Immersed boundary-finite element model of fluid-structure interaction in the aortic root

It has long been recognized that aortic root elasticity helps to ensure efficient aortic valve closure, but our understanding of the functional importance of the elasticity and geometry of the aortic root continues to evolve as increasingly detailed in vivo imaging data become available. Herein, we describe fluid-structure interaction models of the aortic root, including the aortic valve leaflets, the sinuses of Valsalva, the aortic annulus, and the sinotubular junction, that employ a version of Peskin's immersed boundary (IB) method with a finite element (FE) description of the structural elasticity. We develop both an idealized model of the root with three-fold symmetry of the aortic sinuses and valve leaflets, and a more realistic model that accounts for the differences in the sizes of the left, right, and noncoronary sinuses and corresponding valve cusps. As in earlier work, we use fiber-based models of the valve leaflets, but this study extends earlier IB models of the aortic root by employing incompressible hyperelastic models of the mechanics of the sinuses and ascending aorta using a constitutive law fit to experimental data from human aortic root tissue. In vivo pressure loading is accounted for by a backwards displacement method that determines the unloaded configurations of the root models. Our models yield realistic cardiac output at physiological pressures, with low transvalvular pressure differences during forward flow, minimal regurgitation during valve closure, and realistic pressure loads when the valve is closed during diastole. Further, results from high-resolution computations demonstrate that IB models of the aortic valve are able to produce essentially grid-converged dynamics at practical grid spacings for the high-Reynolds number flows of the aortic root

Biomechanical analysis of Ascending Thoracic Aortic Aneurysm (ATAA)

According to the reports of the World Health Organisation (WHO), cardiovascular diseases are the number one cause of death worldwide. Specifically, arterial disease and degeneration are the major reasons for cardiovascular death and disability. Because these diseases are dependent on the changes of the mechanical properties of the arterial wall, it is very important to know as much as possible about the structural composition of arteries. The human aorta is the biggest artery in the body and consists of three main parts, ascending aorta, aortic arch and descending aorta. The walls of the arteries consist of three layers, the intima, media and adventitia, where each of the layers has different physiological functions and therefore distinct mechanical properties. These were investigated using, i.e., uniaxial tensile, inflation or planar biaxial-testing. Purpose of this thesis was to apply the biomechanical approach by mean of numerical and experimental test referring to patient-specific aortic geometries with ascending thoracic aortic aneurysms. However, despite the ample literature and the related scientific and industrial activity in this field, many different phenomena are not yet consolidated. The PhD Thesis is then divided into two main sections: the first is composed by a brief introduction on ATAA, with some background about mechanical properties of soft tissues, the evolution of the constitutive model, some remarks of the continuum. The second section of the thesis is based on the different research activities developed during the PhD

Predictive Models with Patient Specific Material Properties for the Biomechanical Behavior of Ascending Thoracic Aneurysms

International audienceThe aim of this study is to identify the patient-specific material properties of ascending thoracic aortic aneurysms (ATAA) using preoperative dynamic gated Computed Tomography (CT) scans. The identification is based on the simultaneous minimization of two cost functions, which define the difference between model predictions and gated CT measurements of the aneurysm volume at respectively systole and cardiac mid-cycle. The method is applied on 5 patients who underwent surgical repair of their ATAA at the University Hospital Center of St. Etienne. For these patients, the aneurysms were collected and tested mechanically using an in vitro bench. For the sake of validation, the mechanical properties found using the in vivo approach and the in vitro bench were compared. We eventually performed finite-element stress analyses based on each set of material properties. Rupture risk indexes were estimated and compared, 2 showing promising results of the patient-specific identification method based on gated CT

Biomechanical assessment predicts aneurysm-related events in patients with abdominal aortic aneurysm

Objective To test whether aneurysm biomechanical ratio (ABR; a dimensionless ratio of wall stress and wall strength) can predict aneurysm related events. Methods In a prospective multicentre clinical study of 295 patients with an abdominal aortic aneurysm (AAA; diameter ≥ 40 mm), three dimensional reconstruction and computational biomechanical analyses were used to compute ABR at baseline. Participants were followed for at least two years and the primary end point was the composite of aneurysm rupture or repair. Results The majority were male (87%), current or former smokers (86%), most (72%) had hypertension (mean ± standard deviation [SD] systolic blood pressure 140 ± 22 mmHg), and mean ± SD baseline diameter was 49.0 ± 6.9 mm. Mean ± SD ABR was 0.49 ± 0.27. Participants were followed up for a mean ± SD of 848 ± 379 days and rupture (n = 13) or repair (n = 102) occurred in 115 (39%) cases. The number of repairs increased across tertiles of ABR: low (n = 24), medium (n = 34), and high ABR (n = 44) (p = .010). Rupture or repair occurred more frequently in those with higher ABR (log rank p = .009) and ABR was independently predictive of this outcome after adjusting for diameter and other clinical risk factors, including sex and smoking (hazard ratio 1.41; 95% confidence interval 1.09–1.83 [p = .010]). Conclusion It has been shown that biomechanical ABR is a strong independent predictor of AAA rupture or repair in a model incorporating known risk factors, including diameter. Determining ABR at baseline could help guide the management of patients with AAA

