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Keywords:

  • trabecular bone;
  • microstructural parameters;
  • micro-CT;
  • multivariate regression analysis;
  • greater tubercle

Abstract

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS
  5. DISCUSSION
  6. REFERENCES

In the present study the trabecular microstructural parameters (bone volume fraction, trabecular thickness, trabecular separation, trabecular number, connectivity density, degree of anisotropy, and structure model index) of the greater tubercle of the humeral head were measured for human healthy, human osteopenic, ovine, bovine, and porcine bones using micro-computed tomography. Except for trabecular thickness and degree of anisotropy the values of the trabecular microstructural parameters generally differed significantly between species. Thus, only the species for which the implant is designed should be used for in vitro mechanical tests on the stability of implants in trabecular bone. Multivariate regression analysis showed that the microstructural parameters have similar principal interrelations in all species. The most significant relations were found between trabecular thickness and bone volume fraction (median (over all species) p < 0.001), trabecular number and bone volume fraction (p = 0.001), the structural change from plates to rods and bone volume fraction (p < 0.001) as well as between connectivity density and trabecular number (p < 0.001). Trabecular thickness, trabecular number, and the structural change from plates to rods each contributed to the bone volume fraction approximately to the same extent. Based on the similar principal interrelations of the trabecular microstructural parameters found in all investigated species the design of trabecular microstructure in the greater tubercle follows similar phenomenological mechanisms in all species. Thus, in vivo experiments on trabecular bone healing and osteoporosis research for application in humans can be conducted in ovine, bovine, or porcine species. © 2011 Orthopaedic Research Society Published by Wiley Periodicals, Inc. J Orthop Res 30:429–434, 2012

The microstructure of human trabecular bone has frequently been measured and analyzed using a variety of bones including the vertebra, iliac crest, pelvis, femur, tibia, patella, calcaneus, radius, humerus, and mandible.1–12 From comparative studies a wide range of microstructural parameters is reported, depending on donor age, bone type, and bone region.1, 2, 4–11 The variation in the trabecular microstructure between different species has been less frequently investigated. Mullender et al.13 determined trabecular microstructural parameters of the femoral head of five mammalian species (rat, rabbit, Rhesus monkey, pig, and cow) using two-dimensional microscopy. The dimensions of the trabecular structures of the rabbit, monkey, and pig were quite similar, whereas the rat and cow had quite different microstructural trabecular parameters. Swartz et al.14 measured the mid-element diameter and length of trabeculae from humeral and femoral heads of a variety of small, medium-sized, and large mammals, including a diversity of bats and non-flying mammals using two-dimensional macrophotography and photomicrography. The mid-element diameter and length were quite different depending on the species but showed no general dependence on body mass. Many studies have examined trabecular microstructure of the proximal femur and proximal humerus of different species of primates using micro-computed tomography (µCT) with a strong anthropological research background.15–17 Most studies found broad similarities in the trabecular microstructure across primates.

No study has investigated and compared the trabecular microstructure between different non-primate species using three-dimensional measurements and including a comprehensive set of microstructural parameters. Knowledge of interspecies differences between human healthy, human osteopenic, ovine, bovine, and porcine species is of special importance, since these species are used for the in vitro mechanical testing of bone anchoring implants, such as suture anchors,18–21 or for testing the bones directly.22, 23 Furthermore, animal in vivo experiments are commonly carried out to investigate the effect of medical treatments for bone healing and regeneration, which include the analysis of the trabecular microstructure.24, 25 However, it is not clear if and how the results of these tests can be applied from animal to human regarding the trabecular microstructure. Furthermore, no study has investigated the interrelation between trabecular microstructural parameters using multivariate analysis. The present study addresses these issues by measuring and comparing the trabecular microstructure of the greater tubercle of the humeral head in human healthy, human osteopenic, ovine, bovine, and porcine species. The greater tubercle is of great interest for the stability of suture anchors used for the repair of rotator cuff tears.18–21 Furthermore, a recent study found significant differences in the pullout strength of suture anchors at this site between different species.21

In the present study particular emphasis is placed on analyzing the interrelation between the trabecular microstructural parameters using multivariate regression analysis. The multivariate regression analysis avoids spurious relationships caused by confounding variables, which can lead to erroneous conclusions if two variables are directly related to each other (confounding effect in a narrower sense) or even lead to the wrong sign of the relation (Simpson's paradox).26 The interrelation study delivers new insights about the phenomenological mechanisms involved in the design of trabecular microstructure in the greater tubercle that are common for all species. For the first time, the present study includes three-dimensional measurement and comparison of the trabecular microstructure of human healthy, human osteopenic, ovine, bovine, and porcine species and the analysis of the interrelation between the microstructural parameters using multivariate analysis.

