Influence of Orthogonal Overload on Human Vertebral Trabecular Bone Mechanical Properties

Authors

  • Arash Badiei,

    1. Bone and Joint Research Laboratory, Institute of Medical and Veterinary Science, Adelaide, Australia
    2. School of Medical Sciences, Discipline of Pathology, University of Adelaide, Adelaide, Australia
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  • Murk J Bottema,

    1. School of Informatics and Engineering, Flinders University, Adelaide, Australia
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  • Nicola L Fazzalari

    Corresponding author
    1. Bone and Joint Research Laboratory, Institute of Medical and Veterinary Science, Adelaide, Australia
    2. School of Medical Sciences, Discipline of Pathology, University of Adelaide, Adelaide, Australia
    • Address reprint requests to: Nicola Fazzalari, PhD Division of Tissue Pathology, Bone and Joint Research Laboratory, IMVS, Frome Road, Adelaide, South Australia 5000, Australia
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  • The authors state that they have no conflicts of interest.

Abstract

The aim of this study was to investigate the effects of overload in orthogonal directions on longitudinal and transverse mechanical integrity in human vertebral trabecular bone. Results suggest that the trabecular structure has properties that act to minimize the decrease of apparent toughness transverse to the primary loading direction.

Introduction: The maintenance of mechanical integrity and function of trabecular structure after overload remains largely unexplored. Whereas a number of studies have focused on addressing the question by testing the principal anatomical loading direction, the mechanical anisotropy has been overlooked. The aim of this study was to investigate the effects of overload in orthogonal directions on longitudinal and transverse mechanical integrity in human vertebral trabecular bone.

Materials and Methods: T12/L1 vertebral bodies from five cases and L4/L5 vertebral bodies from seven cases were retrieved at autopsy. A cube of trabecular bone was cut from the centrum of each vertebral body and imaged by μCT. Cubes from each T12/L1 and L4/L5 pairs were assigned to either superoinferior (SI) or anteroposterior (AP) mechanical testing groups. All samples were mechanically tested to 10% apparent strain by uniaxial compression according to their SI or AP allocation. To elucidate the extent to which overload in orthogonal directions affects the mechanical integrity of the trabecular structure, samples were retested (after initial uniaxial compression) in their orthogonal direction. After mechanical testing in each direction, apparent ultimate failure stresses (UFS), apparent elastic moduli (E), and apparent toughness moduli (u) were computed.

Results: Significant differences in mechanical properties were found between SI and AP directions in both first and second overload tests. Mechanical anisotropy far exceeded differences resulting from overloading the structure in the orthogonal direction. No significant differences were found in mean UFS and mean u for the first or second overload tests. A significant decrease of 35% was identified in mean E for cubes overloaded in the SI direction and then overloaded in the AP direction.

Conclusions: Observed differences in the mechanics of trabecular structure after overload suggests that the trabecular structure has properties that act to minimize loss of apparent toughness, perhaps through energy dissipating sacrificial structures transverse to the primary loading direction.

INTRODUCTION

Trabecular structure has almost certainly evolved to provide a high level of functionality. Bone strength, the ability of the bone to withstand fracture, is obviously an important property of bone. However, fractures and bone damage are inevitable, and so other desirable properties of bone are its ability to function subsequent to damage and its ability to repair damage. Vertebral fractures, commonly associated with osteoporosis, ranging from mild wedge compressions to severe crush fractures, are believed to be silent in two thirds of women,(1) indicating that, despite structural failure, vertebra remain in a loaded environment where they transmit functional loads through the spine.(2) Further evidence comes from callus formation(2) on individual trabeculae across a number of anatomical sites.(3,4) This indicates that the trabecular structure can sustain damage, undergo repair, and still maintain function. The question of how trabecular structure is able to maintain mechanical integrity and function after sustaining damage remains largely unanswered.

