Modélisation du transport d'eau et du changement de volume dans les neurones et les astrocytes
|Authors:||Lenkeu Lenkeu, Nadège Octavie|
|Advisor:||Doyon, Nicolas; Girouard, Alexandre|
|Abstract:||The holographic microscopy uses interferometry techniques for measuring changes in volume of neurons with an unprecedented accuracy. A major challenge is to relate the measured phase changes with the neuron volume changes and more to relate the extent of these changes volumes to certain properties of neurons such as the activity level of Cation-Chloride Cotransporter (CCC) and some biomechanical properties membranes. The longer term objective is the use of phase changes for detecting changes in the density response of neurons to an osmotic shock which could possibly allow the detection of many kind of pathologies. To understand the information that can be derived from experimental measurements, it is important to understand the relationship between different variables: force pump Na⁺ – K⁺ ATPase, membrane permeability of water, biomechanical properties of the membranes and the phase changes observed by the experimenter. To achieve this, we need some dynamical system skills, we will use the Ordinary Differential Equations (E.D.O) in order to perform the mathematical modeling of the phenomenon illustrating the variation of the membrane volume, as well as the variations in quantities of K⁺, Na⁺ and Cl⁻, which constitute the main ionic composition of astrocytes, which are the cells studied in this project. In this mathematical recall on dynamical systems, we will talk about the bifurcations for a better understanding of the incoming results since we are expecting bifurcations for our model. We will study deeply the E.D.O. system obtained including the search of equilibrium points and their behavior in the phase space, and we will see if there are bifurcations and what is their meaning. The aim being to obtain bifurcations, which would explain the dysfunction of the astrocytes, and would certainly explain the origin of certain neurodegenerative diseases; we will finally see, after studying the model, that there is no bifurcation, nevertheless the simplicity of the model used opens doors to more complex future projects that will perhaps achieve the desired objectives.|
|Document Type:||Mémoire de maîtrise|
|Open Access Date:||24 April 2018|
|Collection:||Thèses et mémoires|
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