An improved trabecular bone model based on Voronoi tessellation.

BACKGROUND AND OBJECTIVE: Accurate numerical and physical models of trabecular bone, correctly representing its complexity and variability, could be highly advantageous in the development of e.g. new bone-anchored implants due to the limited availability of real bone. Several Voronoi tessellation-based porous models have been reported in the literature, attempting to mimic the trabecular bone. However, these models have been limited to lattice rod-like structures, which are only structurally representative of very high-porosity trabecular bone. The objective of this study was to provide an improved model, more representative of trabecular bone of different porosity. METHODS: Boolean operations were utilized to merge scaled Voronoi cells, thereby introducing different structural patterns, controlling porosity and to some extent anisotropy. The mechanical properties of the structures were evaluated using analytical estimations, numerical simulations, and experimental compression tests of 3D-printed versions of the structures. The capacity of the developed models to represent trabecular bone was assessed by comparing some key geometric features with trabecular bone characterized in previous studies. RESULTS: The models gave the possibility to provide pore interconnectivity at relatively low porosities as well as both plate- and rod-like structures. The mechanical properties of the generated models were predictable with numerical simulations as well as an analytical approach. The permeability was found to be better than Sawbones at the same porosity. The models also showed the capability of matching e.g. some vertebral structures for key geometric features. CONCLUSIONS: An improved numerical model for mimicking trabecular bone structures was successfully developed using Voronoi tessellation and Boolean operations. This is expected to benefit both computational and experimental studies by providing a more diverse and representative structure of trabecular bone.

Fracture in porous bone analysed with a numerical phase-field dynamical model.

A dynamic phase-field fracture finite element model is applied to discretized high-resolution three-dimensional computed tomography images of human trabecular bone to analyse rapid bone fracture. The model is contrasted to quasi-static experimental results and a quasi-static phase-field finite element model. The experiment revealed complex stepwise crack evolution with multiple crack fronts, and crack arrests, as the global tensile displacement load was incrementally increased. The quasi-static phase-field fracture model captures the fractures in the experiment reasonably well, and the dynamic model converges towards the quasi-static model when mechanically loaded at low rates. At higher load rates, i.e., at larger impulses, inertia effects significantly contribute to an increased initial global stiffness, higher peak forces and a larger number of cracks spread over a larger volume. Since the fracture process clearly is different at large impulses compared to small impulses, it is concluded that dynamic fracture models are necessary when simulating rapid bone fracture.

Application of phase-field fracture theories and digital volume correlation to synchrotron X-ray monitored fractures in human trabecular bone: A case study.

Fracture processes of trabecular bone have been studied using various approaches over the years. However, reliable methods to analyse fracture at the single trabecula level are limited. In this study, a digital volume correlation (DVC) and a phase-field fracture model are applied and contrasted for human trabecular bone to analyse its failure under global compression at high resolution. A human trabecular bone sample was fractured in situ under synchrotron-based X-ray micro computed tomography (CT). Reconstructed CT data was then used in DVC algorithms to obtain high-resolution displacement fields in the bone at different load steps. A high-resolution specimen-specific structural mesh was discretized from the CT data and used for the phase-field simulation of the fracturing bone. The DVC analysis showed opening mode cracks as well as shear mode cracks. Strains in cracked regions were analysed. The load distribution in the trabecular structure resulted in two completely separated fracture regions in the sample body. A phenomenon that was also captured in the phase-field model. The results encourage us to believe improvements in boundary conditions and material models are worthwhile pursuing. Findings in this study support further development of a phase-field method to analyse fracture in samples with complex morphology, such as trabecular bone, and the capacity of DVC to quantify strains and slowly growing stable fractures during step-wise loading of trabecular bone.

An ex-vivo model for the biomechanical assessment of cement discoplasty.

