Trabecular Homogeneity Index Derived From Plain Radiograph to Evaluate Bone Quality



Radiographic texture analysis has been developed lately to improve the assessment of bone architecture as a determinant of bone quality. We validate here an algorithm for the evaluation of trabecular homogeneity index (HI) in the proximal femur from hip radiographs, with a focus on the impact of the principal compressive system of the trabecular bone, and evaluate its correlation with femoral strength, bone mineral density (BMD), and volumetric trabecular structure parameters. A semiautomatic custom-made algorithm was applied to calculate the HI in the femoral neck and trochanteric areas from radiographs of 178 femoral bone specimens (mean age 79.3 ± 10.4 years). Corresponding neck region was selected in CT scans to calculate volumetric parameters of trabecular structure. The site-specific BMDs were assessed from dual-energy X-ray absorptiometry (DXA), and the femoral strength was experimentally tested in side-impact configuration. Regression analysis was performed between the HI and biomechanical femoral strength, BMD, and volumetric parameters. The correlation between HI and failure load was R2 = 0.50; this result was improved to R2 = 0.58 for cervical fractures alone. The discrimination of bones with high risk of fractures (load <3000 N) was similar for HI and BMD (AUC = 0.87). Regression analysis between the HIs versus site-specific BMDs yielded R2 = 0.66 in neck area, R2 = 0.60 in trochanteric area, and an overall of R2 = 0.66 for the total hip. Neck HI and BMD correlated significantly with volumetric structure parameters. We present here a method to assess HI that can explain 50% of an experimental failure load and determines bones with high fracture risk with similar accuracy as BMD. The HI also had good correlation with DXA and computed tomography–derived data. © 2013 American Society for Bone and Mineral Research.


Occurrence of hip fracture is increasing worldwide as the result of the aging of the population. This is largely related to the decrease of bone mineral density (BMD) with age, which increases the risk of fracture.[1] The current clinical diagnosis of osteoporosis and fracture risk is based on BMD assessed from dual-energy X-ray absorptiometry (DXA), but it has been proven that this method has only a limited ability to predict individual fracture risk.[2-4]

Quantitative computed tomography (CT), peripheral quantitative CT, and magnetic resonance imaging can be used to obtain three-dimensional geometry and architecture of bone in vivo. These methods can be used to supply textural variables that have been shown to be relevant in the assessment of bone quality.[5, 6] Unfortunately, the availability of these volumetric imaging techniques is limited, and they remain as high-cost methods.

Conventional radiography is a low-cost method for evaluating geometry, structure, and fracture risk of bone. A previous method to assess fracture risk was indirectly related to the mineral density of the trabecular bone, using the Singh index.[7] Subsequently, radiographic texture analysis was developed to improve the assessment of bone architecture as a determinant of bone quality instead of bone quantity.[8] Many studies have been conducted to evaluate the trabecular bone structure from radiographs.[9-16]

Homogeneity index (HI) is a parameter derived from the gray-level co-occurrence matrix (GLCM) of a picture, which represents the spatial distribution of gray levels in a picture. The HI evaluates how neighboring pixels are correlated along a defined orientation. While applied to a trabecular area, the HI can calculate the homogeneity of the bone, and to some extent it gives indication of the connectivity of the trabecular fibers: the more connected, the higher the HI. However, the orientation of the fibers has been typically ignored in the literature for calculating the GLCM, and the evaluation of homogeneity index was not a representation of true bone content,[15, 16] resulting in negative correlation between HI and BMD. Finally, to confirm the validity of a method, a large sample size is required for statistical relevance.

The aim of this study was to validate an algorithm for the evaluation of HI derived from plain radiographs, with a focus on the impact of the principal compressive system of the trabecular bone.[17, 18] We hypothesized that using the HI method one could predict mechanical failure load with similar accuracy as with DXA. Furthermore, HI was compared with the BMD assessed by DXA and to the architectural parameters derived from CT scans.

Materials and Methods

Study sample and imaging

For the present study, we used data of 178 cadaver femora (85 males, 93 females, mean age 79.3 ± 10.4 years, range 52 to 100 years) obtained from a larger experimental study at the Institute of Anatomy at the Ludwig Maximilians University of Munich (Germany).[19, 20] The preparation and storage of the samples have previously been described in detail.[20] After the dissection course, excision, and cleaning of the surrounding soft tissue, the proximal femora were radiographed and scanned before being mechanically tested in a sideways fall configuration.

