Nonlinear viscoelastic characterization of bovine trabecular bone

Quantification of long-term nonlinear stress relaxation of bovine trabecular bone

The reliability of computational models in orthopedic biomechanics depends often on the accuracy of the bone material properties. It is widely recognized that the mechanical response of trabecular bone is time-dependent, yet it is often ignored for the sake of simplicity. Previous investigations into the viscoelastic properties of trabecular bone have not explored the relationship between nonlinear stress relaxation and bone mineral density. The inclusion of this behavior could enhance the accuracy of simulations of orthopedic interventions, such as of primary fixation of implants. Although methods to quantify the viscoelastic behavior are known, the time period during which the viscoelastic properties should be investigated to obtain reliable predictions is currently unclear. Therefore, this study aimed to: 1) Investigate the duration of stress relaxation in bovine trabecular bone; 2) construct a material model that describes the nonlinear viscoelastic behavior of uniaxial stress relaxation experiments on trabecular bone; and 3) implement bone density into this model. Uniaxial compressive stress relaxation experiments were performed with cylindrical bovine femoral trabecular bone samples (n = 16) with constant strain held for 24 h. Additionally, multiple stress relaxation experiments with four ascending strain levels with a holding time of 30 min, based on the results of the 24-h experiment, were executed on 18 bovine bone cores. The bone specimens used in this study had a mean diameter of 12.80 mm and a mean height of 28.70 mm. A Schapery and a Superposition model were used to capture the nonlinear stress relaxation behavior in terms of applied strain level and bone mineral density. While most stress relaxation happened in the first 10 min (up to 53 %) after initial compression, the stress relaxation continued even after 24 h. Up to 69 % of stress relaxation was observed at 24 h. Extrapolating the results of 30 min of experimental data to 24 h provided a good fit for accuracy with much improved experimental efficiency. The Schapery and Superposition model were both capable of fitting the repeated stress relaxation in a sample-by-sample approach. However, since bone mineral density did not influence the time-dependent behavior, only the Superposition model could be used for a group-based model fit. Although the sample-by-sample approach was more accurate for an individual specimen, the group based approach is considered a useful model for general application.

Two Orthogonal Nitinol Staples and Combined Nitinol Staple-Screw Constructs for a First Metatarsophalangeal Joint Arthrodesis: A Biomechanical Cadaver Study

BACKGROUND

End-stage hallux metatarsophalangeal (MTP) joint arthritis is commonly treated with arthrodesis using stainless steel or titanium implants. These implants provide static compression that is maximal at the time of implant insertion. Alternatively, nitinol staples are capable of dynamic compression. They have most frequently been used for midfoot arthrodesis procedures. However, their biomechanical performance during hallux MTP arthrodesis has not been described.

METHODS

8 matched pairs of cadaveric feet (4 female, 4 male) were prepared for hallux MTP arthrodesis using cup and cone reamers. Cadaveric pairs were then instrumented with either (1) a transarticular lag screw and dorsal nitinol staple or (2) orthogonal nitinol staples placed dorsally and medially. Walking in a short leg cast for 6 weeks was simulated by applying 90-N forces at 3 Hz to the plantar proximal phalanx for up to 250 000 cycles. Failure was defined as catastrophic implant failure or plantar gapping beyond 7 mm.

RESULTS

15 of 16 specimens failed cyclic loading. All 8 specimens fixed with orthogonal staples failed at an average of 37 ± 81 cycles. 7 of 8 specimens fixed with a dorsal staple and crossed screw failed at 14 900 ± 39 000 cycles. Collectively, 5 specimens failed because of bone fracture (1 in orthogonal staples, 4 in staple-screw group) and 10 failed because of excessive gap formation (7 in orthogonal staples, 3 in staple-screw group). The number of cycles to failure was significantly lower (P = .0469) in the orthogonal staple constructs compared with the dorsal staple and crossed screw constructs.

CONCLUSION

The tested constructs permit significant motion at the first MTP fusion surface during simulated protected weightbearing. Although multiple in vivo factors should be considered when extrapolating results from this cadaveric study, this motion may result in clinical failure with early postoperative weightbearing protocols.

CLINICAL RELEVANCE

We report the first biomechanical evaluation of hallux MTP arthrodesis using modern nitinol staples in 2 separate constructs.