Percutaneous Cement Discoplasty (PCD) is a surgical technique developed to relieve pain in patients with advanced degenerative disc disease characterized by a vacuum phenomenon. It has been hypothesized that injecting bone cement into the disc improves the overall stability of the spinal segment. However, there is limited knowledge on the biomechanics of the spine postoperatively and a lack of models to assess the effect of PCD ex-vivo. This study aimed to develop a biomechanical model to study PCD in a repeatable and clinically relevant manner. Eleven ovine functional spinal units were dissected and tested under compression in three conditions: healthy, injured and treated. Injury was induced by a papain buffer and the treatment was conducted using PMMA cement. Each sample was scanned with micro-computed tomography (CT) and segmented for the three conditions. Similar cement volumes (in %) were injected in the ovine samples compared to volumes measured on clinical PCD CT images. Anterior and posterior disc heights decreased on average by 22.5% and 23.9% after injury. After treatment, the anterior and posterior disc height was restored on average to 98.5% and 83.6%, respectively, of their original healthy height. Compression testing showed a similar stiffness behavior between samples in the same group. A decrease of 51.5% in segment stiffness was found after injury, as expected. The following PCD treatment was found to result in a restoration of stiffness-showing only a difference of 5% in comparison to the uninjured state. The developed ex-vivo model gave an adequate representation of the clinical vacuum phenomena in terms of volume, and a repeatable mechanical response between samples. Discoplasty treatment was found to give a restoration in stiffness after injury. The data presented confirm the effectiveness of the PCD procedure in terms of restoration of axial stiffness in the spinal segment. The model can be used in the future to test more complex loading scenarios, novel materials, and different surgical techniques.

A combined experimental and numerical method to estimate the elastic modulus of single trabeculae.

The elastic modulus at the single trabecular level is an important parameter for the understanding of the mechanical behavior of trabecular bone. Current methods are commonly limited by the irregular trabecular shape and the accuracy of displacement measurement. The aim of this study was to propose a method to estimate the trabecular modulus overcoming some of these limitations. For high-precision displacement measurements, in-situ compression within a synchrotron radiation based X-ray tomograph was used. Trabecular displacements were subsequently estimated by a global digital volume correlation algorithm, followed by high-resolution finite element analyses to account for the irregular geometry. The trabecular elastic moduli were then estimated by comparing the loads from the finite element analyses with those of the experiments. With this strategy, the average elastic modulus was estimated to 3.83 ± 0.54 GPa for three human trabeculae samples. Though limited by the sample size, the demonstrated method shows a potential to estimate the mechanical properties at the single trabecular level.

Porous polylactic acid scaffolds for bone regeneration: A study of additively manufactured triply periodic minimal surfaces and their osteogenic potential.

Three different triply periodic minimal surfaces (TPMS) with three levels of porosity within those of cancellous bone were investigated as potential bone scaffolds. TPMS have emerged as potential designs to resemble the complex mechanical and mass transport properties of bone. Diamond, Schwarz, and Gyroid structures were 3D printed in polylactic acid, a resorbable medical grade material. The 3D printed structures were investigated for printing feasibility, and assessed by morphometric studies. Mechanical properties and permeability investigations resulted in similar values to cancellous bone. The morphometric analyses showed three different patterns of pore distribution: mono-, bi-, and multimodal pores. Subsequently, biological activity investigated with pre-osteoblastic cell lines showed no signs of cytotoxicity, and the scaffolds supported cell proliferation up to 3 weeks. Cell differentiation investigated by alkaline phosphatase showed an improvement for higher porosities and multimodal pore distributions, suggesting a higher dependency on pore distribution and size than the level of interconnectivity.

The effect of two types of resorbable augmentation materials - a cement and an adhesive - on the screw pullout pullout resistance in human trabecular bone.

Augmentation materials, such as ceramic and polymeric bone cements, have been frequently used to improve the physical engagement of screws inserted into bone. While ceramic, degradable cements may ultimately improve fixation stability, reports regarding their effect on early fixation stability have been inconsistent. On the other hand, a newly developed degradable ceramic adhesive that can bond with tissues surrounding the screw, may improve the pullout performance, ensure early stability, and subsequent bony integration. The aim of this study was to investigate failure mechanisms of screw/trabecular bone constructs by comparing non-augmented screws with screws augmented with a calcium phosphate cement or an adhesive, i.e. a phosphoserine-modified calcium phosphate. Pullout tests were performed on screws inserted into trabecular cylinders extracted from human femoral bone. Continuous and stepwise pullout loading was applied with and without real-time imaging in a synchrotron radiation micro-computed tomograph, respectively. Statistical analysis that took the bone morphology into account confirmed that augmentation with the adhesive supported significantly higher pullout loads compared to cement-augmented, or non-augmented screws. However, the adhesive also allowed for a higher injection volume compared to the cement. In-situ imaging showed cracks in the vicinity of the screw threads in all groups, and detachment of the augmentation materials from the trabecular bone in the augmented specimens. Additional cracks at the periphery of the augmentation and the bone-material interfaces were only observed in the adhesive-augmented specimen, indicating a contribution of surface bonding to the pullout resistance. An adhesive that has potential for bonding with tissues, displayed superior pullout resistance, compared to a brushite cement, and may be a promising material for cementation or augmentation of implants.

