Specimen diameter and "side artifacts" in cancellous bone evaluated using end-constrained elastic tension

A graph model to describe the network connectivity of trabecular plates and rods

Introduction: The trabecular network is perceived as a collection of interconnected plate- (P) and rod-like (R) elements. Previous research has highlighted how these elements and their connectivity influence the mechanical properties of bone, yet further work is required to elucidate better the deeply interconnected nature of the trabecular network with distinct element formations conducting forces per their mechanical boundary conditions. Within this network, forces act through elements: a rod or plate with force applied to one end will transmit this force to a component connected to the other end, defining the boundary conditions for the loading of each element. To that end, this study has two aims: First, to investigate the connectivity of individually segmented elements of trabecular bone with respect to their local boundary conditions as defined by the surrounding trabecular network and linking them directly to the bone's overall mechanical response during loading using a mathematical graph model of the plate and rod (PR) Network. Second, we use this model to quantify side artifacts, a known artifact when testing an excised specimen of trabecular bone, where vertical trabeculae lose their load-bearing capacity due to a loss of connectivity, ultimately resulting in a change of the trabecular network topology. Resuts: Connected elements derived from our model predicted apparent elastic modulus by fitting a linear regression (R 2 = 0.81). In comparison, prediction using conventional bone volume fraction results in a lower accuracy (R 2 = 0.72), demonstrating the ability of the PR Network to estimate compressive elastic modulus independent of specimen size or loading boundary condition. Discussion: PR Network models are a novel approach to describing connectivity within the trabecular network and incorporating mechanical boundary conditions within the morphological analysis, thus enabling the study of intrinsic material properties of trabecular bone. Ultimately, PR Network models may be an early predictor or provide further insights into osteo-degenerative diseases.

Mechanical loading of ex vivo bovine trabecular bone in 3D printed bioreactor chambers

Previous ex vivo bone culture methods have successfully implemented polycarbonate (PC) bioreactors to investigate bone adaptation to mechanical load; however, they are difficult to fabricate and have been limited to a 5 mm maximum specimen height. The objective of this study was to validate a custom-made 3D printed MED610TM bioreactor system that addresses the limitations of the PC bioreactor and assess its efficacy in ex vivo bone culture. Twenty-three viable trabecular bone cores (10 mm height by 10 mm diameter) from an 18-month-old bovine sternum were cultured in MED610TM bioreactors with culture medium at 37 °C and 5% CO2 for 21-days. Bone cores were ranked based on their day 0 apparent elastic modulus (Eapp) and evenly separated into a "Load" group (n = 12) and a control group (n = 11). The Load group was loaded five times per week with a sinusoidal strain waveform between -1000 and -5000 με for 120 cycles at 2 Hz. Eapp was assessed on day 0, 8, and 21 using quasi-static tests with a -4000 με applied strain. Over 21-days, the Eapp of Load group samples tended to increase by more than double the control group (53.4% versus 20.9%) and no visual culture contamination was observed. This study demonstrated that bone organ culture in 3D printed MED610TM bioreactors replicated Eapp trends found in previous studies with PC bioreactors. However, further studies are warranted with a larger sample size to increase statistical power and histology to assess cell viability and bone mineral apposition rate.

3D strain analysis of trabecular bone within the osteoarthritic humeral head subjected to stepwise compressive loads

Understanding the local mechanical properties of trabecular bone at the humeral head-neck junction is essential for the safe design of stemless humeral head implants. Recent advancements in mechanical testing coupled with volumetric imaging have allowed for the ability to quantify full-field strain distributions throughout trabecular bone. Within this study, digital volume correlation (DVC) was applied to micro-computed tomography images to investigate the local load carrying characteristics of trabecular bone within osteoarthritic (OA) humeral heads subjected to stepwise loading. A multi-pegged indenter was used to transfer loads from a custom-fabricated loading apparatus to trabecular bone on the resection surface of OA humeral head osteotomies retrieved from patients undergoing total shoulder arthroplasty (TSA). In regions of trabecular bone that eventually fractured, third principal strains were significantly higher (95^th percentile third principal strain = -12,558 μstrain, p < 0.001) compared to regions that did not fracture (95^th percentile third principal strain = -7,806 μstrain). As well, bone volume fraction (p = 0.012), trabecular separation (p = 0.014), and trabecular number (p = 0.007) were found to influence the likelihood of trabecular bone fracture. Collectively, this work has led to a deeper understanding of the local load carrying characteristics of trabecular bone specific to patients receiving TSA for osteoarthritis.