Biomechanical and Microstructural Properties of Subchondral Bone From Three Metacarpophalangeal Joint Sites in Thoroughbred Racehorses

Fatigue-induced subchondral bone (SCB) injury is common in racehorses. Understanding how subchondral microstructure and microdamage influence mechanical properties is important for developing injury prevention strategies. Mechanical properties of the disto-palmar third metacarpal condyle (MCIII) correlate poorly with microstructure, and it is unknown whether the properties of other sites within the metacarpophalangeal (fetlock) joint are similarly complex. We aimed to investigate the mechanical and structural properties of equine SCB from specimens with minimal evidence of macroscopic disease. Three sites within the metacarpophalangeal joint were examined: the disto-palmar MCIII, disto-dorsal MCIII, and proximal sesamoid bone. Two regions of interest within the SCB were compared, a 2 mm superficial and an underlying 2 mm deep layer. Cartilage-bone specimens underwent micro-computed tomography, then cyclic compression for 100 cycles at 2 Hz. Disto-dorsal MCIII specimens were loaded to 30 MPa (n = 10), while disto-palmar MCIII (n = 10) and proximal sesamoid (n = 10) specimens were loaded to 40 MPa. Digital image correlation determined local strains. Specimens were stained with lead-uranyl acetate for volumetric microdamage quantification. The dorsal MCIII SCB had lower bone volume fraction (BVTV), bone mineral density (BMD), and stiffness compared to the palmar MCIII and sesamoid bone (p < 0.05). Superficial SCB had higher BVTV and lower BMD than deeper SCB (p < 0.05), except at the palmar MCIII site where there was no difference in BVTV between depths (p = 0.419). At all sites, the deep bone was stiffer (p < 0.001), although the superficial to deep gradient was smaller in the dorsal MCIII. Hysteresis (energy loss) was greater superficially in palmar MCIII and sesamoid (p < 0.001), but not dorsal MCIII specimens (p = 0.118). The stiffness increased with cyclic loading in total cartilage-bone specimens (p < 0.001), but not in superficial and deep layers of the bone, whereas hysteresis decreased with the cycle for all sites and layers (p < 0.001). Superficial equine SCB is uniformly less stiff than deeper bone despite non-uniform differences in bone density and damage levels. The more compliant superficial layer has an important role in energy dissipation, but whether this is a specific adaptation or a result of microdamage accumulation is not clear.

Three-dimensional finite element analysis of the effect of alveolar cleft bone graft on the maxillofacial biomechanical stabilities of unilateral complete cleft lip and palate

BACKGROUND

The objective is to clarify the effect of alveolar cleft bone graft on maxillofacial biomechanical stabilities, the key areas when bone grafting and in which should be supplemented with bone graft once bone resorption occurred in UCCLP (unilateral complete cleft lip and palate).

METHODS

Maxillofacial CAD (computer aided design) models of non-bone graft and full maxilla cleft, full alveolar cleft bone graft, bone graft in other sites of the alveolar cleft were acquired by processing the UCCLP maxillofacial CT data in three-dimensional modeling software. The maxillofacial bone EQV (equivalent) stresses and bone suture EQV strains under occlusal states were obtained in the finite element analysis software.

RESULTS

Under corresponding occlusal states, the EQV stresses of maxilla, pterygoid process of sphenoid bone on the corresponding side and anterior alveolar arch on the non-cleft side were higher than other maxillofacial bones, the EQV strains of nasomaxillary, zygomaticomaxillary and pterygomaxillary suture on the corresponding side were higher than other maxillofacial bone sutures. The mean EQV strains of nasal raphe, the maximum EQV stresses of posterior alveolar arch on the non-cleft side, the mean and maximum EQV strains of nasomaxillary suture on the non-cleft side in full alveolar cleft bone graft model were all significantly lower than those in non-bone graft model. The mean EQV stresses of bilateral anterior alveolar arches, the maximum EQV stresses of maxilla and its alveolar arch on the cleft side in the model with bone graft in lower 1/3 of the alveolar cleft were significantly higher than those in full alveolar cleft bone graft model.

CONCLUSIONS

For UCCLP, bilateral maxillae, pterygoid processes of sphenoid bones and bilateral nasomaxillary, zygomaticomaxillary, pterygomaxillary sutures, anterior alveolar arch on the non-cleft side are the main occlusal load-bearing structures before and after alveolar cleft bone graft. Alveolar cleft bone graft mainly affects biomechanical stabilities of nasal raphe and posterior alveolar arch, nasomaxillary suture on the non-cleft side. The areas near nasal floor and in the middle of the alveolar cleft are the key sites when bone grafting, and should be supplemented with bone graft when the bone resorbed in these areas.

How Artificial Intelligence and Machine Learning Is Assisting Us to Extract Meaning from Data on Bone Mechanics?

