Loading rate effects on the R-curve behavior of cortical bone

Fracture behavior of human cortical bone with high glycation content under dynamic loading

The present study simulates the fracture behavior of diabetic cortical bone with high levels of advanced glycation end-products (AGEs) under dynamic loading. We consider that the increased AGEs in diabetic cortical bone degrade the materials heterogeneity of cortical bone through a reduction in critical energy release rates of the microstructural features. To simulate the initiation and propagation of cracks, we implement a phase field fracture framework on 2D models of human tibia cortical microstructure. The simulations show that the mismatch between the fracture properties (e.g., critical energy release rate) of osteons and interstitial tissue due to high AGEs contents can change crack growth trajectories. The results show crack branching in the cortical microstructure under dynamic loading is affected by the mismatches related to AGEs. In addition, we observe cortical features such as osteons and cement lines can prevent multiple cracking under dynamic loading even with changing the mismatches due to high AGEs. Furthermore, under dynamic loading, some toughening mechanisms can be activated and deactivated with different AGEs contents. In conclusion, the current findings present that the combination of the loading type and materials heterogeneity of microstructural features can change the fracture response of diabetic cortical bone and its fragility.

Effect of ribose incubation on physical, chemical, and mechanical properties of human cortical bone

Raman spectroscopy (RS) is sensitive to the accumulation of advanced glycation end-products (AGEs), and it measures matrix-sensitive properties that correlate with the fracture toughness of human cortical bone. However, it is unclear whether sugar-mediated accumulation of AGEs affects the fracture toughness of human cortical bone in a manner that is consistent with the negative correlations between amide I sub-peak ratios and fracture toughness. Upon machining 64 single-edge notched beam (SENB) specimens from cadaveric femurs (8 male and 7 female donors between 46 years and 61 years of age), pairs of SENB specimens were incubated in 15 mL of phosphate buffered saline with or without 0.1 M ribose for 4 weeks at 37 °C. After acquiring 10 Raman spectra per bone specimen (n = 32 per incubation group), paired SENB specimens were loaded in three-point bending at a quasi-static or a high loading rate approximating 10-4 s-1 or 10-2 s-1, respectively (n = 16 per incubation group per loading rate). While 2 amide I sub-peak ratios, I1670/I1640 and I1670/I1610, decreased by 3-5% with a 100% increase in AGE content, as confirmed by fluorescence measurements, the ribose incubation to accumulate AGEs in bone did not affect linear elastic (KIc) nor non-linear elastic (KJc) measurements of bone's ability to resist crack growth. Moreover, AGE accumulation did not affect the change in these properties when the loading rate changed. Increasing the loading rate increased KIc but decreased KJc. Ribose incubation did not affect mineral-related RS properties such as mineral-to-matrix ratios, Type B carbonate substitutions, and crystallinity. It did however increase the thermal stability of demineralized bone (differential scanning calorimetry), without affecting the network connectivity of the organic matrix (i.e., maximum slope during a hydrothermal isometric tension test of demineralized bone). In conclusion, RS is sensitive to AGE accumulation via the amide I band (plus the hydroxyproline-to-proline ratio), but the increase in AGE content due to ribose incubation was not sufficient to affect the fracture toughness of human cortical bone.

Effect of organic matrix alteration on strain rate dependent mechanical behaviour of cortical bone

The organic matrix phase of bone plays important role in its mechanical performance, especially in the post-yield regime. Also, the organic phase influences loading rate-dependent behaviour of bone which is relevant during the high-speed loading events. Many diseases, as well as aging, affect the matrix phase of bone which causes compromised mechanical properties. Improved understanding of alterations in the organic matrix phase on mechanical response of bone will be helpful in the mitigation of fractures associated with inferior matrix quality. In the present work, effect of alteration in organic matrix of cortical bone on its strain-rate dependent behaviour was investigated. To produce different amounts of collagen denaturation, bovine cortical bones were heated at the temperature of 180 °C and 240 °C. Further, compression testing was performed at quasi-static strain rates of 10^-4 s^-1 to 10^-2 s^-1 using a conventional testing machine whereas a modified Split Hopkinson Pressure Bar (SHPB) was used for high strain rate (∼10³) testing. Thermal treatment-induced changes in the mineral and organic phases of bone were assessed using X-ray diffraction (XRD) and Fourier-transform infrared-attenuated total reflection (FTIR-ATR) techniques respectively. Compression test results show that thermal treatment of bone up to 180 °C did not affect mechanical properties significantly whereas treating at 240 °C significantly reduced elastic modulus, failure stress and failure strain. Also, thermal denaturation of collagen reduced the strain rate sensitivity of cortical bone at high strain rates. Similar to the compression test observations, nanoindentation results show a significant reduction in elastic modulus and hardness of denatured samples. Further, FTIR results revealed that with the heat treatment of bone, collagen structure undergoes conformational changes at the molecular level. The initial helix structure breakdowns into unordered/random coil structures which subsequently reduced the mechanical competence of bone. The present study provides insight into the effect of organic matrix modification on mechanical behaviour of cortical bone which could be helpful in understanding bone disorders associated with organic matrix phase and development of therapeutic interventions.