Evaluating a theoretical and an empirical model of "side effects" in cancellous bone

Accurate measurement of cancellous bone's apparent elastic modulus, E, is confounded by the experimental artefacts created when trabeculae are severed during specimen preparation. Although standardized axial testing protocols have been developed to deal with the so-called "end effects" caused by severed trabeculae at the loading surfaces, much less attention has been given to the "side effects" around the periphery and the specimen size dependence they create. Two models (one theoretical, one empirical) have been proposed in the literature to predict the reduction in E with decreasing specimen diameter. The current study used finite element method (FEM) modelling to analyze bovine cancellous bone from five different anatomic sites and quantify the changes in E that occurred with specimen diameter. The two models were adapted so that they could predict E based on diameter and architectural parameters (BV/TV, DA, Tb.Sp) alone, without requiring that a "true" modulus be known a priori. Both models fit the data equally well; however, the empirical model gives simpler estimations as a function of trabecular separation (Tb.Sp). A minimum diameter of 5-8 Tb.Sp is recommended.

Multi-scale mechanical and morphological characterisation of sintered porous magnesium-based scaffolds for bone regeneration in critical-sized defects

Magnesium (Mg) and its alloys are very promising degradable, osteoconductive and osteopromotive materials to be used as regenerative treatment for critical-sized bone defects. Under load-bearing conditions, Mg alloys must display sufficient morphological and mechanical resemblance to the native bone they are meant to replace to provide adequate support and enable initial bone bridging. In this study, unique highly open-porous Mg-based scaffolds were mechanically and morphologically characterised at different scales. In situ X-ray computed tomography (XCT) mechanics, digital volume correlation (DVC), electron microscopy and nanoindentation were combined to assess the influence of material properties on the apparent (macro) mechanics of the scaffold. The results showed that Mg exhibited a higher connected structure (38.4mm^-3 and 6.2mm^-3 for Mg and trabecular bone (Tb), respectively) and smaller spacing (245µm and 629µm for Mg and Tb, respectively) while keeping an overall appropriate porosity of 55% in the range of trabecular bone (30-80%). This fully connected and highly porous structure promoted lower local strain compared to the trabecular bone structure at material level (i.e. -22067 ± 8409µε and -40120 ± 18364µε at 6% compression for Mg and trabecular bone, respectively) and highly ductile mechanical behaviour at apparent level preventing premature scaffold failure. Furthermore, the Mg scaffolds exceeded the physiological strain of bone tissue generated in daily activities such as walking or running (500-2000µε) by one order of magnitude. The yield stress was also found to be close to trabecular bone (2.06MPa and 6.67MPa for Mg and Tb, respectively). Based on this evidence, the study highlights the overall biomechanical suitability of an innovative Mg-based scaffold design to be used as a treatment for bone critical-sized defects. STATEMENT OF SIGNIFICANCE: Bone regeneration remains a challenging field of research where different materials and solutions are investigated. Among the variety of treatments, biodegradable magnesium-based implants represent a very promising possibility. The novelty of this study is based on the characterisation of innovative magnesium-based implants whose structure and manufacturing have been optimised to enable the preservation of mechanical integrity and resemble bone microarchitecture. It is also based on a multi-scale approach by coupling high-resolution X-ray computed tomography (XCT), with in situ mechanics, digital volume correlation (DVC) as well as nano-indentation and electron-based microscopy imaging to define how degradable porous Mg-based implants fulfil morphological and mechanical requirements to be used as critical bone defects regeneration treatment.

