Distribution of Young's modulus in the cancellous bone of the proximal canine tibia

Enhanced bone formation in locally-optimised, low-stiffness additive manufactured titanium implants: An in silico and in vivo tibial advancement study

A tibial tuberosity advancement (TTA), used to treat lameness in the canine stifle, provides a framework to investigate implant performance within an uneven loading environment due to the dominating patellar tendon. The purpose of this study was to reassess how we design orthopaedic implants in a load-bearing model to investigate potential for improved osseointegration capacity of fully-scaffolded mechanically-matched additive manufactured (AM) implants. While the mechanobiological nature of bone is well known, we have identified a lower limit in the literature where investigation into exceedingly soft scaffolds relative to trabecular bone ceases due to the trade-off in mechanical strength. We developed a finite element model of the sheep stifle to assess the stresses and strains of homogeneous and locally-optimised TTA implant designs. Using additive manufacturing, we printed three different low-stiffness Ti-6Al-4 V TTA implants: 0.8 GPa (Ti1), 0.6 GPa (Ti2) and an optimised design with a 0.3 GPa cortex and 0.1 GPa centre (Ti3), for implantation in a 12-week in vivo ovine pilot study. Static histomorphometry demonstrated uniform bone ingrowth in optimised low-modulus Ti3 samples compared to homogeneous designs (Ti1 and Ti2), and greater bone-implant contact. Mineralising surfaces were apparent in all implants, though mineral apposition rate was only consistent throughout Ti3. The greatest bone formation scores were seen in Ti3, followed by Ti2 and Ti1. Results from our study suggest lower stiffnesses and higher strain ranges improve early bone formation, and that by accounting for loading environments through rational design, implants can be optimised to improve uniform osseointegration. STATEMENT OF SIGNIFICANCE: The effect of different strain ranges on bone healing has been traditionally investigated and characterised through computational models, with much of the literature suggesting higher strain ranges being favourable. However, little has been done to incorporate strain-optimisation into porous orthopaedic implants due to the trade-off in mechanical strength required to induce these microenvironments. In this study, we used finite element analysis to optimise the design of additive manufactured (AM) titanium orthopaedic implants for different strain ranges, using a clinically-relevant surgical model. Our research suggests that there is potential for locally-optimised AM scaffolds in the use of orthopaedic devices to induce higher strains, which in turn encourages de novo bone formation and uniform osseointegration.

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

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

Morphometrical and biomechanical analyses of a stentless bioprosthetic valve: an implication to avoid potential primary tissue failure

OBJECTIVES

Stentless bioprosthetic valves provide hemodynamic advantages over stented valves as well as excellent durability. However, some primary tissue failures in bioprostheses have been reported. This study was conducted to evaluate the morphometrical and biomechanical properties of the stentless Medtronic Freestyle™ aortic root bioprosthesis, to identify any arising problem areas, and to speculate on a potential solution.

METHODS

The three-dimensional heterogeneity of the stentless bioprosthesis wall was investigated using computed tomography. The ascending aorta and the right, left, and non-coronary sinuses of Valsalva were resected and examined by an indentation test to evaluate their biomechanical properties.

RESULTS

The non-coronary sinus of Valsalva was significantly thinner than the right sinus of Valsalva (p < 0.01). Young's modulus, calculated as an indicator of elasticity, was significantly greater at the non-coronary sinus of Valsalva (430.7 ± 374.2 kPa) than at either the left (190.6 ± 70.6 kPa, p < 0.01) or right sinuses of Valsalva (240.0 ± 56.5 kPa, p < 0.05).

CONCLUSIONS

Based on the morphometrical and biomechanical analyses of the stentless bioprosthesis, we demonstrated that there are differences in wall thickness and elasticity between each sinus of Valsalva. These differences suggest that the non-coronary sinus of Valsalva is the most vulnerable and at greater risk of tissue failure. The exclusion of the non-coronary sinus of Valsalva may be beneficial to mitigate the long-term risks of tissue failure in the stentless bioprosthesis.

