A two-component model of the red blood cell membrane and other mathematical models in medicine

• Autor(a) principal: Meacci, Luca
• Data de Publicação: 2021
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: https://www.teses.usp.br/teses/disponiveis/55/55134/tde-24082021-095359/
• topic: Alzheimer's disease; Biological fluid mechanics; Cancer stem cells; Células-tronco cancerosas; Citoesqueleto; Controle ótimo; COVID-19; COVID-19; Cytoskeleton; Doença de Alzheimer; Fadiga pandêmica; Fluid-solid interactions; Glóbulo vermelho; Interações fluido-sólido; Lipid membrane; Manipulação de partículas; Mathematical modeling; Mecânica biológica dos fluidos; Membrana lipídica; Modelagem matemática; Numerical simulations; Optimal control; Pandemic fatigue; Particles manipulation; Red blood cell; Simulações numéricas

This thesis consists in the presentation of a series of papers for the definition of an original two-component mathematical model for the red blood cell membrane. The model, inspired by the best models currently available, considers the cytoskeleton as a discrete non-linear elastic structure. The novelty of the proposed work is to couple this skeleton with continuum models instead of the more common discrete models (molecular dynamics, particle methods) of the lipid bilayer. The interaction of the solid cytoskeleton with the bilayer, which is a two-dimensional fluid, is done through adhesion forces adapting efficient solid-solid adhesion algorithms. The continuous treatment of the fluid parts is well justified by scale arguments and leads to much more stable and precise numerical problems when, as is the case, the size of the molecules (0:3nm) is much smaller than the overall size (≅ 8000 nm). The most advanced version of the model also takes into account the contribution of the cytosol, modeled as an internal fluid obeying a Newtonian behaviour. The computational formulation of the model can be used to study normal and pathological behavior of red blood cells in slow transient processes. In the papers, many simulations and applications are shown. A certain attention was done to present the mathematical well-posedness of the model. The thesis work was conducted within research activity supporting the National Institute of Science and Technology in Medicine Assisted by Scientific Computing (INCT MACC) of Brazil. The document contains additional published papers containing new proposals of mathematical models with relevant applications in medicine. These additional topics concern the manipulation and optimal control of particles in micro-fluids, the modeling of progress and treatment of diseases such as cancer with the presence of cancer stem cells and Alzheimers disease, and an epidemiological model on the COVID-19 spread that mimics the social reaction due to pandemic fatigue.