A number of studies have attempted to address this question. Fyhrie and Schaffler(5) reported a qualitative assessment of the mechanisms of failure in human vertebral trabecular bone when loaded in the anatomical superoinferior direction. Their observations indicate that when large compressive strains are applied to vertebral trabecular bone, the majority of the damage is limited to elements transverse to the loading direction, with damage to vertical elements being mainly microscopic “internal matrix microdamage.” They did not study whether the failure mechanisms during transverse loading would have similar outcomes. Fazzalari et al.(6) carried out monotonic mechanical testing on intertrochanteric biopsies from the proximal femur and evaluated the microdamage postfailure. Their observations showed a link between age, structural microdamage, and mechanical integrity. However, the relationship between the principal axis of loading of the proximal femur and the spatial arrangement of the structure of trabecular bone is much more complex compared with that of the vertebral body. Therefore, whereas not directly applicable to the vertebral body, their study does provide insight into some of the general failure mechanisms of trabecular bone. Similarly, studies by Keaveny et al. of the postyield mechanics of bovine tibial(2) and human vertebral trabecular bone(7) and Kopperdahl et al.(8) of whole vertebral bodies provided further insight into the failure mechanisms of trabecular bone. These overload-release-reload studies highlighted many aspects of trabecular bone damage behavior, including observations that indicate postyield behavior may be dominated by the ultrastructural material properties of trabecular bone.(2,7,8) These studies provided information on the damage behavior of trabecular bone after overloading in the principal anatomical loading direction. The authors did not study whether off-axis (transverse) loading would result in similar observations.

Although the aforementioned studies focus on the principal anatomical loading direction, the structural and mechanical anisotropy is largely overlooked. A number of studies have considered monotonic failure mechanics of vertebral trabecular bone in orthogonal directions.(9–11) These studies focused on the relative difference between failure loads in orthogonal directions and not the influence of failure mechanics orthogonal to initial failure. With findings by Mosekilde and Viidik(10) showing that the vertebral strength anisotropy index (ratio of longitudinal to transverse strength) increases with age, the question regarding the mechanical relationship between longitudinal and transverse elements and the consequences of that relationship on global mechanical integrity arises. The aim of this study was to investigate the effect of initial overload on the mechanical integrity of trabecular bone in the orthogonal direction to the initial overload.

MATERIALS AND METHODS

The study included vertebral bodies from 12 cases (9 men and 3 women) with a median age of 68 yr (range, 53–83 yr). At postmortem examination, the T12/L1 vertebral bodies from five cases (four men and one woman) and the L4/L5 vertebral bodies from the remaining seven (five men and two women) were collected.

All vertebral bodies were wrapped in saline-soaked gauze and stored at −30°C immediately after collection. A cube of trabecular bone 10 × 10 × 10 mm was obtained from the centrum of each vertebral body by cutting through the frozen vertebral bodies using a low-speed diamond blade saw (Model 660; Southbay) under constant water irrigation. A goniometer mounted on the saw ensured the trabecular bone alignment of all cubes corresponded to the superoinferior and anteroposterior alignments of their vertebral bodies. Exact dimensions of cubes were measured using digital calipers.

Cubes from each T12/L1 and L4/L5 pair were assigned to either superoinferior (SI) or anteroposterior (AP) mechanical testing groups using a random selection process; a random number generator (Matlab; Mathworks) provided a number between 0 and 1 and cubes assigned to SI for numbers >0.5 and AP for ≤0.5. Because cube pairs were collected from adjacent vertebral bodies, once one of the pair was assigned to an SI or AP group, the adjacent cube was automatically assigned to the other group. Final assignments resulted in three, two, four, and three (T12, L1, L4, and L5, respectively) cubes assigned to SI and two, three, three, and four (T12, L1, L4, and L5, respectively) cubes assigned to AP.

