Mathematical Study of the Perturbation of Magnetic Fields Caused by Erythrocytes.

The purpose of this chapter is the mathematical study of the perturbation of a homogeneous static magnetic field caused by the embedding of a red blood cell. Analytical expressions for the magnetic potential and the magnetic strength vector are derived. From the obtained results, it emerges that the magnetic field inside the red blood cell is not uniform and the magnitude depends on the orientation of the erythrocyte.

A Multiscale Mathematical Model for Tumor Growth, Incorporating the GLUT1 Expression.

We propose a multiscale mathematical model for the avascular tumor growth. At the cellular scale, the model takes into account the biochemical environment, the different phases of the tumor cell cycle, the cells signaling, and cellular mechanics through a bioenergetics approach. A mathematical function is employed, namely, the "health function," that stands for the cells' biochemical energy in tumor's different regions, with respect to the carrying capacity of the extracellular matrix (ECM) and the metabolic processes of tumor cells.

Qualitative Differences Between the Semi-separable and the "Almansi-Type" Stokes Stream Function Expansions in the Study of Biological Fluids.

The creeping motion of a Newtonian fluid around particles simulating the relative motion of biological fluids such as blood plasma flow past red blood cells can be modeled through Stokes equations in spheroidal coordinates. By employing a stream function ψ, the irrotational and the rotational Stokes flow are described through a second- and a fourth-order elliptic-type partial differential equations: Eψ = 0 and Eψ = 0, respectively. Firstly, the complete set of the solution expansion has been obtained, in terms of particular combinations of Gegenbauer functions, in separable and semiseparable forms.

A Microscale Mathematical Blood Flow Model for Understanding Cardiovascular Diseases.

The blood plasma flow through a swarm of red blood cells in capillaries is modeled as an axisymmetric Stokes flow within inverted prolate spheroidal solid-fluid unitary cells. The solid internal spheroid represents a particle of the swarm, while the external spheroid surrounds the spheroidal particle and contains the analogous amount of fluid that corresponds to the fluid volume fraction of the swarm. Analytical expansions for the components of the flow velocity are obtained by introducing a stream function ψ which satisfies the fourth-order partial differential equation Eψ = 0.

Stress transfer at the nanoscale on graphene ribbons of regular geometry.

The knowledge of the mechanism of stress transfer from a polymer matrix to a 2-dimensional nano-inclusion such as a graphene flake is of paramount importance for the design and the production of effective nanocomposites. For efficient reinforcement the shape of the inclusion must be accurately controlled since the axial stress transfer from matrix to the inclusion is affected by the axial-shear coupling observed upon loading of a flake of irregular geometry. Herein, we study true axial phenomena on regular- exfoliated-graphene micro-ribbons which are perfectly aligned to the loading direction.