Numerical modelling of cardiovascular disease

Introduction

Atherosclerosis, a disease of the large arteries, is the primary cause of heart disease and stroke. In westernized societies, it is underlying cause of about 50% of all deaths. Atherosclerosis is a multi – factorial process, which requires extensive accumulation of smooth muscle cells within the intima of the affected artery. The form and content of the advanced lesions of atherosclerosis demonstrate the results of three fundamental biological processes. These are: (1) accumulation of smooth muscle cells, together with variable numbers of accumulated macrophages and T-lymphocytes; (2) formation by the proliferated smooth muscle cells of large amounts of connective tissue matrix, including collagen, elastic fibers and proteoglycans; and (3) accumulation of lipid and free cholesterol within the cells as well as in the surrounding connective tissues. The distribution of lipid and connective tissue in these lesions determines whether they are stable or are at risk of rupture and thrombosis. The factors which influence to artery disease are the increased levels of cholesterol, hypertension, and the incidence of cigarette smoking, diabetes, age or male gender and the occurrence of coronary artery disease. The atherosclerotic plaque progression is associated with mechanical, biochemical, biological and genetic reactions. Blood flows in artery’s lumen and forces to arterial wall with effects to endothelial permeability, gene expression, arterial wall mechanics and smooth muscle cells proliferation.

Atherosclerosis is characterized by the accumulation of species from blood flow to arterial wall. These species can be lipids, other molecules or cells. We model the biological mechanisms, which concern to atherosclerotic plaque initialization and progression. The LDL transfer from blood flow in the artery wall is the first step in modelling atherosclerotic plaque progression. The next step is the computation of a rate of growth based on this lipid accumulation. In the section of modelling mass transfer, outside the molecular (LDL) transfer, can be added the cell (monocytes) flux in the blood, their adhesion up to endothelial surface and the penetration to the intima. The difference with molecule transfer is the large size of cell in comparison with molecules such as LDL.

The objective of the research is to develop and validate a model for the mass transfer from the blood flow to the artery wall based on blood flow, arterial wall mechanics, biological factors and gene expression which indicates the region of the development and the growth rate of the atherosclerotic plaque progress.

Modelling of atherosclerosis

We model the shear dependent transport properties of LDL in carotid artery bifurcation. The artery wall is assumed to be one homogenous layer which LDL can penetrate. We use the Finite Element Method to couple and solute the fluid dynamics and the solute dynamics equations. Navier – Stokes equations are employed to model the blood flow and the Darcy’s Law to model the transmural flow in the artery wall. The mass transport properties of solute at the lumen and at the endothelium were modeled using the Convection – Diffusion equation. Our results show that the concentration is related to the wall shear stress. The model indicates that LDL accumulates near to endothelial membrane and especially in regions where the wall shear stress is low. Maximum concentration of the macromolecule appears at the outer walls of the carotid artery branches, which is in agreement with experimental data.

Computational modelling of atherosclerosis is used for the better understanding of its underlying processes and for plaque growth prediction. Estimation of wall shear stress requires the blood flow modelling and offers prediction of regions potential for plaque growth assuming that regions of low wall shear stress are correlated with the arterial wall thickness change. In our lab, blood flow modelling is performed in large datasets which consist of human coronary and carotid arteries reconstructed in three-dimensional space using intravascular ultrasound, angiography, magnetic resonance imaging and computed tomography. In addition, we study low density lipoprotein transport since lipid accumulation in the arterial wall is the initial stage of the plaque formation. Plaque growth modelling implementing differential equations used for estimation of lipid oxidation, macrophages differentiation and foam cells formation is a main research direction. Finally, rigid wall and Fluid Structure Interaction (FSI) simulations are performed focusing on the estimation of a crucial index which is the Fractional Flow Reserve (FFR) value.

Cardiovascular imaging

Cardiovascular imaging is used in the current medical practice in order to diagnose or provide prognosis of atherosclerosis. Image types used for atherosclerosis diagnosis and prognosis include the Intravascular Ultrasound (IVUS), the angiography, the computed tomography (CT), the magnetic resonance imaging (MRI) and the optical coherence tomography. However, these images provide to the medical experts 2D representations of the arteries, making the diagnosis a difficult and rather subjective process.

In order to overcome the limits of the 2D representation of images, 3D artery reconstruction algorithms have been developed, for all the above imaging modalities with very high accuracy. The research that has been conducted in this area offers a set of tools to the cardiologists to reconstruct automatically models of arterial segments and arterial trees in 3D, that represent the geometry of the artery and pinpoint specific places with stenoses.

Moreover, research has been conducted for the development of plaque characterization algorithms that provide a classification of the different plaque types existing in the arterial images. The Figure below shows indicative images processed with segmentation or plaque characterization algorithms. A further development in this research area is the reconstruction and visualization of the plaque type in 3D.

Stent deployment

Innovation on lifestyle and medication has changed the treatment of atherosclerosis but still there are some patient cases, in whom a mechanical intervention is required. For instance, in high risk patients, a more invasive treatment is followed, such as arterial by-pass or PCI (Percutaneous Coronary Intervention). In Coronary artery bypass grafting (CABG), arterial or vein conduits (grafts) are used to bypass the occluded arterial region. In PCI, a balloon- catheter is inflated and in turn the arterial wall and arterial lumen are dilated and blood flow is restored. Stenting is a combination of angioplasty and stent implantation, where the tubular wire mesh is positioned in the stenosed arterial region, inflated and permanently left in order to prevent arterial recoil and restenosis. The evolution of stents has resulted in improved clinical outcome, however there are still some issues that should be taken into consideration, such as the induced local arterial injury, the possibility of in-stent restenosis (ISR), as well as, the risk for stent thrombosis (ST).

Computational simulations appeal as a useful and effective tool for investigating the mechanical performance of  stents and evaluating the arterial implications coming from different stent designs and materials, a process that cannot be fully assessed through in bench or animal experiments. Towards this direction, several research teams have provided valuable information, either by performing computational simulations of stent deployment inside idealized arteries, or even utilizing patient specific imaging data for the reconstructing the arterial segments. Different stent deployment techniques have been also approached, including displacement driven or pressure driven stent inflation approaches. The inclusion or exclusion of the balloon component was also one of the parameters that have been investigated.

In our stent deployment modeling approach, we studied the performance of the Leader Plus stent expansion inside a patient specific coronary arterial segment focusing on the arterial stresses in the contact region with the stent as well as in the stresses in the stent device.

The unexpanded configuration of the three-dimensional (3D) finite element model consisted of the 3D reconstructed arterial segment and the 3D Leader Plus stent design. ANSYS 14.5 (Ansys Canonsburg, PA) software was used for the creation of the model and for the post processing of the results. The mesh was created with 3D higher order 10 node elements. The mesh sensitivity was implemented with a convergence criterion of the maximum von Mises stresses being within 5%. Stent deployment was performed following a pressure driven approach through the application of a pressure directly to the inner stent surface.

Boundary conditions

The stent was initially placed in the arterial stenosis region. The ends of the artery were not allowed to move or rotate, appropriate boundary conditions allowed the movement in the axial and radial directions of the stent, whereas stent inflation was enabled by a pressure of 1.5MPa. This non-linear problem was solved based on the Newton-Raphson’s method.

Results

Stent expansion was achieved under uniform pressure, however due to the unsymmetry of the stenosed arterial region, stent struts deformed non-uniformly (Fig xxx). The investigation of the stent response is of great importance since high stent stresses can result in stent fracture and consequently in arterial injury. High stresses, approximately 550MPa, were observed in the stent connectors.

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