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

Ph.DDOCTOR OF PHILOSOPH

Hip fractures : A biomechanical analysis of fracture strength prediction, prevention, and repair

Due to the aging population, hip fracture incidence has been increasing over the past decades. Measurements of bone mineral density with dual energy X-ray absorptiometry are the gold standard for hip fracture risk assessment, where patients with a low bone density have a high risk of fracture. However, many people that are not diagnosed to be at risk, still fracture their hip. Calculations of bone strength using subject-specific finite element (FE) models, can improve fracture risk prediction, but further improvement is required.Patients with a high fracture risk are often prescribed pharmaceutical treatment in order to increase bone density systemically. As systemic response to treatment is limited, other options to prevent fractures by improving the bone strength are investigated. One of those options is the injection of biomaterials in the femoral neck. In case of a hip fracture due to a low-energy fall, total hip replacement is generally preferred over joint-preserving methods like fixation using a dynamic hip screw. Screw fixation comes with a risk of screw instability, especially in low-density bone. Bone cements can be used to improve fixation of orthopaedic implants and fracture fixation devices. Calcium sulphate/hydroxyapatite (CaS/HA) is an injectable biomaterial that has been used, for example, to reinforce collapsed vertebrae and to stabilize wrist fractures. The work presented in the thesis aims to improve fracture risk prediction, and fracture prevention and repair methods with use of CaS/HA. This is achieved through a combination of experimental mechanical tests at organ and tissue scale, and development and thorough validation of FE models of the proximal femur.In the first part of this thesis, 12 cadaveric femora were used in an experiment where the bones were loaded until fracture in a configuration developed to replicate a fall to the side. During loading, high-speed cameras were used to image both the medial and lateral side of the femoral neck allowing for full-field strain measurements using digital image correlation. The femora were imaged with clinical CT before and micro-CT before and after mechanical testing. Using the acquired CT images, FE models were developed at two different resolutions to determine their ability to capture the fracture force, fracture location and surface strains. The FE models based on the clinical CT images were able to accurately capture the fracture force and identify regions where the bone would fracture. These models could also capture the strains with high accuracy. However, the strains were not predicted as accurately in regions with high surface irregularity. The models based on the micro-CT images could show with higher accuracy how the strains were distributed around local porosity (e.g., due to vascularization) in the femoral neck and how these influenced the fracture pattern.The thesis continues with an investigation of fracture prevention and repair methods through the use of CaS/HA. The ability of CaS/HA to increase the fracture strength of the proximal femur for fracture prevention and its ability to stabilize a dynamic hip screw used for fracture repair was investigated. The increase in fracture strength was investigated using FE models. These models showed that CaS/HA can increase the fracture strength of the femur approximately 20% when injected close to the cortex in the lateral neck. Pullout tests using a dynamic hip screw were performed on synthetic bone blocks and femoral heads from hip fracture patients. In the synthetic blocks, CaS/HA significantly increased the pullout strength. However, in the human bone the stability of the screw was not improved, because the cement could not easily spread into the threads of the screws. The mechanical behaviour of CaS/HA and bone was further investigated using high-resolution synchrotron X-ray tomography. Cylindrical trabecular bone specimens with and without CaS/HA were imaged with tomography during in-situ loading of the samples. The images revealed that CaS/HA reinforced the bone, and that CaS/HA is a brittle material that will crack before the bone.To conclude, in this thesis FE models are presented showing accurate prediction of fracture strength, which can be used for improved fracture risk assessments. Furthermore, the work provides insight in how CaS/HA behaves mechanically and how it can be used to increase the fracture strength and to stabilize fixation devices in the femur, improving fracture prevention and fracture repair methods