MATERIALS AND METHODS

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS
  5. DISCUSSION
  6. REFERENCES

Sixteen human humeri were collected from human donors aged between 30 and 93 years at the time of death. The humeri had no signs of any surgical intervention or pathologic condition. Eight fresh ovine, eight bovine, and eight porcine humeri were collected from animals between 4 and 6 months old. The specimens were obtained within 24 h post-mortem. The bone mineral densities (BMD) of the proximal trabecular bone of the human humeral heads were measured using a 64-slice computed tomography (CT) system (Somatom Sensation 64, Siemens AG, Erlangen, Germany). Based on the BMD measurements, eight humeral heads having a BMD >100 mg Ca-HA/ml were considered as healthy and eight humeral heads having a BMD <80 mg Ca-HA/ml were considered as osteopenic.

Rectangular trabecular bone samples with a size of 10 mm × 10 mm × 10 mm were cut out from the center of the greater tubercle perpendicular to the bone surface using a high precision band saw with water irrigation (EXAKT GmbH, Norderstedt, Germany). Using the same anatomical position for all specimens assures a good comparability between the specimens, since it is known that the bone density can vary with location within the humeral head.27, 28 The bone samples were scanned using µCT (µCT 20, SCANCO Medical AG, Brüttisellen, Switzerland) with an isotropic resolution of 26 µm.

The µCT scans were analyzed using the SCANCO IPL (Image Processing Language) software.5, 7, 29 After thresholding using an adaptive procedure the following microstructural parameters of the trabecular bone were measured directly and three-dimensionally. The bone volume fraction (BV/TV) was calculated using a tetrahedron meshing technique for the bone volume, the mean trabecular thickness (Tb.Th.) and the mean trabecular separation (Tb.Sp.) were determined by fitting maximal spheres inside and between the trabecular structure, respectively, the trabecular number (Tb.N.) was calculated as the inverse of the mean distance between the mid-axes of the trabecular structures, the degree of anisotropy (DA) was calculated as the ratio between the maximum and minimum radius of the mean intercept length (MIL) ellipsoid and the connectivity density (Conn.D.) was derived from the Euler number.3, 7, 29 Additionally, the structure model index (SMI) was calculated, which distinguishes between plate-like and rod-like trabecular structures.5 An SMI of 0 indicates an ideal plate-like structure and an SMI of 3 indicates an ideal rod-like structure. The direct and three-dimensional assessment of the microstructural parameters does not require any model assumption in contrast to the widely used indirect two-dimensional method where a model such as the plate model has to be assumed. Using the indirect approach the accuracy of the calculated parameters is not assured due to the complex nature of trabecular bone.7, 9, 29 Furthermore, in the indirect approach most microstructural parameters are derived from very few basic parameters, so that the microstructural parameters have a strong interrelation by definition. To account for the dependence of the trabecular microstructural parameters on the depth position relative to the bone surface11, 27, 28 the bone samples were divided into two volumes of interest (VOIs) of different depth positions. The first VOI starts directly beneath the cortical layer and ends 5 mm beneath the cortical layer (subcortical region) and the second VOI starts 5 mm beneath the cortical layer and ends 10 mm beneath the cortical layer (inner region). The microstructural parameters were measured separately in each VOI.

