Age- and sex-related characteristics in cortical thickness of femoral diaphysis for young and elderly subjects

Abstract

Introduction

Cortical thickness of the femoral diaphysis is assumed to be a preferred parameter in the assessment of the structural adaptation by mechanical use and biological factors. This study aimed to investigate the age- and sex-specific characteristics in cortical thickness of the femoral diaphysis between young and elderly non-obese people.

Materials and methods

This study investigated 34 young subjects (21 men and 13 women; mean age: 27 ± 8 years) and 52 elderly subjects (29 men and 23 women; mean age: 70 ± 6 years). Three-dimensional (3D) cortical thickness of the femoral diaphysis was automatically calculated for 5000–8000 measurement points using the high-resolution cortical thickness measurement from clinical CT data. In 12 assessment regions created by combining three heights (proximal, central, and distal diaphysis) and four areas of the axial plane at 90° (medial, anterior, lateral, and posterior areas) in the femoral coordinate system, the standardized thickness was assessed using the femoral length.

Results

As per the trends, (1) there were no differences in medial and lateral thicknesses, while the posterior thickness was greater than the anterior thickness, (2) the thickness in men was higher than that in women, and (3) the thickness in young subjects was higher than that in elderly subjects.

Conclusions

The results of this study are of clinical relevance as reference points to clarify the causes of various pathological conditions for diseases of the lower extremities.

Appendix

Treece et al. [16] assume that the cortical layer is locally flat and of uniform thickness, at least within the extent of the imaging system’s point spread function (PSF). They can then model the CT values along the line as a convolution of the ‘real’ density with an in-plane and an out-of plane PSF. The real density variation y over distance x is assumed to be piecewise constant, with different values in the surrounding tissue, the cortex and the trabecular bone. This can be expressed as the summation of two step functions:

$$y\left(x\right)={y}_{0}+\left({y}_{1}-{y}_{0}\right)H\left(x-{x}_{0}\right)+\left({y}_{2}-{y}_{1}\right)H\left(x-{x}_{1}\right)$$

where y₀; y₁ and y₂ are the CT values in the surrounding tissue, cortical and trabecular bone, respectively, x₀ and x₁ are the locations of the outer and inner cortical surfaces, and H(x) is a unit step function. The in-plane PSF g_i was modeled as a normalized Gaussian function:

$${g}_{\mathrm{i}}\left(x\right)=\frac{e\frac{{x}^{2}}{{\sigma }^{2}}}{\sigma \sqrt{\pi }}$$

where σ represents the extent of the blur. The out-of-plane PSF g_o is the result of the interaction between the CT slice thickness and the orientation of the cortical layer with respect to the imaging plane. This can be expressed as a rectangular function:

$${g}_{0}\left(x\right)=\frac{1}{2\mathrm{r}}\left[H\left(x+r\right)-H\left(x-r\right)\right]$$

where the extent of blur 2r is calculated from s, the CT slice thickness, and a, the angle the cortical surface normal makes with the imaging plane:

$$r=\frac{s}{2}\mathrm{tan}a$$

Hence, the fully blurred CT values y_blur are given

$${y}_{\mathrm{b}\mathrm{l}\mathrm{u}\mathrm{r}}\left(x\right)={y}_{0}+\iint \frac{{y}_{1}-{y}_{0}}{2r\sigma \sqrt{\pi }}\left[{e}^{-\frac{{\left(x+r-{x}_{0}\right)}^{2}}{{\sigma }^{2}}}-{e}^{-\frac{{\left(x-r-{x}_{0}\right)}^{2}}{{\sigma }^{2}}}\right]+\frac{{y}_{2}-{y}_{1}}{2r\sigma \sqrt{\pi }}\left[{e}^{-\frac{{\left(x+r-{x}_{1}\right)}^{2}}{{\sigma }^{2}}}-{e}^{-\frac{{\left(x-r-{x}_{1}\right)}^{2}}{{\sigma }^{2}}}\right]dxdx$$

except for the special case r = 0, when:

$${Y}_{\mathrm{b}\mathrm{l}\mathrm{u}\mathrm{r},r=0}\left(x\right)={y}_{0}+\int \frac{{y}_{1}-{y}_{0}}{\sigma \sqrt{\pi }}{e}^{-\frac{{(x-{x}_{0})}^{2}}{{\sigma }^{2}}}+\frac{{y}_{2}-{y}_{1}}{\sigma \sqrt{\pi }}{e}^{-\frac{{\left(x-{x}_{1}\right)}^{2}}{{\sigma }^{2}}}dx$$

The true cortical thickness t_r is then:

$${t}_{\mathrm{r}}={t}_{\mathrm{m}}\mathrm{cos}a=\left({x}_{1}-{x}_{0}\right)\mathrm{cos}a$$

where t_m is the measured in-plane thickness.