Dramatic advancements in interdisciplinary research with the fourth paradigm of science, especially the implementation of computer science, nourish the potential for artificial intelligence (AI), machine learning (ML), and artificial neural network (ANN) algorithms to be applied to studies concerning mechanics of bones. Despite recent enormous advancement in techniques, gaining deep knowledge to find correlations between bone shape, material, mechanical, and physical responses as well as properties is a daunting task. This is due to both complexity of the material itself and the convoluted shapes that this complex material forms. Moreover, many uncertainties and ambiguities exist concerning the use of traditional computational techniques that hinders gaining a full comprehension of this advanced biological material. This book chapter offers a review of literature on the use of AI, ML, and ANN in the study of bone mechanics research. A main question as to why to implement AI and ML in the mechanics of bones is fully addressed and explained. This chapter also introduces AI and ML and elaborates on the main features of ML algorithms such as learning paradigms, subtypes, main ideas with examples, performance metrics, training algorithms, and training datasets. As a frequently employed ML algorithm in bone mechanics, feedforward ANNs are discussed to make their taxonomy and working principles more readily comprehensible to researchers. A summary as well as detailed review of papers that employed ANNs to learn from collected data on bone mechanics are presented. Reviewing literature on the use of these data-driven tools is essential since their wider application has the potential to: improve clinical assessments enabling real-time simulations; avoid and/or minimize injuries; and, encourage early detection of such injuries in the first place.

On challenges in clinical assessment of hip fracture risk using image-based biomechanical modelling: a critical review

INTRODUCTION

Hip fracture is a common health risk among elderly people, due to the prevalence of osteoporosis and accidental fall in the population. Accurate assessment of fracture risk is a crucial step for clinicians to consider patient-by-patient optimal treatments for effective prevention of fractures. Image-based biomechanical modeling has shown promising progress in assessment of fracture risk, and there is still a great possibility for improvement. The purpose of this paper is to identify key issues that need be addressed to improve image-based biomechanical modeling.

MATERIALS AND METHODS

We critically examined issues in consideration and determination of the four biomechanical variables, i.e., risk of fall, fall-induced impact force, bone geometry and bone material quality, which are essential for prediction of hip fracture risk. We closely inspected: limitations introduced by assumptions that are adopted in existing models; deficiencies in methods for construction of biomechanical models, especially for determination of bone material properties from bone images; problems caused by separate use of the variables in clinical study of hip fracture risk; availability of clinical information that are required for validation of biomechanical models.

RESULTS AND CONCLUSIONS

A number of critical issues and gaps were identified. Strategies for effectively addressing the issues were discussed.

Influence of non-enzymatic glycation on the mechanical properties of cortical bone

Poor bone quality induced by non-enzymatic glycation (NEG) of bone tissue in patients with type 2 diabetes mellitus (T2DM) is regarded as the major factor of bone fragility and affecting bone mechanical properties. A comprehensive and systemic mechanical investigation for evaluating the effect of NEG on bone was still lacking. In order to provide additional information for the bone quality of T2DM, the effects of NEG on mechanical properties of cortical bone were investigated in terms of elastoplasticity, fracture toughness and viscoelasticity. All samples of cortical bone, including the samples of strength test (n = 20), fracture toughness test (n = 40, quasi-static and fall-like conditions with displacement rates of 10^-3 mm/s and 10 mm/s, respectively) and stress relaxation test (n = 20), were harvested from bovine tibiae. The samples of each test were equally divided into incubated-control group and ribose-incubated group. All mechanical tests were performed after incubating all samples for 15 days. Post-yield strain (p = 0.014), post-yield energy (p < 0.0001) and damage fraction (p = 0.040) of ribose-incubated group were significantly lower than those of incubated-control group, but secant modulus (p = 0.029) of ribose-incubated group was significantly higher than that of incubated-control group. In quasi-static condition, the plastic contribution J_pl of fracture toughness (p = 0.043) of ribose-incubated group was significantly lower than that of incubated-control group. In fall-like condition, there were no differences in J_pl, elastic contribution J_el and J-integral in both two groups. The quasi-static J_el (p < 0.0001, p < 0.0001) of incubated-control and ribose-incubated groups and J-integral (p = 0.007) of incubated-control group were all significantly higher than those of fall-like condition. In stress relaxation test, initial modulus E₀ (p = 0.040) and equilibrium modulus (p = 0.029) of ribose-incubated group were significantly higher than those of incubated-control group. Reductions of relaxation modulus, which were the differences between two adjacent time points within 700 s-3000 s for ribose-incubated group, were significantly lower than those of incubated-control group. NEG could decrease the post-yield properties and quasi-static facture toughness of cortical bone, especially the plastic contribution of quasi-static fracture toughness. It could also decrease the viscoelasticity of cortical bone. The present study confirmed the negative effects of NEG on the mechanical properties of cortical bone in terms of elastoplasticity, fracture toughness and viscoelasticity, but NEG had no significant effect on the fracture toughness of cortical bone at fall-like loading. These results provided more evidence for increased fragility of cortical bone in patients with T2DM.