Replicating dynamic humerus motion using an industrial robot

Transhumeral percutaneous osseointegrated prostheses provide upper-extremity amputees with increased range of motion, more natural movement patterns, and enhanced proprioception. However, direct skeletal attachment of the endoprosthesis elevates the risk of bone fracture, which could necessitate revision surgery or result in loss of the residual limb. Bone fracture loads are direction dependent, strain rate dependent, and load rate dependent. Furthermore, in vivo, bone experiences multiaxial loading. Yet, mechanical characterization of the bone-implant interface is still performed with simple uni- or bi-axial loading scenarios that do not replicate the dynamic multiaxial loading environment inherent in human motion. The objective of this investigation was to reproduce the dynamic multiaxial loading conditions that the humerus experiences in vivo by robotically replicating humeral kinematics of advanced activities of daily living typical of an active amputee population. Specifically, 115 jumping jack, 105 jogging, 15 jug lift, and 15 internal rotation trials-previously recorded via skin-marker motion capture-were replicated on an industrial robot and the resulting humeral trajectories were verified using an optical tracking system. To achieve this goal, a computational pipeline that accepts a motion capture trajectory as input and outputs a motion program for an industrial robot was implemented, validated, and made accessible via public code repositories. The industrial manipulator utilized in this study was able to robotically replicate over 95% of the aforementioned trials to within the characteristic error present in skin-marker derived motion capture datasets. This investigation demonstrates the ability to robotically replicate human motion that recapitulates the inertial forces and moments of high-speed, multiaxial activities for biomechanical and orthopaedic investigations. It also establishes a library of robotically replicated motions that can be utilized in future studies to characterize the interaction of prosthetic devices with the skeletal system, and introduces a computational pipeline for expanding this motion library.

What is the influence of two strain rates on the relationship between human cortical bone toughness and micro-structure?

Cortical bone fracture mechanisms are well studied under quasi-static loading. The influence of strain rate on crack propagation mechanisms needs to be better understood, however. We have previously shown that several aspects of the bone micro-structure are involved in crack propagation, such as the complete porosity network, including the Haversian system and the lacunar network, as well as biochemical aspects, such as the maturity of collagen cross-links. The aim of this study is to investigate the influence of strain rate on the toughness of human cortical bone with respect to its microstructure and organic non-collagenous composition. Two strain rates will be considered: quasi-static loading (10−4 s−1), a standard condition, and a higher loading rate (10−1 s−1), representative of a fall. Cortical bone samples were extracted from eight female donors (age 50–91 years). Three-point bending tests were performed until failure. Synchrotron radiation micro-computed tomography imaging was performed to assess bone microstructure including the Haversian system and the lacunar system. Collagen enzymatic cross-link maturation was measured using a high performance liquid chromatography column. Results showed that that under quasi-static loading, the elastic contribution of the fracture process is correlated to both the collagen cross-links maturation and the microstructure, while the plastic contribution is correlated only to the porosity network. Under fall-like loading, bone organization appears to be less linked to crack propagation.

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.