The values of the microstructural parameters were compared between the species using the global one-way ANOVA. When significance was shown, the Bonferroni multiple comparison test was utilized to assess the individual differences among the species. The interrelation of the microstructural parameters was determined using multivariate linear regression analysis including the t-test for calculating the probability value of the regression coefficients. The multivariate regression analysis considers the interrelations between all parameters simultaneously, that is, it adjusts the relation between two parameters for other influencing parameters so that confounding biases are avoided. In detail, the data points are fit to the following multivariate linear regression equation using the ordinary least squares method

  • equation image(1)

where xi is the dependent variable, xj are the independent variables, aij are the corresponding regression coefficients, ai0 is the intercept, and n is the number of variables. The matrix of the probability values (pij) of the regression coefficients is symmetric. The regression coefficients can be normalized in terms of the standard deviations of the corresponding independent and dependent variables, so that they are independent from scaling of the variables. By evaluating the standardized regression coefficients the strengths of the regressions can be compared between each other. The standardized regression coefficients (βij) can be obtained from the regression coefficients via the following equation

  • equation image(2)

where σj is the standard deviation of the independent variable (xj) and σi is the standard deviation of the dependent variable (xi). A probability value (p) of <0.05 (two-sided) was considered significant for all analyses.

RESULTS

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS
  5. DISCUSSION
  6. REFERENCES

The trabecular microstructural parameters in the subcortical and inner region are summarized in Tables 1a and 1b, respectively. Among all parameters, Conn.D. differed most significantly between the species. Tb.Th. and DA showed the smallest differences among the species; both values did not differ significantly between any two species. Tb.Sp. and SMI increased and BV/TV, Tb.N., and Conn.D. decreased with depth in all species. In particular, the porcine and bovine species showed a strong decrease of BV/TV of over 60% from the subcortical to the inner region, which was significantly stronger than in human healthy, human osteopenic, and ovine species.

Table 1a. Trabecular Microstructural Parameters (Mean ± Standard Deviation) in the Subcortical Region
 Human HealthyHuman Osteop.OvineBovinePorcine
BV/TV0.15 ± 0.050.09 ± 0.020.18 ± 0.010.22 ± 0.040.34 ± 0.05
Tb.Th. (mm)0.14 ± 0.030.12 ± 0.010.12 ± 0.010.13 ± 0.020.17 ± 0.02
Tb.Sp. (mm)0.72 ± 0.100.90 ± 0.130.54 ± 0.040.53 ± 0.040.41 ± 0.04
Tb.N. (1/mm)1.31 ± 0.161.09 ± 0.121.74 ± 0.121.80 ± 0.112.15 ± 0.16
DA2.13 ± 0.211.88 ± 0.301.85 ± 0.131.61 ± 0.271.84 ± 0.17
Conn.D. (1/mm3)3.91 ± 0.782.91 ± 0.809.24 ± 1.8710.19 ± 1.1910.19 ± 3.08
SMI1.21 ± 0.581.51 ± 0.290.79 ± 0.200.56 ± 0.33−0.18 ± 0.47
Table 1b. Trabecular Microstructural Parameters (Mean ± Standard Deviation) in the Inner Region
 Human HealthyHuman Osteop.OvineBovinePorcine
BV/TV0.13 ± 0.070.07 ± 0.030.15 ± 0.020.07 ± 0.030.13 ± 0.04
Tb.Th. (mm)0.17 ± 0.040.13 ± 0.020.13 ± 0.010.15 ± 0.050.10 ± 0.01
Tb.Sp. (mm)0.92 ± 0.131.08 ± 0.130.69 ± 0.091.22 ± 0.360.61 ± 0.07
Tb.N. (1/mm)1.06 ± 0.140.91 ± 0.091.38 ± 0.180.84 ± 0.261.59 ± 0.16
DA1.25 ± 0.081.32 ± 0.131.55 ± 0.121.68 ± 0.321.34 ± 0.09
Conn.D. (1/mm3)3.13 ± 0.982.05 ± 0.785.79 ± 1.882.22 ± 1.219.16 ± 2.05
SMI1.70 ± 0.731.93 ± 0.581.23 ± 0.321.92 ± 0.401.60 ± 0.54