Hinge location and apical drill holes in opening wedge high tibial osteotomy: A finite element analysis

At the time of medial opening wedge high tibial osteotomy (HTO) to realign the lower limb and offload medial compartment knee osteoarthritis, unwanted fractures can propagate from the osteotomy apex. The aim of this study was to use finite element (FE) analysis to determine the effect of hinge location and apical drill holes on cortical stresses and strains in HTO. A monoplanar medial opening wedge HTO was created above the tibial tuberosity in a composite tibia. Using the FE method, intact lateral hinges of different widths were considered (5, 7.5, and 10 mm). Additional apical drill holes (2, 4, and 6 mm diameters) were then incorporated into the 10 mm hinge model. The primary outcome measure was the maximum principal strain in the cortical bone surrounding the hinge axis. Secondary outcomes included the force required for osteotomy opening, minimum principal strain, and mean cortical bone stresses (maximum principal/minimum principal/von Mises). Larger intact hinges (10 mm) were associated with higher cortical bone maximum principal strain and stress, lower minimum principal strain/stress, and required greater force to open. Lateral cortex strain concentrations were present in all scenarios, but extended to the joint surface with the 10 mm hinge. Apical drill holes reduced the mean cortical bone maximum principal strain adjacent to the hinge axis: 2 mm hole 6% reduction; 4 mm 35% reduction; and 6 mm 55% reduction. Incorporating a 4-mm apical drill hole centered 10 mm from the intact lateral cortex maintains a cortical bone hinge, minimizes cortical bone strains and reduces the force required to open the HTO; thus improving control.

A predictive model for creep deformation following vertebral compression fractures

Many vertebral compression fractures continue to collapse over time, resulting in spinal deformity and chronic back pain. Currently, there is no adequate screening strategy to identify patients at risk of progressive vertebral collapse. This study developed a mathematical model to describe the quantitative relationship between initial bone damage and progressive ("creep") deformation in human vertebrae. The model uses creep rate before damage, and the degree of vertebral bone damage, to predict creep rate of a fractured vertebra following bone damage. Mechanical testing data were obtained from 27 vertebral trabeculae samples, and 38 motion segments, from 26 human spines. These were analysed to evaluate bone damage intensity, and creep rates before and after damage, in order to estimate the model parameter, p, which represents how bone damage affects the change of creep rate after damage. Results of the model showed that p was 1.38 (R² = 0.72, p < 0.001) for vertebral trabeculae, and 1.48 for motion segments (R² = 0.22, p = 0.003). These values were not significantly different from each other (P > 0.05). Further analyses revealed that p was not significantly influenced by cortical bone damage, endplate damage, disc degeneration, vertebral size, or vertebral areal bone mineral density (aBMD) (P > 0.05). The key determinant of creep deformation following vertebral compression fracture was the degree of trabecular bone damage. The proposed model could be used to identify the measures of bone damage on routine MR images that are associated with creep deformation so that a screening tool can be developed to predict progressive vertebral collapse following compression fracture.

A finite element analysis of tibial tritanium cones without stems in varying bone defects

BACKGROUND

In the UK around 10% of hip and knee arthroplasties are revision operations. At revision total knee arthroplasty (rTKA), bone loss management is critical to achieving a stable bone-implant construct. Though tritanium cones have been used to manage bone defects in rTKA, their biomechanical performance with varying defects remains unknown.

METHODS

Uncontained tibial bone defects at four anatomic locations, with varying depths and widths (Type T2A and T2B) were investigated computationally in a composite tibia which was subjected to four loading scenarios. The ability of the tritanium cone to replace the tibial bone defect was examined using the outcome measures of bone strain distribution and interface micromotions.

RESULTS

It was found that anterior and lateral defects do not significantly alter the strain distribution compared with intact bone. For medial defects, strain distribution is sensitive to defect width; while strain distributions for posterior defects are associated with defect width and depth. In general, micromotions at the bone-implant interface are small and are primarily influenced by defect depth.