Intrinsic mechanical behavior of femoral cortical bone in young, osteoporotic and bisphosphonate-treated individuals in low- and high energy fracture conditions

Bisphosphonates are a common treatment to reduce osteoporotic fractures. This treatment induces osseous structural and compositional changes accompanied by positive effects on osteoblasts and osteocytes. Here, we test the hypothesis that restored osseous cell behavior, which resembles characteristics of younger, healthy cortical bone, leads to improved bone quality. Microarchitecture and mechanical properties of young, treatment-naïve osteoporosis, and bisphosphonate-treated cases were investigated in femoral cortices. Tissue strength was measured using three-point bending. Collagen fibril-level deformation was assessed in non-traumatic and traumatic fracture states using synchrotron small-angle x-ray scattering (SAXS) at low and high strain rates. The lower modulus, strength and fibril deformation measured at low strain rates reflects susceptibility for osteoporotic low-energy fragility fractures. Independent of age, disease and treatment status, SAXS revealed reduced fibril plasticity at high strain rates, characteristic of traumatic fracture. The significantly reduced mechanical integrity in osteoporosis may originate from porosity and alterations to the intra/extrafibrillar structure, while the fibril deformation under treatment indicates improved nano-scale characteristics. In conclusion, losses in strength and fibril deformation at low strain rates correlate with the occurrence of fragility fractures in osteoporosis, while improvements in structural and mechanical properties following bisphosphonate treatment may foster resistance to fracture during physiological strain rates.

The fracture mechanics of human bone: influence of disease and treatment

Aging and bone diseases are associated with increased fracture risk. It is therefore pertinent to seek an understanding of the origins of such disease-related deterioration in bone's mechanical properties. The mechanical integrity of bone derives from its hierarchical structure, which in healthy tissue is able to resist complex physiological loading patterns and tolerate damage. Indeed, the mechanisms through which bone derives its mechanical properties make fracture mechanics an ideal framework to study bone's mechanical resistance, where crack-growth resistance curves give a measure of the intrinsic resistance to the initiation of cracks and the extrinsic resistance to the growth of cracks. Recent research on healthy cortical bone has demonstrated how this hierarchical structure can develop intrinsic toughness at the collagen fibril scale mainly through sliding and sacrificial bonding mechanisms that promote plasticity. Furthermore, the bone-matrix structure develops extrinsic toughness at much larger micrometer length-scales, where the structural features are large enough to resist crack growth through crack-tip shielding mechanisms. Although healthy bone tissue can generally resist physiological loading environments, certain conditions such as aging and disease can significantly increase fracture risk. In simple terms, the reduced mechanical integrity originates from alterations to the hierarchical structure. Here, we review how human cortical bone resists fracture in healthy bone and how changes to the bone structure due to aging, osteoporosis, vitamin D deficiency and Paget's disease can affect the mechanical integrity of bone tissue.

Bone as a Structural Material

As one of the most important natural materials, cortical bone is a composite material comprising assemblies of tropocollagen molecules and nanoscale hydroxyapatite mineral crystals, forming an extremely tough, yet lightweight, adaptive and multi-functional material. Bone has evolved to provide structural support to organisms, and therefore its mechanical properties are vital physiologically. Like many mineralized tissues, bone can resist deformation and fracture from the nature of its hierarchical structure, which spans molecular to macroscopic length-scales. In fact, bone derives its fracture resistance with a multitude of deformation and toughening mechanisms that are active at most of these dimensions. It is shown that bone's strength and ductility originate primarily at the scale of the nano to submicrometer structure of its mineralized collagen fibrils and fibers, whereas bone toughness is additionally generated at much larger, micro- to near-millimeter, scales from crack-tip shielding associated with interactions between the crack path and the microstructure. It is further shown how the effectiveness with which bone's structural features can resist fracture at small to large length-scales can become degraded by biological factors such as aging and disease, which affect such features as the collagen cross-linking environment, the homogeneity of mineralization, and the density of the osteonal structures.

Effects of fatigue induced damage on the longitudinal fracture resistance of cortical bone

As a composite material, cortical bone accumulates fatigue microdamage through the repetitive loading of everyday activity (e.g. walking). The accumulation of fatigue microdamage is thought to contribute to the occurrence of fragility fractures in older people. Therefore it is beneficial to understand the relationship between microcrack accumulation and the fracture resistance of cortical bone. Twenty longitudinally orientated compact tension fracture specimens were machined from a single bovine femur, ten specimens were assigned to both the control and fatigue damaged groups. The damaged group underwent a fatigue loading protocol to induce microdamage which was assessed via fluorescent microscopy. Following fatigue loading, non-linear fracture resistance tests were undertaken on both the control and damaged groups using the J-integral method. The interaction of the crack path with the fatigue induced damage and inherent toughening mechanisms were then observed using fluorescent microscopy. The results of this study show that fatigue induced damage reduces the initiation toughness of cortical bone and the growth toughness within the damage zone by three distinct mechanisms of fatigue-fracture interaction. Further analysis of the J-integral fracture resistance showed both the elastic and plastic component were reduced in the damaged group. For the elastic component this was attributed to a decreased number of ligament bridges in the crack wake while for the plastic component this was attributed to the presence of pre-existing fatigue microcracks preventing energy absorption by the formation of new microcracks.

