Osteoporosis International

, Volume 20, Issue 2, pp 323–333

Using Radon transform of standard radiographs of the hip to differentiate between post-menopausal women with and without fracture of the proximal femur

Authors

    • Department of RadiologyUniversity of Munich
  • J. Lutz
    • Department of RadiologyUniversity of Munich
  • M. Körner
    • Department of RadiologyUniversity of Munich
  • W. Mutschler
    • Department of Trauma SurgeryUniversity of Munich
  • M. Reiser
    • Department of RadiologyUniversity of Munich
  • K.-J. Pfeifer
    • Department of RadiologyUniversity of Munich
Original Article

DOI: 10.1007/s00198-008-0663-6

Cite this article as:
Boehm, H.F., Lutz, J., Körner, M. et al. Osteoporos Int (2009) 20: 323. doi:10.1007/s00198-008-0663-6

Abstract

Summary

Texture features based on the Radon transform were extracted from clinical radiographs of the hip in post-menopausal women. The novel algorithm allowed us to identify patients with fracture of the proximal femur and may provide an alternative to measuring bone mineral density in predicting the fracture-risk in osteoporosis, especially where densitometry is regionally unavailable.

Introduction

The aim of this study is to introduce an algorithm for differentiation between patients with and without fracture of the hip using parameters based on the Radon transform (RT) and applied to standard radiographs of the proximal femur and to compare the results with bone mineral density (BMD).

Methods

The study comprised 50 post-menopausal women (78.6 ± 11.5 years of age), including 25 patients with hip fracture and 25 age-matched controls. We obtained lumbar and femoral BMD and standard femoral radiographs. In the radiographs we analysed trabecular patterns of the hip in a region-of-interest of 57 x 29 mm using the RT. From the histogram-representation of the RT, we extracted several characteristic parameters. By ROC and discriminant-analysis, we assessed the statistical power of both methods.

Results

For correct differentiation between fracture and non-fracture cases by femoral BMD, area-under-the-curve (AUC) was 0.78; AUC for the RT-based parameters ranged from 0.73 to 0.8. By combination of densitometric and textural information in a multivariate model the fracture status of 84% of subjects was predicted correctly, identification of fracture cases rose to 88%.

Conclusion

Identification of fracture patients by RT applied to femoral radiographs was feasible and seemed to have a discriminative potential comparable to that of standard densitometry. In the future, the new method may provide an alternative to DXA or in conjunction with conventional densitometry may enhance the detection of patients with elevated risk of hip fracture.

Keywords

Fracture riskIn vivoOsteoporosisProximal femurRadiographic texture analysisRadon transform

Introduction

Due to aging populations the incidence of osteoporosis and associated fractures becomes an increasingly relevant issue for the public health institutions of industrialized nations. Fractures of the hip represent the worst complication of osteoporosis with a mortality of close to 25% to 30% during the first post-traumatic year [13]. Prediction of fracture risk is a major focus of osteoporosis research and, over the years, has been approached from different angles.

The current WHO-definition of osteoporosis [4] is based on bone mineral density (BMD) obtained by dual energy X-ray absorptiometry (DXA), which is still the clinically most widely available parameter for diagnosis and follow-up of the disease. BMD is closely correlated with the compressive strength of bone in vitro and serves as a predictor of fracture risk under in vivo conditions [510]. However, there exists a considerable overlap in the BMD results between individuals who have fractured and those who have not [1113]. From the point of view of evidence-based medicine, DXA is still the method of choice for fracture prediction, though. Among the more promising, experimentally successful methods for assessment of bone fragility are procedures involving high-resolution imaging modalities in conjunction with sophisticated image processing techniques. A major concern is that these experimental procedures are either very costly and/or involve significant amounts of radiation exposure. Therefore they are of limited use as far as future application in clinical practice for screening for osteoporosis is concerned [1416].

Clinically far more available than DXA is conventional X-ray imaging. Trabecular bone structure is visible in great detail on standard radiographs and many attempts have been made to quantify the quality of the structure and assess its relationship to osteoporosis and BMD. The spectrum of methods ranges from visual scoring systems, such as the Singh-index [17], through to sophisticated computerised methods based on non-linear methods, such as fractals and Fourier spectrum analysis [18, 19].

