found that there is a significant strong positive correlation between the final wound area and the minimal wound area. The high correlation between the wound area after 4 days and the final/minimal wound area makes it possible for physicians to predict the most probable time evolution of the wound of the patient. However, the collagen density ratio at the time when the wound area reaches its equilibrium and minimum, cannot indicate the degree of wound contractions, whereas at the 4th day post-wounding, when the collagen is accumulating from null, there is a strong negative correlation between the area and the collagen density ratio. Further, under the circumstances that we modelled, the probability that patients will end up with 5% contraction is about 0.627.Numerical Analysi
Point forces in elasticity equation and their alternatives in multi dimensions
Full text linkDeep 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 simulate traction forces exerted by (myo)fibroblasts. Since the size of cells (e.g. (myo)fibroblasts) 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 to simulate the traction forces exerted by the skin cells. In the current paper, we treat the forces that are directed normal to the cell boundary and toward the cell centre. Since it can be shown that there exists no smooth solution, at least not in H1 for solutions to the governing momentum balance equation, we analyse the convergence and quality of approximation. Furthermore, the expected finite element problems that we get necessitate to scrutinize alternative model formulations, such as the use of smoothed Dirac Delta distributions, or the so-called smoothed particle approach as well as the so-called ‘hole’ approach where cellular forces are modelled through the use of (natural) boundary conditions. In this paper, we investigate and attempt to quantify the conditions for consistency between the various approaches. This has resulted into error analyses in the L2-norm of the numerical solution based on Galerkin principles that entail Lagrangian basis functions. The paper also addresses well-posedness in terms of existence and uniqueness. The current analysis has been performed for the linear steady-state (hence neglecting inertia and damping) momentum equations under the assumption of Hooke's law.Numerical Analysi
Upscaling between an agent-based model (smoothed particle approach) and a continuum-based model for skin contractions
Full text linkSkin 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 surrounding extracellular matrix (ECM). Modelling is done in multiple scales: agent-based modelling on the microscale and continuum-based modelling on the macroscale. In this manuscript we present some results from our study of the connection between these scales. For the one-dimensional case, we managed to rigorously establish the link between the two modelling approaches for both closed-form solutions and finite-element approximations. For the multi-dimensional case, we computationally evidence the connection between the agent-based and continuum-based modelling approaches.Numerical Analysi
Simulating sprouting angiogenesis: Using a new 3D substrate dependent cell-based model
No full textAngiogenesis1 is the biological mechanism by which new blood vessels sprout from existing ones. It differs from vasculogenesis, which is the de novo growth of the primary vascular network from initially dispersed endothelial cells (ECs). Vasculogenesis is predominant in embryonic tissue whilst new vasculature in the adult body arises mostly from angiogenesis. ECs, lining the inside of blood vessels, react to different angiogenic stimuli and inhibitors. Among the stimuli is the vascular endothelial growth factor (VEGF) which is up-regulated in tissue where the vascular structure is damaged or insufficiently developed to meet oxygen demand. The identification of the processes involved in angiogenesis is quite recent and has stirred increased interest in therapeutic and clinical applications according to Carmeliet et al. [1]. One can think of tissue repair in wound beds, inhibition of growth of tumorous tissue or vascular reform during the female reproductive cycle. Rossiter et al. [2] showed that VEGF induced angiogenesis is crucial for wound healing in an experiment where wounds were inflicted upon normal and VEGF-deficient mice. New vasculature ensures supply of oxygen and lymphocytes and disposal of carbon dioxide and lactates, accelerating wound healing and tissue reconstruction. The increased creation of new vasculature around tumorous tissue is believed to follow the same process and inhibiting angiogenesis is therefore an important topic in clinical studies on cancer treatment. Biochemical laboratory experiments can be hard, time consuming, expensive or unethical. Computational models can be used to provide an easy, quick and cheap way to get insights that would otherwise require laboratory experiments. The understanding of biological processes needs quantification and in this sense mathematical formulation of the relations involved becomes useful. Their mathematical interpretation and experimental verification is an iterative process resulting in better understanding of the process itself. Computer simulation will never make laboratory experiments obsolete, but it can provide guidance in targeting viable hypotheses before conducting in vitro or in vivo experiments. Mathematical modeling of biological cellular processes dates back to the simulation by Glazier and Graner in 1992. They describe natural sorting behavior of different cell types [3] and different re-arrangement patterns driven by