The behavior of cancellous bone from quasi-static to dynamic strain rates with emphasis on the intermediate regime

Insights into the mechanical interaction between an active cranial implant and the skull subjected to moderate impact loadings

In the context of cochlear implants, which are now widely used, and innovative active devices, the cranial implantation of electronic devices raises new questions about the mechanical interactions between the implant and the skull. The aim of this study was to build a methodology using experimental data and numerical simulations to evaluate the mechanical interactions between the skull and the WIMAGINE® active cranial implant intended for use for tetraplegic patients. A finite element model of the implant housing and a simplified model of the three-layered skull were developed. 2.5 J-hammer impact tests were performed on implant housings and ovine cadaver heads for model calibration. The two models were then combined to analyze the interactions between the skull and the implant and compared against impact tests. The implant dissipates a certain amount of the impact energy which could be a parameter to include in implant design in addition to the implant integrity, tending to increase the implant stiffness. The non-implanted as well as the implanted lamb heads demonstrated an overall good resistance to the impact tests. The models correlated well with the experimental data, and improvements of the model through more realistic geometry (CT-scans) and more complex material behavior could now be implemented. Such a model could then be used with human head geometries and help for future implant design optimizations using numerical models of the implant-skull and even implant-head complex.

Johnson-Cook Parameter Identification for Commercially Pure Titanium at Room Temperature under Quasi-Static Strain Rates

BACKGROUND

To simulate mechanical shocks on an intracranial implant called WIMAGINE®, Clinatec chose a Johnson-Cook model to account for the viscoplastic behavior of grade 2 titanium in a dynamic study using Radioss©.

METHODS

Thirty tensile specimens were subjected to tensile tests at room temperature, and the influence of the strain rate (8 × 10-3 and 8 × 10-2 s-1) and sandblasting was analyzed. Relaxations were included in the tests to analyze viscosity phenomena.

RESULTS

A whole set of parameters was identified for the elastic and plastic parts. Strain rate influence on stress was negligible at these strain rates. As expected, the sandblasting hardened the material during the tests by decreasing the hardening parameters, while local necking occurred at an earlier strain.

CONCLUSIONS

This article provides the parameters of a Johnson-Cook model to simulate the elastoplastic behavior of pure titanium (T40, grade 2) in Finite Element Model (FEM) software.

Dynamic behaviors and protection mechanisms of sulcata tortoise carapace

This paper presents the compressive behavior of tortoise carapace at high strain rates and its protection mechanisms under impact loading. Both experimental and numerical results are reported. Tortoise is a land-based desert-dwelling animal taxonomically classified in the order of Testudines. The carapace is the dome-shaped upper part of the tortoise shell that protects its body from predator attacks. The carapace structure is composed of four layers formed as a composite structure with a porous core. The outer surface is keratin scutes made of fibrous structural proteins. The remaining layers are bone-like materials which are dorsal cortex, cancellous interior and ventral cortex. The compressive behavior at high rate of deformation is examined using split Hopkinson pressure bar (SHPB) technique. The results shown in the stress-strain plot illustrate a strain-rate hardening effect. The impact test is conducted using a gas gun with 6.35-mm diameter steel bearing balls as projectiles. The responses of carapace sample under a range of impact velocities are investigated to analyze its protection mechanisms. The numerical model of impact test is created to obtain an insight into mechanical behaviors of the carapace structure that cannot be observed in the experiments. The strain rate dependent material model is defined based on the SHPB test results. The distributions of stress and rebound velocity are presented and discussed.

Shear behavior of human skull bones

A shear-punch test (SPT) experimental method was developed to address the lack of shear deformation and failure response data for the human skull as a function of local bone microarchitecture. Improved understanding of skull deformation and fracture under varying stress-states helps implement mechanism-based, multi-axial material models for finite element analysis for optimizing protection strategies. Shear-punch coupons (N = 47 specimens) were extracted from right-parietal and frontal bones of three fresh-frozen-thawed human skulls. The specimens were kept as full through-thickness or segmented into the three skull constituent layers: the inner and outer cortical tables and the middle porous diploë. Micro-computed x-ray tomography (μCT) before and after SPT provided the bone volume fraction (BVF) as a function of depth for correlation to shear mechanisms in the punched volumes. Digital image correlation was used to track displacement of the punch above the upper die to minimize compliance error. Five full-thickness specimens were subjected to partial indentation loading to investigate the process of damage development as a function of BVF and depth. It was determined that BVF dominates the shear yield and ultimate strength of human skull bone, but the imposed uniaxial loading rate (0.001 and 0.1 s^-1) did not have as strong a contribution (p = 0.181-0.806 > 0.05) for the shear yield and ultimate strength of the skull bone layer specimens. Shear yield and ultimate strength data were highly correlated to power law relationships of BVF (R² = 0.917-0.949). Full-thickness and partial loaded SPT experiments indicate the diploë primarily dictates the shear strength of the intact structure.

