Mathematical modelling of angiogenesis using continuous cell-based models

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)...

Simulation of Front Instabilities in Density-Driven Flow, Using a Reactive Transport Model for Biogrout Combined with a Randomly Distributed Permeability Field

Biogrout is a method to strengthen granular soil, which is based on microbial-induced carbonate precipitation. To model the Biogrout process, a reactive transport model is used. Since high flow rates are undesirable for the Biogrout process, the model equations can be solved with a standard Galerkin finite element method. The Biogrout process...

A Reactive Transport Model for Biogrout Compared to Experimental Data

Biogrout is a method for reinforcement of granular soil. In the Biogrout process, calcium carbonate is produced. This solid connects the grains, and therefore the strength of the soil is increased. The calcium carbonate is formed with the use of micro-organisms. Experiments and numerical simulations have been performed to demonstrate the process...

Short Review of Computational Models for Single Cell Deformation and Migration

This short review communication aims at enumerating several modeling efforts that have been performed to model cell migration and deformation. To optimize and improve medical treatments against diseases like cancer, ischemic wounds or pressure ulcers, it is of vital importance to understand the underlying biological mechanisms. Such biological...

Particle methods to solve modelling problems in wound healing and tumor growth

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...

Semi-stochastic cell-level computational modelling of cellular forces

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...

Towards a Mathematical Formalism for Semi-stochastic Cell-Level Computational Modeling of Tumor Initiation

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...

In silico cell and tissue science

Interactive mathematical model of self-healing in carbonated cementitious materials

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...

Modeling of a self-healing process in blast furnace slag cement exposed to accelerated carbonation

In the current research, a mathematical model for the post-damage improvement of the carbonated blast furnace slag cement (BFSC) exposed to accelerated carbonation is constructed. The study is embedded within the framework of investigating the effect of using lightweight expanded clay aggregate, which is incorporated into the impregnation of the...

A phenomenological model for chemico-mechanically induced cell shape changes during migration and cell–cell contacts

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...

Stability analysis for a peri-implant osseointegration model

We investigate stability of the solution of a set of partial differential equations, which is used to model a peri-implant osseointegration process. For certain parameter values, the solution has a ‘wave-like’ profile, which appears in the distribution of osteogenic cells, osteoblasts, growth factor and bone matrix. This ‘wave-like’ profile...

A mathematical model and analytical solution for the fixation of bacteria in biogrout

Biogrout is a new method for soil reinforcement, which is based on microbialinduced carbonate precipitation. Bacteria and reactants are flushed through the soil, resulting in calcium carbonate precipitation and consequent soil reinforcement. Bacteria are crucially important in the Biogrout process since they catalyse the reaction. Hence, to...

A finite-element model for healing of cutaneous wounds combining contraction, angiogenesis and closure

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...

A pilot study of a phenomenological model of adipogenesis in maturing adipocytes using Cahn–Hilliard theory

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...

A semi-stochastic cell-based formalism to model the dynamics of migration of cells in colonies

We consider the movement and viability of individual cells in cell colonies. Cell movement is assumed to take place as a result of sensing the strain energy density as a mechanical stimulus. The model is based on tracking the displacement and viability of each individual cell in a cell colony. Several applications are shown, such as the dynamics...

Application of the numerical density-enthalpy method to the multi-phase flow through a porous medium

In this paper we apply a new method to solve multi-phase fluid flow problem for 1D1D and 2D2D fluid systems. This method is developed at TNO and presented in [1] for spatially homogeneous systems. We call this method the numerical density-enthalpy method (or ??-hh method) because density-enthalpy phase diagrams (or ??-hh diagrams) play an...

A suite of sharp interface models for solid-state transformations in alloys

The work deals in particular with dissolution and growth of particles in solid-state alloys. Several models are presented and numerical solution procedures are summarized briefly. Further, some analytic solutions are considered shortly, which are useful to validate the numerical solutions. One model, which incorporates surface energy effects is...