Composite Finite Elements for Trabecular Bone Microstructures

In many medical and technical applications, numerical simulations need to be performed for objects with interfaces of geometrically complex shape. We focus on the biomechanical problem of elasticity simulations for trabecular bone microstructures. The goal of this dissertation is to develop and implement an efficient simulation tool for finite element simulations on such structures, so-called composite finite elements. We will deal with both the case of material/void interfaces (complicated domains) and the case of interfaces between different materials (discontinuous coefficients). In classical finite element simulations, geometric complexity is encoded in tetrahedral and typically unstructured meshes. Composite finite elements, in contrast, encode geometric complexity in specialized basis functions on a uniform mesh of hexahedral structure. Other than alternative approaches (such as e.g. fictitious domain methods, generalized finite element methods, immersed interface methods, partition of unity methods, unfitted meshes, and extended finite element methods), the composite finite elements are tailored to geometry descriptions by 3D voxel image data and use the corresponding voxel grid as computational mesh, without introducing additional degrees of freedom, and thus making use of efficient data structures for uniformly structured meshes. The composite finite element method for complicated domains goes back to Wolfgang Hackbusch and Stefan Sauter and restricts standard affine finite element basis functions on the uniformly structured tetrahedral grid (obtained by subdivision of each cube in six tetrahedra) to an approximation of the interior. This can be implemented as a composition of standard finite element basis functions on a local auxiliary and purely virtual grid by which we approximate the interface. In case of discontinuous coefficients, the same local auxiliary composition approach is used. Composition weights are obtained by solving local interpolation problems for which coupling conditions across the interface need to be determined. These depend both on the local interface geometry and on the (scalar or tensor-valued) material coefficients on both sides of the interface. We consider heat diffusion as a scalar model problem and linear elasticity as a vector-valued model problem to develop and implement the composite finite elements. Uniform cubic meshes contain a natural hierarchy of coarsened grids, which allows us to implement a multigrid solver for the case of complicated domains. Besides simulations of single loading cases, we also apply the composite finite element method to the problem of determining effective material properties, e.g. for multiscale simulations. For periodic microstructures, this is achieved by solving corrector problems on the fundamental cells using affine-periodic boundary conditions corresponding to uniaxial compression and shearing. For statistically periodic trabecular structures, representative fundamental cells can be identified but do not permit the periodic approach. Instead, macroscopic displacements are imposed using the same set as before of affine-periodic Dirichlet boundary conditions on all faces. The stress response of the material is subsequently computed only on an interior subdomain to prevent artificial stiffening near the boundary. We finally check for orthotropy of the macroscopic elasticity tensor and identify its axes.Zusammengesetzte finite Elemente für trabekuläre Mikrostrukturen in Knochen In vielen medizinischen und technischen Anwendungen werden numerische Simulationen für Objekte mit geometrisch komplizierter Form durchgeführt. Gegenstand dieser Dissertation ist die Simulation der Elastizität trabekulärer Mikrostrukturen von Knochen, einem biomechanischen Problem. Ziel ist es, ein effizientes Simulationswerkzeug für solche Strukturen zu entwickeln, die sogenannten zusammengesetzten finiten Elemente. Wir betrachten dabei sowohl den Fall von Interfaces zwischen Material und Hohlraum (komplizierte Gebiete) als auch zwischen verschiedenen Materialien (unstetige Koeffizienten). In klassischen Finite-Element-Simulationen wird geometrische Komplexität typischerweise in unstrukturierten Tetraeder-Gittern kodiert. Zusammengesetzte finite Elemente dagegen kodieren geometrische Komplexität in speziellen Basisfunktionen auf einem gleichförmigen Würfelgitter. Anders als alternative Ansätze (wie zum Beispiel fictitious domain methods, generalized finite element methods, immersed interface methods, partition of unity methods, unfitted meshes und extended finite element methods) sind die zusammengesetzten finiten Elemente zugeschnitten auf die Geometriebeschreibung durch dreidimensionale Bilddaten und benutzen das zugehörige Voxelgitter als Rechengitter, ohne zusätzliche Freiheitsgrade einzuführen. Somit können sie effiziente Datenstrukturen für gleichförmig strukturierte Gitter ausnutzen. Die Methode der zusammengesetzten finiten Elemente geht zurück auf Wolfgang Hackbusch und Stefan Sauter. Man schränkt dabei übliche affine Finite-Element-Basisfunktionen auf gleichförmig strukturierten Tetraedergittern (die man durch Unterteilung jedes Würfels in sechs Tetraeder erhält) auf das approximierte Innere ein. Dies kann implementiert werden durch das Zusammensetzen von Standard-Basisfunktionen auf einem lokalen und rein virtuellen Hilfsgitter, durch das das Interface approximiert wird. Im Falle unstetiger Koeffizienten wird die gleiche lokale Hilfskonstruktion verwendet. Gewichte für das Zusammensetzen erhält man hier, indem lokale Interpolationsprobleme gelöst werden, wozu zunächst Kopplungsbedingungen über das Interface hinweg bestimmt werden. Diese hängen ab sowohl von der lokalen Geometrie des Interface als auch von den (skalaren oder tensorwertigen) Material-Koeffizienten auf beiden Seiten des Interface. Wir betrachten Wärmeleitung als skalares und lineare Elastizität als vektorwertiges Modellproblem, um die zusammengesetzten finiten Elemente zu entwickeln und zu implementieren. Gleichförmige Würfelgitter enthalten eine natürliche Hierarchie vergröberter Gitter, was es uns erlaubt, im Falle komplizierter Gebiete einen Mehrgitterlöser zu implementieren. Neben Simulationen einzelner Lastfälle wenden wir die zusammengesetzten finiten Elemente auch auf das Problem an, effektive Materialeigenschaften zu bestimmen, etwa für mehrskalige Simulationen. Für periodische Mikrostrukturen wird dies erreicht, indem man Korrekturprobleme auf der Fundamentalzelle löst. Dafür nutzt man affin-periodische Randwerte, die zu uniaxialem Druck oder zu Scherung korrespondieren. In statistisch periodischen trabekulären Mikrostrukturen lassen sich ebenfalls Fundamentalzellen identifizieren, sie erlauben jedoch keinen periodischen Ansatz. Stattdessen werden makroskopische Verschiebungen zu denselben affin-periodischen Randbedingungen vorgegeben, allerdings durch Dirichlet-Randwerte auf allen Seitenflächen. Die Spannungsantwort des Materials wird anschließend nur auf einem inneren Teilbereich berechnet, um künstliche Versteifung am Rand zu verhindern. Schließlich prüfen wir den makroskopischen Elastizitätstensor auf Orthotropie und identifizieren deren Achsen