Curve Skeleton and Moments of Area Supported Beam Parametrization in Multi-Objective Compliance Structural Optimization

This work addresses the end-to-end virtual automation of structural optimization up to the derivation of a parametric geometry model that can be used for application areas such as additive manufacturing or the verification of the structural optimization result with the finite element method. A holistic design in structural optimization can be achieved with the weighted sum method, which can be automatically parameterized with curve skeletonization and cross-section regression to virtually verify the result and control the local size for additive manufacturing. is investigated in general. In this paper, a holistic design is understood as a design that considers various compliances as an objective function. This parameterization uses the automated determination of beam parameters by so-called curve skeletonization with subsequent cross-section shape parameter estimation based on moments of area, especially for multi-objective optimized shapes. An essential contribution is the linking of the parameterization with the results of the structural optimization, e.g., to include properties such as boundary conditions, load conditions, sensitivities or even density variables in the curve skeleton parameterization. The parameterization focuses on guiding the skeletonization based on the information provided by the optimization and the finite element model. In addition, the cross-section detection considers circular, elliptical, and tensor product spline cross-sections that can be applied to various shape descriptors such as convolutional surfaces, subdivision surfaces, or constructive solid geometry. The shape parameters of these cross-sections are estimated using stiffness distributions, moments of area of 2D images, and convolutional neural networks with a tailored loss function to moments of area. Each final geometry is designed by extruding the cross-section along the appropriate curve segment of the beam and joining it to other beams by using only unification operations. The focus of multi-objective structural optimization considering 1D, 2D and 3D elements is on cases that can be modeled using equations by the Poisson equation and linear elasticity. This enables the development of designs in application areas such as thermal conduction, electrostatics, magnetostatics, potential flow, linear elasticity and diffusion, which can be optimized in combination or individually. Due to the simplicity of the cases defined by the Poisson equation, no experts are required, so that many conceptual designs can be generated and reconstructed by ordinary users with little effort. Specifically for 1D elements, a element stiffness matrices for tensor product spline cross-sections are derived, which can be used to optimize a variety of lattice structures and automatically convert them into free-form surfaces. For 2D elements, non-local trigonometric interpolation functions are used, which should significantly increase interpretability of the density distribution. To further improve the optimization, a parameter-free mesh deformation is embedded so that the compliances can be further reduced by locally shifting the node positions. Finally, the proposed end-to-end optimization and parameterization is applied