The multivariate regression analysis was performed for all species separately (unpooled data). The multivariate regression analysis including all measured microstructural parameters revealed a very strong (equation image) and highly significant (p < 0.001) multicollinearity between Tb.N. and Tb.Sp. for all species. The simple relation between both parameters is plotted in Figure 1. A strong multicollinearity can lead to large standard errors and a high variability in parameter estimates30; to avoid these numerical problems Tb.Sp. was omitted from further multivariate regression analyses. In the multivariate regression of BV/TV against Conn.D., DA, Tb.Th., Tb.N., and SMI, BV/TV was a significant positive function of Tb.Th. and Tb.N. and a significant negative function of SMI for all species. Table 2 shows the mean (over all species) standardized regression coefficients as well as the corresponding median (over all species) probability values. The mean (over all species) coefficient of determination (R2) was 0.980. Based on the high R2 and the high and significant regression coefficients a high multicollinearity between BV/TV and Tb.Th., Tb.N., and SMI can be assumed and therefore BV/TV was not considered for the further multivariate regression analysis. The relation between Conn.D. and Tb.N. was highly significantly (p < 0.001) positive for all species in the multivariate regression analysis including Conn.D., DA, Tb.Th., Tb.N., and SMI. The simple function of Conn.D. versus Tb.N. is plotted in Figure 2. In addition, the standardized regression coefficients between SMI and Tb.Th., DA and Conn.D., and DA and Tb.N. had a probability value of <0.1 in four of the five species and the same sign in all species. The mean (over all species) standardized regression coefficients and the median (over all species) probability values of these relations are given in Tables 3a and 3b, respectively.

thumbnail image

Figure 1. Tb.Sp. as function of Tb.N. for all species.

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Table 2. Mean (over All Species) Standardized Regression Coefficients (β) and Median (over All Species) Probability Values (p) of the Multivariate Regression of BV/TV against Conn.D., DA, Tb.Th., Tb.N., and SMI (n.s.: Not Significant)
 Conn.D.DATb.Th.Tb.N.SMI
βn.s.n.s.0.4040.681−0.527
pn.s.n.s.<0.0010.001<0.001
thumbnail image

Figure 2. Conn.D. as function of Tb.N. for all species.

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Table 3a. Mean (over All Species) Standardized Regression Coefficients of the Multivariate Regression Analysis Including Conn.D., DA, Tb.Th., Tb.N., and SMI
 Conn.D.DATb.Th.Tb.N.SMI
Conn.D.n.s.−0.349n.s.1.114n.s.
DA−1.257n.s.n.s.1.412n.s.
Tb.Th.n.s.n.s.n.s.n.s.−0.714
Tb.N.0.7560.329n.s.n.s.n.s.
SMIn.s.n.s.−0.352n.s.n.s.
Table 3b. Median (over All Species) Probability Values of the Multivariate Regression Analysis Including Conn.D., DA, Tb.Th., Tb.N., and SMI
 Conn.D.DATb.Th.Tb.N.
DA0.059   
Tb.Th.n.s.n.s.  
Tb.N.<0.0010.043n.s. 
SMIn.s.n.s.0.005n.s.

DISCUSSION

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS
  5. DISCUSSION
  6. REFERENCES

The values of the measured microstructural parameters of the human healthy humerus fit very well in the general range obtained for different human bones using the same processing software as in the present study.7 In general, the values of the microstructural parameters differed largely between the species (Tables 1a and 1b). However, Tb.Th. showed quite small differences among all species, which were also found for the rabbit, monkey, pig, and cow in the literature.13 In addition, all microstructural parameters in general showed a high dependence on the depth position, however, the magnitude of the change depended on the species. The decrease of BV/TV in the greater tubercle with depth found in the present study was also observed by Meyer et al.28 The increase of Tb.Sp. and SMI and the decrease of BV/TV, Tb.N., and Conn.D. with depth was documented in the literature for the femur and tibia as well.11 In summary the values of the microstructural parameters generally depended on the species and on the depth position. Thus, for in vitro mechanical tests of the stability of bone anchoring implants in trabecular bone only the species for which the implant is intended, that is, typically human healthy or human osteopenic bone, should be used. Other species such as ovine, bovine, or porcine bone will not reproduce the same trabecular conditions as in the human.

