Mathematical model describing erythrocyte sedimentation rate. Implications for blood viscosity changes in traumatic shock and crush syndrome

BACKGROUND: The erythrocyte sedimentation rate (ESR) is a simple and inexpensive laboratory test, which is widespread in clinical practice, for assessing the inflammatory or acute response. This work addresses the theoretical and experimental investigation of sedimentation a single and multiple particles in homogeneous and heterogeneous (multiphase) medium, as it relates to their internal structure (aggregation of solid or deformed particles). METHODS: The equation system has been solved numerically. To choose finite analogs of derivatives we used the schemes of directional differences. RESULTS: (1) Our model takes into account the influence of the vessel wall on group aggregation of particles in tubes as well as the effects of rotation of particles, the constraint coefficient, and viscosity of a mixture as a function of the volume fraction. (2) This model can describe ESR as a function of the velocity of adhesion of erythrocytes; (3) Determination of the ESR is best conducted at certain time intervals, i.e. in a series of periods not exceeding 5 minutes each; (4) Differential diagnosis of various diseases by means of ESR should be performed using the aforementioned timed measurement of ESR; (5) An increase in blood viscosity during trauma results from an increase in rouleaux formation and the time-course method of ESR will be useful in patients with trauma, in particular, with traumatic shock and crush syndrome. CONCLUSION: The mathematical model created in this study used the most fundamental differential equations that have ever been derived to estimate ESR. It may further our understanding of its complex mechanism

A Neuron-Glial Perspective for Computational Neuroscience

International audienceThere is growing excitement around glial cells, as compelling evidence point to new, previously unimaginable roles for these cells in information processing of the brain, with the potential to affect behavior and higher cognitive functions. Among their many possible functions, glial cells could be involved in practically every aspect of the brain physiology in health and disease. As a result, many investigators in the field welcome the notion of a Neuron-Glial paradigm of brain function, as opposed to Ramon y Cayal's more classical neuronal doctrine which identifies neurons as the prominent, if not the only, cells capable of a signaling role in the brain. The demonstration of a brain-wide Neuron-Glial paradigm however remains elusive and so does the notion of what neuron-glial interactions could be functionally relevant for the brain computational tasks. In this perspective, we present a selection of arguments inspired by available experimental and modeling studies with the aim to provide a biophysical and conceptual platform to computational neuroscience no longer as a mere prerogative of neuronal signaling but rather as the outcome of a complex interaction between neurons and glial cells