to verify a linear elasto-static optimization result for and to satisfy local size constraint for the manufacturing with selective laser melting of a heat transfer optimization result for a heat sink of a CPU. For the elasto-static case, the parameterization is adjusted until a certain criterion (displacement) is satisfied, while for the heat transfer case, the manufacturing constraints are satisfied by automatically changing the local size with the proposed parameterization. This heat sink is then manufactured without manual adjustment and experimentally validated to limit the temperature of a CPU to a certain level.:TABLE OF CONTENT III I LIST OF ABBREVIATIONS V II LIST OF SYMBOLS V III LIST OF FIGURES XIII IV LIST OF TABLES XVIII 1. INTRODUCTION 1 1.1 RESEARCH DESIGN AND MOTIVATION 6 1.2 RESEARCH THESES AND CHAPTER OVERVIEW 9 2. PRELIMINARIES OF TOPOLOGY OPTIMIZATION 12 2.1 MATERIAL INTERPOLATION 16 2.2 TOPOLOGY OPTIMIZATION WITH PARAMETER-FREE SHAPE OPTIMIZATION 17 2.3 MULTI-OBJECTIVE TOPOLOGY OPTIMIZATION WITH THE WEIGHTED SUM METHOD 18 3. SIMULTANEOUS SIZE, TOPOLOGY AND PARAMETER-FREE SHAPE OPTIMIZATION OF WIREFRAMES WITH B-SPLINE CROSS-SECTIONS 21 3.1 FUNDAMENTALS IN WIREFRAME OPTIMIZATION 22 3.2 SIZE AND TOPOLOGY OPTIMIZATION WITH PERIODIC B-SPLINE CROSS-SECTIONS 27 3.3 PARAMETER-FREE SHAPE OPTIMIZATION EMBEDDED IN SIZE OPTIMIZATION 32 3.4 WEIGHTED SUM SIZE AND TOPOLOGY OPTIMIZATION 36 3.5 CROSS-SECTION COMPARISON 39 4. NON-LOCAL TRIGONOMETRIC INTERPOLATION IN TOPOLOGY OPTIMIZATION 41 4.1 FUNDAMENTALS IN MATERIAL INTERPOLATIONS 43 4.2 NON-LOCAL TRIGONOMETRIC SHAPE FUNCTIONS 45 4.3 NON-LOCAL PARAMETER-FREE SHAPE OPTIMIZATION WITH TRIGONOMETRIC SHAPE FUNCTIONS 49 4.4 NON-LOCAL AND PARAMETER-FREE MULTI-OBJECTIVE TOPOLOGY OPTIMIZATION 54 5. FUNDAMENTALS IN SKELETON GUIDED SHAPE PARAMETRIZATION IN TOPOLOGY OPTIMIZATION 58 5.1 SKELETONIZATION IN TOPOLOGY OPTIMIZATION 61 5.2 CROSS-SECTION RECOGNITION FOR IMAGES 66 5.3 SUBDIVISION SURFACES 67 5.4 CONVOLUTIONAL SURFACES WITH META BALL KERNEL 71 5.5 CONSTRUCTIVE SOLID GEOMETRY 73 6. CURVE SKELETON GUIDED BEAM PARAMETRIZATION OF TOPOLOGY OPTIMIZATION RESULTS 75 6.1 FUNDAMENTALS IN SKELETON SUPPORTED RECONSTRUCTION 76 6.2 SUBDIVISION SURFACE PARAMETRIZATION WITH PERIODIC B-SPLINE CROSS-SECTIONS 78 6.3 CURVE SKELETONIZATION TAILORED TO TOPOLOGY OPTIMIZATION WITH PRE-PROCESSING 82 6.4 SURFACE RECONSTRUCTION USING LOCAL STIFFNESS DISTRIBUTION 86 7. CROSS-SECTION SHAPE PARAMETRIZATION FOR PERIODIC B-SPLINES 96 7.1 PRELIMINARIES IN B-SPLINE CONTROL GRID ESTIMATION 97 7.2 CROSS-SECTION EXTRACTION OF 2D IMAGES 101 7.3 TENSOR SPLINE PARAMETRIZATION WITH MOMENTS OF AREA 105 7.4 B-SPLINE PARAMETRIZATION WITH MOMENTS OF AREA GUIDED CONVOLUTIONAL NEURAL NETWORK 110 8. FULLY AUTOMATED COMPLIANCE OPTIMIZATION AND CURVE-SKELETON PARAMETRIZATION FOR A CPU HEAT SINK WITH SIZE CONTROL FOR SLM 115 8.1 AUTOMATED 1D THERMAL COMPLIANCE MINIMIZATION, CONSTRAINED SURFACE RECONSTRUCTION AND ADDITIVE MANUFACTURING 118 8.2 AUTOMATED 2D THERMAL COMPLIANCE MINIMIZATION, CONSTRAINT SURFACE RECONSTRUCTION AND ADDITIVE MANUFACTURING 120 8.3 USING THE HEAT SINK PROTOTYPES COOLING A CPU 123 9. CONCLUSION 127 10. OUTLOOK 131 LITERATURE 133 APPENDIX 147 A PREVIOUS STUDIES 147 B CROSS-SECTION PROPERTIES 149 C CASE STUDIES FOR THE CROSS-SECTION PARAMETRIZATION 155 D EXPERIMENTAL SETUP 15

