Modeling of the early stage of atherosclerosis with emphasis on the regulation of the endothelial permeability.

In this paper, we develop a mathematical model for the early stage of atherosclerosis, as a chronic inflammatory disease. It includes also processes that are relevant for the "thickening" of the vessel walls, and prepares a more complete model including also the later stages of atherosclerosis. The model consists of partial differential equations: Navier-Stokes equations modeling blood flow, Biot equations modeling the fluid flow inside the poroelastic vessel wall, and convection/chemotaxis-reaction-diffusion equations modeling transport, signaling and interaction processes initiating inflammation and atherosclerosis. The main innovations of this model are: a) quantifying the endothelial permeability to low-density-lipoproteins (LDL) and to the monocytes as a function of WSS, cytokines and LDL on the endothelial surface; b) transport of monocytes on the endothelial surface, mimicking the monocytes adhesion and rolling; c) the monocytes influx in the lumen, as a function of factor increasing monocytopoiesis; d) coupling between Navier-Stokes system, Biot system and convection/chemotaxis-reaction-diffusion equations. Numerical simulations of a simplified model were performed in an idealized two-dimensional geometry in order to investigate the dynamics of endothelial permeability, and the growth and spread of immune cells populations and their dependence in particular on low-density-lipoprotein and wall-shear stress.

Hydrodynamics of a free-flowing leukocyte toward the endothelial wall.

Leukocyte recruitment is an essential stage of the inflammatory response and although the molecular mechanisms of this process are relatively well known, the influence of the hydrodynamic effects that govern the inflammatory response are still under study. In this paper we made use of the images and experimental parameters obtained by intravital microscopy in an in vivo animal model of inflammation to track the leukocytes trajectories and measure their velocities and diameters. Using a recent validated mathematical model describing the coupled deformation-flow of an individual leukocyte in a microchannel, numerical simulations of an individual and of two leukocytes under flow were performed. The results showed that velocity plays an important role in the motion, deformation and attraction of the cells during an inflammatory response. In fact, for higher inlet velocities the cell movement along the endothelial wall is accelerated and the attraction forces break faster. These results highlight the role of the mechanical properties of the blood, namely the ones influenced by the velocity field, in the case of inflammation.

The effect of ventricular volume increase in the amplitude of intracranial pressure.

We study the impact of vascular pulse in the cerebrospinal fluid (CSF) pressure measured on the lateral cerebral ventricles, as well as its sensitivity with respect to ventricular volume change. Recent studies have addressed the importance of the compliance capacity in the brain and its relation to arterial pulse abortion in communicating hydrocephalus. Nevertheless, this mechanism is not fully understood. We propose a fluid-structure interaction (FSI) model on a 3 D idealized geometry based on realistic physiological and morphological parameters. The computational model describes the pulsatile deformation of the third ventricle due to arterial pulse and the resulting CSF dynamics inside brain pathways. The results show that when the volume of lateral ventricles increases up to 3.5 times, the amplitudes of both average and maximum pressure values, computed on the lateral ventricles surface, substantially decrease. This indicates that the lateral ventricles expansion leads to a dumping effect on the pressure exerted on the walls of the ventricles. These results strengthen the possibility that communicant hydrocephalus may, in fact, be a natural response to reduce abnormal high intracranial pressure (ICP) amplitude. This conclusion is in accordance with recent hypotheses suggesting that communicant hydrocephalus is related to a disequilibrium in brain compliance capacity.

Bicuspid aortic valve aortopathies: An hemodynamics characterization in dilated aortas.

Bicuspid aortic valve (BAV) aortopathy remains of difficult clinical management due to its heterogeneity and further assessment of related aortic hemodynamics is necessary. The aim of this study was to assess systolic hemodynamic indexes and wall stresses in patients with diverse BAV phenotypes and dilated ascending aortas. The aortic geometry was reconstructed from patient-specific images while the aortic valve was generated based on patient-specific measurements. Physiologic material properties and boundary conditions were applied and fully coupled fluid-structure interaction (FSI) analysis were conducted. Our dilated aortic models were characterized by the presence of abnormal hemodynamics with elevated degrees of flow skewness and eccentricity, regardless of BAV morphotype. Retrograde flow was also present. Both features, predicted by flow angle and flow reversal ratios, were consistently higher than those reported for non-dilated aortas. Right-handed helical flow was present, as well as elevated wall shear stress (WSS) on the outer ascending aortic wall. Our results suggest that the abnormal flow associated with BAV may play a role in aortic enlargement and progress it further on already dilated aortas.

