Mathematical modelling of angiogenesis in wound healing: Comparison of theory and experiment.
Mathematical Modelling of Cancer Stem Cells Population Behavior
Recent discovery of cancer stem cells in tumorigenic tissues has raised many questions about their nature, origin, function and their behavior in cell culture. Most of current experiments reporting a dynamics of cancer stem cell populations in culture show the eventual stability of the percentages of these cell populations in the whole population of cancer cells, independently of the starting conditions. In this paper we propose a mathematical model...
Mathematical modelling of molecule evolution in protocells
In this article, we analyse the process of the emergence of RNA polynucleotides located in an enclosed environment, at an early stage of the RNA world. Therefore we prepared a mathematical model, composed of a set of differential equations, which simulates the behaviour of an early biological system bounded by a protocell membrane. There is evidence that enclosed environments were available on the primordial Earth. There are also experimental proofs that RNA strands can develop in these formations....
Mathematical modelling of profiled haemodialysis: A simplified approach.
Mathematical modelling of the effects of mitotic inhibitors on avascular tumour growth.
Mathematical modelling of the interleukin-2 T-cell system: A comparative study of approaches based on ordinary and delay differential equations.
Mathematical modelling of the response of breast cancer to drug therapy.
Mathematical modelling of tumour angiogenesis and the action of angiostatin as a protease inhibitor.
Mathematical Modelling of Tumour Dormancy
Many tumours undergo periods in which they apparently do not grow but remain at a roughly constant size for extended periods. This is termed tumour dormancy. The mechanisms responsible for dormancy include failure to develop an internal blood supply, individual tumour cells exiting the cell cycle and a balance between the tumour and the immune response to it. Tumour dormancy is of considerable importance in the natural history of cancer. In many cancers, and in particular in breast cancer, recurrence...
Mathematical modelling of tumour invasion and metastasis.
Mathematical models and numerical simulations for the P53-Mdm2 network.
Mathematical Models of Dividing Cell Populations: Application to CFSE Data
Flow cytometric analysis using intracellular dyes such as CFSE is a powerful experimental tool which can be used in conjunction with mathematical modeling to quantify the dynamic behavior of a population of lymphocytes. In this survey we begin by providing an overview of the mathematically relevant aspects of the data collection procedure. We then present an overview of the large body of mathematical models, along with their assumptions and uses,...
Mathematical models of the complete course of HIV infection and AIDS.
Mathematical models of tumor growth systems
We study a class of parabolic-ODE systems modeling tumor growth, its mathematical modeling and the global in time existence of the solution obtained by the method of Lyapunov functions.
Mathematical properties of DNA structure in 3-dimensional space.
Mean transit time and mean residence time for linear diffusion-convection-reaction transport system.
Mechanisms of Cell Motion in Confined Geometries
We present a simple mechanism of cell motility in a confined geometry, inspired by recent motility assays in microfabricated channels. This mechanism relies mainly on the coupling of actin polymerisation at the cell membrane to geometric confinement. We first show analytically using a minimal model of polymerising viscoelastic gel confined in a narrow channel that spontaneous motion occurs due to polymerisation alone. Interestingly, this mechanism...
Media/psychological impact on multiple outbreaks of emerging infectious diseases.
Medical cost trajectories and onsets of cancer and noncancer diseases in US elderly population.
Medical image – based computational model of pulsatile flow in saccular aneurisms
Saccular aneurisms, swelling of a blood vessel, are investigated in order (i) to estimate the development risk of the wall lesion, before and after intravascular treatment, assuming that the pressure is the major factor, and (ii) to better plan medical interventions. Numerical simulations, using the finite element method, are performed in three-dimensional aneurisms. Computational meshes are derived from medical imaging data to take into account both between-subject and within-subject anatomical...