The structure-mechanical relationship of palm vascular tissue

The structure-mechanical relationship of palm sheath is studied with numerical and experimental methods. The cellular structure of the vascular tissue is rebuilt with an image-based reconstruction method and used to create finite element models. The validity of the models is firstly verified with the results from the tensile tests. Then, the cell walls inside each of the specific regions (fiber cap, vessel, xylem, etc.) are randomly removed to obtain virtually imperfect structures. By comparing the magnitudes of performance degradation in the different imperfect structures, the influences of each region on the overall mechanical performances of the vascular tissue are discussed. The longitudinal stiffness and yield strength are sensitive to the defects in the vessel regions. While in the transverse directions (including the radial and tangential directions), the parenchymatous tissue determines the mechanical properties of the vascular tissue. Moreover, the hydraulic, dynamic response and energy absorption behavior of the vascular tissue are numerically explored. The flexibility of natural palm tissue enhances its impact resistance. Under the quasi-static compression, the cell walls connecting the fiber cap and the vessel dissipate more energy. The dominant role of the fiber cap in the plastic energy dissipation under high-speed impact is observed. And the radially-arranged fiber cap also allows the palm tissue to improve its tangential mechanical performances under hydraulic pressure.

Fracture resistance of human cortical bone across multiple length-scales at physiological strain rates

While most fracture-mechanics investigations on bone have been performed at low strain rates, physiological fractures invariably occur at higher loading rates. Here, at strain rates from 10(-5) to 10(-1) s(-1), we investigate deformation and fracture in bone at small length-scales using in situ small-angle x-ray scattering (SAXS) to study deformation in the mineralized collagen fibrils and at the microstructural level via fracture-mechanics experiments to study toughening mechanisms generating toughness through crack-tip shielding. Our results show diminished bone toughness at increasing strain rates as cracks penetrate through the osteons at higher strain rates instead of deflecting at the cement lines, which is a prime toughening mechanism in bone at low strain rates. The absence of crack deflection mechanisms at higher strain rates is consistent with lower intrinsic bone matrix toughness. In the SAXS experiments, higher fibrillar strains at higher strain rates suggest less inelastic deformation and thus support a lower intrinsic toughness. The increased incidence of fracture induced by high strain rates can be associated with a loss in toughness in the matrix caused by a strain rate induced stiffening of the fibril ductility, i.e., a "locking-up" of the viscous sliding and sacrificial bonding mechanisms, which are the origin of inelastic deformation (and toughness) in bone at small length-scales.

Effects of gamma radiation sterilization and strain rate on compressive behavior of equine cortical bone

OBJECTIVES

Gamma radiation has been widely used for sterilization of bone allograft. However, sterilization by gamma radiation damages the material properties of bone which is a major clinical concern since bone allograft is used in load bearing applications. While the degree of this damage is well investigated for quasi-static and cyclic loading conditions, there does not appear any information on mechanical behavior of gamma-irradiated cortical bone at high speed loading conditions. In this study, the effects of gamma irradiation on high strain rate compressive behavior of equine cortical bone were investigated using a Split Hopkinson Pressure Bar (SHPB). Quasi-static compression testing was also performed.

METHODS

Equine cortical bone tissue from 8year old retired racehorses was divided into two groups: non-irradiated and gamma-irradiated at 30kGy. Quasi-static and high strain rate compression tests were performed at average strain rates of 0.0045/s and 725/s, respectively.

RESULTS

Agreeing with previous results on the embrittlement of cortical bone when gamma-irradiated, the quasi-static results showed that gamma-irradiation significantly decreased ultimate strength (9%), ultimate strain (27%) and toughness (41%), while not having significant effect on modulus of elasticity, yield strain and resilience. More importantly, contrary to what is typically observed in quasi-static loading, the gamma-irradiated bone under high speed loading showed significantly higher modulus of elasticity (45%), ultimate strength (24%) and toughness (26%) than those of non-irradiated bone, although the failure was at a similar strain.