Radiographs were obtained using a Faxitron X-ray system (Model 43885A; Faxitron, Hewlett Packard, McMinnville, OR, USA) and digitized together with a calibration scale using a scanner at a spatial resolution of 600 dpi. DXA scans of the femora were obtained using a standard narrow fan beam scanner (GE Lunar Prodigy, GE Lunar Corp., Madison, WI, USA) with the femoral specimens submerged in a water bath. Standard positioning was used across all specimens, and both total (corresponding to the whole upper femur) and site-specific femoral BMDs were evaluated using the software provided by the manufacturer. CT scans were performed for 130 of the femora using a 16-row multidetector CT scanner (Sensation 16; Siemens Medical Solutions, Erlangen, Germany). A high-resolution protocol (bone kernel) with a slice thickness of 0.75 mm was used.[21]

The femurs were mechanically tested, simulating a fall on the greater trochanter as previously presented.[19, 20] Briefly, femora were positioned with an angle of 10° between horizontal plane and shaft axis with internal rotation of 15° for the neck; loads were then applied to the greater trochanter through a pad at a rate of 6.6 mm/second. The failure load was determined from the load-deformation curve and the fracture type classified to cervical, trochanteric, and shaft fractures using the standard AO classification. Descriptive statistics of the materials are presented in the Table 1.

Table 1. Descriptive Statistics for Geometry, BMD per Location, and Failure Load (n = 178)
ParameterMean (SD)Range
Head diameter (cm)4.75 (0.16)3.81–5.82
Neck diameter (cm)3.28 (0.38)2.62–5.34
Neck BMD (g/cm2)0.71 (0.17)0.22–1.19
Trochanteric BMD (g/cm2)0.66 (0.17)0.19–1.16
Total BMD (g/cm2)0.80 (0.19)0.27–1.31
Failure load (N)3998 (1464)664–8156

Evaluation of the homogeneity index

Image processing was performed with a custom-made algorithm developed under MATLAB (version 7.1, MathWorks, Natick, MA, USA) with a graphical interface allowing the user to select a region of interest (ROI) in the radiograph. In this study, ROIs were chosen relative to the overall size of the bone to fit within the fibers, with a size of 140 × 140 pixels for bones with head diameters between 45 mm and 50 mm (each 5-mm difference from this interval decreases or increases the ROI size by 10 × 10 pixels). Two ROIs were defined, one within the main compressive system (inferomedial neck, at the neck/head transition area) and one within the main tensile system (trochanteric area) (Fig. 1). Image preprocessing was then applied: A noise threshold was followed by median filtering 3 × 3 and, subsequently, disk-shaped morphological top and bottom hat operations were performed.

Figure 1.

Selection of the regions of interest (ROI). (A) Trochanteric and (C) femoral neck: filtered and rotated along the main trabecular orientation. (B, D) Corresponding gradient-based pictures. The trochanteric (TA) and neck (NA) areas used for site-specific BMD assessment are delimited by the dotted lines.

Fourier transform was applied to the ROI to evaluate the trabecular main orientation (TMO) by fitting a line to extract the TMO in the frequency domain. The angle α between the TMO and the shaft axis was then calculated in the space domain and the data within the ROI were rotated to obtain textural alignment along TMO (Fig. 1A, C).

A gradient-based gray-level image was then calculated solely perpendicular to TMO in the neck area (Fig. 1D) but both perpendicular and aligned with TMO for the trochanteric ROI (Fig. 1B). Similarly, a GLCM was calculated perpendicular to the TMO in the neck ROI but averaged from both the perpendicular and parallel orientations related to the TMO (0° and 90°) in the trochanteric area. A distance of one pixel was selected in the evaluation of the GLCMs. First column and first row were cropped from the GLCM, removing the values corresponding to empty spaces in the bone. HI, which measures the closeness of the distribution of elements near the diagonal of the GLCM, was calculated as follows:

display math(1)

HI was normalized by the number of fibers, derived from the thickness of the bone using the formula:[2]

display math(2)

The thickness of the bone was estimated from a site-specific bone width. For the neck/head transition area, the thickness was estimated to be 0.8*head width [cm]. For the trochanteric area, bone thickness was estimated to be equal to the neck width [cm]. The flowchart for evaluation of the HI is presented in Fig. 2. The root mean square coefficients of variation (CVrms) have been previously reported as 1.5% and 0.7% for the head and neck widths (diameters), respectively.[22]

Figure 2.

Flowchart of the image processing to obtain the homogeneity index (HI) of the trabecular structure.

