Computational modeling of fracture biomechanics in cerebral aneurysms using a phase field model in thin shells

La evaluación de indicadores de riesgo en medicina es de larga trayectoria y de fundamental importancia dada la imperiosa necesidad de contar con marcadores que permitan evaluar situaciones de diagnóstico complejas, que se presentan a diario en los centros de salud. La ruptura de aneurismas intracraneales es la causa más común de hemorragia subaracnoidea espontánea, la cual posee una elevada tasa de morbimortalidad. Las aneurismas intracraneales poseen una prevalencia mucho mayor que su tasa de rotura espontánea, lo cual se encuentra agravado por los riesgos asociados con la intervención para su oclusión. Al presente, el mecanismo de ruptura de los aneurismas intracraneales no es completamente entendido, por lo tanto, es importante desarrollar herramientas tecnológicas que permitan brindar apoyo en el diagnóstico clínico y en la planificación de la intervención para su oclusión.Recientes estudios han mostrado que los modelos de campo de fase son idóneos por su estructura matemática (formulación variacional) para representar la propagación de fracturas en tejidos biológicos blandos e.g. arterias humanas, las cuales se comportan como un material débilmente anisótropo. En este proyecto, mediante el empleo de modelos de campo de fase, se determinará aquellas zonas propensas a romper (mayor daño). En este trabajo se considera que el saco aneurismático como sus arterias adyacentes se pueden representar mediante un medio continuo cuyas propiedades geométricas y materiales varían en función de si representan la patología aneurismática o la arteria, por ejemplo el espesor de la pared y el módulo de Young. Mientras que la cinemática de la deformación mecánica se rige por la teoría de láminas delgadas de Kirchhoff-Love geométricamente no lineal.Con el objetivo de determinar indicadores de ruptura y tomando en consideración la premisa de que los aneurismas se rompen cuando la fuerza ejercida sobre la pared supera el umbral de resistencia del tejido, se realizará un análisis estadístico sobre la base de datos AneuriskWeb consistente en 100 pacientes. El estudio combinará indicadores morfométricos clásicos con otros basados en el daño aparente producido por el estrés mecánico. Además, se espera poder caracterizar mecánicamente las zonas donde se observa mayor daño y la sensibilidad ante la aplicación de cargas externas con el fin de desarrollar una herramienta versátil y robusta de cara a planificar la intervención endovascular que conlleve un menor riesgo de ruptura.The assessment of risk markers has a longstanding and a fundamental importance in medicine, which is driven by the need to evaluate complex diagnosis situations, occurring daily in health centers. Rupture of intracranial saccular aneurysms is the most common cause of spontaneous subarachnoid hemorrhage which has significant morbidity and mortality. Intracranial aneurysms have the peculiarity that its prevalence is much higher than the rate of spontaneous rupture, which is compounded by the risks associated with the clinical treatments for their occlusion. Currently, the rupture mechanism is not fully understood, therefore, it is important to develop appropriate tools that allow to provide support in the clinical diagnosis and in the planning of the intervention for its occlusion.Recent studies have shown that phase field models are suitable due to their mathematical structure to represent the propagation of fractures in soft biological tissues e.g. human arteries, which behave as a weakly anisotropic material. In this project, through the use of phase field models, the regions prone to breaking around of the aneurysm neck will be determined. In this work it is considered that the aneurysm sac, as its adjacent arteries, can be represented by a continuous medium whose geometric and material properties vary depending on whether they represent the aneurysm pathology or the parent vessels, for example the thickness of the wall and the Young's modulus. While the kinematics of mechanical deformation is governed by the theory of Kirchhoff-Love of geometrically nonlinear thin shells.In order to determine reliable rupture indicators and taking into account the premise that aneurysms are broken when the force exerted on the wall exceeds the tissue resistance threshold, a statistical analysis will be performed based on the AneuriskWeb data consisting of 100 patients. The study will combine classic morphometric descriptors with others based on the apparent damage produced by mechanical stress. In addition, by developing a versatile and robust computational tool, it is expected to mechanically characterize the areas where greater damage is observed and those wich are more sensitive to the application of external loads, such that the treatment and endovascular intervention entail a lower risk of rupture