In previous work, we have demonstrated the great potential of an algorithm for characterization of trabecular bone structure based on the standard Hough transform (SHT) [20, 21]. The SHT-based parameters are of use with respect to predicting the ultimate fracture load of cubic bone samples depicted by high-resolution MRI. Equivalent to the SHT is the Radon transform (RT) [22, 23], which has recently been used to assess the trabecular orientation of avian bone by Pontzer et al. [24]. In general, the SHT and RT serve as global analysis tools capable of detecting parameterized patterns such as straight lines or struts, which are suitable approximations of trabecular bone textures. According to Pontzer et al. (2006) the peaks in the density distribution of the projection domain correspond to the predominant orientation of maximum bone density, i.e., the trabecular architecture. One of the great advantages of both RT and SHT is their robustness with respect to noise or structural gaps in the pattern under study.

Objective

The current study was designed to test the hypothesis that quantitative texture features obtained from the Radon transform of standard radiographic projections of the proximal femur can be used to characterize the trabecular pattern and provide a means to differentiate between subjects with hip fractures and controls. Results of the novel approach were compared with the discriminatory power of bone densitometry.

Materials and methods

Patients, diagnostic imaging, and bone mineral density

The study comprised 50 post-menopausal women aged 78.6 + 11.5 yrs, who were consecutively admitted to the Department of Trauma Surgery of our hospital for suspected fractures of the hip or pelvis due to a fall from standing height. Twenty-five of the patients had confirmed fractures of the hip; the other 25 subjects were age-matched controls in whom fractures of the proximal femur were excluded. None of the patients had been previously diagnosed with or treated for osteoporosis. Patients with a history of metabolic or metastatic bone disease as well as past hip-fracture or prosthetic implants at the proximal femur were ruled out.

For diagnostic imaging we used a clinical CR device equipped with a standard Bucky table (Optitop 150/50/80 HC, Siemens, Erlangen/Germany). Radiographs of the pelvis were acquired in posterior-anterior projection at tube voltages of 80 kV, focal spot size 0.6 mm and a tube-film-distance of 115 cm using a storage phosphor cassette system (Agfa CR/MD 4.0, Agfa, Mortsel/Belgium) with an optical resolution of four line-pairs per millimeter. Wherever possible, a femur positioning device was used to rotate the legs such that the femoral neck axis was oriented horizontally to the imaging plane. The radiographs of the proximal femur met the following quality criteria:
  1. 1.

    The lesser and greater trochanter were clearly projected.

     
  2. 2.

    Trabecular structures were clearly visible in the femoral neck and the head.

     
  3. 3.

    No peri-articular calcification of soft tissue or vascular structures masked any part of the proximal femur.

     

It has to be kept in mind, that the trabecular pattern visible in the radiograph is the result of superposition of many layers of individual calcified elements assembled in a complex structure in 3D. For this reason—to stress the difference—we will use the term trajectory rather than trabecula.

In 12 of the cases with fractures of the hip, the left side was affected, in 13 cases the right side. For all patients, the diagnostic work-up included conventional imaging of the pelvis following the protocol described above as well as measurement of bone mineral density (BMD) at the proximal femur and lumbar spine by dual X-ray absorptiometry (DXA) using a clinical narrow fan beam scanner with multi-view image reconstruction (GE Lunar Prodigy, GE Lunar Corporation, Madison, WI/USA). This investigation was approved by the hospital ethical committee, and informed consent was obtained form all patients. All data were acquired during the course of regular clinical examinations and later retrieved from the PACS for evaluation. Patients were not exposed to any additional radiation for the benefit of our study. Diagnostic assessment of bone mineral density was conducted within one week of hospitalization. In the patients with hip fracture, BMD of the contra-lateral hip was obtained. The densitometric parameters at the hip were evaluated from the automatically located, standardized regions-of-interest (ROI) in the femoral neck, the trochanteric region, the shaft and the total hip by the software implemented in the scanner (enCore, software version 9.30.044).