CT-scan processing

CT scans of 130 bones were available (65 males, 65 females). The CT scans were processed, and pictures aligned along the femoral neck axis were generated using the software ClearCanvas (version 2.0, ClearCanvas Inc., Toronto, Canada) and were then exported as TIFF files. A script was developed under Matlab to select the ROI in the similar neck/head transition area as defined from the radiographs. The average Hounsfield Unit of the volumetric ROI within the femoral neck was then calculated for each bone. CT images of the volumetric ROI were then analyzed using Bruker Skyscan (Kontich, Belgium) CTAn software. Image contrast was first enhanced by 75% within 4 pixels mask and the average of the same size mask was used as the threshold level. These thresholded images were then subjected to 3D structural analysis. The CT analysis process is presented in Fig. 3.

Figure 3.

Left: Set of CT slices, in which the ROIs are selected from the slice located in the middle of the femoral neck axis and extended to all scans within the femoral neck. Center: ROI of each CT slice. Right: reconstructed trabecular bone.

Statistical analysis

The intra- and interobserver repeatability of the HI was evaluated for all the bones in each region. The selection of the ROI was performed two times with a 1-week interval for the intra-observer repeatability. The interobserver repeatability was performed within three users, one being the first data from the intra-observer repeatability. For all repeatability estimations, the precision was calculated as coefficient of variation using the root mean square method.

Regression analysis was performed between the adjusted HI values and their corresponding site-specific BMDs assessed by DXA. Total HI of each bone was averaged from adjusted neck and trochanteric HIs and was compared with the total BMD values derived from DXA as well as the experimental failure load. Finally, the adjusted neck HI was compared with the experimental failure loads of cervical fractures solely (n = 86) and the adjusted trochanteric HI for the trochanteric fracture loads solely (n = 67). Power trend lines were used in each regression analysis involving HI.

A cut-off value of 3000 N was used to determine bones with high risk of fracture, suggested by Amin and colleagues to be the threshold of proximal femur strength for both women and men.[23] Receiver operating characteristic (ROC) analysis was used to assess the ability of HI and BMD to discriminate these bones.

Because of nonlinearity between the data, Spearman's correlation analysis was performed between the unadjusted and adjusted neck HI and the parameters extracted from the reconstructed model derived from the CT scans of the corresponding area. Pearson method was used for neck BMD and volumetric parameters.


The results of the intra- and interobserver repeatability in the assessment of the HI per area are presented in Table 2.

Table 2. Repeatability (CVrms) of the Adjusted Homogeneity Index From the Textural Image Analysis (n = 178)a
 Neck areaTrochanteric area
  • aRepeated three times by the same observer for intra-observer calculations and by three observers in interobserver calculations.

While comparing the experimental failure load with the total HI and the total BMD, the regression analysis results were R2 = 0.50 and R2 = 0.60, respectively (Fig. 4). For cervically fractured cases (n = 86), the relationships increased to R2 = 0.58 and R2 = 0.63 when compared with the HI and BMD in the neck area. For trochanteric fractures (n = 67), the relationship with trochanteric HI was R2 = 0.40, whereas for the trochanteric BMD it was R2 = 0.71. For femoral shaft fractures (n = 25), the corresponding relationships were R2 = 0.40 for total HI and R2 = 0.26 for total BMD.

Figure 4.

Regression analysis between the adjusted homogeneity index and BMD and the experimental failure load. Top: All bones pooled together (n = 178): total HI (left) and total BMD (right). Middle: Cervically fractured bones (n = 86): neck HI (left) and neck BMD (right). Bottom: Trochanterically fractured bones (n = 67): trochanteric HI (left) and trochanteric BMD (right).

Using a cut-off value of 3000 N, 48 of the 178 bones were considered to have high risk of fracture. ROC analysis to discriminate these bones gave similar results using either total HI or total BMD (Fig. 5). The area under the curves was 0.873 (95% confidence interval [CI] 0.819–0.927) for the total HI and 0.871 (95% CI 0.811–0.932) for the total BMD.

Figure 5.

Receiver operating characteristic (ROC) curves for the prediction of femurs at risk with hip strength below 3000 N (48 bones versus 130 controls).

Regression analysis results (Fig. 6) between the adjusted HI and corresponding BMD were R2 = 0.66 and R2 = 0.60 for the neck and trochanteric areas, respectively, and R2 = 0.66 between total BMD and total HI of each bone.

Figure 6.

Regression analysis between the adjusted homogeneity index by location and their corresponding BMD assessed from DXA (n = 178).