Misalignment Error in Cancellous Bone Apparent Elastic Modulus Depends on Bone Volume Fraction and Degree of Anisotropy

Cancellous bone is an anisotropic structure with architectural and mechanical properties that vary due to both skeletal site and disease state. This anisotropy means that, in order to accurately and consistently measure the mechanical properties of cancellous bone, experiments should be performed along the primary mechanical axis (PMA), that is, the orientation in which the mechanical properties are at their maximum value. Unfortunately, some degree of misalignment will always be present, and the magnitude of the resulting error is expected to be architecture dependent. The goal of this work is to quantify the dependence of the misalignment error, expressed in terms of change in apparent elastic modulus (ΔE), on both the bone volume fraction (BV/TV) and the degree of anisotropy (DA). Finite element method (FEM) models of bovine cancellous bone from five different skeletal sites were created at 5 deg and 20 deg from the PMA determined for each region. An additional set of models was created using image dilation/erosion steps in order to control for BV/TV and better isolate the effect of DA. Misalignment error was found to increase with increasing DA and decreasing BV/TV. At 5 deg misaligned from the PMA, error is relatively low (&lt;5%) in all cases but increases to 8–24% error at 20 deg. These results suggest that great care is needed to avoid introducing misalignment error into experimental studies, particularly when studying regions with high anisotropy and/or low bone volume fraction, such as vertebral or osteoporotic bone.

Failure behaviour of rat vertebrae determined through simultaneous compression testing and micro-CT imaging

Skeletal fractures, including those resulting from osteoporosis, result in significant healthcare and societal costs on an annual basis. Therefore, it is important to understand the mechanisms by which these fractures occur. Incremental compression testing combined with micro-CT imaging has been used to visualize the progression of failure in trabecular bone samples; however, these studies have ignored the potential contributions of the cortical shell. In the current study, incremental compression testing with simultaneous micro-CT imaging was performed on rat vertebrae from multiple disease states (healthy control, osteoporotic, osteoporotic + treatment). These tests allowed the progression of failure through an entire vertebral body to be visualized for the first time. Three distinct failure modes were observed throughout all specimens, independent of disease state. Two of these failure modes (types I and II), which were observed in 93% of all specimens, were associated with the vascular apertures in the vertebrae's dorsal and ventral surfaces. This behaviour is likely caused by the stress concentrations in the cortical shell resulting from the apertures themselves, coupled with the reduced trabecular bone volume adjacent to them. These results suggest that the combined contributions of both the cortical shell and trabecular bone must be considered when studying the compressive failure behaviour of rat vertebrae.

Experimental and computational micromechanics at the tibial cement-trabeculae interface

Aseptic loosening of the tibial component in cemented total knee arthroplasty remains a major concern. We hypothesize that micromotion between the cement and trabeculae leads to increased circulation of interstitial fluid which in turn causes fluid-induced resorption of the trabeculae. Another mechanism for implant loosening is trabecular strain shielding. Using a newly developed experimental setup and digital image correlation (DIC) methods we were able to measure micromotion and strains in lab-prepared cement-trabeculae interface specimens (n=4). Finite element (FE) models of these specimens were developed to determine whether differences in micromotion and strain in morphologically varying specimens could be simulated accurately. Results showed that the measured micromotion and strains correlated well with FE model predictions (r(2)=0.59-0.85; r(2)=0.66-0.90). Global specimen strains measured axially matched well with the FE model strains (r(2)=0.87). FE model cement strains showed an increasing trend with distance from the cement border. The influence of loss of trabecular connectivity at the specimen edges was studied using our FE model results. Micromotion values at the outer edge of the specimens were higher than the specimen interior when considering a very thin outer edge (0.1mm). When the outer edge thickness was increased to about one trabecular length (0.8mm), there was a drop in the median and peak values. Using the experimental and modelling approach outlined in this study, we can further study the mechanisms that lead to loss of interlock between cement and trabeculae at the tibial interface.