Identification of effective elastic modulus using modal analysis; application to canine cancellous bone

Mechanical properties of cancellous bone is of increasing interest due to its involvement in aging pathologies and oncology. Characterization of fragile bone tissue is challenging and available methodologies include quasi-static compressive tests of small size specimens, ultrasound and indentation techniques. We hypothesized that modal analysis of flexure beams could be a complementary methodology to obtain Young modulus. The sampling methodology was adapted such that the uniqueness of the linear dynamic response was available to determine the elastic modulus from natural frequencies and mode shapes. In a first step, the methodology was validated using a synthetic bone model as control. Then, water-jet cutting allowed collecting fourteen small beam-like specimens in canine distal femurs. X-ray microtomography confirmed the microarchitecture preservation, the homogeneity and the isotropy at the specimen scale to derive effective properties. The first natural frequency in clamped-free boundary conditions was used to obtain mean values of Young modulus, which ranged from 210 MPa to 280 MPa depending on the specimen collection site. Experimental tests were rapid and reproducible and our preliminary results were in good agreement with literature data. In conclusion, beam modal analysis could be considered for exploring mechanical properties of fragile and scarce biological tissues.

Anisotropic and strain rate-dependent mechanical properties and constitutive modeling of the cancellous bone from piglet cervical vertebrae

BACKGROUND AND OBJECTIVE

Characterizing the mechanical properties of the cancellous bone from the cervical vertebrae of child or child surrogate is important for the development of spine finite element models and the investigation of injury mechanism, however, there is currently no public data available as far as we know.

METHODS

Compression tests were conducted on the specimens from the cervical vertebrae of 8-week-old piglets (child surrogates) in axial and radial directions at the strain rates of 0.01, 0.1, 1 and 10/s. The influences of directionality and strain rate on the mechanical properties of the vertebral cancellous bone were statistically investigated. The typical transversely isotropic model, which was added a strain rate item and a plasticity item, was implemented into LS-DYNA finite element code. Based on the material subroutine code, simulation was conducted on the vertebral tissue under compression in axial and radial directions at different strain rates.

RESULTS

The mechanical properties of the cancellous bone of cervical vertebrae were obtained and most of the stress-strain curves showed major linear elastic stage and short plastic stage before fracture. Significant anisotropic behavior was observed for the vertebral tissue in axial and radial directions. The elastic modulus, ultimate stress,yield stress, and ultimate strain of the speimens in axial direction was obtained, with on average, 2.5 ± 0.6 times, 2.1 ± 0.15 times, and 2.1 ± 0.1 times higher and 0.86 ± 0.076 times lower respecitvely, than those in radial direction. In addition, with the strain rate varying from 0.01/s to 10/s, the mechanical parameters, like elastic modulus, yield and ultimte stresses exhibited significant strain rate effect, however, no significant difference was found for the ultimate strain.

CONCLUSIONS

The cervical vertebrae showed significant anisotropic and strain rate-dependent behaviors. The self-developed subroutine codes based on the strain rate-dependent transversely isotropic elastic and plastic constitutive model can simulate the behaviors well.

Simulation analysis of impact damage to the bone tissue surrounding a dental implant

Dental implant may suffer transient external impacts. To simulate the effect of impact forces on bone damage is very important for evaluation of damage and guiding treatment in clinics. In this study, an animal model was established by inserting an implant into the femoral condyle of New Zealand rabbit. Implant with good osseointegration was loaded with impact force. A three-dimensional finite element model was established based on the data of the animal model. Damage process to bone tissue was simulated with Abaqus 6.13 software combining dynamic mechanical properties of the femur. The characteristics of bone damage were analyzed by comparing the results of animal testing with numerical simulation data. After impact, cortical bone around the implant and trabecular at the bottom of the implant were prone to damage. The degree of damage correlated with the direction of loading and the magnitude of the impact. Lateral loading was most likely performed to damage cancellous bone. The stress wave formed by the impact force can damage the implant–bone interface and peri-implant trabeculae. The data from numerical simulations were consistent with data from animal experiments, highlighting the importance of a thorough examination and evaluation based on the patient’s medical history.

