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Matrix Concentration of Insulin-like Growth Factor I (IGF-I) is Negatively Associated with Biomechanical Properties of Human Tibial Cancellous Bone Within Individual Subjects

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Abstract

Insulin-like growth factor-I (IGF-I), abundant in bone matrix, is believed to play an important role during bone development and remodeling. To our knowledge, however, few studies have addressed the relationship between the concentration of IGF-I in bone matrix and the biomechanical properties of bone tissue. In this study, forty-five cylindrical specimens of cancellous bone were harvested from six human tibiae and scanned using microcomputed tomography (μCT). The bone volume fraction (BV/TV) was calculated from three-dimensional (3D) μCT images. Mechanical tests were then performed on a servohydraulic testing system to determine the strength and stiffness of cancellous bone. Following mechanical testing, the concentration of IGF-I in bone matrix was measured by using an enzyme-linked immunoabsorbent assay (ELISA). Within each subject, the concentration of IGF-I in bone matrix had significant (P < 0.01) negative correlations with the bone volume fraction, strength, and stiffness of cancellous bone. In particular, the anterior quadrant of the proximal tibia was significantly (P < 0.02) greater in IGF-I matrix concentration and marginally significantly lower in strength (P = 0.053) and stiffness (P = 0.059) than the posterior quadrant. The negative correlations between the cancellous bone matrix concentration of IGF-I and cancellous bone biomechanical properties within subjects found in this study may help us understand the variation of the biomechanical properties of cancellous bone in proximal human tibiae.

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Acknowledgments

This study was supported by National Institutes of Health grants AR40776, AR44712, AR47434, and AR049343.

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Authors and Affiliations

  1. Bone and Joint Center, Department of Orthopaedic Surgery, Henry Ford Health System, Detroit, Michigan, USA

    X. N. Dong, Y. N. Yeni, B. Zhang, C. M. Les, G. J. Gibson & D. P. Fyhrie

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  1. X. N. Dong
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Correspondence to X. N. Dong.

Appendix

Appendix

A.1 Correlation coefficients with repeated observations

Because there were multiple specimens of cancellous bone from each subject (i.e., pseudoreplication), it could be misleading to perform statistical analyses by combining all cancellous bone specimens from several subjects and then calculating the correlation as if the data were a simple sample. Although forty-five cylindrical specimens of cancellous bone were harvested, there were only six actual independent observations, which was equal to the number of subjects used in the present study. This is similar to the problem of multiple physiological measurements from individual patients as discussed by Altman and Bland [40].

A.2 Correlation within subjects

It is sometimes useful to introduce additional variables into a regression model, to account for the effects of nominal scale variables (i.e., categorical variables such as subject) on the response variable [41].

For example, we might be considering fitting the model

$$ {\rm{BV/TV = a}}\,{\rm{ + }}\,{\rm{b}}\;{\rm{IGF - I}} $$
(1)

where BV/TV is the bone volume fraction of cancellous bone, IGF-I is the concentration of IGF-I in bone matrix, a is the intercept, and b is the slope. However, this model does not take account of the variability between subjects.

Therefore, we might be interested in determining the effect of subject variations on BV/TV. There are six levels of the nominal scale variable (i.e., six subjects). Therefore, five dummies are required for the regression model [41–43]. Our regression model could then be expanded to

$$ {\rm{BV/TV}}\,{\rm{ = a}}\,{\rm{ + b IGF - I + d}}_{\rm{1}} {\rm{ D}}_{{\rm{1 }}} {\rm{ + d}}_{\rm{2}} {\rm{ D}}_{{\rm{2 }}} {\rm{ + d}}_{\rm{3}} {\rm{ D}}_{\rm{3}} {\rm{ + d}}_{\rm{4}} {\rm{ D}}_{{\rm{ 4}}} {\rm{ + d}}_{\rm{5}} {\rm{ D}}_{\rm{5}} $$
(2)

where D1, D2, D3, D4, and D5 are dummy variables that account for average inter-individual variation. The five dummy variables can be used to represent six levels of a categorical variable (subject). The use of these dummy variables accounts for pseudoreplication and will yield significantly more accurate predictions of the dependent variable than will the preceding model without dummy variables (Equation 1). The method is also known as analysis of covariance and is equivalent to fitting parallel lines through each subject’s data [43].

We can make use of the analysis of variance (ANOVA) table associated with the multiple regression model [32]. The residual sum of squares in the table represents the variations about those lines fitted to each subject. We remove the variation due to the subjects and express the variation in the bone volume fraction to the matrix concentration of IGF-I as a proportion of what remains (Sum of squares for IGF-I)/(Sum of square for IGF-I + Residual sum of squares). This proportion is also called the coefficient of determination (R2) for a multiple regression. The P value is calculated from the F test in the associated analysis of variance table.

A.3 Correlation between subjects

If we want to know whether subjects with high average values of IGF-I concentration also tend to have high average values of biomechanical properties, we can use the correlation between the subject means of the independent and dependent variables. We can calculate the mean values of IGF-I concentration and the biomechanical properties for each of six subjects. The 45 pairs of measurements from which these means were calculated were given in the Figures 2–4. Here we are interested in whether the average IGF-I concentration for a subject is related to the subject’s average biomechanical properties.

We can calculate the Pearson correlation coefficient and the Spearman correlation coefficient for the mean concentration of IGF-I in bone matrix and the average biomechanical properties by using simple linear correlation and rank correlation analysis, respectively [41].

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Dong, X.N., Yeni, Y.N., Zhang, B. et al. Matrix Concentration of Insulin-like Growth Factor I (IGF-I) is Negatively Associated with Biomechanical Properties of Human Tibial Cancellous Bone Within Individual Subjects. Calcif Tissue Int 77, 37–44 (2005). https://doi.org/10.1007/s00223-004-0140-y

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