Quantifying the regional variations in the mechanical properties of cancellous bone of the tibia using indentation testing and quantitative computed tomographic imaging

Finite element models apply material properties using experimentally derived density–modulus equations and computed tomographic image data, yet numerous different equations exist in the literature. The purpose of this study was to experimentally evaluate the distribution of mechanical properties through the proximal tibia and compare with those predicted using existing density–modulus equations. Indentation testing was performed on five cadaveric tibiae, with four slices removed from the proximal epiphysis and metaphysis of each. Elastic modulus and yield strength were identified for each test and grouped into nine transverse regions. These regions were identified on computed tomographic scans, and four density–modulus equations from the literature applied. Errors between measured and predicted modulus were then calculated. Elastic modulus and yield strength varied regionally, with the bone located closest to the joint and in the condyles being strongest and the intercondylar region the weakest. The optimal relationship for predicting modulus varied depending on anatomical region, but generally was best predicted by the Goulet equation. The regions of high strength identified in this study (condyles and proximal regions) can serve as improved sites of attachment for orthopedic devices and should be preserved during surgery, if possible. The substantial regional variations observed herein (almost a threefold change in modulus across different regions) should be incorporated into finite element models and applied using the Goulet density–modulus equation.

Rabbit knee joint biomechanics: motion analysis and modeling of forces during hopping

Although the rabbit hindlimb has been commonly used as an experimental animal model for studies of osteoarthritis, bone growth and fracture healing, the in vivo biomechanics of the rabbit knee joint have not been quantified. The purpose of this study was to investigate the kinematic and kinetic patterns during hopping of the adult rabbit, and to develop a model to estimate the joint contact force distribution between the tibial plateaus. Force platform data and three-dimensional motion analysis using infrared markers mounted on intracortical bone pins were combined to calculate the knee and ankle joint intersegmental forces and moments. A statically determinate model was developed to predict muscle, ligament and tibiofemoral joint contact forces during the stance phase of hopping. Variations in hindlimb kinematics permitted the identification of two landing patterns, that could be distinguished by variations in the magnitude of the external knee abduction moment. During hopping, the prevalence of an external abduction moment led to the prediction of higher joint contact forces passing through the lateral compartment as compared to the medial compartment of the knee joint. These results represent critical data on the in vivo biomechanics of the rabbit knee joint, which allow for comparisons to both other experimental animal models and the human knee, and may provide further insight into the relationships between mechanical loading, osteoarthritis, bone growth, and fracture healing.

Grafting of massive tibial subchondral bone defects in a caprine model using beta-tricalcium phosphate versus autograft

OBJECTIVE

This study evaluated the ability of beta-tricalcium phosphate particles (beta-TCP) and autograft (AUTO) to maintain joint surface morphology when used to supplement massive subchondral bone defects in a caprine model.

DESIGN

This was a prospective, parallel arm study with 2 experimental arms and a control group.

METHODS

Unilateral, 11 mm diameter, 25 mm deep cylindrical defects were created in tibial subchondral bone of anesthetized goats (n = 16) and filled with autograft or beta-tricalcium phosphate particles. The contralateral limbs served as internal controls. Goats were killed at 3 months and both tibiae harvested. Molds made of the tibial plateau surface were used to create positive casts from which medial and lateral tibial plateau surfaces of both experimental (beta-tricalcium phosphate particles, autograft) and control limbs were digitized in 3 dimensions. Mirror images of the medial condyle surface contours from the controls were superimposed onto the experimental surfaces and deviations were compared using a Student t test (alpha = 0.05). Tibiae were then cut sagittally into medial (biomechanics) and lateral (histology) halves. Compressive modulus within the defect area was assessed by indentation to 2.0 mm at 0.2 mm per second using a 6-mm diameter pin. Specimens from the lateral tibial plateau were processed for undecalcified histology and the area of bone within the defect region measured. The articular surface of 86% of the autograft and 0% of the beta-tricalcium phosphate particles group had degenerative changes, with 29% of autograft goats exhibiting large-scale plateau collapse. Mean surface deviation for autograft was significantly greater than for beta-tricalcium phosphate particles (2.19 +/- 1.49 mm versus 0.78 +/- 0.19 mm), as was maximum surface deviation (11.19 +/- 8.02 mm versus 4.39 +/- 1.33 mm) (P < 0.05). The compressive modulus within the defect area for control animals was significantly higher than the experimental groups (P < 0.05). Significantly more bone was regenerated within beta-tricalcium phosphate particle-grafted defects compared to autograft (P < 0.05). These results indicated that beta-tricalcium phosphate particles might be a useful graft material for local repair of load bearing skeletal sites such as depressed tibial plateau fractures.

