Catálogo de publicaciones - libros

We address the following question: Can one sustain, on the basis of mathematicalmodels, that for cancer cells, the loss of control by circadian rhythm favours a faster populationgrowth? This question, which comes from the observation that tumour growth in mice isenhanced by experimental disruption of the circadian rhythm, may be tackled by mathematicalmodelling of the cell cycle. For this purpose we consider an age-structured population modelwith control of death (apoptosis)rates and phase transitions, and two eigenvalues: one for periodic control coefficients (via a variant of Floquet theory in infinite dimension)and one forconstant coefficients (taken as the time average of the periodic case). We show by a direct proofthat, surprisingly enough considering the above-mentioned observation, the periodic eigenvalue is always greater than the steady state eigenvalue when the sole apoptosis rate is concerned. We also show by numerical simulations when transition rates between the phases of the cell cycle are concerned, that, without further hypotheses, no natural hierarchy between the two eigenvalues exists. This at least shows that, if such models are to take into account the above-mentioned observation, control of death rates inside phases is not sufficient, and that transition rates between phases are a key target in proliferation control.

A quantitative understanding of the bone remodeling process is of considerable biomedical and practical biotechnological interest to support the application of layer manufacturing techniques to produce scaffolds for surgical applications. Osteoclasts and osteoblasts play a principal role in different models of the bone multicellular unit operating in bone and display a rich spectrum of behaviour. The goal of this work is to show that it is possible to capture the cyclic dynamics of operating cells. The central idea of the mathematical model is that the regulatory nature of osteocytes is the basis of the cyclic-like behaviour associated with the system (remodeling process)as a whole. We developed this model taking due account of the apoptosis of osteocytes as a possible regulation loop in bone remodeling control. By applying the ordinary differential equations technique to the model, we show cyclic modes over a wide range of constants that have clear biological relevance. Simulations show that for a particular range of constants the model exhibits a torus-like quasi-steady state. Further investigation into these simulations indicates the existence of a surface in the osteoclasts-osteoblasts-osteocytes-bone space, that could be interpreted as a conservative value confirming the substrate-energy regenerative capability of the bone remodeling system. It is suggested that the nature of this recovering potential is directed against both mechanical and biochemical damage to the bone.

Atherosclerotic lesions are predominantly localised to arterial bifurcations and bends, and are highly correlated with areas of low wall shear stress (WSS), but the underlying reason for this localisation is not fully understood. A key role is played by the endothelial cells, which regulate the transport of materials from the bloodstream to the artery wall and secrete vasoactive agents that modulate vascular tone. A mathematical model is presented, exploring the link between arterial geometry, WSS and factors related to atherogenesis. The model simulates the cellular response to the fluid shear stress on the cell membrane and the binding of ligands to cell surface receptors. This is used to calculate the rate of production of nitric oxide (NO), which is a potent vasodilator and anti-atherogenic factor. It is hypothesised that the section of endothelium adjacent to a region of recirculating flow is most at risk of developing atherosclerotic plaque, due to reduced bioavailability of NO.

In vivo applications of biocompatible magnetic nanoparticles in a carrier liquid controlled by an external magnetic field from outside the body have recently been proposed for specific drug delivery such as in locoregional cancer therapies or the occlusion aneurysms. They can also be used as guided contrast agents in myocardial imaging after myocardial infarction. However, the choice of the optimal clinical setting still remains a challenge for all of the mentioned applications. A numerical heterogeneous multiscale model can be used for an optimal a priori determination of the free parameters and might help to overcome this problem.

A mathematical model of water flow between dialysis fluid in the peritoneal cavity and blood through the capillary wall and homogeneous interstitium driven by high hydrostatic and osmotic pressure of dialysis fluid is formulated. The model is based on nonlinear equations of reaction-diffusion-convection type. Numerical simulations provide the distribution profiles for hydrostatic pressure, glucose concentration, and water flux in the tissue for different times from the infusion of dialysis fluid into the peritoneal cavity for different transport parameters that represent clinical treatments of peritoneal dialysis.

We discuss a model for the interaction between the parasite and the immune system in Chagas disease, by separately describing the intracellular and extracellular parasite stages. The solution of the case where two antibody species are active is worked out in detail, and a diagram showing the differents outcomes of the model is obtained. Our predictions accurately reproduce experimental data on the infection evolution during the acute phase of the disease and lead to an estimate of the damage generated by direct parasite action

We consider the numerical simulation of a time-dependent taxis-diffusion-reaction model of fracture healing in mice using the method of lines. The partial differential equation problem has an axi-symmetric structure and this is employed to properly reduce the model to an equivalent problem in two-dimensional (2D) space leading subsequently to an efficient spatial discretisation. Special care is given to respect conservation of mass and the non-negativity of the solution. The numerical simulation results are contrasted to those obtained from a simplistic reduction of the axi-symmetric model to 2D space (at the same computational cost).We observe quantitative and qualitative differences.

We introduce a score to classify the severity of patients by analysing the information content of clinical time series.

The inference of regulatory networks from microarray data relies on expression measures to identify gene activity patterns. However, currently existing xpression measures are not the direct measurements of mRNA concentration one would ideally need for an accurate determination of gene regulation. If the development of expression measures is to advance to the point where absolute target concentrations can be estimated, it is essential to have an understanding of physical processes leading to observed microarray data. We survey here the performance of existing expression measures for oligonucleotide microarrays and describe recent progress in developing physical dynamic adsorption models relating measured fluorescent dye intensities to underlying target mRNA concentration.

We have shown for a dataset of computationally predicted alternative splice sites how inherent information can be utilized to validate the predictions by applying statistics on different features typical for splice sites. As a promising splice site feature we investigated the frequencies of binding motifs in the context of exonic and intronic splice site flanks and between the alternative and reference splice sites. We show that both partitions of splice sites can statistically be separated not only by their distance to the splice signal consensus but also via frequencies of splice regulatory protein (SRp) binding motifs in the splice site environment.