Trabecular bone cubes were imaged using a Skyscan 1072 X-ray μCT system (Skyscan; 80 kV, 120 μA, 1-mm Al filter, and four-frame averaging) providing a spatial resolution of ∼16 × 16 × 16 μm. Tomographic images obtained from scanning were smoothed with a Gaussian filter using CTAn software (Skyscan) to reduce noise.(12) Next, images were segmented to either a bone or background phase (i.e., binary) using custom written software in Matlab (Mathworks) using Otsu's global thresholding algorithm.(13) A CTAn component-labeling routine was used on the 3D structure to remove any unconnected components.(14) The trabecular structure was analyzed to obtain global average architectural parameters. Standard model-independent 3D algorithms were used to calculate the bone volume fraction (BV/TV; %), specific surface (BS/BV; mm2/mm3), total surface (BS/TV; mm2/mm3), trabecular thickness (Tb.Th; μm), trabecular separation (Tb.Sp; μm), and trabecular number (Tb.N; /mm).(12,15–17) The preferential alignment of the trabecular structure was quantified using the degree of anisotropy (DA). DA is a scalar quantity defined as the ratio between the maximum and minimum of the ellipsoid that best describes the mean intercept length based anisotropy of the 3D structure.(18–20) DA = 1 indicates isotropy, whereas DA > 1 indicates anisotropy or preferential alignment. Trabecular bone pattern factor (TBPf; /mm) was computed to quantitatively describe the ratio of intertrabecular connectivity. TBPf is an index of relative surface convexity or concavity.(21) In the case of well-connected trabecular bone, TBPf has small values, and in the case of isolated trabeculae, TBPf results in larger values. Structure model index (SMI) was computed to quantify the prevalence of rod-like and plate-like elements within the trabecular structure, where an ideal plate, ideal cylinder, and ideal sphere have SMI values of 0, 3, and 4, respectively.(22) Connectivity was measured by computing the number of redundant elements in the trabecular structure through the Euler number.(18,19) The connectivity density (Conn.D; /mm3) was defined as the connectivity, normalized by the volume of the structure.(18) The algorithms and definitions of these parameters are also described elsewhere.(12,15–18,21–23) All parameters were computed using CTAn software provided by the manufacturer of the μCT system. To ensure the principal trabecular orientation of cubes corresponded to the anatomical trabecular alignment, principal orientation within each cube was measured (mean ± SD) using custom written software (Matlab; Mathworks) for both coronal (86 ± 19°) and sagittal (86 ± 9°) planes.

All mechanical testing was carried out on a universal testing machine (Hounsfield, H25KM) controlled by a personal computer and custom-designed software. All samples were tested to 10% apparent strain by uniaxial compression according to their SI or AP allocation. Thus, cubes assigned to SI were positioned such that anatomical SI was parallel to the load train, whereas cubes assigned to AP were positioned such that anatomical AP was parallel to the load train. The compressive load was produced by displacement (rate of 1 mm/min) of a screw-driven upper platen onto unsupported samples placed on a lower fixed platen.(6,9,10,24) Strain was measured using the displacement of platens.(6,9) As suggested by Fazzalari et al.,(6) a 0.14-mm-thick layer of latex (Skin Shield; Livingstone Pty) was used on each end of the bone cubes to provide stability for free trabecular ends and maximize the contact area between sample and the machine. To minimize the effects of misalignment, a pivoting platen was used in the load train.(10,24) All tests were stopped at 10% apparent strain.

To elucidate to what extent structural elements in the orthogonal directions to overload affect the mechanical integrity of cubes, all cubes were consecutively mechanically tested, to 10% apparent strain, in the direction orthogonal to the initial test. Thus, cubes initially assigned to SI were first overloaded in the SI direction and then overloaded in the AP direction. This group will be referred to as S/A (Fig. 1). Similarly, cubes initially assigned to AP were first overloaded in the AP direction and then overloaded in the SI direction. This group will be referred to as A/S (Fig. 1). Because of the nature of the experiment described above, the standard platen test had to be used in place of the protocol suggested by Keaveny et al.(25) for compression tests involving trabecular bone, because samples could not be embedded in brass endcaps.

Figure Figure 1.

Schematic diagram of the overload experiments. For the SI group, the first overload was in the superoinferior direction (SI) followed by a second overload in the anteroposterior direction (S/A). For the AP group, the first overload was in the anteroposterior direction (AP) followed by a second overload in the superoinferior direction (A/S).

After mechanical testing, cube dimensions and data from the load-deformation curves were used to compute the apparent ultimate failure stresses (UFS), apparent elastic moduli (E), and apparent toughness moduli (u) for both first and second overloads. Failure was defined as the point of maximal stress in the stress-strain curve, elastic modulus as the maximal slope of the elastic region of the stress-strain curve and modulus of toughness as the area under the stress-strain curve up to the point of failure.(2,6,9,10,24,26,27) Machine compliance was tested using the protocol suggested by Turner and Burr.(24) No correction was applied for machine compliance as machine stiffness was found to be greater than the apparent stiffness of trabecular bone samples.(24)

Regression analyses (least squares linear analyses) were used to test relationships between variables. Statistical differences between group means were tested using ANOVA and Student's t-test. Tukey's posthoc test was used to identify groups that achieved significance from ANOVA. Statistical differences in regression line slopes were analyzed using analysis of covariance (ANCOVA). Statistical analyses were performed using both Matlab (Mathworks) and SPSS (SPSS Inc.).