Passive biomechanics of abdominal aortic aneurysms

En esta tesis se estudia la respuesta elástica de aneurismas aórticos abdominales (AAA), buscando ahondar en su conocimiento y con la finalidad de proveer un mejor criterio de decisión para la realización, o no, de una intervención quirúrgica para la reparación de la lesión. Parámetros biomecánicos como la tensión pico de la pared arterial (singlas en inglés: PWS) o el riesgo de ruptura de la pared arterial (siglas en inglés: PWRR) han mostrado ser una alternativa posible y prometedora a ser utilizada para determinar el riesgo de ruptura. De la misma manera, el entender la biomecánica pasiva de los AAA permite realizar una evaluación más correcta de las tensiones, lo que se puede realizar mediante el uso de modelos de material adecuados para los tejidos junto con modelos geométricos fiables en los que se apliquen condiciones de frontera realistas. Esta tesis presenta un novedoso algoritmo iterativo para determinar la geometría cero-presión de un AAA para pacientes específicos, la cual supera las limitaciones de las metodologías existentes y permite una mejor estimación de las tensiones. La importancia de este algoritmo se debe a que los modelos de AAA de pacientes específicos son generados a partir de imágenes médicas de CT (tomografía axial computarizada) sincronizadas en las cuales la arteria está bajo presión, por lo tanto la identificación de la geometría cero-presión de AAAs permite una estimación más realista de la respuesta mecánica de la pared arterial. La metodología permite considerar el comportamiento hiperelástico anisótropo de la pared arterial, su espesor y la presencia del trombo intraluminal (ILT). Resultados en doce geometrías de de AAAs, paciente específico, indican que el algorítmo es computacionalmente tratable y eficiente, a la vez que preserva el volumen global del modelo. Adicionalmente, una comparación de resultados de PWS calculados usando geometría cero-presión y geometría basada en CT al aplicar la presión sistólica indica que los resultados a partir de geometría CT subestiman (significativamente) la tensión pico de la pared arterial en casos de modelos isótropo y anisótropo de la pared arterial. Adicionalmente, en base a los resultados experimentales publicados para la pared arterial del aneurisma y aorta sana, los resutados de esta tesis no encuentran diferencias significativas entre el uso de un modelo de material isótropo o anisótropo. Con respecto al ILT, el cual es un pseudo-tejido que se desarrolla a partir de sangre coagulada y se encuentra en la mayor parte de los AAAs de tamaño relevante, algunos estudios sugieren que las características mecánicas del ILT pueden estar relacionadas con el riesgo de ruptura del AAA, aunque existe una gran controversia en este respecto. Esta tesis investiga como la constitución y topología del ILT influye en la magnitud y localización de las tensiones pico en la pared arterial. El ILT, isótropo y no homogéneo, puede aparecer como un tejido flexible (una capa) o rígido (fibrótico multicapa). El estudio se extendió a 21 AAAs, pacientes específicos, (diámetro: 4.2-5.4 cm) que fueron reconstruidos a partir de imágenes CT y analizados numéricamente empleando el algoritmo de tirón propuesto para identificar la geometría cero presión. Los resultados indican que la PWS está mayormente correlacionada con el volumen de ILT (¿=0.44, p=0.05) y con el espesor de capa mínimo de ILT (¿=0.73, p=0.001) que con el diámetro máximo de AAA (¿=0.05, p=0.82). En promedio la PWS fue un 20% (desv estándar 12%) más alta para modelos en los que se usaron modelos suaves de ILT en lugar de modelos rígidos de ILT (p<0.001). La localización del PWS está altamente correlacionada con los puntos de menor espesor de ILT, en las secciones de máximo diámetro del AAA, y esto fue independiente de la rigidez del ILT. Adicionalmente, la heterogeneidad del ILT, i.e. la composición espacial de trombo suave o rígido, puede influenciar sustancialmente la tensión de la pared arterial. El presente estudio está limitado a identificar la influencia de factores biomecánicos, el cómo estos resultados se trasladan a la evaluación del riesgo de ruptura de AAA debe ser desarrollado a partir de estudios clínicos.The passive biomechanics of abdominal aortic aneurysms (AAA) is studied, seeking to deepen in its knowledge and with the aim of providing better decision criteria to undergo surgical intervention for AAA repair. Biomechanical parameters as the peak wall stress (PWS) or the peak wall rupture risk (PWRR) have shown to be a feasible and promising alternative that can be used to better ascertain the risk of rupture. In addition, the understanding of the passive biomechanics of AAA allows obtaining a more accurate stress assessment, which can be done by using appropriate material models for the tissues along with accurate geometric models and more realistic boundary conditions for the lesion. This thesis presents a novel iterative algorithm to determine the zeropressure geometry of a patient-specific AAA that overcomes limitations on existing methodologies and allows a better estimation of the stresses. The importance of this algorithm lays in that patient-specific AAA models are generated from gated CT (Computer Tomography) medical images in which the artery is under pressure (diastolic), therefore the identification of the AAA zero pressure geometry would allow for a more realistic estimate of the aneurismal wall mechanics. The methodology allows considering the anisotropic hyperelastic behavior of the aortic wall, its thickness and accounts for the presence of the intraluminal thrombus (ILT). The results on twelve patientspecific AAA geometric models indicate that the procedure is computational tractable and efficient, and preserves the global volume of the model. In addition, a comparison of the peak wall stress computed with the zero pressure and CT-based geometries during systole indicate that computations using CTbased geometric models underestimate (significantly) the peak wall stress for both, isotropic and anisotropic material models of the arterial wall. In addition, based on the reported experimental results for aneurysmal and aortic wall mechanics, no significant differences among isotropic and anisotropic material models have been found. With respect to the ILT, which is a pseudo-tissue that develops from coagulated blood and it is found in most AAAs of clinically relevant size, a number of studies have suggested that ILT mechanical characteristics may be related to AAA risk of rupture, even though there is still great controversy on this regard. This thesis investigates how ILT constitution and topology influence the magnitude and location of PWS. ILT is isotropic and inhomogeneous and may appear as a soft (single-layered) or stiff (multilayered fibrotic) tissue. An extended study was conducted involving twenty-one patient-specific AAAs (diameter: 4.2-5.4 cm) which were reconstructed from CT images and biomechanically analyzed using the proposed methodology. Results indicated that PWS correlated stronger with ILT volume (ρ=0.44, p=0.05) and the minimum thickness of the ILT layer (ρ=0.73, p=0.001) than with maximum AAA diameter (ρ=0.05, p=0.82). In average PWS was 20% (SD 12%) higher for FE models that used a soft instead of stiff ILT models (p<0.001). PWS location strongly correlated with sites of minimum ILT thickness in the section of maximum AAA diameter and was independent from the ILT stiffness. In addition, ILT heterogeneity, i.e. the spatial composition of soft and stiff thrombus tissue, can considerably influence the stress in the AAA wall. The present study is limited to the identification of influential biomechanical factors, and how its findings translate to an AAA rupture risk assessment remains to be explored by clinical studies