CONCLUSIONS

Our models show that the cone is an acceptable choice for bone defect management in rTKA. Since all observed micromotions were small, successful osteointegration would be expected in all types of uncontained defects considered in this study. Tritanium cones safely accommodate uncontained tibial defects up to 10 mm deep and extending up to 9 mm from the centre of the cone. Medial and posteriorly based defects managed with symmetric cones display the greatest bone strains and asymmetric cones may be useful in this context.

Metaphyseal cones in revision total knee arthroplasty: The role of stems

Aims

Metaphyseal tritanium cones can be used to manage the tibial bone loss commonly encountered at revision total knee arthroplasty (rTKA). Tibial stems provide additional fixation and are generally used in combination with cones. The aim of this study was to examine the role of the stems in the overall stability of tibial implants when metaphyseal cones are used for rTKA.

Methods

This computational study investigates whether stems are required to augment metaphyseal cones at rTKA. Three cemented stem scenarios (no stem, 50 mm stem, and 100 mm stem) were investigated with 10 mm-deep uncontained posterior and medial tibial defects using four loading scenarios designed to mimic activities of daily living.

Results

Small micromotions (mean < 12 µm) were found to occur at the bone-implant interface for all loading cases with or without a stem. Stem inclusion was associated with lower micromotion, however these reductions were too small to have any clinical significance. Peak interface micromotion, even when the cone is used without a stem, was too small to effect osseointegration. The maximum difference occurred with stair descent loading. Stress concentrations in the bone occurred around the inferior aspect of each implant, with the largest occurring at the end of the long stem; these may lead to end-of-stem pain. Stem use is also found to result in stress shielding in the bone along the stem.

Conclusion

When a metaphyseal cone is used at rTKA to manage uncontained posterior or medial defects of up to 10 mm depth, stem use may not be necessary.

Cite this article:Bone Joint Res. 2020;9(4):162–172.

Time-dependent behaviour of demineralised trabecular bone - Experimental investigation and development of a constitutive model

Trabecular bone is a cellular composite material comprising primarily of mineral and organic phases and its mechanical response to loads is time-dependent. The contribution of the organic phase to the time-dependent behaviour of bone is not yet understood. We investigated the time-dependent response of demineralised trabecular bone through tensile multiple-load-creep-unload-recovery experiments. We found that demineralised trabecular bone's time-dependent response is nonlinearly related to the applied stress levels - it stiffens with increased stress levels. Our results also indicated that the time-dependent behaviour is associated with the original bone volume ratio (BV/TV). Irrecoverable strain exists, even at the low strain levels, but are not associated with BV/TV. Furthermore, we found that the nonlinear viscoelastic model can accurately predict the time-dependent behaviour of the trabecular bone's organic phase, which can be incorporated together with the properties of mineral to generate a composite model of bone. This study will help to provide a better understanding of this natural composite material.

Length scale parameter of single trabecula in cancellous bone

In this paper, the material length scale parameter of the modified couple stress theory for trabecular bones is studied. For this reason, experimental data for the buckling of single wet and dry trabeculae from the subchondral region of the human medial tibial plateau are used from the literature. A material length scale parameter is extracted using the modified couple stress theory-based buckling relation and the experimental results. This parameter can capture the size-dependent behavior of trabeculae and can be beneficial for micro-mechanical investigation of trabecular bones. In addition, this paper proposes a size-dependent length scale parameter for trabeculae to estimate the buckling behaviors of dry and wet trabeculae, more accurately. Therefore, this paper confirms that the softening (weakening) effects of the modified couple stress theory and size-dependent behavior of the material length scale parameter can be considered for some special cases, and additionally, a correct value for the length scale parameter of the trabecula is revealed.

Effect of loading frequency on deformations at the bone-implant interface

This study considers the time-dependent behaviour of bone in the context of loosening of metal implants, which is one of the typical complications of joint replacement and fracture-fixation surgeries. We employed viscoelastic properties developed from our previous experimental studies for trabecular bone in a representative bone-implant construct, which was subjected to cyclic loading at varying loading frequencies. We found that the separation between the bone and the implant is a function of loading frequency and increases with number of loading cycles applied. Our analysis shows that at the start of cyclic loading, a higher frequency results in a lower displacement response of bone at the bone-implant interface; however, after the bone-implant system has been subjected to a large number of cycles (>500 cycles in this study), higher interfacial displacements are observed at higher loading frequencies. In other words, higher loading frequencies will not result in bone-implant separation if limited number of cycles are applied. In all cases, interfacial displacements increase as bone volume ratio decreases. This simple approach can be used to evaluate the mechanical environment in bone-implant systems due to cyclic loading which commonly used time-independent models that are unable to simulate. The approach can also be used to evaluate implant loosening due to cyclic loading.

