On the major role played by the curvature of intracranial aneurysms walls in determining their mechanical response, local hemodynamics, and rupture likelihood

The properties of intracranial aneurysms (IAs) walls are known to be driven by the underlying hemodynamics adjacent to the IA sac. Different pathways exist explaining the connections between hemodynamics and local tissue properties. The emergence of such theories is essential if one wishes to compute the mechanical response of a patient-specific IA wall and predict its rupture. Apart from the hemodynamics and tissue properties, one could assume that the mechanical response also depends on the local morphology, more specifically, the wall curvature, with larger values at highly-curved wall portions. Nonetheless, this contradicts observations of IA rupture sites more often found at the dome, where the curvature is lower. This seeming contradiction indicates a complex interaction between local hemodynamics, wall morphology, and mechanical response, which warrants further investigation. This was the main goal of this work. We accomplished this by analysing the stress and stretch fields in different regions of the wall for a sample of IAs, which have been classified based on particular local hemodynamics and local curvature. Pulsatile numerical simulations were performed using the one-way fluid-solid interaction strategy implemented in OpenFOAM (solids4foam toolbox). We found that the variable best correlated with regions of high stress and stretch was the wall curvature. Additionally, our data suggest a connection between the local curvature and local hemodynamics, indicating that the curvature is a property that could be used to assess both mechanical response and hemodynamic conditions, and, moreover, to suggest new metrics based on the curvature to predict the likelihood of rupture.Comment: Preprint submitted to Acta Biomaterialia, with 27 pages and 11 figure

Anisotropic behaviour of human gallbladder walls

Inverse estimation of biomechanical parameters of soft tissues from non-invasive measurements has clinical significance in patient-specific modelling and disease diagnosis. In this paper, we propose a fully nonlinear approach to estimate the mechanical properties of the human gallbladder wall muscles from in vivo ultrasound images. The iteration method consists of a forward approach, in which the constitutive equation is based on a modified Hozapfel–Gasser–Ogden law initially developed for arteries. Five constitutive parameters describing the two orthogonal families of fibres and the matrix material are determined by comparing the computed displacements with medical images. The optimisation process is carried out using the MATLAB toolbox, a Python code, and the ABAQUS solver. The proposed method is validated with published artery data and subsequently applied to ten human gallbladder samples. Results show that the human gallbladder wall is anisotropic during the passive refilling phase, and that the peak stress is 1.6 times greater than that calculated using linear mechanics. This discrepancy arises because the wall thickness reduces by 1.6 times during the deformation, which is not predicted by conventional linear elasticity. If the change of wall thickness is accounted for, then the linear model can used to predict the gallbladder stress and its correlation with pain. This work provides further understanding of the nonlinear characteristics of human gallbladder

A methodology for the derivation of unloaded abdominal aortic aneurysm geometry with experimental validation

In this work, we present a novel method for the derivation of the unloaded geometry of an abdominal aortic aneurysm (AAA) from a pressurized geometry in turn obtained by 3D reconstruction of computed tomography (CT) images. The approach was experimentally validated with an aneurysm phantom loaded with gauge pressures of 80, 120, and 140mm Hg. The unloaded phantom geometries estimated from these pressurized states were compared to the actual unloaded phantom geometry, resulting in mean nodal surface distances of up to 3.9% of the maximum aneurysm diameter. An in-silico verification was also performed using a patient-specific AAA mesh, resulting in maximum nodal surface distances of 8 lm after running the algorithm for eight iterations. The methodology was then applied to 12 patient-specific AAA for which their corresponding unloaded geometries were generated in 5-8 iterations. The wall mechanics resulting from finite element analysis of the pressurized (CT image-based) and unloaded geometries were compared to quantify the relative importance of using an unloaded geometry for AAA biomechanics. The pressurized AAA models underestimate peak wall stress (quantified by the first principal stress component) on average by 15% compared to the unloaded AAA models. The validation and application of the method, readily compatible with any finite element solver, underscores the importance of generating the unloaded AAA volume mesh prior to using wall stress as a biomechanical marker for rupture risk assessment

Mathematical and Numerical Modeling of Healthy and Unhealthy Cerebral Arterial Tissues