RESULTS

Bone architecture

No significant difference (p > 0.05) in BV/TV or architectural parameters was found between men and women. Similarly, no statistically significant difference (p > 0.05) was observed for mean BV/TV between pairwise combinations of cubes (Table 1), between cubes from T12/L1 and those from L4/L5 (Table 2), or between cubes assigned to SI and those assigned to AP testing groups (Table 3).

Table Table 1.. Mean ± SD of μCT-Based BV/TV and Architectural Parameters of Cubes From the Spinal Segments T12, L1, L4, and L5
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Table Table 2.. Mean ± SD of μCT-Based BV/TV and Architectural Parameters of Cubes From T12/L1 and L4/L5 Pairings
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Table Table 3.. Mean ± SD of μCT-Based BV/TV and Architectural Parameters of Cubes Assigned to SI and AP Testing Groups
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Statistically significant differences in SMI were identified between cubes from L4 vertebrae and those from both T12 (p = 0.02) and L1 (p = 0.04) vertebrae (Table 1). No statistically significant (p > 0.05) differences in architectural parameters were observed for any other pairwise combination of cubes. Significant differences were also found for mean Tb.N (p = 0.03), DA (p = 0.01), TBPf (p = 0.04), and SMI (p = 0.01) between T12/L1 and L4/L5 cubes (Table 2). However, no significant differences in architectural parameters were found between cubes assigned SI and those assigned to AP testing directions (Table 3).

First overload in the SI and AP directions

Mean UFS, mean E, and mean u were significantly (p < 0.05) greater in the SI group than in the AP group (76%, 84%, and 61%, respectively), with the expected strong positive linear relationship between UFS and E(28,29) seen in both groups (r2 = 0.95, p < 0.001 and r2 = 0.70, p < 0.001, respectively).

UFS was positively correlated to BV/TV in both SI and AP groups (Table 4; Figs. 2A and 2B), whereas u was only significantly correlated to BV/TV in the SI group (Table 4). E was positively correlated to BV/TV in both the SI [ESI = 0.16(BV/TVSI)2.5] and AP [EAP = 0.01(BV/TVAP)2.9] groups (Table 4). Different linear relationships between trabecular architecture and mechanics were observed in the two groups. In the SI group, significant linear relationships were observed between UFS and Tb.Th, whereas significant linear relationships were observed between u and both BS/TV and Tb.N. Significant linear relationships between E and BS/BV and E and Tb.Th were also observed (Table 4). In the AP group, significant linear relationships between UFS and the architectural parameters BS/TV, Tb.Sp, Tb.N, and Conn.D were found. The same set of architectural parameters was also significantly correlated with E (Table 4). No significant linear relationships were identified between u and any of the architectural parameters in this group (Table 4).

Table Table 4.. Coefficient of Determination (r2) and Significance Between First Overload Mechanical Parameters and μCT-Based BV/TV and Architectural Parameters for Sample From SI and AP Groups
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Figure Figure 2.

(A) Relationship between UFS and BV/TV for SI mechanical tests. SI indicates first overload results from the SI group, and A/S indicates superoinferior overload results from samples with prior AP overload. UFSSI = 0.334BV/TVSI – 2.16 (nSI = 12, r2SI = 0.77, p < 0.001); UFSA/S = 0.170BV/TVA/S – 0.55 (nA/S = 12, r2A/S = 0.38, p < 0.04). Regression lines for SI data are shown as a solid line, and regression lines for A/S data are shown as a broken line. No significant difference was found between the slopes of the regression lines (p = 0.08). (B) Relationship between UFS and BV/TV for AP mechanical tests. AP indicates first overload results from the AP group, and S/A indicates anteroposterior overload results from samples with prior SI overload. UFSAP = 0.069BV/TVAP – 0.41, (nAP = 12, r2AP = 0.54, p < 0.007); UFSS/A = 0.066BV/TVS/A – 0.42 (nS/A = 12, r2S/A = 0.67, p < 0.002). Regression line for AP data is shown as a solid line, and regression line for S/A data is shown as a broken line. No significant difference was found between the slopes of the regression lines (p = 0.88).

Second overload in the orthogonal direction

Mean UFS, mean E, and mean u were significantly greater in the A/S group compared with S/A group (77%, 89%, and 46%, respectively), similar to the relationship seen in the SI and AP groups. As expected,(28,29) in the A/S and S/A groups, UFS was positively correlated with E (r2 = 0.92, p < 0.001 and r2 = 0.49, p = 0.01, respectively).

