This review is devoted to recent developments in blood flow modelling. It begins with the discussion of blood rheology and its non-Newtonian properties. After that we will present some modelling methods where blood is considered as a heterogeneous fluid composed of plasma and blood cells. Namely, we will describe the method of Dissipative Particle Dynamics and will present some results of blood flow modelling. The last part of this paper deals with one-dimensional global models of blood circulation. We will explain the main ideas of this approach and will present some examples of its application.

The complex phenomena underlying mechanical contraction of cardiac cells and their influence in the dynamics of ventricular contraction are extremely important in understanding the overall function of the heart. In this paper we generalize previous contributions on the active strain formulation and propose a new model for the excitation-contraction coupling process. We derive an evolution equation for the active fiber contraction based on configurational forces, which is thermodynamically consistent. Geometrically, we link microscopic and macroscopic deformations giving rise to an orthotropic contraction mechanism that is able to represent physiologically correct thickening of the ventricular wall. A series of numerical tests highlights the importance of considering orthotropic mechanical activation in the heart and illustrates the main features of the proposed model

The process of platelet activation and blood coagulation is quite complex and not yet completely understood. Recently, a phenomenological meaningful model of blood coagulation and clot formation in flowing blood that extends existing models to integrate biochemical, physiological and rheological factors, has been developed. The aim of this paper is to present results from a computational study of a simplified version of this coupled fluid‐biochemistry model. A generalized Newtonian model with shear‐thinning viscosity has been adopted to describe the flow of blood. To simulate the biochemical changes and transport of various enzymes, proteins and platelets involved in the coagulation process, a set of coupled advection–diffusion–reaction equations is used. Three‐dimensional numerical simulations are carried out for the whole model in a straight vessel with circular cross‐section, using a finite volume semi‐discretization in space, on structured grids, and a multistage scheme for time integration. Clot formation and growth are investigated in the vicinity of an injured region of the vessel wall. These are preliminary results aimed at showing the validation of the model and of the numerical code.