The Spearman's correlation showed variable correlations between the adjusted neck HI and the trabecular parameters from the corresponding areas of the CT scans (Table 3). The correlations were slightly better for the neck BMD values using the Pearson's method, but not statistically different, with an exception for the averaged Hounsfield Unit (p < 0.001).

Table 3. Volumetric Trabecular Parameters Defined From the CT Scans and Their Correlation Coefficients With the Unadjusted/Adjusted Neck Homogeneity Indices (HI) (Spearman) and Neck BMD (Pearson) (n = 130)
ParameterMean (SD)HIAdjusted HINeck BMD
  • HU = Hounsfield Unit.
  • #p < 0.05,
  • *p < 0.001.
Average HU348 (100)0.70*0.61*0.84*
Structure model index0.36 (0.24)−0.46*−0.61*−0.64*
Trabecular pattern factor−0.23 (0.10)−0.45*−0.57*−0.59*
Bone volume fraction48.3 (2.7)0.47*0.54*0.65*
Trabecular number0.13 (0.01)0.42*0.48*0.51*
Trabecular separation3.82 (0.22)−0.40*−0.42*−0.50*
Euler number−1437 (410)−0.14−0.43*−0.28*
Intersection surface6494 (932)0.080.41*0.32*
Bone surface density0.54 (0.03)0.31*0.32*0.36*
Trabecular thickness3.60 (0.10)0.160.18#0.34*


In the present study, we validated an algorithm for the evaluation of HI from texture analysis of conventional radiographs, with a focus on the impact of the principal compressive system of the trabecular bone. The results show that homogeneity index evaluated as a trabecular parameter from hip radiograph can be used to assess bone quality. HI can discriminate femurs with high risk of fracture with similar accuracy as DXA. The high intra- and interobserver repeatability demonstrated the robustness of the method, with similar repeatability as the ones previously reported.[15, 24-26]

In our analysis, the ROIs were located in the middle of the principal tensile and compressive systems. Ignoring bone size and keeping the same ROI size for each bone might have altered the results for bones with smaller size by selecting areas outside the principal systems and eventually giving a lower HI value. The impact of the compressive system[17, 18] was represented in the femoral neck ROI by applying the gradient-based method and the orientation of the GLCM solely perpendicular to the fibers. Although the averaging of four different orientations (0°, 45°, 90°, and 135°) is typically used in the literature to ensure rotational invariance,[15, 16] here we orientated the GLCM perpendicular to the TMO to reflect the anisotropy of the trabecular bone. The compressive system is more obvious and is well represented in the neck ROI, whereas the orientation of the tensile system was less straightforward and its intensity was smaller in the trochanteric ROI. Because of this constraint and the presence of a secondary tensile group in this region,[27] the gradient-based method and the GLCM calculation were applied both perpendicularly and along the TMO in the trochanteric area. In addition, to evaluate the true bone content inside the ROI, we cropped the first row and column of the GLCM before calculating the HI to remove the values related to empty spaces, resulting in a positive correlation with BMD values. The HI was then adjusted to the thickness of the bone in the considered location, which correction was based on a representative anatomical measurement of the corresponding area. The normalization used here is directly related to the amount of fibers. Under the assumption that a thicker bone will present more layers of fibers, its corresponding higher distribution of values within the GLCM will result in a “lowered” HI that was corrected by the normalization. The adjusted HI results appeared to reflect better the volumetric trabecular parameters (Table 3) and correlate more strongly with BMD and failure load than the unadjusted HI values (data not shown).

The total averaged HI was able to explain half of the variability of the experimental failure load (R2 = 0.50), mimicking a fall on the greater trochanter. For cervical fracture cases, it was to be expected that the adjusted neck HI would give a better correlation to the failure load (R2 = 0.58) than total HI. However, the results obtained for trochanteric fractures and adjusted trochanteric HI were quite low (R2 = 0.40), which could be justified by the fact that the organization is better captured by the HI method in the neck area than the trochanteric area.