UFS showed significant and positive linear correlation with BV/TV in both the A/S (Fig. 2A) and S/A groups (Fig. 2B; Table 5). No significant difference was observed between the slope of the regression lines for the SI and A/S (p = 0.08, Fig. 2A) or the AP and S/A (p = 0.88, Fig. 2B) groups. No significant relationship was found between E and BV/TV (Table 5).

Table Table 5.. Coefficient of Determination (r2) and Significance Between Second Overload Mechanical Parameters and μCT-Based BV/TV and Architectural Parameters
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Linear relationships between the mechanical parameters and the architectural parameters for the second overload tests showed a contrast to those seen in the first overload tests. In the A/S group, TBPf was the only architectural parameter to show a significant linear relationship with mechanical parameters (Table 5). In the S/A group, Tb.Th was the only architectural parameter to show a significant linear relationship to UFS, whereas both BS/TV and Tb.Th were identified as having significant linear relationships with u. None of the architectural parameters showed a significant linear correlation to E (Table 5).

Differences in SI to AP mechanical properties (UFS, E, and u) were greater than differences identified in SI or AP mechanical properties after overloading in the orthogonal direction. Mechanical properties were significantly greater in SI than AP (UFS: 76%, E: 84%, and u: 61%) and significantly greater in A/S than S/A (UFS: 77%, E: 89%, and u: 46%) compared with the differences found between SI and A/S (UFS: 9%, E: 10%, and u: 10%, p > 0.05; Table 6) or between AP and S/A (UFS: 15%, u: 20%; p > 0.05). However, mean E was significantly greater in the AP group than the S/A group (p = 0.03; Table 7). No significant difference (p = 0.89) was found between the slopes of the regression lines between UFS and E for SI and A/S (Fig. 3A) or AP and S/A (p = 0.24; Fig. 3B).

Table Table 6.. Mean ± SD and Percent Difference From Mechanical Tests in the SI Direction
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Table Table 7.. Mean ± SD and Percent Difference From Mechanical Tests in the AP Direction
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Figure Figure 3.

(A) Relationship between UFS and E for SI mechanical tests. SI indicates first overload results from the SI group, and A/S indicates superoinferior overload results from samples with prior AP overload. UFSSI = 0.020ESI + 0.07 (nSI = 12, r2SI = 0.95, p < 0.001); UFSA/S = 0.020EA/S + 0.05 (nA/S = 12, r2A/S = 0.92, p < 0.001). Regression line for SI data is shown as a solid line, and regression line for A/S data is shown as a broken line. The two regression lines overlap. No significant difference was found between the slopes of the regression lines (p = 0.89). (B) Relationship between UFS and E for AP mechanical tests. AP indicates first overload results from the AP group, and S/A indicates anteroposterior overload results from samples with prior SI overload. UFSAP = 0.020EAP + 0.13 (nAP = 12, r2AP = 0.70, p < 0.001); UFSS/A = 0.034ES/A + 0.06 (nS/A = 12, r2S/A = 0.48, p < 0.02). Regression line for AP data is shown as a solid line, and regression line for S/A data is shown as a broken line. No significant difference was found between the slopes of the regression lines (p = 0.24).

DISCUSSION

The mean magnitudes of UFS and E for the SI and AP groups were similar to those reported by Mosekilde et al.(10) and others,(9,30,31) with slight differences likely to be caused by difference in cohort age and test protocols. In addition, relationships between bone volume fraction and mechanical parameters for these groups were similar to those reported by others.(9,29,31)

A number of investigators(9–11) have shown the presence of mechanical anisotropy in vertebral trabecular bone, and results from this study complement those findings. SI mechanical properties were greater than AP mechanical properties, despite the fact that there was no significant difference in global BV/TV or global architecture between cubes randomly assigned to the SI and AP groups. Even after overload in the orthogonal direction, UFS, E, and u were greater in magnitude for the A/S group than the S/A group. Hence, the mechanical anisotropy observed in this study and by others(9–11) was still present after the trabecular structure was mechanically overloaded in the orthogonal direction. Moreover, the mechanical anisotropy was greater when comparing SI with AP or A/S with S/A than differences found before and after overload in the orthogonal direction. Thus, mechanical anisotropy resulted in greater differences between SI and AP mechanical properties compared with differences resulting from overloading the structure in the orthogonal direction.