A variational model of fracture for tearing brittle thin sheets

Tearing of brittle thin elastic sheets, possibly adhered to a substrate, involves a rich interplay between nonlinear elasticity, geometry, adhesion, and fracture mechanics. In addition to its intrinsic and practical interest, tearing of thin sheets has helped elucidate fundamental aspects of fracture mechanics including the mechanism of crack path selection. A wealth of experimental observations in different experimental setups is available, which has been often rationalized with insightful yet simplified theoretical models based on energetic considerations. In contrast, no computational method has addressed tearing in brittle thin elastic sheets. Here, motivated by the variational nature of simplified models that successfully explain crack paths in tearing sheets, we present a variational phase-field model of fracture coupled to a nonlinear Koiter thin shell model including stretching and bending. We show that this general yet straightforward approach is able to reproduce the observed phenomenology, including spiral or power-law crack paths in free standing films, or converging/diverging cracks in thin films adhered to negatively/positively curved surfaces, a scenario not amenable to simple models. Turning to more quantitative experiments on thin sheets adhered to planar surfaces, our simulations allow us to examine the boundaries of existing theories and suggest that homogeneous damage induced by moving folds is responsible for a systematic discrepancy between theory and experiments. Thus, our computational approach to tearing provides a new tool to understand these complex processes involving fracture, geometric nonlinearity and delamination, complementing experiments and simplified theories.Fil: Li, Bin. Universidad Politécnica de Catalunya; España. Sorbonne Université; Francia. Centre National de la Recherche Scientifique; FranciaFil: Millán, Raúl Daniel. Universidad Nacional de Cuyo. Facultad de Ciencias Aplicadas a la Industria; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. Universidad Politécnica de Catalunya; EspañaFil: Torres Sánchez, Alejandro. Universidad Politécnica de Catalunya; EspañaFil: Roman, Benoît. Centre National de la Recherche Scientifique; Francia. Sorbonne Université; FranciaFil: Arroyo Balaguer, Marino. Universidad Politécnica de Catalunya; Españ

Modeling and enhanced sampling of molecular systems with smooth and nonlinear data-driven collective variables

Collective variables (CVs) are low-dimensional representations of the state of a complex system, which help us rationalize molecular conformations and sample free energy landscapes with molecular dynamics simulations. Given their importance, there is need for systematic methods that effectively identify CVs for complex systems. In recent years, nonlinear manifold learning has shown its ability to automatically characterize molecular collective behavior. Unfortunately, these methods fail to provide a differentiable function mapping high-dimensional configurations to their low-dimensional representation, as required in enhanced sampling methods. We introduce a methodology that, starting from an ensemble representative of molecular flexibility, builds smooth and nonlinear data-driven collective variables (SandCV) from the output of nonlinear manifold learning algorithms. We demonstrate the method with a standard benchmark molecule, alanine dipeptide, and show how it can be non-intrusively combined with off-the-shelf enhanced sampling methods, here the adaptive biasing force method. We illustrate how enhanced sampling simulations with SandCV can explore regions that were poorly sampled in the original molecular ensemble. We further explore the transferability of SandCV from a simpler system, alanine dipeptide in vacuum, to a more complex system, alanine dipeptide in explicit water.Peer ReviewedPostprint (published version

Solmec: an efficient c++ library to solve linear and nonlinear elasticity problems

A C++ library based on local maximum-entropy approximation schemes to solve linear and nonlinear elasticity problem is presented. The available tools are briefly described, and several implementation details are also mentioned. Selected numerical examples are shown in order to illustrate the capabilities of the library. The current and future developments are indicated.Peer Reviewe

Numerical integration by using local-node gauss-hermite cubature

A local–node numerical integration scheme for meshless methods is presented in this work. The distinguishing characteristic of the introduced scheme is that not support mesh or grid to perform numerical integration is needed, besides the fact that gauss cubature points for each node are generated in a properly fashion and that the extension of the methodology to high dimensions is straightforward. The numerical integration is computed with the Gauss–Hermite cubature formulas, and the partition of unity is employed to introduce the Gaussian weight in a natural way. Selected numerical tests in two-dimensions are used to illustrate the validity of the proposed methodology. Although the obtained results are encouraging, the behavior of the integration error is not still well understood when the dimensionless parameter which control the width of the Gaussian kernel varies

