Method to geometrically personalize a detailed finite element model of the spine

To date, developing geometrically personalized and detailed solid finite element models of the spine remains a challenge, notably due to multiple articulations and complex geometries. To answer this problem, a methodology based on a free form deformation technique (kriging) was developed to deform a detailed reference finite element mesh of the spine (including discs and ligaments) to the patient-specific geometry of 10 and 82-year old asymptomatic spines. Different kriging configurations were tested: with or without smoothing, and control points on or surrounding the entire mesh. Based on the results, it is recommended to use surrounding control points and smoothing. The mean node to surface distance between the deformed and target geometries was 0.3 mm ± 1.1. Most elements met the mesh quality criteria (95%) after deformation, without interference at the articular facets. The method’s novelty lies in the deformation of the entire spine at once, as opposed to deforming each vertebra separately, with surrounding control points and smoothing. This enables the transformation of reference vertebrae and soft tissues to obtain complete and personalized FEMs of the spine with minimal post-processing to optimize the mesh. Biomechanics

An X-FEM and Level Set computational approach for image-based modeling. Application to homogenization.

International audienceThe advances in material characterization by means of imaging techniques require powerful computational methods for numerical analysis. The present contribution focuses on highlighting the advantages of coupling the Extended Finite Elements Method (X-FEM) and the level sets method, applied to solve microstructures with complex geometries. The process of obtaining the level set data starting from a digital image of a material structure and its input into an extended finite element framework is presented. The coupled method is validated using reference examples and applied to obtain homogenized properties for heterogeneous structures. Although the computational applications presented here are mainly two dimensional, the method is equally applicable for three dimensional problems

Patient specific finite volume modeling for intraosseous PMMA cement flow simulation in vertebral cancellous bone

Ph.DDOCTOR OF PHILOSOPH

A novel contact interaction formulation for voxel-based micro-finite-element models of bone

Voxel-based micro-finite-element (μFE) models are used extensively in bone mechanics research. A major disadvantage of voxel-based μFE models is that voxel surface jaggedness causes distortion of contact-induced stresses. Past efforts in resolving this problem have only been partially successful, ie, mesh smoothing failed to preserve uniformity of the stiffness matrix, resulting in (excessively) larger solution times, whereas reducing contact to a bonded interface introduced spurious tensile stresses at the contact surface. This paper introduces a novel "smooth" contact formulation that defines gap distances based on an artificial smooth surface representation while using the conventional penalty contact framework. Detailed analyses of a sphere under compression demonstrated that the smooth formulation predicts contact-induced stresses more accurately than the bonded contact formulation. When applied to a realistic bone contact problem, errors in the smooth contact result were under 2%, whereas errors in the bonded contact result were up to 42.2%. We conclude that the novel smooth contact formulation presents a memory-efficient method for contact problems in voxel-based μFE models. It presents the first method that allows modeling finite slip in large-scale voxel meshes common to high-resolution image-based models of bone while keeping the benefits of a fast and efficient voxel-based solution scheme

Metodología para la reconstrucción 3D de estructuras craneofaciales y su utilización en el método de elementos finitos

Este artículo describe la implementación de una metodología para la reconstrucción 3D de estructuras anatómicas craneofaciales conformadas por tejidos duros y blandos a partir de imágenes biomédicas para ser utilizadas en aplicaciones que involucren el método de elementos finitos en bioingeniería. La metodología inicia con el desarrollo de un software de procesamiento de imágenes biomédicas en formato DICOM (Digital Imaging Standard for Medical Images) realizado en lenguaje C que provee la nube de puntos de la estructura anatómica, a partir de la cual se construyen y optimizan las superficies que finalmente son las que conforman un sólido que puede ser exportado a ANSYS 10.0r. Este proceso se llevó a cabo utilizando los software de modelación geométrica ProENGINEER WILDFIRE 3.0r y GID 8.0r. Se reconstruyeron estructuras como mandíbula, hueso temporal y algunas piezas dentales de manera satisfactoria, conservando sus características anatómicas, obteniendo un modelo geométrico que permitió efectuar simulaciones biomecánicas por medio del método de los elementos finitos en ANSYS 10.0r. La metodología implementada proporcionó una mayor capacidad de detalle en la modelación geométrica de estructuras anatómicas, y a su vez posibilitó la realización de una aplicación biomecánica sin incurrir en simplificaciones como la omisión del hueso esponjoso y la inadecuada asignación de las propiedades mecánicas mandibulares, de modo que se pudiera afectar la calidad de los resultados. Aunque la validación del estudio se realizó a partir de la acción de un dispositivo de ortodoncia sobre la mandíbula, la metodología desarrollada podría aplicarse a la evaluación de otros problemas que involucren estructuras anatómicas diferentes. PACS: 87.57.C-, 87.57.N-, 87.85.Pq, 87.85.Ox MSC: 92C5

