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A distributed-parameter (one-dimensional) anatomically detailed model for the arterial network of the arm is developed in order to carry out hemodynamics simulations. This work focuses on the specific aspects related to the model set-up. In this regard, stringent anatomical and physiological considerations have been pursued in order to construct the arterial topology and to provide a systematic estimation of the involved parameters. The model comprises 108 arterial segments, with 64 main arteries...
A mathematical model of mixing food in rumen is presented. The model is based on the idea of the Baker Transformation, but exhibits some different phenomena: the transformation does not mix points at all in some parts of the phase space (and under some conditions mixes them strongly in other parts), as observed in ruminant animals.
A mathematical model of the tumour growth along a blood vessel is proposed. The
model employs the mixture theory approach to describe a tissue which consists of cells, extracellular
matrix and liquid. The growing tumour tissue is supposed to be surrounded by the host
tissue. Tumours where complete oxydation of glucose prevails are considered. Special attention is
paid to consistent description of oxygen consumption and growth processes based on the energy
balance. A finite difference numerical...
This paper is devoted to solving of dynamic problems in biomechanics that require
detailed study of fast processes. Numerical method of characteristics is used to model the
temporal development of the processes with high accuracy.
While drawing a link between the papers contained in this issue and those present in a previous one (Vol. 2, Issue 3), this introductory article aims at putting in evidence some trends and challenges on cancer modelling, especially related to the development of multiphase and multiscale models.
Blood rheology is completely determined by its major corpuscles which are erythrocytes,
or red blood cells (RBCs). That is why understanding and correct mathematical description
of RBCs behavior in blood is a critical step in modelling the blood dynamics. Various
phenomena provided by RBCs such as aggregation, deformation, shear-induced diffusion and
non-uniform radial distribution affect the passage of blood through the vessels. Hence,
they have...
In this paper, we compare a biomechanics empirical model of the heart fibrous structure to two models obtained by a non-periodic homogenization process. To this end, the two homogenized models are simplified using the small amplitude homogenization procedure of Tartar, both in conduction and in elasticity. A new small amplitude homogenization expansion formula for a mixture of anisotropic elastic materials is also derived and allows us to obtain a third simplified model.
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