Computational analysis of blood flow and stress patterns in the aorta of patients with Marfan syndrome

Personalised external aortic root support (PEARS) was designed to prevent progressive aortic dilatation, and the associated risk of aortic dissection, in patients with Marfan syndrome by providing an additional support to the aorta. The objective of this thesis was to understand the biomechanical implications of PEARS surgery as well as to investigate the altered haemodynamics associated with the disease and its treatment. Finite element (FE) models were developed using patient-specific aortic geometries reconstructed from pre and post-PEARS magnetic resonance (MR) images of three Marfan patients. The wall and PEARS materials were assumed to be isotropic, incompressible and linearly elastic. A static load on the inner wall corresponding to the patients’ pulse pressure was applied with a zero-displacement constraint at all boundaries. Results showed that peak aortic stresses and displacements before PEARS were located at the sinuses of Valsalva but following PEARS surgery, they were shifted to the aortic arch, at the intersection between the supported and unsupported aorta. The zero-displacement constraint at the aortic root was subsequently removed and replaced with downward motion measured from in vivo images. This revealed significant increases in the longitudinal wall stress, especially in the pre-PEARS models. Computational fluid dynamics (CFD) models were developed to evaluate flow characteristics. The correlation-based transitional Shear Stress Transport (SST-Tran) model was adopted to simulate potential transitional and turbulence flow during part of the cardiac cycle and flow waveforms derived from phase-contrast MR images were imposed at the inlets. Qualitative patterns of the haemodynamics were similar pre- and post-PEARS with variations in mean helicity flow index (HFI) of -10%, 35% and 20% in the post-PEARS aortas of the three patients. A fluid-structure interaction (FSI) model was developed for one patient, pre- and post-PEARS in order to examine the effect of wall compliance on aortic flow as well as the effect of pulsatile flow on wall stress. This model excluded the sinuses and was based on the laminar flow assumption. The results were similar to those obtained using the rigid wall and static structural models, with minor quantitative differences. Considering the higher computational cost of FSI simulations and the relatively small differences observed in peak wall stress, it is reasonable to suggest that static structural models would be sufficient for wall stress prediction. Additionally, aortic root motion had a more profound effect on wall stress than wall compliance. Further studies are required to assess the statistical significance of the findings outlined in this thesis. Recommendations for future work were also highlighted, with emphasis on model assumptions including material properties, residual stress and boundary conditions.Open Acces

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