Nitinol Compression Staples in Foot and Ankle Surgery

Nitinol compression implants are fast and simple to insert and have a high radiographic union rate for midfoot and hindfoot arthrodeses. Applications of nitinol technology in orthopedic surgery are rapidly expanding with the improved and broadened portfolio of implants available.

The risk of loosening of extramedullary fracture fixation devices

Extramedullary devices that use screws, pins or wires are used extensively to treat fractures in normal and diseased bone. A common failure mode is implant loosening at the bone-screw/pin/wire interface before fracture healing occurs. This review first considers the fundamental mechanics of the bone-fixator construct with focus on interfacial strains that result in loosening. It then evaluates the time-independent and time-dependent material models of bone that have been used to simulate and predict loosening. It is shown that the recently developed time-dependent models are capable of predicting loosening due to cyclic loads in bone of varying quality.

The effect of malalignment on proximal tibial strain in fixed-bearing unicompartmental knee arthroplasty: A comparison between metal-backed and all-polyethylene components using a validated finite element model

Objectives

Elevated proximal tibial bone strain may cause unexplained pain, an important cause of unicompartmental knee arthroplasty (UKA) revision. This study investigates the effect of tibial component alignment in metal-backed (MB) and all-polyethylene (AP) fixed-bearing medial UKAs on bone strain, using an experimentally validated finite element model (FEM).

Methods

A previously experimentally validated FEM of a composite tibia implanted with a cemented fixed-bearing UKA (MB and AP) was used. Standard alignment (medial proximal tibial angle 90°, 6° posterior slope), coronal malalignment (3°, 5°, 10° varus; 3°, 5° valgus), and sagittal malalignment (0°, 3°, 6°, 9°, 12°) were analyzed. The primary outcome measure was the volume of compressively overstrained cancellous bone (VOCB) < -3000 µε. The secondary outcome measure was maximum von Mises stress in cortical bone (MSCB) over a medial region of interest.

Results

Varus malalignment decreased VOCB but increased MSCB in both implants, more so in the AP implant. Varus malalignment of 10° reduced the VOCB by 10% and 3% in AP and MB implants but increased the MSCB by 14% and 13%, respectively. Valgus malalignment of 5° increased the VOCB by 8% and 4% in AP and MB implants, with reductions in MSCB of 7% and 10%, respectively. Sagittal malalignment displayed negligible effects. Well-aligned AP implants displayed greater VOCB than malaligned MB implants.

Conclusion

All-polyethylene implants are more sensitive to coronal plane malalignments than MB implants are; varus malalignment reduced cancellous bone strain but increased anteromedial cortical bone stress. Sagittal plane malalignment has a negligible effect on bone strain.

Cite this article: I. Danese, P. Pankaj, C. E. H. Scott. The effect of malalignment on proximal tibial strain in fixed-bearing unicompartmental knee arthroplasty: A comparison between metal-backed and all-polyethylene components using a validated finite element model. Bone Joint Res 2019;8:55–64. DOI: 10.1302/2046-3758.82.BJR-2018-0186.R2.

Strain state dependent anisotropic viscoelasticity of tendon-to-bone insertion

Tendon-to-bone insertion tissues may be considered as functionally-graded connective tissues, providing a gradual transition from soft tendon to hard bone tissue, and functioning to alleviate stress concentrations at the junction of these tissues. The tendon-to-bone insertion tissues demonstrate pronounced viscoelastic behavior, like many other biological tissues, and are designed by the nature to alleviate stress at physiological load rates and strains states. In this paper we present experimental data showing that under biaxial tension tendon-to-bone insertion demonstrates rate-dependent behavior and that stress-strain curves for the in-plane components of stress and strain become less steep when strain rate is increased, contrary to a typical viscoelastic behavior, where the opposite trend is observed. Such behavior may indicate the existence of a protective viscoelastic mechanism reducing stress and strain during a sudden increase in mechanical loading, known to exist in some biological tissues. The main purpose of the paper is to show that such viscoelastic stress reduction indeed possible and is thermodynamically consistent. We, therefore, propose an anisotropic viscoelasticity model for finite strain. We identify the range of parameters for this model which yield negative viscoelastic contribution into in-plane stress under biaxial state of strain and simultaneously satisfy requirements of thermodynamics. We also find optimal parameters maximizing the observed protective viscoelastic effect for this particular state of strain. This model will be useful for testing and describing viscoelastic materials and for developing interfaces for dissimilar materials, considering rate effect and multiaxial loadings.