the differential adhesion hypothesis [4]. This hypothesis states that cells of different types have specific potential energies upon adhesion, driving sorting behavior. In these simulations, the cellular Potts model2 (CPM) is used. A CPM for vasculogenesis based on this work was made byMerks et al. [5, 6] in which a layer of partial differential equations (PDEs) models the chemoattractants. Later, Merks added Vascular Endothelial cadherin (VE-cadherin) caused contact-inhibited chemotaxis to simulate angiogenic-like sprout formation [7]. From an initial clump of ECs in the model sprouting behavior appears. Merks postulates that both vasculogenesis and angiogenesis must be driven by the same principles. To produce these results, a generic library called the Tissue Simulation Toolkit (TST) was written in C++ starting from 2004 modeling the CPM described by Glazier et al. [4] in a generic way. Merks [7] extensively describes the advantages of a cell based approach over a continuum approach that is widely used in mathematical biology. Although his CPM is a nice method that increases insight in the angiogenic process, it is computationally heavy, limiting the scalability of the tractable problem domain. Vermolen and Gefen [8] described tissue behavior using a semi-stochastic cell-based formalism to model the migration of cells in colonies in the context of wound healing, tumor growth, bone ingrowth and contraction formation. Movement of cells is assumed to be the result of a strain energy density working as a mechanical stimulus. Like the CPM, the model tracks displacement and viability of individual cells. The aim of this study is to adapt this semi-stochastic cell-based formalism to describe angiogenesis, hence connecting this modeling approach to the subject ofMerks’ work. The need for such a model is clearly stated in the discussion of Vermolen’s work [9]. Thanks to the computational less heavy character in comparison with the CPM, we hope to be able to simulate larger areas to get a better glance at large scale behavior whilst still being able to benefit from the cell-based character of the model. We also improve the biochemical model for the degrading of the substrate by the cells and formulate all relevant parameters based on local properties. The challenge is to translate the advantages of Merks’ CPM, like cell shape specific behavior, tracking of elongation patterns and cell-cell contact behavior, to this new formalism without compromising the computational simplicity. To verify our simulation results with biochemical experiments, this study is performed in collaboration with the Dermatology Department of the VU Medical Center. This department does in vitro laboratory research on many processes that occur in the skin, for example the role of endothelial cells during skin wound healing. The first aim of this research is tomimic their in vitro angiogenesis sprouting assay using our computational model, simulating the response to different chemical stimuli like VEGF. Formulating a way to visually and numerically compare the laboratory work to the simulated results is key to making the model applicable in practice.Numerical AnalysisApplied mathematicsElectrical Engineering, Mathematics and Computer Scienc
A Cellular Automata Model of Oncolytic Virotherapy in Pancreatic Cancer
No full textOncolytic 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 use of probabilistic principles. The migration of injected viruses (as therapy) is modeled by diffusion through the tissue. The resulting diffusion–reaction equation with smoothed point viral sources is discretized by the finite difference method and integrated by the IMEX approach. Furthermore, Monte Carlo simulations are done to quantitatively evaluate the correlations between various input parameters and numerical results. As we expected, our model is able to simulate the pancreatic cancer growth at early stages, which is calibrated with experimental results. In addition, the model can be used to predict and evaluate the therapeutic effect of oncolytic virotherapy.Numerical Analysi
High-speed predictions of post-burn contraction using a neural network trained on 2D-finite element simulations
No full textSevere 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 contraction can be expensive from a computational point of view, we use machine learning to replace these simulations such that we have a cheap alternative. The current study deals with a feed-forward neural network that we trained with 2D finite element simulations based on morphoelasticity. We focus on the evolution of the scar shape, wound area, and total strain energy, a measure of discomfort, over time. The results show average goodness of fit (R2) of 0.9979 and a tremendous speedup of 1815000X. Further, we illustrate the applicability of the neural network in an online medical app that takes the patient's age into account.Numerical Analysi
Mathematical modelling of angiogenesis and contraction occuring during wound healing in soft tissues
No full textWound contraction and angiogenesis are two important processes in the proliferative stage of wound healing. In this thesis a novel mathematical model on angiogenesis is presented. Furthermore this new angiogenesis model is coupled with an already existing model for wound contraction.Numerical AnalysisApplied mathematicsElectrical Engineering, Mathematics and Computer Scienc
Semi-stochastische aanpak van migratie, sterfte en deling in geïnfecteerde celkolonies
No full textApplied mathematicsElectrical Engineering, Mathematics and Computer Scienc
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