Over the last two decades, we have witnessed an increasing application of mathematical models and numerical simulations for the study of the cardiovascular system. Indeed, both tools provide an important contribution to the analysis of the functioning of the different components of the cardiovascular system (i.e. heart, vessels and blood) and of their interactions either in physiological and pathological conditions. For this reason, reliable constitutive models for the cardiac, arterial and venous tissues as well as for the blood are an essential prerequisite for a number of different objectives that range from the improved diagnostic to the study of the onset and development of cardiovascular diseases (e.g atherosclerosis or aneurysms). This work focuses on the mathematical and numerical modeling of healthy and unhealthy cerebral arterial tissue. In particular, it presents a detailed analysis of different constitutive models for the arterial tissue by means of finite element numerical simulations of arterial wall mechanics and fluid-structure interaction problems occurring in hemodynamics. Hyperelastic isotropic and anisotropic constitutive laws are considered for the description of the passive mechanical behavior of the vessels. An anisotropic multi-mechanism model, specifically proposed for the cerebral arterial tissue, for which the activation of the collagen fibers occurs at finite strains is employed. Firstly, the constitutive laws are numerically validated by considering numerical simulations of static inflation tests on a cylindrical geometry representing a specimen of anterior cerebral artery. With this regard, the material parameters for the constitutive law are obtained from the data fitting of experimental measurements obtained on the same vessel. The constitutive models are critically discussed according to their capability of describing the physiogical highly nonlinear behavior of arteries and on other numerical aspects related to the computational simulation of arterial wall mechanics. Afterwards, simulations of the blood flow and vessel wall interactions are carried out on idealized blood vessels in order to analyze the influence of the modeling choice for the arterial wall on hemodynamic and mechanical quantities that are commonly considered as indicators of physiological or pathological conditions of arteries. We also consider the numerical simulations of unhealthy cerebral arterial tissues by taking into account the mechanical weakening of the vessel wall that occurs during early development stages of cerebral aneurysms by means of static inflation and FSI simulations. We employ both isotropic and anisotropic models study the effects of the mechanical degradation on hemodynamic and mechanical quantities of interest. The FSI simulations are carried out both on idealized geometries of blood vessels and on domains representing idealized and anatomically realistic cerebral aneurysms

Multiscale modelling of intracranial aneurysm evolution: A novel Patient-specific Fluid-Solid-Growth (p-FSG) framework incorporating endothelial mechanobiology

IAs (intracranial aneurysms) affect 2-5% of the adult population with a high fatality rate upon rupture. However, the rupture rate is around 0.1%-1% per year which indicates most aneurysms are stable. This leads to a strong demand for clinicians to have a better understanding of the aneurysm stability for treatment planning. Aneurysm stability is thought to be linked to its mechanical environment from both the blood flow and the pulsatile pressure giving the mechanistic signals to vascular cells. A cascade of subsequently biological reactions through the routine of cellular mechanotransduction within the aneurysm tissue determine the development of aneurysms. It is envisaged that mechanistic modelling of biological processes that govern aneurysm growth may help to distinguish between vulnerable and stable aneurysms. We developed an integrated Patient-specific Fluid-Solid-Growth (p-FSG) framework for simulating the growth of existing intracranial aneurysms. An aneurysm and connected arteries are modelled as fibre-reinforced nonlinear elastic soft-tissue in the commercial software ANSYS. Computational Fluid Dynamics (CFD) simulation quantifies haemodynamic stimuli that act on endothelial cells. Here, we link the morphology of the cells (spindle, hexagonal) to a novel flow metric (Anisotropic Ratio, AR) that characterizes the oscillatory nature of the flow pattern. We then proposed a hypothesis that the endothelial permeability could be regarded as a function of the morphology of endothelial cells which is associated to the growth and remodelling of the aneurysmal tissue. Mass density of elastin and collagen decreases in the region of high endothelial permeability via the inflammatory pathway. Collagen growth (mass changes) is driven by stretch based stimuli of fibroblast cells. Collagen remodelling employs a stress-mediated method that restores the Cauchy stress on collagen fibres to homeostatic levels in the course of the aneurysm enlargement. Principal destructive and self-protective activities during the aneurysm evolution involving elastin, collagen fibres, endothelial cells and fibroblasts are mathematically represented by our p-FSG framework. Our research suggests that the collagen growth function is a vital mechanism for the stability of aneurysms. This is the first framework models the aneurysm evolution on the basis of the patient-specific aneurysm geometry. Also, we incorporated the functionality of endothelial cells quantified by a novel flow metric to the aneurysm growth and remodelling (G&R) model. This automatic p-FSG framework fully integrated into ANSYS engineering software provides a foundational platform for modelling the aneurysm growth and might become a practical tool in the estimation of aneurysm stability

Numerical modelling of the fluid-structure interaction in complex vascular geometries

A complex network of vessels is responsible for the transportation of blood throughout the body and back to the heart. Fluid mechanics and solid mechanics play a fundamental role in this transport phenomenon and are particularly suited for computer simulations. The latter may contribute to a better comprehension of the physiological processes and mechanisms leading to cardiovascular diseases, which are currently the leading cause of death in the western world. In case these computational models include patient-specific geometries and/or the interaction between the blood flow and the arterial wall, they become challenging to develop and to solve, increasing both the operator time and the computational time. This is especially true when the domain of interest involves vascular pathologies such as a local narrowing (stenosis) or a local dilatation (aneurysm) of the arterial wall. To overcome these issues of high operator times and high computational times when addressing the bio(fluid)mechanics of complex geometries, this PhD thesis focuses on the development of computational strategies which improve the generation and the accuracy of image-based, fluid-structure interaction (FSI) models. First, a robust procedure is introduced for the generation of hexahedral grids, which allows for local grid refinements and automation. Secondly, a straightforward algorithm is developed to obtain the prestress which is implicitly present in the arterial wall of a – by the blood pressure – loaded geometry at the moment of medical image acquisition. Both techniques are validated, applied to relevant cases, and finally integrated into a fluid-structure interaction model of an abdominal mouse aorta, based on in vivo measurements