No significant difference was found between the SI and A/S groups in terms of mean UFS and mean u. Similarly, no significant difference was found between the AP and S/A groups in terms of mean UFS and mean u. In contrast, E was found to be 35% less in the S/A group than the AP group. No such difference was found between SI and A/S groups. These results suggest that overloading in the AP direction had little effect on the SI mechanical integrity, whereas overloading in the SI direction had the effect of reducing the apparent elastic modulus in the AP direction. This, combined with the observation that apparent ultimate failure stress was not significantly different from the cubes mechanically tested under first overload, suggests the energy required to cause failure, that is, modulus of toughness, is determined by strain to failure. This property acts as a protection mechanism for the maintenance of a functional trabecular structure.

These findings are supported by the work of Fyhrie and Schaffler(5) and others.(2,7,8,32,33) Fyhrie and Schaffler took cubes of vertebral trabecular bone and performed uniaxial mechanical testing past the point of failure. Samples were analyzed both macro- and microscopically. They found that macroscopic damage from SI testing resulted in little or no structural damage to SI trabecular elements, with virtually all damage restricted to horizontal trabecular elements transverse to the SI loading direction. These horizontal elements were found to have failed by (1) “fracturing off at the base from connection to a vertical trabecula,” (2) “split along the axis,” or (3) “broken in the middle.” Microscopic examination highlighted that superoinferior elements were grossly intact but did “sustain internal matrix microdamage.” They suggested that these failure mechanisms allow trabecular bone to recover its initial form even though the apparent elastic modulus of the structure would be diminished. They suggest this pattern of damage is a mechanism that may allow the trabecular bone to heal and restore close to original function. The observations of Fyhrie and Schaffler(5) go part way to explaining why, in this study, a 35% decrease in apparent elastic modulus was noted in cubes overloaded in the SI direction than overloaded in the AP direction (S/A group). In this study, even though no micro- or macroscopic examinations were carried out, the range and magnitude of UFS in combination with the fact that mechanical tests were overload tests suggests that the damage sustained to the trabecular structure would have been similar to that observed by Fyhrie and Schaffler.

Fyhrie and Schaffler did not look at the effect of transverse element failure on longitudinal elements. In this case, this study's results suggest that the failure mechanism for AP compression differs from that of SI compression. This is further supported by the observations that mechanical anisotropy differences, that is, SI versus AP, were greater than differences induced through overloading in the orthogonal direction. This highlights a structural property that may have significant influence on trabecular bone damage mechanics.

Keaveny et al.(2) carried out postfailure tests on bovine proximal tibia trabecular bone, where reduced-section cylinders of trabecular bone were tested to different strains (1%, 2.5%, 4%, and 5.5%), unloaded to 0% strain, and reloaded to 9% strain. They found that modulus was reduced in all tests, whereas strains of ≥2.5% were required to produce reductions in strength. In general, their findings suggest that compromising the trabecular structure leads to a greater reduction in modulus than strength. Comparable findings were also shown in human vertebral trabecular bone(7) and in the whole vertebral body.(8) Similar to the hypotheses of Fyhrie and Schaffler,(5) Keaveny et al. suggested that trabecular bone has ultrastructural material properties that aid the trabecular structure in maintaining function and healing subsequent to damage.

Wang et al.(32) mechanically tested samples of bovine proximal tibia bone by compressive overloading followed by torsional overloading. In a subsequent study, Wang and Niebur(33) mechanically tested similar bovine proximal tibia samples by torsional overloading followed by compressive overloading. In each study, a number of microdamage variables were measured. In comparing the two studies, Wang et al. concluded that the percentage of the original microcracks that propagated because of compressive overloading followed by torsional overloading were significantly greater than those from torsional overloading followed by compressive overloading.(33) Although the type of bone and the modes of loading differ to this study, Wang et al. provided insight into the underlying mechanisms of trabecular bone damage properties and further supported the notion that material properties at the ultrastructural level help to dissipate energy and increase the energy required to cause failure.(6,32)

Taken together, the findings of these previous studies and this study suggest a complex relationship between the failure mechanisms and mechanical roles of longitudinal and transverse elements of the vertebral body. One explanation of the observations is that, in addition to the mechanical support role of the transverse elements, they may have a significant role in the dissipation of energy during trauma to the trabecular structure. In effect, they may act as sacrificial elements in a crumple-zone allowing energy to be dissipated away from the main longitudinal elements, thereby minimizing damage to these primary elements, analogous to the crumple zones in modern vehicles. In the context of aging and osteoporosis, one could speculate that the loss or reduction in the thickness of these transverse elements(34,35) would result in the trabecular structure having less protection and thus resulting in more significant damage during trauma, which, if not given the appropriate time and conditions to heal, would result in further damage leading to failure.