Crack nucleation and propagation in microcrystalline-cellulose based granules subject to uniaxial and triaxial load.

Cracking patterns in four kinds of granules, based on the common pharmaceutical excipient microcrystalline cellulose (MCC) and subject to compressive load, were examined. The initial pore structure and the location of initial failure under uniaxial compression were assessed using X-ray micro-computed tomography, whereas contact force development and onset of cracking under more complex compressive load were examined using a triaxial testing apparatus. Smoothed particle hydrodynamics (SPH) simulations were employed for numerical analysis of the stress distributions prior to cracking. For granules subject to uniaxial compression, initial cracking always occurred along the meridian and the precise location of the crack depended on the pore structure. Likewise, for granules subject to triaxial compression, the fracture plane of the primary crack was generally parallel to the dominant loading direction. The occurrence of cracking was highly dependent on the triaxiality ratio, i.e. the ratio between the punch displacements in the secondary and dominant loading directions. Compressive stresses in the lateral directions, induced by triaxial compression, prevented crack opening and fragmentation of the granule, something that could be verified by simulations. These results provide corroboration as well as further insights into previously observed differences between confined and unconfined compression of granular media.

Cellulose nanopaper structures of high toughness.

Cellulose nanofibrils offer interesting potential as a native fibrous constituent of mechanical performance exceeding the plant fibers in current use for commercial products. In the present study, wood nanofibrils are used to prepare porous cellulose nanopaper of remarkably high toughness. Nanopapers of different porosities and from nanofibrils of different molar mass are prepared. Uniaxial tensile tests are performed and structure-property relationships are discussed. The high toughness of highly porous nanopaper is related to the nanofibrillar network structure and high mechanical nanofibril performance. Also, molar mass correlates with tensile strength. This indicates that nanofibril fracture controls ultimate strength. Furthermore, the large strain-to-failure means that mechanisms, such as interfibril slippage, also contributes to inelastic deformation in addition to deformation of the nanofibrils themselves.

Young's modulus of trabecular bone at the tissue level: A review.

The tissue-level Young's modulus of trabecular bone is important for detailed mechanical analysis of bone and bone-implant mechanical interactions. However, the heterogeneity and small size of the trabecular struts complicate an accurate determination. Methods such as micro-mechanical testing of single trabeculae, ultrasonic testing, and nanoindentation have been used to estimate the trabecular Young's modulus. This review summarizes and classifies the trabecular Young's moduli reported in the literature. Information on species, anatomic site, and test condition of the samples has also been gathered. Advantages and disadvantages of the different methods together with recent developments are discussed, followed by some suggestions for potential improvement for future work. In summary, this review provides a thorough introduction to the approaches used for determining trabecular Young's modulus, highlights important considerations when applying these methods and summarizes the reported Young's modulus for follow-up studies on trabecular properties. STATEMENT OF SIGNIFICANCE: The spongy trabecular bone provides mechanical support while maintaining a low weight. A correct measure of its mechanical properties at the tissue level, i.e. at a single-trabecula level, is crucial for analysis of interactions between bone and implants, necessary for understanding e.g. bone healing mechanisms. In this study, we comprehensively summarize the Young's moduli of trabecular bone estimated by currently available methods, and report their dependency on different factors. The critical review of different methods with recent updates is intended to inspire improvements in estimating trabecular Young's modulus. It is strongly suggested to report detailed information on the tested bone to enable statistical analysis in the future.

Trabecular deformations during screw pull-out: a micro-CT study of lapine bone.

The mechanical fixation of endosseous implants, such as screws, in trabecular bone is challenging because of the complex porous microstructure. Development of new screw designs to improve fracture fixation, especially in high-porosity osteoporotic bone, requires a profound understanding of how the structural system implant/trabeculae interacts when it is subjected to mechanical load. In this study, pull-out tests of screw implants were performed. Screws were first inserted into the trabecular bone of rabbit femurs and then pulled out from the bone inside a computational tomography scanner. The tests were interrupted at certain load steps to acquire 3D images. The images were then analysed with a digital volume correlation technique to estimate deformation and strain fields inside the bone during the tests. The results indicate that the highest shear strains are concentrated between the inner and outer thread diameter, whereas compressive strains are found at larger distances from the screw. Tensile strains were somewhat smaller. Strain concentrations and the location of trabecular failures provide experimental information that could be used in the development of new screw designs and/or to validate numerical simulations.