A novel ultrasound indentation system for measuring biomechanical properties of in vivo soft tissue

Technologies for soft tissue analysis are advancing at a rapid place. For instance, elastography, which provides soft tissue strain images, is starting to be tried in clinical practice as a tool for diagnosing cancer. Soft tissue deformation modeling and analysis is also an active area of research that has application in surgery planning and treatment. Typically, quantitative soft tissue analysis uses nominal values of soft tissue biomechanical properties. However, in practice, soft tissue properties can vary significantly between individuals. Hence, for soft tissue methodologies to reach their full potential as patient-specific techniques, there is a need to develop ways to efficiently measure soft tissue mechanical properties in vivo. This paper describes a prototype real-time ultrasound (US) indentation test system developed to meet this need. The system is based on the integration of a force sensor and an optical tracking system with a commercial US machine integrated with a suite of analysis methodologies. In a study on a single-layer phantom, we used the system to compare various methods of estimating linear elastic properties (via a theoretical approximation, 2-D finite element analysis, 3-D finite element analysis and a standard material-testing method). In a second study on a three-layer gelatin phantom, we describe a new finite-element-based inverse solution for recovering the Young's moduli of each layer to show how the system can estimate properties of internal components of soft tissue. Finally, we show how the system can be used to derive a modified quasilinear viscoelastic (QVL) model on real breast tissue.

Comparison of failure characteristics of a range of cancellous bone-bone cement composites

Over the past decade, orthopedic surgery has embraced an increase in the depth of cement penetration into the adjacent cancellous bone structure. The resultant interdigitation transforms this zone into a thick layer of continuous interpenetrating composite material. The failure behavior of the composite formed with a number of potential bone cements with different bonding ability was investigated. The cancellous bone-cement composites exhibit considerable resistance to crack extension, and in situ optical observation indicates that the contribution of the cancellous bone is analogous to that of a typical fiber bridging process. The critical stress intensity factor and the work of fracture have been used to quantify the failure characteristics of the cancellous bone-cement composites. The nature of the crack propagation through these cement-bone composites was also captured via optical microscopy, and scanning electron microscopic images were taken of the failure surfaces. The R-curve behavior, or crack extension characteristic, of the cancellous bone-cement composite was also determined. The interesting outcome is that the cancellous bone-PMMA (poly-methylmethacrylate) composite, despite the absence of chemical bonding with bone, required the highest energy to fracture. In addition, the dimensional stability of the cement has a great effect on the interface.

Autologous bone marrow stromal cells loaded onto porous hydroxyapatite ceramic accelerate bone repair in critical-size defects of sheep long bones

The ability of marrow-derived osteoprogenitor cells to promote repair of critical-size tibial gaps upon autologous transplantation on a hydroxyapatite ceramic (HAC) carrier was tested in a sheep model. Conditions for in vitro expansion of sheep bone marrow stromal cells (BMSC) were established and the osteogenic potential of the expanded cells was validated. Ectopic implantation of sheep BMSC in immunocompromised mice led to extensive bone formation. When used to repair tibial gaps in sheep, cell-loaded implants (n = 2) conducted a far more extensive bone formation than did cell-free HAC cylinders (n = 2) over a 2-month period. In cell-loaded implants, bone formation was found to occur both within the internal macropore space and around the HAC cylinder while in control cell-free implants, bone formation was limited mostly to the outer surface and was not observed in most of the inner pores. As tested in an indentation assay, the stiffness of the complex HAC-bone material was found to be higher in cell-loaded implants compared to controls. Our pilot study on a limited number of large-sized animals suggests that the use of autologous BMSC in conjunction with HAC-based carriers results in faster bone repair compared to HAC alone. Potentially this combination could be used clinically in the treatment of extensive long bone defects.

Mechanical and morphological variation of the human lumbar vertebral cortical and trabecular bone

The nanoindentation technique was used to characterize the variation in the elastic modulus and hardness of human lumbar vertebral cortical and trabecular bone. The elastic modulus (and in most cases, the hardness as well) of axially aligned trabeculae cut in the transverse direction was significantly greater than in other orientations of vertebral cortical and trabecular bone. In all cases, the elastic modulus and hardness of bone in the load-bearing direction was greater than in corresponding bone types cut in the other directions. Scanning electron micrographs of cortical shell revealed the Haversian-like canal systems expected in secondary cortical bone, but it was difficult to differentiate by morphology cortical from trabecular bone in the human lumbar vertebrae.