Combined exposure to big endothelin-1 and mechanical loading in bovine sternal cores promotes osteogenesis

Increased bone formation resulting from mechanical loading is well documented; however, the interactions of the mechanotransduction pathways are less well understood. Endothelin-1, a ubiquitous autocrine/paracrine signaling molecule promotes osteogenesis in metastatic disease. In the present study, it was hypothesized that exposure to big endothelin-1 (big ET1) and/or mechanical loading would promote osteogenesis in ex vivo trabecular bone cores. In a 2×2 factorial trial of daily mechanical loading (-2000με, 120cycles daily, "jump" waveform) and big ET1 (25ng/mL), 48 bovine sternal trabecular bone cores were maintained in bioreactor chambers for 23days. The bone cores' response to the treatment stimuli was assessed with percent change in core apparent elastic modulus (ΔEapp), static and dynamic histomorphometry, and prostaglandin E2 (PGE2) secretion. Two-way ANOVA with a post hoc Fisher's LSD test found no significant treatment effects on ΔEapp (p=0.25 and 0.51 for load and big ET1, respectively). The ΔEapp in the "no load + big ET1" (CE, 13±12.2%, p=0.56), "load + no big ET1" (LC, 17±3.9%, p=0.14) and "load + big ET1" (LE, 19±4.2%, p=0.13) treatment groups were not statistically different than the control group (CC, 3.3%±8.6%). Mineralizing surface (MS/BS), mineral apposition (MAR) and bone formation rates (BFR/BS) were significantly greater in LE than CC (p=0.037, 0.0040 and 0.019, respectively). While the histological bone formation markers in LC trended to be greater than CC (p=0.055, 0.11 and 0.074, respectively) there was no difference between CE and CC (p=0.61, 0.50 and 0.72, respectively). Cores in LE and LC had more than 50% greater MS/BS (p=0.037, p=0.055 respectively) and MAR (p=0.0040, p=0.11 respectively) than CC. The BFR/BS was more than two times greater in LE (p=0.019) and LC (p=0.074) than CC. The PGE2 levels were elevated at 8days post-osteotomy in all groups and the treatment groups remained elevated compared to the CC group on days 15, 19 and 23. The data suggest that combined exposure to big ET1 and mechanical loading results in increased osteogenesis as measured in biomechanical, histomorphometric and biochemical responses.

Relationship between sample volumes and modulus of human vertebral trabecular bone in micro-finite element analysis

Micro-finite element (μFE) models have been widely used to assess the biomechanical properties of trabecular bone. How to choose a proper sample volume of trabecular bone, which could predict the real bone biomechanical properties and reduce the calculation time, was an interesting problem. Therefore, the purpose of this study was to investigate the relationship between different sample volumes and apparent elastic modulus (E) calculated from μFE model. 5 Human lumbar vertebral bodies (L1-L5) were scanned by micro-CT. Cubic concentric samples of different lengths were constructed as the experimental groups and the largest possible volumes of interest (VOI) were constructed as the control group. A direct voxel-to-element approach was used to generate μFE models and steel layers were added to the superior and inferior surface to mimic axial compression tests. A 1% axial strain was prescribed to the top surface of the model to obtain the E values. ANOVA tests were performed to compare the E values from the different VOIs against that of the control group. Nonlinear function curve fitting was performed to study the relationship between volumes and E values. The larger cubic VOI included more nodes and elements, and more CPU times were needed for calculations. E values showed a descending tendency as the length of cubic VOI decreased. When the volume of VOI was smaller than (7.34mm(3)), E values were significantly different from the control group. The fit function showed that E values approached an asymptotic values with increasing length of VOI. Our study demonstrated that apparent elastic modulus calculated from μFE models were affected by the sample volumes. There was a descending tendency of E values as the length of cubic VOI decreased. Sample volume which was not smaller than (7.34mm(3)) was efficient enough and timesaving for the calculation of E.