Spinal aging

The age distribution of the global population is shifting upwards. As a result, clinicians worldwide are faced with an increasing number of spinal disorders related to the elderly and spinal aging. Spinal pathology in the elderly specifically includes osteoporosis and osteoporotic vertebral compression fractures and degenerative spinal deformity. The impact of spinal disorders on health-related quality of life is more severe than the impact of many common diseases, such as cardiovascular diseases or type 2 diabetes. Spinal disorders affect more than 1.7 billion people worldwide and represent significant economic costs to society by the utilization of vast amounts of healthcare resources and by indirect costs such as loss of productivity. With the aging of our population the burden of spinal disorders on society is estimated to increase even further. Spinal aging encompasses a set of spinal disorders which are complex and heterogeneous with highly individualized surgical planning. As this patient category is associated with multiple medical comorbidities, decreased mobility, poor balance, and a greater propensity to falling, more patient tailored and multidisciplinary treatment strategies will be needed. Due to the confluence of an aging population and an increased capacity and willingness by the spinal community to manage difficult problems in older patients, it is essential that, when designing and implementing therapeutic strategies, clinicians must consider all of these factors. By shared decision making, medical and technical knowledge from surgeons is combined with values and preferences from patients in order to achieve effective and safe treatment modalities and ensure adequate patient support. This thesis addresses both clinical and preclinical aspects of spinal aging. In anticipation of an aging population, the main motivation of this thesis was to emphasize the significant and growing burden of spinal disorders in the elderly; to optimize current conservative and operative treatment for spinal aging; and to argue that allocation of resources to the management of spinal disorders should be a priority for our healthcare economy

Mechanics of Biomaterials

The mechanical behavior of biomedical materials and biological tissues are important for their proper function. This holds true, not only for biomaterials and tissues whose main function is structural such as skeletal tissues and their synthetic substitutes, but also for other tissues and biomaterials. Moreover, there is an intimate relationship between mechanics and biology at different spatial and temporal scales. It is therefore important to study the mechanical behavior of both synthetic and livingbiomaterials. This Special Issue aims to serve as a forum for communicating the latest findings and trends in the study of the mechanical behavior of biomedical materials

Reduction in mesenchymal stem cell numbers in premature aging DNA repair deficient TTD mice

Background: Mice carrying mutations in DNA repair genes often show signs of accelerated ageing and therefore can be used as a model system to study age related diseases like osteoporosis. It has been shown that TTD mice, carrying a mutation in the nucleotide excision repair gene XPD (xeroderma pigmentosa group D), display features of ageing related osteoporosis as well as adipose tissue hypoplasia. Since both cell types involved, osteoblasts as well as adipocytes, arise from the same mesenchymal stem cell population, the aim of the current project was to study the number, proliferation and differentiation potential of these cells in TTD compared to wild type (WT) mice. This might provide us with useful information concerning the mechanism behind age-related osteoporosis and the loss of adipose tissue.Methods: Bone marrow from old TTD and WT mice was cultured under osteogenic or adipogenic conditions and analysed for alkaline phosphatase activity (ALP), mineralisation (osteoblast) and lipid deposition (adipocyte).Results: Under osteogenic conditions the number of ALP-positive colonies after 9 and 14 days of culture was significantly decreased (p=0.02) in TTD compared to WT mice. The rate at which new ALP-positive colonies are formed between day 9 and day 14 of culture has not changed between TTD and WT mice, indicating that the decrease in colony number is not due to a delay in differentiation. Mineralisation of ALP-positive colonies did not seem to be affected, with a borderline significant decrease on day 14 at the onset of mineralisation but no significant changes on day 21 of culture. Lipid deposition was strongly reduced in TTD compared to WT mice (p=0.01) after 35 days of culture.Conclusions: The observed reduction in osteoblast and adipocyte differentiation indicates a reduction of mesenchymal stem cell numbers in TTD mice. This reduction in mesenchymal stem cell numbers and the corresponding decline in osteoblast differentiation could explain the premature osteoporotic features observed in TTD mice. In line with this, the reduction of mesenchymal stem cells and adipocyte differentiation may underlie the adipose tissue hypoplasia observed in TTD mice