Mesh construction and computational analysis of the biomechanics of an endovascular intervention in cerebral aneurysms using Kirchhoff–Love shells

The mechanism of aneurysm rupture is still not fully understood. The rupture risk of the intervention may increase during endovascular occlusions of cerebral aneurysms due to a localized load in the parent vessel close to the neck, a common day-to-day situation. As a first attempt on the road towards developing a plausible analysis capable of dealing with many cases in a statistical sense, we describe the deformation kinematics using a geometrically nonlinear thin shell model under Kirchhoff-Love’s assumptions in conjunction with a simplistic Kirchhoff-St. Venant’s hyperelastic material model. Though it cannot assess the artery’s complexity, this more straightforward yet not trivial approach enable us to statistically study the application of a concentrated load in many locations, which mimics the action of an instrument during the endovascular treatment. We performed numerical simulations on 34 cases from the AneuriskWeb Database. We present preliminary results considering a smoothly varying thickness between the parent vessel and the aneurysm dome, focusing in the mesh construction process and loading.Fil: Muzi, Nicolás. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. Universidad Nacional de Cuyo. Facultad de Ciencias Aplicadas a la Industria; ArgentinaFil: Camussoni, Francesco. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; ArgentinaFil: Moyano, Luis Gregorio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Universidad Nacional de Cuyo; ArgentinaFil: Millán, Raúl Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. Universidad Nacional de Cuyo; ArgentinaXLII Ibero Latin American Congress on Computational Methods in Engineering; III Pan-American Congress on Computational MechanicsRío de JaneiroBrasilAssociação Brasileira de Métodos Computacionais em Engenhari

Second order convex maximum entropy approximants with applications to high order PDE

We present a new approach for second order maximum entropy (max-ent) meshfree approximants that produces positive and smooth basis functions of uniform aspect ratio even for non-uniform node sets, and prescribes robustly feasible constraints for the entropy maximization program defining the approximants. We examine the performance of the proposed approximation scheme in the numerical solution by a direct Galerkin method of a number of partial differential equations (PDEs), including structural vibrations, elliptic second order PDEs, and fourth order PDEs for Kirchhoff-Love thin shells and for a phase field model describing the mechanics of biomembranes. The examples highlight the ability of the method to deal with non-uniform node distributions, and the high accuracy of the solutions. Surprisingly, the first order meshfree max-ent approximants with large supports are competitive when compared to the proposed second order approach in all the tested examples, even in the higher order PDEs.Peer ReviewedPostprint (author's final draft

Fracture toughening and toughness asymmetry induced by flexoelectricity

Cracks generate the largest strain gradients that any material can withstand. Flexoelectricity (coupling between strain gradient and polarization) must therefore play an important role in fracture physics. Here we use a self-consistent continuum model to evidence two consequences of flexoelectricity in fracture: the resistance to fracture increases as structural size decreases, and it becomes asymmetric with respect to the sign of polarization. The latter phenomenon manifests itself in a range of intermediate sizes where piezo- and flexoelectricity compete. In BaTiO3 at room temperature, this range spans from 0.1 to 50 nm, a typical thickness range for epitaxial ferroelectric thin films.Fil: Abdollahi, Amir. Universidad Politécnica de Catalunya; EspañaFil: Peco Regales, Christian. Universidad Politécnica de Catalunya; EspañaFil: Millán, Raúl Daniel. Universidad Politécnica de Catalunya; España. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Arroyo Balaguer, Marino. Universidad Politécnica de Catalunya; EspañaFil: Catalan, Gustau. Institut Catalá de Recerca I Estudis Avançats; España. Institut Catala de Nanociéncia i Nanotecnologia; EspañaFil: Arias, Irene. Universidad Politécnica de Catalunya; España. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Computational geometry and biomechanical analysis of an endovascular intervention in cerebral aneurysms using Kirchhoff–Love shells of nonuniform thickness