It has been suggested by Amin and colleagues[23] that the value of 3000 N represents a critical level in skeletal fragility for both sexes, this value being in line with the previous study of Orwoll and colleagues.[28] According to these publications, we used the value of 3000 N as a cut-off to separate bones with high fracture risk from others. Eventually, the discrimination of these specific bones using ROC curve analysis gave similar results for HI and BMD. This supports the hypothesis that analysis of structural parameters from radiographic pictures can replace DXA-based BMD to discriminate bone with high fracture risk.[29, 30]

The regression analysis between BMD assessed by DXA and the HI resulted in higher correlations than the ones previously published involving GLCM parameters,[15, 16, 25, 26] especially in the neck area. Better results were obtained in the middle of the compressive system (R2 = 0.66) than in the middle of the tensile system (R2 = 0.60). Finally, the averaged HI of the two ROIs within the principal compressive and tensile systems gave a good correlation (R2 = 0.66) when compared with the total BMD assessed by DXA. All the regression analyses showed nonlinear power trendlines, which could be justified by the fact that the HI is limited by the value 1 (corresponding to a pure white picture); the lesser amount of bone that exists in the selected ROI, the faster the homogeneity value decreases.

As previously suggested, parameters extracted from texture analysis can be compared with three-dimensional architecture.[12] The correlation between HI and volumetric parameters was only performed in the inferomedial neck area to display the bone architecture,[31, 32] the area being considered representative of hip strength.[25, 32] All the correlations reported here were similar to the ones found in literature between co-occurrence matrix parameters and volumetric parameters,[24, 33] even if the imaging methods used previously were different (micro-CT and high-resolution digital X-ray device). Results of the correlation analysis were slightly better for BMD[33, 34] than for HI but were not statistically different from each other. An exception to this statement was the averaged volumetric Hounsfield Unit, which is directly related to the volumetric BMD of the reconstructed model, explaining the high correlation obtained with the BMD assessed from DXA. However, the correlation with the HI remained strong, supporting the results previously obtained from the regression analysis with the data from DXA. Similarly, the HI was well correlated with the bone volume fraction, with this parameter representing the bone volume/total volume ratio and being related to bone strength.[35]

The trabecular pattern factor reflects the connectedness of structures, and the structure model index is a topological index for estimating the characteristic form in terms of plates and rods composing the 3D structure. Both of these parameters are inversely associated with the presence of cracks in trabecular bone,[36] and it has been suggested that damages tend to occur in rodlike trabeculae.[35, 36] Thus, cracks in the cancellous bone fibers affect the GLCM and eventually decrease the HI value. This hypothesis is supported with the good correlation between these volumetric parameters and the HI.

The strength of the present study is the large sample size (178 cadaver femurs) being significantly larger than in previous studies.[9-16] However, there are some limitations in our methodology. First, this study is based on cadaver material. For in vivo applications, the radiographic structure analysis would require extra filtering to remove the artifacts caused by the soft tissues and pelvis. Second, the ROIs used in this method do not correspond to the ones used by the manufacturer's standard hip analysis software to assess the BMDs from DXA (Fig. 1). The method developed here solely focused on the principal tensile and compressive systems to avoid high variations of the homogeneity within the ROI. However, despite this mismatch, the results reported here were statistically significant and suggest that the assessment of BMD in the exact same location as the HI might give even better correlations. Third, the adjustments of the HI with the bone thickness per specific area were based on anatomical measurement assessed from the radiograph; however, these parameters still remain as approximations of the real thickness. Finally, the protocol to digitize the radiographs was not exactly the same for all the bones in this study. The radiographs have been digitally scanned between the years 1998 and 2003, with some changes in the resolutions and acquisition parameters depending on the years. To keep a relevant sample size of imaging material, the pictures were preprocessed to have the same resolution and were normalized with similar noise removal.

In conclusion, the homogeneity index can discriminate femurs with high risk of fracture with similar accuracy as DXA. HI itself can explain half of the experimental failure load and, additionally, HI showed a good correlation with BMD derived from DXA and moderate to strong correlations with volumetric parameters from CT scans in a large sample set of cadaver femurs. The results obtained here suggest that the evaluation of HI might offer a low-cost substitute to the DXA-based BMD assessment, as conventional radiography is available worldwide. Further clinical studies are needed to confirm the applicability of the method in fracture risk assessment.


All authors state that they have no conflicts of interest.


Mr Sauli Herrala is acknowledged for his help in statistical analysis. This study was financially supported by the Finnish Funding Agency for Technology and Innovation, the Academy of Finland, the National Doctoral Programme of Musculoskeletal Disorders and Biomaterials, and Deutsche Forschungsgemeinschaft Grant DFG LO 730/2-2.

Authors' roles: Study conception and design: JT, TJ, SS. Data collection: JT, JH, MF, PP, VK, TL, FE. Data analysis: JT, JH, MF, SS. Data interpretation: JT, JH, TJ, SS. Drafting of manuscript: JT. Revising the manuscript critically for important intellectual content: All authors. Approving the final version of the manuscript: All authors.