BV/TV was a significant function of Tb.Th., Tb.N., and SMI in all species; a smaller thickness, a lower number and a structural change from plates to rods of the trabeculae each result in a lower BV/TV. The standardized regression coefficients of Tb.Th., Tb.N., and SMI have similar magnitudes (Table 2). Thus, Tb.Th., Tb.N., and SMI each contribute to a similar extent to changes in BV/TV. The positive influences of Tb.Th.1, 7, 9, 10, 12 and Tb.N. (and thus the negative influence of Tb.Sp.)1, 4, 6, 10, 12 and the negative influence of SMI5, 7, 9, 12 on BV/TV are mentioned in the literature, but the influences of the microstructural parameters were not analyzed simultaneously using multivariate analysis and only one species was considered. Moreover, the approximately equally strong influences of Tb.Th., Tb.N., and SMI on BV/TV have not been mentioned in the literature. Quantitatively, the authors can generally agree to the concept of changes in trabecular microstructure with aging developed by Weinstein and Hutson that closely spaced, thick trabecular plates, characteristic of a young person and high bone volume, are transformed into a widely spaced array of thin bars and struts, typical of the elderly and low bone volume.1

In all species, Conn.D. was significantly positively related to Tb.N. (Fig. 2; Tables 3a and 3b), which is in accordance with the literature.2–4, 12 Through the intermediation of Tb.N., Conn.D., and BV/TV were positively simple correlated using univariate (simple) regression analysis in conformance with the literature2–4, 12; the mean (over all species) R2 was 0.39 and the median (over all species) p-value was 0.004. Since, as the present study has found, BV/TV is strongly correlated with Tb.Th., Tb.N., and SMI and in addition simply correlated with Conn.D., BV/TV alone carries information on Tb.Th., Tb.N., SMI, and Conn.D. Therefore, BV/TV alone can describe the mechanical properties of trabecular bone for the most part in a predefined testing direction.4, 6, 23, 24, 31 However, the mechanical bone properties are, in addition to the dependence on BV/TV, a strong function of the testing direction and thus anisotropy parameters.4, 8, 31 Based on the finding of the present study that anisotropy is largely independent on BV/TV, parameters which describe the anisotropy may improve the prediction of mechanical properties considerably.

In the multivariate regression analysis Tb.Sp. was omitted due to the multicollinearity between Tb.N. and Tb.Sp. (Fig. 1); the omission of Tb.Sp. (and not Tb.N.) was arbitrary, the multivariate regression analysis including Tb.N. instead of Tb.Sp. led to the same significant results as the analysis described in the present study (data not shown). The results of the present study cannot be extrapolated with certainty to other published studies since the literature studies analyzed the microstructural parameters by means of univariate analysis methods and therefore are biased by the confounding effect. An example for the confounding effect is the relation between Conn.D. and BV/TV in the present study; in no species was a significant relation observed between both variables using multivariate regression analysis, however, in four of the five species the relation was significant using univariate regression analysis. Additionally, many literature studies mentioned used indirect two-dimensional measurement methods assuming the plate-model, which can result in inaccurate measurements of the microstructural parameters as mentioned in the Materials and Methods Section. The resolution of the µCT scans was 26 µm in the present study, which is far lower than the lowest measured values, which was about 100 µm for Tb.Th. for human osteopenic and porcine bones. Thus, the trabecular microstructure was resolved with sufficient precision. Body mass was not included as a variable in the analysis since humans and quadrupeds are expected to have very different loading magnitudes in the humerus relative to body mass. This view is supported by the study of Swartz et al.14 that found that trabecular size parameters are not functions of body mass. Furthermore, the present study has shown that the interrelations of the trabecular microstructural parameters are similar among the species without considering the body mass.

In summary, the present study has shown that the values of the trabecular microstructural parameters of the greater tubercle generally differ among species. Thus, for in vitro mechanical tests on the implant stability in trabecular bone only the species for which the implant is designed should be used. However, all investigated species had similar principal interrelations of the trabecular microstructural parameters. The strongest relations are between BV/TV and Tb.Th., Tb.N., and SMI, each having a similar strength, and between Conn.D. and Tb.N. Based on these interrelation findings, the design of trabecular microstructure in the greater tubercle follows similar phenomenological mechanisms in all species. Thus, in vivo experiments on trabecular bone healing and osteoporosis research for application in humans can be conducted in ovine, bovine, or porcine species, however, the results must be expressed relative to a control group of the same species.

REFERENCES

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS
  5. DISCUSSION
  6. REFERENCES