Time-dependent behaviour of bone accentuates loosening in the fixation of fractures using bone-screw systems

Aims

Loosening is a well-known complication in the fixation of fractures using devices such as locking plates or unilateral fixators. It is believed that high strains in the bone at the bone-screw interface can initiate loosening, which can result in infection, and further loosening. Here, we present a new theory of loosening of implants. The time-dependent response of bone subjected to loads results in interfacial deformations in the bone which accumulate with cyclical loading and thus accentuates loosening.

Methods

We used an 'ideal' bone-screw system, in which the screw is subjected to cyclical lateral loads and trabecular bone is modelled as non-linear viscoelastic and non-linear viscoelastic-viscoplastic material, based on recent experiments, which we conducted.

Results

We found that the interfacial deformation in the bone increases with the number of cycles, and the use of a non-linear viscoelastic-viscoplastic model results in larger deformations, some of which are irrecoverable. There is an apparent trend in which interfacial deformations increase with increasing porosity of bone.

Conclusion

The developed time-dependent model of the mechanical behaviour of bone permits prediction of loosening due to cyclical loads, which has not been possible previously. Application of this model shows that implant loosening will be accentuated by cyclical loading due to physiological activities, and the risks of loosening are greater in osteoporotic patients.Cite this article: S. Xie, K. Manda, P. Pankaj. Time-dependent behaviour of bone accentuates loosening in the fixation of fractures using bone-screw systems. Bone Joint Res 2018;7:580-586. DOI: 10.1302/2046-3758.710.BJR-2018-0085.R1.

Brillouin spectroscopy and radiography for assessment of viscoelastic and regenerative properties of mammalian bones

Biomechanical properties of mammalian bones, such as strength, toughness, and plasticity, are essential for understanding how microscopic-scale mechanical features can link to macroscale bones' strength and fracture resistance. We employ Brillouin light scattering (BLS) microspectroscopy for local assessment of elastic properties of bones under compression and the efficacy of the tissue engineering approach based on heparin-conjugated fibrin (HCF) hydrogels, bone morphogenic proteins, and osteogenic stem cells in the regeneration of the bone tissues. BLS is noninvasive and label-free modality for probing viscoelastic properties of tissues that can give information on structure-function properties of normal and pathological tissues. Results showed that MCS and BPMs are critically important for regeneration of elastic and viscous properties, respectively, HCF gels containing combination of all factors had the best effect with complete defect regeneration at week nine after the implantation of bone grafts and that the bones with fully consolidated fractures have higher values of elastic moduli compared with defective bones.

Mechanical Stimuli in the Local In Vivo Environment in Bone: Computational Approaches Linking Organ-Scale Loads to Cellular Signals

PURPOSE OF REVIEW

Connecting organ-scale loads to cellular signals in their local in vivo environment is a current challenge in the field of bone (re)modelling. Understanding this critical missing link would greatly improve our ability to anticipate mechanotransduction during different modes of stimuli and the resultant cellular responses. This review characterises computational approaches that could enable coupling links across the multiple scales of bone.

RECENT FINDINGS

Current approaches using strain and fluid shear stress concepts have begun to link organ-scale loads to cellular signals; however, these approaches fail to capture localised micro-structural heterogeneities. Furthermore, models that incorporate downstream communication from osteocytes to osteoclasts, bone-lining cells and osteoblasts, will help improve the understanding of (re)modelling activities. Incorporating this potentially key information in the local in vivo environment will aid in developing multiscale models of mechanotransduction that can predict or help describe resultant biological events related to bone (re)modelling. Progress towards multiscale determination of the cell mechanical environment from organ-scale loads remains elusive. Construction of organ-, tissue- and cell-scale computational models that include localised environmental variation, strain amplification and intercellular communication mechanisms will ultimately help couple the hierarchal levels of bone.

From Tension to Compression: Asymmetric Mechanical Behaviour of Trabecular Bone's Organic Phase

Trabecular bone is a cellular composite material comprising primarily of mineral and organic phases with their content ratio known to change with age. Therefore, the contribution of bone constituents on bone's mechanical behaviour, in tension and compression, at varying load levels and with changing porosity (which increases with age) is of great interest, but remains unknown. We investigated the mechanical response of demineralised bone by subjecting a set of bone samples to fully reversed cyclic tension-compression loads with varying magnitudes. We show that the tension to compression response of the organic phase of trabecular bone is asymmetric; it stiffens in tension and undergoes stiffness reduction in compression. Our results indicate that demineralised trabecular bone struts experience inelastic buckling under compression which causes irreversible damage, while irreversible strains due to microcracking are less visible in tension. We also identified that the values of this asymmetric mechanical response is associated to the original bone volume ratio (BV/TV).