SIGNIFICANCE

Under high speed loading, the mechanical properties of bone allografts were not degraded by irradiation, in contrast to the degradation measured in this and prior studies under quasi-static loading. This result calls into question the assumption that bone allograft is always degraded by gamma irradiation, regardless of loading conditions. However, it needs further investigation to be translated positively in a clinical setting.

Evaluation of the influence of strain rate on Colles' fracture load

Colles' fracture, a transverse fracture of the distal radius bone, is one of the most frequently observed osteoporotic fractures resulting from low energy or traumatic events, associated with low and high strain rates, respectively. Although experimental studies on Colles' fracture were carried out at various loading rates ranging from static to impact loadings, there is no systematic study in the literature that isolates the influence of strain rate on Colles' fracture load. In order to provide a better understanding of fracture risk, the current study combines experimental material property measurements under varying strain rates with computational modeling and presents new information on the effect of strain rate on Colles' fracture. The simulation results showed that Colles' fracture load decreased with increasing strain rate with a steeper change in lower strain rates. Specifically, strain rate values (0.29s(-1)) associated with controlled falling without fracture corresponded to a 3.7% reduction in the fracture load. On the other hand, the reduction in the fracture load was 34% for strain rate of 3.7s(-1) reported in fracture inducing impact cadaver experiments. Further increase in the strain rate up to 18s(-1) led to an additional 22% reduction. The most drastic reduction in fracture load occurs at strain rates corresponding to the transition from controlled to impact falling. These results are particularly important for the improvement of fracture risk assessment in the elderly because they identify a critical range of loading rates (10-50mm/s) that can dramatically increase the risk of Colles' fracture.

The effect of strain rate on fracture toughness of human cortical bone: a finite element study

Evaluating the mechanical response of bone under high loading rates is crucial to understanding fractures in traumatic accidents or falls. In the current study, a computational approach based on cohesive finite element modeling was employed to evaluate the effect of strain rate on fracture toughness of human cortical bone. Two-dimensional compact tension specimen models were simulated to evaluate the change in initiation and propagation fracture toughness with increasing strain rate (range: 0.08-18 s(-1)). In addition, the effect of porosity in combination with strain rate was assessed using three-dimensional models of micro-computed tomography-based compact tension specimens. The simulation results showed that bone's resistance against the propagation of a crack decreased sharply with increase in strain rates up to 1 s(-1) and attained an almost constant value for strain rates larger than 1 s(-1). On the other hand, initiation fracture toughness exhibited a more gradual decrease throughout the strain rates. There was a significant positive correlation between the experimentally measured number of microcracks and the fracture toughness found in the simulations. Furthermore, the simulation results showed that the amount of porosity did not affect the way initiation fracture toughness decreased with increasing strain rates, whereas it exacerbated the same strain rate effect when propagation fracture toughness was considered. These results suggest that strain rates associated with falls lead to a dramatic reduction in bone's resistance against crack propagation. The compromised fracture resistance of bone at loads exceeding normal activities indicates a sharp reduction and/or absence of toughening mechanisms in bone during high strain conditions associated with traumatic fracture.

Compressive mechanical properties of bovine cortical bone under varied loading rates

Bone tissue functions in varied mechanical systems of the body under static and dynamic conditions. Therefore, it is essential to understand the mechanical responses of bone at varied loading rates, especially those at fast loading rates. This study has investigated the effect of loading rate on the compressive mechanical properties of bovine cortical bone. Bone specimens of 3.85 mm in diameter and 7.7 mm in length were compressed longitudinally with the loading rates of 2 to 2000 mm/s (corresponding strain rates of 0.26 to 260 s−1). As a result, bovine cortical bone showed high linear elasticity when the loading rate was slow, and exhibited three definite regions of linear elasticity, plastic deformation, and densification at faster loading rates. The elastic modulus showed no dependency on the loading rate. Compressive strength, strain at fracture, and toughness increased as the loading rate increased under the condition that the loading rates were slower than each critical loading rate of 1000, 100, and 1500 mm/s, respectively. However, all showed no significant changes when the loading rates were faster than the corresponding critical loading rates. In conclusion, as the loading rate increased, changes in the compressive mechanical parameters were different depending on the parameter and the loading rate range. Compressive mechanical behaviour of bovine cortical bone showed a brittle nature under high strain rates (strain rates > 13 s−1). These findings should be reflected in the biomimetic simulation of biomaterials for bone tissue repair and engineering.