En la actualidad, los mecanismos de ruptura de aneurismas intracraneales no han sido caracterizados en su totalidad. El riesgo de ruptura durante la intervención endovascular de oclusión podría incrementarse debido a cargas localizadas en regiones cercanas al cuello del aneurisma, una situación común durante el procedimiento. Como un primer acercamiento al desarrollo de un análisis aplicable a una gran cantidad de casos con relevancia estadística, describimos la cinemática de deformación mediante un modelo de láminas delgadas geométricamente no lineales bajo la teoría de Kirchhoff-Love, en conjunto con un modelo material hiperelástico de Kirchhoff-St. Venant. Si bien este modelo no refleja la complejidad del tejido arterial, este enfoque nos permite considerar la aplicación de una carga localizada en múltiples ubicaciones de la arteria para una base de datos con número significativo de casos, imitando el efecto de un microcatéter utilizado en el tratamiento endovascular. Realizamos simulaciones numéricas en 4 casos de la base de datos AneuriskWeb, y presentamos resultados preliminares considerando un espesor variable entre la arteria y el domo del aneurisma, poniendo el foco en la construcción de las mallas de superficie y en los experimentos realizados.The mechanism of aneurysm rupture is still not fully understood. The rupture risk of the intervention may increase during endovascular occlusion of cerebral aneurysms due to a localized load in the parent vessel close to the neck, a common dayto-day situation. As a first attempt on the road towards developing a plausible analysis capable of dealing with many cases in a statistical sense, we describe the deformation kinematics using a geometrically nonlinear thin shell model under KirchhoffLove’s assumptions in conjunction with a simplistic Kirchhoff-St. Venant’s hyperelastic material model. Though it cannot assess the artery’s complexity, this more straightforward yet not trivial approach enables us to statistically study the application of a concentrated load in many locations, which mimics the action of an instrument during the endovascular treatment. We performed numerical simulations on 4 cases from the AneuriskWeb Database. We present preliminary results considering a smoothly varying thickness between the parent vessel and the aneurysm dome, focusing on the mesh construction process and loading.Fil: Muzi, Nicolás. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. Universidad Nacional de Cuyo. Facultad de Ciencias Aplicadas a la Industria; ArgentinaFil: Camussoni, Francesco. Comisión Nacional de Energía Atómica. Gerencia del Área de Investigaciones y Aplicaciones No Nucleares. Gerencia de Física (cab). División Física Estadística; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; ArgentinaFil: Moyano, Luis Gregorio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Investigaciones y Aplicaciones No Nucleares. Gerencia de Física (cab). División Física Estadística; ArgentinaFil: Millán, Raúl Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. Universidad Nacional de Cuyo. Facultad de Ciencias Aplicadas a la Industria; Argentin

Cell-based maximum entropy approximants for three-dimensional domains: Application in large strain elastodynamics using the meshless total Lagrangian explicit dynamics method

We present the cell-based maximum entropy (CME) approximants in E3 space by constructing the smooth approximation distance function to polyhedral surfaces. CME is a meshfree approximation method combining the properties of the maximum entropy approximants and the compact support of element-based interpolants. The method is evaluated in problems of large strain elastodynamics for three-dimensional (3D) continua using the well-established meshless total Lagrangian explicit dynamics method. The accuracy and efficiency of the method is assessed in several numerical examples in terms of computational time, accuracy in boundary conditions imposition, and strain energy density error. Due to the smoothness of CME basis functions, the numerical stability in explicit time integration is preserved for large time step. The challenging task of essential boundary condition (EBC) imposition in noninterpolating meshless methods (eg, moving least squares) is eliminated in CME due to the weak Kronecker-delta property. The EBCs are imposed directly, similar to the finite element method. CME is proven a valuable alternative to other meshless and element-based methods for large-scale elastodynamics in 3D. A naive implementation of the CME approximants in E3 is available to download at https://www.mountris.org/software/mlab/cme.Fil: Mountris, Konstantinos A.. Universidad de Zaragoza; EspañaFil: Bourantas, George C.. University of Western Australia; AustraliaFil: Millán, Raúl Daniel. Universidad Nacional de Cuyo. Facultad de Ciencias Aplicadas a la Industria; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; ArgentinaFil: Joldes, Grand R.. University of Western Australia; AustraliaFil: Miller, Karol. Cardiff University; Reino Unido. University of Western Australia; AustraliaFil: Pueyo, Esther. Centro de Investigacion Biomedica En Red.; España. Universidad de Zaragoza; EspañaFil: Wittek, Adam. University of Western Australia; Australi