Are regional variations in bone growth related to mechanical stress and strain parameters?

A three-dimensional finite element analysis was used to quantify the patterns of mechanical stresses within the rabbit distal femur growth plate, and test the hypothesis that these patterns are correlated to measured patterns of bone growth rates. This investigation of normal development is the first step toward improving our understanding of the role of mechanical factors in bone growth abnormalities. Rabbits from five age groups ranging from 1 to 42 days were evaluated, and four different loading conditions were analyzed, representing specific time points in the normal gait cycle. Finite element models generated directly from micro-computed tomography images of the distal femurs identified regional variations in stress and strain parameters, similar to the variations in bone growth rates measured using fluorochrome labeling. A linear regression analysis supports the hypothesis that high compressive stresses are correlated with lower bone growth rates. However, for the loading conditions considered in this study, the variations in mechanical stress and strain parameters explain no more than 15% of the overall variations in bone growth rates. The greatest variations in both growth rates and mechanical stresses were present in the anterior frontal plane from the 42 day age group, in which correlations between reduced bone growth rates and compressive stresses were much stronger (r2 up to 0.80).

A new method for theoretical analysis of static indentation test

A new mathematical method was developed to study the indentation problem of an infinite elastic layer overlaid on a rigid foundation. Rigid, flat-ended cylindrical or spherical indenters are pressed onto the upper surface of the elastic layer causing a small deformation mode. Shear stresses between the indenter and the layer are assumed negligible and the layer is assumed to be either bonded or unbonded to the rigid foundation. The problem is equivalent to a mixed boundary-value problem of the theory of elasticity. Instead of using the Fredholm integral equation reported in the literature, the new approach obtained closed-form solutions through an infinite series. Convergence can be achieved using less than 10 terms of the series.

Initial in vitro stability of the tibial component in a canine model of cementless total knee replacement

The tibial component of a canine cementless total knee replacement model was used to determine the degree to which pegs and screws contributed to the initial in vitro stability of the device. Three implant designs were investigated: (1) a four-peg implant in which cortical bone screws passed through the pegs, (2) the four-peg implant without adjuvant screw fixation, and (3) a flat implant with screws placed in the same positions as in the first design. For measuring the interface motion, the tibial component and proximal tibia were modeled as rigid bodies and an experimental method was developed which permitted all six degrees of freedom of the motion between these two objects to be determined. In tests performed to validate this methodological approach, the potential confounding influences of tibial deformation and differential amounts of tibial deformation with the use of screws or pegs were shown to be minimal, supporting the use of the rigid-body method. In general, the areas of greatest motion were at the periphery of the bone-implant interface, regardless of whether or not screws or pegs were used. The components secured with screws had up to five-fold reductions in interface motion compared to components which had pegs but lacked screw fixation. Components with pegs and screws and components with screws only had the same amount of interface motion. Thus, in the presence of screw fixation, the addition of pegs did not increase the stability of the tibial component.

Effects of fixation technique on displacement incompatibilities at the bone-implant interface in cementless total knee replacement in a canine model

Bone-implant displacements can be caused by rigid body motion and by differences in material properties of the implant and bone. In the present study of the tibial component in total knee replacement, we tested a series of tibial component fixation designs to determine how certain design features influenced the magnitude of the tangential displacement between the component and supporting bone in a canine model. The transverse expansion of the proximal tibia under static axial loading was measured in the intact tibia and then in the same bone following implantation of tibial components with different interface characteristics: cementless flat smooth, cementless flat porous-coated, cementless flat porous-coated with screws, cementless pegged porous-coated, cementless pegged porous-coated with screws, cemented pegged, and cemented pegged with screws. In all cases, the magnitude of the transverse expansion increased with higher applied loads. When the statistical analysis was restricted to the cementless interfaces, the presence/absence of the porous coating, the presence/absence of pegs, and the use of screws had no significant influence on tibial expansion. However, in an analysis including the cemented and cementless pegged components, tibial expansion was reduced with the use of screws. The magnitude of the interface motion due to these displacement incompatibilities was approximately fivefold lower than the amount of interface motion related to rigid body motion found in a separate study with the canine model. The measured expansion was similar in the intact tibiae and the implanted tibiae, suggesting that the transverse constraint in the canine proximal tibia must be provided by the surrounding cortical ring rather than the subchondral bone.