Model-based segmentation and registration of multimodal medical images

Ph.DDOCTOR OF PHILOSOPH

Developing a modeling and simulation framework for human thermoregulation for voxelized domains

Doctor of PhilosophyDepartment of Mechanical and Nuclear EngineeringAmir BahadoriSteven J EckelsSince the 1980s, various models have been developed to simulate human thermoregulation. These models have undergone many modifications, maturing from simple geometrical shapes to more advanced polygon meshes. However, state-of-the-art models still lack the flexibility to be person specific and simulate thermoregulation with anatomical accuracy. Computational human phantoms (CHP), such as voxel phantoms, are anthropomorphic models developed from person-specific medical imaging data. These models provide the flexibility to represent a person-specific simulation domain with anatomical accuracy. However, using voxel phantoms for thermoregulation is challenging. This dissertation focuses on the challenges of using voxel phantoms for thermoregulation simulation and proposes solutions to overcome them. The first challenge associated with voxel phantoms is the stair-step effect introduced due to the cuboidal nature of voxels. To understand and quantify the surface area error due to the stair-step effect, a sphere was used, as a sphere represents the worst-case scenario for 3D curved domains. The overestimation of surface area for a sphere was found to be 50 %. Many solutions are available in the literature to reduce this error, but all of them rely on an unstructured mesh. To maintain the structured nature inherent in voxel phantoms, a structured cleaving method was developed. This method divides a pixel into four triangles and a voxel into 24 tetrahedrons. Using the smoothing method described in this dissertation, the overestimation of the surface area of a sphere was reduced to 16 %. This method was further tested on four tumors obtained from MRI scans. The overestimation of surface area for these tumors was reduced from 47% to 17% on average using the structured cleaving method. The second challenge of thermoregulation models lies in the multiphysics aspect of thermoregulation. Blood flow in vasculature is predominantly modeled as one-dimensional, whereas the blood flow in capillary beds is modeled as three-dimensional. This results in a mixed-dimensional mesh of vasculature and the tissue-capillary bed. This mixed-dimensional coupling was addressed using the Dirac distribution function and algorithm obtained from the literature. This algorithm was further advanced by adding multiscale coupling due to the difference in mesh resolutions of segmented vasculature and tissue voxels. The mixed-dimensional, multi-scale mesh was used to create a blood flow - heat transfer coupled solver and simulate this multi-physics phenomenon on frog tongue data obtained from the literature. The resulting framework is called the Voxelized Multi-Physics Simulation Framework (VoM-PhyS), which provides a strong foundation for a full-body thermoregulation simulation. The third challenge with any voxel domain generated from imaging data is associated with voxel resolution. Due to the dimensional scale of blood vessels, not all vessels are captured in a given voxel resolution. This loss of segmentable vascular data results in discontinuous blood vessels. The pre-capillary vessels, like arterioles, provide the highest resistance to blood flow. Due to the resolution limitations, these pre-capillary vessels are modeled with the tissue as a porous domain. In other words, using the porous media method, pre-capillary vessels get modeled with a capillary bed in a tissue voxel. This results in a loss of information that could have been modeled if the pre-capillary vessels were segmented and modeled distinct from capillary bed. The vessels can only be modeled if a very high image resolution is used, which would also increase the computational cost of the entire simulation domain. Instead, a mathematical representation of the pressure drop induced in these unsegmented blood vessels is used. A part of this dissertation focuses on developing a mathematical equation to calculate the pressure drop parameter, which can be used to accurately model the flow resistance offered by pre-capillary vessels and simulate blood flow. This dissertation provides the equations to calculate the pressure drop parameters for any given vasculature and tissue domain, provided the total pressure drop across the simulation domain and the total blood steady-state flow rate are known. These equations provide deeper insight into vascular resistance and strengthen the VoM-PhyS Framework by allowing the flexibility to reduce the mesh size and computational memory requirements. The effect of substituting segmented vessels with mathematical pressure drop parameters on heat transfer is analyzed by simulating a 3D vascular domain of 32 terminal vessels and five generations of bifurcation. Each generation is successively removed and substituted with the pressure drop parameter to analyze the error in heat transfer due to a lack of segmentation data. To reduce this error, two methods are proposed and demonstrated to show considerable energy error reduction