Effects of bone damage on creep behaviours of human vertebral trabeculae

A subgroup of patients suffering with vertebral fractures can develop progressive spinal deformities over time. The mechanism underlying such clinical observation, however, remains unknown. Previous studies suggested that creep deformation of the vertebral trabeculae may play a role. Using the acoustic emission (AE) technique, this study investigated effects of bone damage (modulus reduction) on creep behaviours of vertebral trabecular bone. Thirty-seven human vertebral trabeculae samples were randomly assigned into five groups (A to E). Bones underwent mechanical tests using similar experimental protocols but varied degree of bone damage was induced. Samples first underwent creep test (static compressive stress of 0.4MPa) for 30min, and then were loaded in compression to a specified strain level (0.4%, 1.0%, 1.5%, 2.5%, and 4% for group A to E, respectively) to induce different degrees of bone damage (0.4%, no damage control; 1.0%, yield strain; 1.5%, beyond yield strain, 2.5% and 4%, post-ultimate strains). Samples were creep loaded (0.4MPa) again for 30min. AE techniques were used to monitor bone damage. Bone damage increased significantly from group A to E (P<0.05), with >30% of modulus reduction in group D and E. Before compressive loading, creep deformation was not different among the five groups and AE hits in creep test were rare. After compressive loading, creep deformation was significantly greater in group D and E than those in other groups (P<0.05). The number of AE hits and other AE measurements during creep test were significantly greater in group D and E than in group A, B, and C (P<0.05 for all). Data suggested that with the increase of vertebral trabecular bone damage, substantial creep deformation may occur even when the vertebra was under physiological loads. The boosted creep deformation observed may be attributed to newly created trabecular microfractures. Findings provide a possible explanation as to why some vertebral fracture patients develop progressive spinal deformity over time.

Micro Finite Element models of the vertebral body: Validation of local displacement predictions

The estimation of local and structural mechanical properties of bones with micro Finite Element (microFE) models based on Micro Computed Tomography images depends on the quality bone geometry is captured, reconstructed and modelled. The aim of this study was to validate microFE models predictions of local displacements for vertebral bodies and to evaluate the effect of the elastic tissue modulus on model’s predictions of axial forces. Four porcine thoracic vertebrae were axially compressed in situ, in a step-wise fashion and scanned at approximately 39μm resolution in preloaded and loaded conditions. A global digital volume correlation (DVC) approach was used to compute the full-field displacements. Homogeneous, isotropic and linear elastic microFE models were generated with boundary conditions assigned from the interpolated displacement field measured from the DVC. Measured and predicted local displacements were compared for the cortical and trabecular compartments in the middle of the specimens. Models were run with two different tissue moduli defined from microindentation data (12.0GPa) and a back-calculation procedure (4.6GPa). The predicted sum of axial reaction forces was compared to the experimental values for each specimen. MicroFE models predicted more than 87% of the variation in the displacement measurements (R² = 0.87–0.99). However, model predictions of axial forces were largely overestimated (80–369%) for a tissue modulus of 12.0GPa, whereas differences in the range 10–80% were found for a back-calculated tissue modulus. The specimen with the lowest density showed a large number of elements strained beyond yield and the highest predictive errors. This study shows that the simplest microFE models can accurately predict quantitatively the local displacements and qualitatively the strain distribution within the vertebral body, independently from the considered bone types.

Time Dependent Behaviour of Trabecular Bone at Multiple Load Levels

The deformation of bone when subjected to loads is not instantaneous but varies with time. To investigate this time-dependent behaviour sixteen bovine trabecular bone specimens were subjected to compressive loading, creep, unloading and recovery at multiple load levels corresponding to apparent strains of 2000-25,000 με. We found that: the time-dependent response of trabecular bone comprises of both recoverable and irrecoverable strains; the strain response is nonlinearly related to applied load levels; and the response is linked to bone volume fraction. Although majority of strain is recovered after the load-creep-unload-recovery cycle some residual strain always exists. The analysis of results indicates that trabecular bone becomes stiffer initially and then experiences stiffness degradation with the increasing load levels. Steady state creep rate was found to be dependent on applied stress level and bone volume fraction with a power law relationship.