Impact of CCSVI on cerebral haemodynamics: a mathematical study using MRI angiographic and flow data.

BACKGROUND: The presence of abnormal anatomy and flow in neck veins has been recently linked to neurological diseases. The precise impact of extra-cranial abnormalities such as stenoses remains unexplored. METHODS: Pressure and velocity fields in the full cardiovascular system are computed by means of a global mathematical model that accounts for the relationship between pulsating cerebral blood flow and intracranial pressure. RESULTS: Our model predicts that extra-cranial strictures cause increased pressure in the cerebral venous system. Specifically, there is a predicted pressure increase of about 10% in patients with a 90% stenoses. Pressure increases are related to significant flow redistribution with flow reduction of up to 70% in stenosed vessels and consequent flow increase in collateral pathways. CONCLUSIONS: Extra-cranial venous strictures can lead to pressure increases in intra-cranial veins of up to 1.3 mmHg, despite the shielding role of the Starling resistor. The long-term clinical implications of the predicted pressure changes are unclear.

A mathematical model for filtration and macromolecule transport across capillary walls.

Metabolic substrates, such as oxygen and glucose, are rapidly delivered to the cells of large organisms through filtration across microvessels walls. Modelling this important process is complicated by the strong coupling between flow and transport equations, which are linked through the osmotic pressure induced by the colloidal plasma proteins. The microvessel wall is a composite media with the internal glycocalyx layer exerting a strong sieving effect on macromolecules, with respect to the external layer composed by the endothelial cells. The physiological structure of the microvessel is represented as the superimposition of two membranes with different properties; the inner membrane represents the glycocalyx, while the outer membrane represents the surrounding endothelial cells. Application of the mass conservation principle and thermodynamic considerations lead to a model composed of two coupled second-order ordinary differential equations for the hydrostatic and osmotic pressures, one, expressing volumetric mass conservation and the other, which is non-linear in the unknown osmotic pressure, expressing macromolecules mass conservation. Despite the complexity of the system, the assumption that the properties of the layers are piece-wise constant allows us to obtain analytical solutions for the two pressures. This solution is in agreement with experimental observations, which contrary to common belief, show that flow reversal cannot occur in steady-state conditions unless the hydrostatic pressure in the lumen drops below physiologically plausible values. The observed variations of the volumetric flux and the solute mass flux in case of a significant reduction of the hydrostatic pressure at the lumen are in qualitative agreement with observed variations during detailed experiments reported in the literature. On the other hand, homogenising the microvessel wall into a single-layer membrane with equivalent properties leads to a very different distribution of pressure across the microvessel walls, not consistent with observations.

Numerical and analytical study of an atherosclerosis inflammatory disease model.

We study a reaction-diffusion mathematical model for the evolution of atherosclerosis as an inflammation process by combining analytical tools with computer-intensive numerical calculations. The computational work involved the calculation of more than sixty thousand solutions of the full reaction-diffusion system and lead to the complete characterisation of the ω-limit for every initial condition. Qualitative properties of the solution are rigorously proved, some of them hinted at by the numerical study.

Space-time adaptive numerical methods for geophysical applications.

In this paper we present high-order formulations of the finite volume and discontinuous Galerkin finite-element methods for wave propagation problems with a space-time adaptation technique using unstructured meshes in order to reduce computational cost without reducing accuracy. Both methods can be derived in a similar mathematical framework and are identical in their first-order version. In their extension to higher order accuracy in space and time, both methods use spatial polynomials of higher degree inside each element, a high-order solution of the generalized Riemann problem and a high-order time integration method based on the Taylor series expansion. The static adaptation strategy uses locally refined high-resolution meshes in areas with low wave speeds to improve the approximation quality. Furthermore, the time step length is chosen locally adaptive such that the solution is evolved explicitly in time by an optimal time step determined by a local stability criterion. After validating the numerical approach, both schemes are applied to geophysical wave propagation problems such as tsunami waves and seismic waves comparing the new approach with the classical global time-stepping technique. The problem of mesh partitioning for large-scale applications on multi-processor architectures is discussed and a new mesh partition approach is proposed and tested to further reduce computational cost.

Activation of renal erythropoietic factor by phosphorylation.

Renal erythropoietic factor (REF) serves as a substrate for a cyclic nucleotide-dependent protein kinase. The phosphorylation of REF is associated with increased erythropoietic activity. Conversely, REF isolated from hypoxic rats is a poor phosphate acceptor. These findings and the presence of a positive correlation between erythropoietin levels and urinary excretion of adenosine 3',5' monophosphate (cyclic-AMP) in anemic individuals suggest that the cyclic-AMP-protein kinase system plays an important role in the activation of REF.