João Janela

Sensitivity of hemodynamics in a patient specific cerebral aneurysm to vascular geometry and blood rheology

Newtonian and generalized Newtonian mathematical models for blood flow are compared in two different reconstructions of an anatomically realistic geometry of a saccular aneurysm, obtained from rotational CTA and differing to within image resolution. The sensitivity of the flow field is sought with respect to geometry reconstruction procedure and mathematical model choice in numerical simulations. Taking as example a patient specific intracranial aneurysm located on an outer bend under steady state simulations, it is found that the sensitivity to geometry variability is greater, but comparable, to the one of the rheological model. These sensitivities are not quantifiable a priori. The flow field exhibits a wide range of shear stresses and slow recirculation regions that emphasize the need for careful choice of constitutive models for the blood. On the other hand, the complex geometrical shape of the vessels is found to be sensitive to small scale perturbations within medical imaging resolution. The sensitivity to mathematical modeling and geometry definition are important when performing numerical simulations from in vivo data, and should be taken into account when discussing patient specific studies since differences in wall shear stress range from 3% to 18%.

A 3D non-Newtonian fluid-structure interaction model for blood flow in arteries

The mathematical modelling and numerical simulation of the human cardiovascular system is playing nowadays an important role in the comprehension of the genesis and development of cardiovascular diseases. In this paper we deal with two problems of 3D modelling and simulation in this field, which are very often neglected in the literature. On the one hand blood flow in arteries is characterized by travelling pressure waves due to the interaction of blood with the vessel wall. On the other hand, blood exhibits non-Newtonian properties, like shear-thinning, viscoelasticity and thixotropy. The present work is concerned with the coupling of a generalized Newtonian fluid, accounting for the shear-thinning behaviour of blood, with an elastic structure describing the vessel wall, to capture the pulse wave due to the interaction between blood and the vessel wall. We provide an energy estimate for the coupling and compare the numerical results with those obtained with an equivalent fluid-structure interaction model using a Newtonian fluid.

Shear-thinning effects of hemodynamics in patient-specific cerebral aneurysms.

Two different generalized Newtonian mathematical models for blood flow, derived for the same experimental data, are compared, together with the Newtonian model, in three different anatomically realistic geometries of saccular cerebral aneurysms obtained from rotational CTA. The geometries differ in size of the aneurysm and the existence or not of side branches within the aneurysm. Results show that the differences between the two generalized Newtonian mathematical models are smaller than the differences between these and the Newtonian solution, in both steady and unsteady simulations.

Towards a Geometrical Multiscale Approach to Non-Newtonian Blood Flow Simulations

In this paper we address some problems that arise when modelling the human cardiovascular system. On one hand, blood is a complex fluid and in many situations Newtonian models may not be capable of capturing important aspects of blood rheology, for example its shear-thinning viscosity, viscoelasticity or yield stress. On the other hand, the geometric complexity of the cardiovascular system does not permit the use of full three-dimensional (3D) models in large regions. We deal with these problems by using a relatively simple non-Newtonian model capturing the shear-thinning behaviour of blood in a confined region of interest, and coupling it with a zero dimensional (0D) model (also called lumped parameters model) accounting for the remaining circulatory system. More specifically, the 0D system emulates the global circulation, providing proper boundary conditions to the 3D model.