Dependence of anisotropy of human lumbar vertebral trabecular bone on quantitative computed tomography-based apparent density

Most studies investigating human lumbar vertebral trabecular bone (HVTB) mechanical property-density relationships have presented results for the superior-inferior (SI), or "on-axis" direction. Equivalent, directly measured data from mechanical testing in the transverse (TR) direction are sparse and quantitative computed tomography (QCT) density-dependent variations in the anisotropy ratio of HVTB have not been adequately studied. The current study aimed to investigate the dependence of HVTB mechanical anisotropy ratio on QCT density by quantifying the empirical relationships between QCT-based apparent density of HVTB and its apparent compressive mechanical properties--elastic modulus (E(app)), yield strength (σ(y)), and yield strain (ε(y))--in the SI and TR directions for future clinical QCT-based continuum finite element modeling of HVTB. A total of 51 cylindrical cores (33 axial and 18 transverse) were extracted from four L1 human lumbar cadaveric vertebrae. Intact vertebrae were scanned in a clinical resolution computed tomography (CT) scanner prior to specimen extraction to obtain QCT density, ρ(CT). Additionally, physically measured apparent density, computed as ash weight over wet, bulk volume, ρ(app), showed significant correlation with ρ(CT) [ρ(CT) = 1.0568 × ρ(app), r = 0.86]. Specimens were compression tested at room temperature using the Zetos bone loading and bioreactor system. Apparent elastic modulus (E(app)) and yield strength (σ(y)) were linearly related to the ρ(CT) in the axial direction [E(SI) = 1493.8 × (ρ(CT)), r = 0.77, p < 0.01; σ(Y,SI) = 6.9 × (ρ(CT)) − 0.13, r = 0.76, p < 0.01] while a power-law relation provided the best fit in the transverse direction [E(TR) = 3349.1 × (ρ(CT))(1.94), r = 0.89, p < 0.01; σ(Y,TR) = 18.81 × (ρ(CT))(1.83), r = 0.83, p < 0.01]. No significant correlation was found between ε(y) and ρ(CT) in either direction. E(app) and σ(y) in the axial direction were larger compared to the transverse direction by a factor of 3.2 and 2.3, respectively, on average. Furthermore, the degree of anisotropy decreased with increasing density. Comparatively, ε(y) exhibited only a mild, but statistically significant anisotropy: transverse strains were larger than those in the axial direction by 30%, on average. Ability to map apparent mechanical properties in the transverse direction, in addition to the axial direction, from CT-based densitometric measures allows incorporation of transverse properties in finite element models based on clinical CT data, partially offsetting the inability of continuum models to accurately represent trabecular architectural variations.

Apparent elastic modulus of ex vivo trabecular bovine bone increases with dynamic loading

Although it is widely known that bone tissue responds to mechanical stimuli, the underlying biological control is still not completely understood. The purpose of this study was to validate required methods necessary to maintain active osteocytes and minimize bone tissue injury in an ex vivo three-dimensional model that could mimic in vivo cellular function. The response of 22 bovine trabecular bone cores to uniaxial compressive load was investigated by using the ZETOS bone loading and bioreactor system while perfused with culture medium for 21 days. Two groups were formed, the "treatment" group (n = 12) was stimulated with a physiological compressive strain (4000 µε) in the form of a "jump" wave, while the "control" group (n = 10) was loaded only during three measurements for apparent elastic modulus on days 3, 10, and 21. At the end of the experiment, apoptosis and active osteocytes were quantified with histological analysis, and bone formation was identified by means of the calcium-binding dye, calcein. It was demonstrated that the treatment group increased the elastic modulus by 61%, whereas the control group increased by 28% (p<0.05). Of the total osteocytes observed at the end of 21 days, 1.7% (±0.3%) stained positive for apoptosis in the loaded group, whereas 2.7% (±0.4%) stained positive in the control group. Apoptosis in the center of the bone cores of both groups at the end of 21 days was similar to that observed in vivo. Therefore, the three-dimensional model used in this research permitted the investigation of physiological responses to mechanical loads on morphology adaptation of trabecular bone in a controlled defined load and chemical environment.