Unlike previous studies investigating trabecular bone damage,(2,5,7,8) here μCT-based model-independent architectural parameters were also measured. Results comparing architectural parameters with SI and AP group mechanics showed results similar to those found by other investigators.(36–38) In the SI group, significant relationships were observed between UFS, E, and u and a number of architectural parameters, including BS/BV, BS/TV, Tb.Th, and Tb.N (Table 4). In contrast, architectural parameters showed a different contribution to the AP group mechanical properties, where UFS and E showed significant relationships to BS/TV, Tb.Sp, Tb.N, and Conn.D, and no significant relationships were identified between u and any architectural parameters (Table 4). These results highlight that, in AP loading, the spatial arrangement and connectivity of the trabecular structures play a more significant role than just Tb.Th. This is in contrast to longitudinal loading and further supports the notion that there are differences between longitudinal and AP element response to mechanical loading.

With the A/S and S/A groups, the relationships between mechanical parameters and architecture were different to that seen for the SI and AP groups. Significant relationships were found with TBPf, Tb.Th, and BS/TV for the A/S and S/A groups (Table 5). The relationship between UFS and u with BV/TV was weaker for the A/S tests than the first overload mechanical results of the SI group, yet for S/A tests, this relationship was even stronger than that seen for the AP group. The fact that no statistically significant differences were found between the A/S and SI groups for mean UFS, mean E, and mean u, yet the relationship between architectural and mechanical parameters were different, indicates that the structural basis for the relationship must have changed. This, together with the observation that a significant 35% reduction in E was found between the S/A and AP groups, also indicates differences in mechanical response between AP and longitudinal directions.

Work by Keaveny et al.(25) suggested that the platen compression test has inherent systemic and random errors that contribute to underestimation of mechanical properties. The protocol presented by Keaveny et al. includes embedding samples in brass endcaps. In this study, each sample was tested twice, once in each of the two directions. This precludes the use of endcaps. Also, whereas the suggested protocol is of importance in determining absolute values, the systemic errors addressed by the protocol of Keaveny et al. are not critical in this study because differences between errors are examined. As such, the mechanical testing protocol presented is valid. In addition, cube dimensions were measured once before initial mechanical testing. These cube dimensions were used throughout the experiment, even though mechanical testing would have induced small changes to the cube dimensions. Given the observations of Fyhrie and Schaffler(5) that, on average, after release of compressive load, at least 96% of the original height of vertebral cubes samples compressed to 85% of their original height is regained, errors induced by the use of the original cube dimensions were considered negligible.

Given this study's small sample size, a certain degree of uncertainty resulting from the distribution of samples from different vertebral levels was expected. Slight differences in mechanical properties were expected between vertebral levels. However, the analyses suggested the spread was even. Architectural differences identified included differences in Tb.N, DA, TBPf, and SMI between T12/L1 and L4/L5 cubes. However, because cubes from T12/L1 and L4/L5 were distributed between the SI and AP groups, variability was also distributed between groups. Similarly, variability introduced by differences in SMI between T12 and L4 and L1 and L4 were also distributed between the SI and AP groups.

In summary, this study highlighted differences between the longitudinal and AP elements of vertebral trabecular bone. Differences in mechanical response were found between SI and AP directions after overload in the orthogonal direction. The mechanical anisotropy of vertebral trabecular bone far exceeded any differences induced by overloading the structure in the orthogonal direction. Similarly, underlying relationships between trabecular architecture and mechanical properties were also found to be different for the two directions. These observations suggest that the trabecular structure has properties that minimize loss of apparent toughness, perhaps through energy dissipating sacrificial structures transverse to the primary loading direction.

Acknowledgements

The authors thank H Tsangari and R Davies for cutting the cubes from the vertebral bodies. Thanks are extended to the mortuary staff of the Division of Tissue Pathology (IMVS) for sample collection, the Department of Orthopaedic and Trauma (University of Adelaide) for access to the biomechanics laboratory, and Adelaide Microscopy (University of Adelaide) for access to the μCT imaging facilities. We also thank Drs Ian Parkinson and Julia Kuliwaba for suggestions on the manuscript. This work was supported by funding from the NH&MRC, APA scholarships, and the University of Adelaide.

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