High-speed X-ray visualization of dynamic crack initiation and propagation in bone

The initiation and propagation of physiological cracks in porcine cortical and cancellous bone under high rate loading were visualized using high-speed synchrotron X-ray phase-contrast imaging (PCI) to characterize their fracture behaviors under dynamic loading conditions. A modified Kolsky compression bar was used to apply dynamic three-point flexural loadings on notched specimens and images of the fracture processes were recorded using a synchronized high-speed synchrotron X-ray imaging set-up. Three-dimensional synchrotron X-ray tomography was conducted to examine the initial microstructure of the bone before high-rate experiments. The experimental results showed that the locations of fracture initiations were not significantly different between the two types of bone. However, the crack velocities in cortical bone were higher than in cancellous bone. Crack deflections at osteonal cement lines, a prime toughening mechanism in bone at low rates, were observed in the cortical bone under dynamic loading in this study. Fracture toughening mechanisms, such as uncracked ligament bridging and bridging in crack wake were also observed for the two types of bone. The results also revealed that the fracture toughness of cortical bone was higher than cancellous bone. The crack was deflected to some extent at osteon cement line in cortical bone instead of comparatively penetrating straight through the microstructures in cancellous bone. STATEMENT OF SIGNIFICANCE: Fracture toughness is with great importance to study for crack risk prediction in bone. For those cracks in bone, most of them are associated with impact events, such as sport accidents. Consequently, we visualized, in real-time, the entire processes of dynamic fractures in notched cortical bone and cancellous bone specimens using synchrotron X-ray phase contrast imaging. The onset location of crack initiation was found independent on the bone type. We also found that, although the extent was diminished, crack deflections at osteon cement lines, a major toughening mechanism in transversely orientated cortical bone at quasi-static rate, were still played a role in resisting cracking in dynamically loaded specimen. These finding help researchers to understand the dynamic fracture behaviors in bone.

Quasi-static and dynamic in vitro mechanical response of 3D printed scaffolds with tailored pore size and architectures

Scaffold-based Tissue Engineering represents the most promising approach for the regeneration of load bearing skeletal tissues, in particular bone and cartilage. Scaffolds play major role in this process by providing a physical template for cells to adhere and proliferate whilst ensuring an adequate biomechanical support at the defect site. Whereas the quasi static mechanical properties of porous polymeric scaffolds are well documented, the response of these constructs under high strain compressive rates remain poorly understood. Therefore, this study investigates, for the first time, the influence of pore size and geometry on the mechanical behaviour of Polycaprolactone (PCL) scaffolds under quasi static and dynamic conditions. 3D printed scaffolds with varied pore sizes and geometries were obtained using different filament distances (FD) and lay-down patterns, respectively. In particular, by fixing the lay-down pattern at 0/90° and varying the FD between 480 and 980 μm it was possible to generate scaffolds with square pores with dimensions in the range of 150-650 μm and porosities of 59-79%. On the other hand, quadrangular, hexagonal, triangular and complex pore geometries with constant porosity (approx. 70%) were obtained at a fixed FD of 680 μm and imposing four different lay-down patterns of 0/90, 0/60/120, 0/45/90/135 and 0/30/60/90/120/150°, respectively. The mechanical response of printed scaffolds was assessed under two different compression loading regimes spanning five distinct strain rates, from 10^-2 to 2000 s^-1, using two different apparatus: a conventional screw-driven testing machine (Instron 4483) and a Split Hopkinson pressure bar (SHPB) equipped with a set of A201 Flexi-force™ (FF) force sensors and a pulse shaper. Our results show that the mechanical properties of PCL scaffolds are not strain rate sensitive between 1300 and 2000 s^-1 and these strongly depend on the pore size (porosity) rather than pore geometry. Those findings are extremely relevant for the engineering of bone tissue scaffolds with enhanced mechanical stability by providing new data describing the mechanical response of these constructs at high strain rates as well as the at the transition between quasi static and dynamic regimes.

Rate and age-dependent damage elasticity formulation for efficient hip fracture simulations

Prediction of bone failure is beneficial in a range of clinical situations from screening of osteoporotic patients with high fracture risk to assessment of protective equipment against trauma. Computational efficiency is an important feature to consider when developing failure models for iterative applications, such as patient-specific diagnosis or design of orthopaedic devices. The authors previously developed a methodology to generate efficient mesoscale structural full bone models. The aim of this study was to implement a damage elasticity formulation representative of an elasto-plastic material model with age and strain rate dependencies compatible with these structural models. This material model was assessed in the prediction of femoral fractures in longitudinal compression and side fall scenarios. The simulations predicted failure loads and fracture patterns in good agreement with reported results from experimental studies. The observed influence of strain rate on failure load was consistent with literature. The superiority of a simplified elasto-plastic formulation over an elasto-brittle bone material model was assessed. This computationally efficient damage elasticity formulation was capable of capturing fracture development after onset.