Numerical simulations of a 3D fluid-structure interaction model for blood flow in an atherosclerotic artery.

The inflammatory process of atherosclerosis leads to the formation of an atheromatous plaque in the intima of the blood vessel. The plaque rupture may result from the interaction between the blood and the plaque. In each cardiac cycle, blood interacts with the vessel, considered as a compliant nonlinear hyperelastic. A three dimensional idealized fluid-structure interaction (FSI) model is constructed to perform the blood-plaque and blood-vessel wall interaction studies. An absorbing boundary condition (BC) is imposed directly on the outflow in order to cope with the spurious reflexions due to the truncation of the computational domain. The difference between the Newtonian and non-Newtonian effects is highlighted. It is shown that the von Mises and wall shear stresses are significantly affected according to the rigidity of the wall. The numerical results have shown that the risk of plaque rupture is higher in the case of a moving wall, while in the case of a fixed wall the risk of progression of the atheromatous plaque is higher.

A synthetic model for blood coagulation including blood slip at the vessel wall.

Modeling blood coagulation has taken various directions in recent years, depending on the aspects that authors wish to emphasize. In this paper we want to address an issue that has been systematically ignored in the relevant literature, namely the effect of blood slip at the vessels wall. The presence of a slip results in an increased supply of activated platelets to the clotting site. We calculate such a contribution showing that, in extreme cases, it can be even dominant. Indeed, raising the concentration of activated platelets induces an acceleration of thrombin production and eventually of the whole clot progression. The model explains the difference between arterial and venous thrombi. We confine to the coagulation stage known as "propagation phase" in the context of the so called cell based model. The paper is preparatory for a deeper analysis in which the clotting process is coupled to blood rheology and that will be carried out in the future by the same authors. At the present stage, the extremely complex biochemistry has been simplified adopting a leaner, though virtual, system of diffusion-convection-reaction equations, in the optics of providing "modular" models, that can be reduced or enlarged so to meet specific modeling requirements.

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.

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%.

Blood coagulation dynamics: mathematical modeling and stability results.

The hemostatic system is a highly complex multicomponent biosystem that under normal physiologic conditions maintains the fluidity of blood. Coagulation is initiated in response to endothelial surface vascular injury or certain biochemical stimuli, by the exposure of plasma to Tissue Factor (TF), that activates platelets and the coagulation cascade, inducing clot formation, growth and lysis. In recent years considerable advances have contributed to understand this highly complex process and some mathematical and numerical models have been developed. However, mathematical models that are both rigorous and comprehensive in terms of meaningful experimental data, are not available yet. In this paper a mathematical model of coagulation and fibrinolysis in flowing blood that integrates biochemical, physiologic and rheological factors, is revisited. Three-dimensional numerical simulations are performed in an idealized stenosed blood vessel where clot formation and growth are initialized through appropriate boundary conditions on a prescribed region of the vessel wall. Stability results are obtained for a simplified version of the clot model in quiescent plasma, involving some of the most relevant enzymatic reactions that follow Michaelis-Menten kinetics, and having a continuum of equilibria.

Study of geometrical uncertainty stemming from different reconstruction procedures on the flow field for a peripheral bypass graft.

The geometry of conduits derived from in vivo image data is subject to acquisition and reconstruction errors. This results in a degree of uncertainty in defining the bounding geometry for a patient-specific anatomical conduit. The impact of the conduit geometry uncertainty should be considered with respect to haemodynamic clinically relevant measures that may alter the perception and evaluation of prognosis and diagnosis. These are commonly fluid mechanic stresses on or near the wall. Taking an example of a peripheral bypass graft configuration, we examine the effects of image threshold on the geometry. Thresholding approaches are chosen from the existing image segmentation community and are based on clustering schemes. Two novel methods are also introduced. The geometries are reconstructed using a partition-of-unity implicit function approach from the stack of segmented cross-sections that yields a piecewise linear triangulated mesh. Methods to quantify the differences resulting in the virtual model reconstruction from the different thresholding methods are based on the distance between the models and the surface mean curvature.