Biomechanical Modeling of Vertebral Mechanobiological Growth and of the Deformation Process in Adolescent Idiopathic Scoliosis

RÉSUMÉ La scoliose idiopathique chez l’adolescent est une déformation tridimensionnelle du rachis se développant durant la croissance. Plusieurs études rapportent que la progression de la déformation scoliotique est influencée par des facteurs biomécaniques. La déformation scoliotique, l’asymétrie de la balance du rachis et l’activité musculaire sont responsables du chargement asymétrique sur les plaques de croissances. Ces facteurs modifient la répartition entre le côté concave-convexe du taux de croissance et, par conséquent, conduit à un cercle vicieux de progression de la déformation scoliotique. Le processus biomécanique de la progression de la scoliose a été étudié dans la littérature en considérant principalement une composante de chargement axiale pour la représentation de la croissance. L’objectif général de ce projet est d’étudier la biomécanique multiaxiale de la progression scoliotique. Le but spécifique du projet est de vérifier que le processus de déformation, impliquant la croissance et sa modulation mécanobiologique par des charges multi-axiales, est stimulable numériquement par la méthode des éléments finis, et que ces charges multi-axiales exercées sur les plaques de croissance épiphysaires sont responsables des déformations caractéristiques des vertèbres et rachis scoliotiques. Le chargement utilisé pour simuler la pathologie consiste en des forces primaires axiales asymétriques combinées à des forces secondaires de cisaillement et de torsion. Afin d’atteindre ce but, le projet a été divisé en trois parties. La première partie a consisté à faire une étude comparative de deux techniques de modélisation afin de simuler les concepts de croissance mécanobiologique. La seconde partie a consisté à développer un nouveau modèle de croissance mécanobiologique, basé sur l’énergie de stimulation, afin de représenter les déformations vertébrales résultant du chargement multiaxial. La troisième partie a consisté à soumettre le nouveau modèle numérique à différents cas de chargements et à analyser leurs influences sur la croissance et sur la progression de la scoliose. Dans la première partie, les formulations analytiques de la croissance mécanobiologique développées par Stokes et coll. (1990) et Carter et coll. (1988) ont été comparées entre elles à l’aide d’un modèle par éléments finis d’une vertèbre thoracique. La vertèbre et la plaque de croissance adjacente supérieure ont été modélisées par des éléments solides 3D linéaires.----------ABSTRACT Adolescent idiopathic scoliosis is a three dimensional deformity of spine that mostly occurs during the growth spurt. It is generally accepted that the progression of scoliotic deformities is influenced by biomechanical factors. Asymmetrical loading of vertebral growth plates resulting from an initial scoliotic curve or asymmetric balance or muscle recruitment are modifying the concave-convex side growth rate, thus leading to a vicious circle of scoliosis progression. The mechanobiological process of scoliosis was previously investigated, but mainly considering the axial loading component for growth. The general objective of this project was to study the multi-axial biomechanics of scoliosis progression. The specific objective was to model the deformation process, including the spinal growth and mechanobiological growth modulation due to multi-axial loads, and analyze how these loads are involved in the resulting characteristic scoliotic deformities. This tested pathomechanism presents the primary loading characteristics of asymmetric axial forces combined with secondary shear and torsion. In order to address the proposed research objectives, this project was divided into three parts. The first one was a comparative study and analysis of two modeling techniques to simulate existing concepts of mechanobiological growth. The second part was the development of a novel model of mechanobiological growth based on energy stimulus that enabled to represent the vertebral changes due to multi-axial loading. In the last part, this model was exploited to simulate the effect of different loads and analyze how they influence the growth process and how they relate to the scoliotic pathomechanism. In the first part, the analytical formulation of mechanobiological growth developed by Stokes et al. (1990) and Carter et al. (1988) was compared using a finite element model representing a thoracic vertebra as solid elements. Stokes’s model only concerned axial stress, while Carter’s model involved multi-axial stresses. The epiphyseal growth plates were represented using three layers similar to those found in the vertebral bodies: a loading sensitive area, a growth area, and a mineralized area. The two mechanobiological growth models were numerically integrated into the growth plate model. The two models were further used to simulate vertebral growth modulation resulting from different physiological loading conditions applied o