A Review of Mathematical Models for the Formation of\ud Vascular Networks

Mainly two mechanisms are involved in the formation of blood vasculature: vasculogenesis and angiogenesis. The former consists of the formation of a capillary-like network from either a dispersed or a monolayered population of endothelial cells, reproducible also in vitro by specific experimental assays. The latter consists of the sprouting of new vessels from an existing capillary or post-capillary venule. Similar phenomena are also involved in the formation of the lymphatic system through a process generally called lymphangiogenesis.\ud \ud A number of mathematical approaches have analysed these phenomena. This paper reviews the different modelling procedures, with a special emphasis on their ability to reproduce the biological system and to predict measured quantities which describe the overall processes. A comparison between the different methods is also made, highlighting their specific features

Cell orientation under stretch: Stability of a linear viscoelastic model

The sensitivity of cells to alterations in the microenvironment and in particular to external mechanical stimuli is significant in many biological and physiological circumstances. In this regard, experimental assays demonstrated that, when a monolayer of cells cultured on an elastic substrate is subject to an external cyclic stretch with a sufficiently high frequency, a reorganization of actin stress fibres and focal adhesions happens in order to reach a stable equilibrium orientation, characterized by a precise angle between the cell major axis and the largest strain direction. To examine the frequency effect on the orientation dynamics, we propose a linear viscoelastic model that describes the coupled evolution of the cellular stress and the orientation angle. We find that cell orientation oscillates tending to an angle that is predicted by the minimization of a very general orthotropic elastic energy, as confirmed by a bifurcation analysis. Moreover, simulations show that the speed of convergence towards the predicted equilibrium orientation presents a changeover related to the viscous–elastic transition for viscoelastic materials. In particular, when the imposed oscillation period is lower than the characteristic turnover rate of the cytoskeleton and of adhesion molecules such as integrins, reorientation is significantly faster

Pathophysiology of Bowel Dysfunction in Multiple Sclerosis and the potential for targeted treatment

Bowel symptoms (constipation and/or faecal incontinence) affect the vast majority of patients with multiple sclerosis (MS), but the pathophysiology is unclear and treatment remains empirical. The primary hypothesis of this thesis is that involvement of the spinal cord by the disease is central to the development of bowel symptoms, and this is tested in the first two studies: 1. A study of the overlap in prevalence of bladder symptoms in patients with MS and bowel symptoms. 2. A study of rectal compliance, as an important reflection of both the gut’s neural tone and its ability to hold content, in comparison to patients with supraconal spinal cord injury and normal controls. The secondary hypothesis is that residual spinal cord function can represent a potential target of treatment, and this is tested in studies 3 and 4: 3. A prospective observational study of bowel biofeedback in symptomatic MS patients. 4. A prospective observational study of transanal irrigation in symptomatic MS patients. Study 1 shows that the prevalence of bladder symptoms – determined by spinal cord disease - is higher in patients with bowel symptoms than in the general population of MS sufferers. The second study shows that rectal compliance - as an index of the spinal reflex activity regulating autonomic rectal function – is altered in patients with MS according to the clinical degree of spinal cord involvement by the disease. A similar pattern is followed for symptoms of constipation, but not faecal incontinence. The two treatment studies showed that: Biofeedback improves bowel symptoms and 5-seconds-endurance squeeze pressure. Improvement of sphincter pressure could be the result of behavioural changes, inducing physiological changes through residual efferent pathways in the spinal cord. Transanal irrigation is effective to treat bowel symptoms in patients who fail biofeedback

Multi-scale analysis and modelling of collective migration in biological systems

Collective migration has become a paradigm for emergent behaviour in systems of moving and interacting individual units resulting in coherent motion. In biology, these units are cells or organisms. Collective cell migration is important in embryonic development, where it underlies tissue and organ formation, as well as pathological processes, such as cancer invasion and metastasis. In animal groups, collective movements may enhance individuals' decisions and facilitate navigation through complex environments and access to food resources. Mathematical models can extract unifying principles behind the diverse manifestations of collective migration. In biology, with a few exceptions, collective migration typically occurs at a 'mesoscopic scale' where the number of units ranges from only a few dozen to a few thousands, in contrast to the large systems treated by statistical mechanics. Recent developments in multi-scale analysis have allowed linkage of mesoscopic to micro- and macroscopic scales, and for different biological systems. The articles in this theme issue on 'Multi-scale analysis and modelling of collective migration' compile a range of mathematical modelling ideas and multi-scale methods for the analysis of collective migration. These approaches (i) uncover new unifying organization principles of collective behaviour, (ii) shed light on the transition from single to collective migration, and (iii) allow us to define similarities and differences of collective behaviour in groups of cells and organisms. As a common theme, self-organized collective migration is the result of ecological and evolutionary constraints both at the cell and organismic levels. Thereby, the rules governing physiological collective behaviours also underlie pathological processes, albeit with different upstream inputs and consequences for the group. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'

A note on light velocity anisotropy

It is proved that in experiments on or near the Earth, no anisotropy in the one-way velocity of light may be detected. The very accurate experiments which have been performed to detect such an effect are to be considered significant tests of both special relativity and the equivalence principleComment: 8 pages, LaTex, Gen. Relat. Grav. accepte

Modeling sand slides by a mechanics-based degenerate parabolic equation

Avalanching plays a crucial role in granular materials dynamics, in particular in the evolution of the shape of the leeward side of sand dunes. This paper presents a physically-based mathematical model capable of reproducing the kinematic evolution of the surface of sand piles and to obtain eventually the stationary configurations, in the presence of external sources as well. Simulation results with different boundary conditions and geometries are reported in order to show the high flexibility of the model. The model is also validated by means of comparison with the experimental results of different authors

Microfluidic mixing of low viscosity Boger fluids

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.This study is focused on the development of low viscosity Boger fluids and on the investigation of their elasticity on emulsion formation. Non-Newtonian continuous phases (Boger fluids) made of two different molecular weight Polyacrylamide in water plus glycerol solutions were used. While, as Newtonian continuous phase, a water plus glycerol solution showing the same viscosity as the non-Newtonian one was prepared and as dispersed phase silicon oil was used. Visualization of these emulsions flowing through a micromixer was useful in order to extract quantitative informations of their behavior, such as the velocity profile and droplets’ size distribution. Then the formation of vortex upstream of a divergent-convergent configuration has been shown as the wall migration effect, which drives droplets away from the walls and toward the center of the microcapillary investigated

Gut dysfunction in patients with multiple sclerosis and the role of spinal cord involvement in the disease.

Bowel and bladder symptoms are highly prevalent in patients with multiple sclerosis (MS). Bladder dysfunction (affecting 75% of these patients) is caused by disease in the spinal cord, whilst the pathophysiology of bowel dysfunction is unknown. Pathways regulating both the organs lie in close proximity to the spinal cord, and coexistence of their dysfunction might be the result of a common pathophysiology. If so, the prevalence of bladder symptoms should be greater in patients with MS and bowel symptoms. This hypothesis is tested in the study. We also evaluated how patient-reported symptoms quantify bowel dysfunction