The combined use of experimental and mathematical models can lead to a better understanding of fracture healing. In this study, a mathematical model, which was originally established by Bailón-Plaza and van der Meulen (J Theor Biol 212:191-209, 2001), was applied to an experimental model of a semi-stabilized murine tibial fracture. The mathematical model… (More)
Linearly-implicit two-step peer methods are successfully applied in the numerical solution of ordinary differential and differential-algebraic equations. One of their strengths is that even high-order methods do not show order reduction in computations for stiff problems. With this property, peer methods commend themselves as time-stepping schemes in finite… (More)
In this paper we consider the numerical solution of 2D systems of certain types of taxis-diiusion-reaction equations from mathematical biology. By spatial discretization these PDE systems are approximated by systems of positive, nonlinear ODEs (Method of Lines). The aim of this paper is to examine the numerical integration of these ODE systems for low to… (More)
The processes of wound healing and bone regeneration and problems in tissue engineering have been an active area for mathematical modeling in the last decade. Here we review a selection of recent models which aim at deriving strategies for improved healing. In wound healing, the models have particularly focused on the inflammatory response in order to… (More)
This paper describes the main building blocks of a simulation environment of the OSI Network Layer of packet-switching networks. The need for such a tool is presented and pitfalls of previous solutions are described. Remedies provided by the most recent solution are discussed. Architecture, organisation, and architectural decisions are explained.
— We investigate how additional links added randomly to a network connection topology affect the phase transition from the free flow state to the congested state in packet-switching networks (PSNs). For the purpose of our study we have identified that the OSI Network Layer is the most important layer of the OSI reference model. For this layer we developed… (More)
Splitting methods are a frequently used approach for the solution of large stiff initial value problems of ordinary differential equations with an additively split right-hand side function. Such systems arise, for instance, as method of lines discretizations of evolutionary partial differential equations in many applications. We consider the choice of… (More)
Angiogenesis – the process by which new blood vessels grow into a tissue from surrounding parent vessels – is an important process in many areas of medicine. Here we consider the numerical simulation of a PDE model of tumor-induced angiogenesis. It contains convection (migration), diffusion and reaction terms. Despite the restriction to one specific model,… (More)