From the height and weight of each patient, we calculated the body mass index (BMI) according to the formula:
$$BMI = {{\left( {weight\;in\;kilograms} \right)} \mathord{\left/{\vphantom {{\left( {weight\;in\;kilograms} \right)} {\left( {height\;in\;meters} \right)^2 .}}} \right.\kern-\nulldelimiterspace} {\left( {height\;in\;meters} \right)^2 .}}$$
(1)

Quantitative image analysis

Preprocessing

We measured the distribution of trabecular patterns in standard radiographs of the hip in predefined rectangular regions-of-interest (ROI) using the Radon transform. The ROIs were aligned with the femoral neck axis and have an edge length of 160 × 80 pixels corresponding to dimensions of 57 × 29 mm in the film plane (Fig. 1).
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Fig. 1

For each patient, a rectangular region-of-interest (ROI) with edge length 160 × 80 pixels in the proximal femur was selected for quantification of textural properties by Radon transform

The methodological difficulty with radiographic images is the fact that image acquisition conditions can cause intensity and contrast variations between images, making it difficult to evaluate bone structure or density accurately. To tackle this issue and for enhancement and segmentation of the trabecular image components, we introduced a normalization and binarization step by local median filtering: all image pixels with gray-values higher than the median gray-value of the neighboring pixels within a radial distance d were assigned a value of “1”, otherwise “0”. Empirically, a kernel size of 12 pixels was best suited to calculate the texture parameters based on the RT for the image data of our patients. The binarized image was processed further by removal of “noise”, i.e., elimination of solitary pixels that did not contribute to trabecular image components (Fig. 2).
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Fig. 2

Representative examples of image sections from the proximal femur of a patient with hip fracture (femoral BMD = 0.65 g/cm2, left panel) and an age-matched control (BMD = 0.72 g/cm2, right panel). Note the reduced number of arc-like trabeculae in the fracture patient in comparison to the control

Radon transform

The Radon transform of a function f (x,y) is defined as the integral along a straight line defined by its distance ρ from the origin and its angle of inclination θ with θ ranging from 0 ≤ θ ≤  π [25]. The RT is basically a mapping of the spatial domain (x,y), i.e., the original image in 2D, onto the projection domain (ρ, θ), with each point corresponding to a straight line in the spatial domain (Fig. 3). On the other hand, each point in the spatial domain is represented by a sine curve in the projection domain. The different sine curves in the projection domain corresponding to image points that are arranged on the same straight line will all intersect in a single location in the projection domain and will increase the intensity of that particular point of intersection. Thus, high-intensity points in the projection domain signify well defined linearly structured patterns in the original image, which, in the case of the radiographic projections of trabecular bone, are the trabecular trajectories.
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Fig. 3

Typical projection-domain-representation of trabecular texture after Radon transform. Note the sinusoidal curves intersecting at various locations in the image plane: intensity values at intersections correspond to the number of pixels that are arranged in the same straight line in the original image

We used the RT-procedure for binarized images as implemented in IDL 6.2 software (Research Systems Inc., Boulder,Co/USA). The values for all pixels in a given row are summed, creating a column of row-intensity values; this process is repeated iteratively as the image is rotated 179 times by 1°. A row matrix comprising 163 bins was used for RT projection with resulting length of 0.36 mm per bin.

Extraction of textural parameters

For each patient we computed the histogram H of the intensity values of the Radon transform of the ROI in the proximal femur (Fig. 4). The binsize of H was 1. H took on a characteristic shape for each patient (Figs. 4, 5).
https://static-content.springer.com/image/art%3A10.1007%2Fs00198-008-0663-6/MediaObjects/198_2008_663_Fig4_HTML.gif
Fig. 4

Histogram-representation of the intensities in the projection-domain-representation of trabecular texture after Radon transform. The dashed line corresponds to the fracture patient the solid line to the control (see Fig. 2). Note the relative shift of the solid curve towards the right, indicating larger numbers of pixels assembled in straight lines (i.e., trabecular trajectories)

https://static-content.springer.com/image/art%3A10.1007%2Fs00198-008-0663-6/MediaObjects/198_2008_663_Fig5_HTML.gif
Fig. 5

Results of ROC analysis for correct identification of fracture patients. The solid line signifies the RT-based parameter maxH (AUC = 0.8), the dashed line represents femoral T-score (AUC = 0.78)

We defined the parameters maxH (maximum of H), skewH (skewness), kurtH (kurtosis), madH (mean absolute deviation) with
$$skewH = \sum {\left( {H_i - \overline H } \right)^3 ,} $$
(2)
$$kurtH = \sum {\left( {H_i - \overline H } \right)^4 - 3,} $$
(3)
$$madH = n^{ - 1} \sum {\left| {H_i - \overline H } \right|} ,$$
(4)
$$\overline H $$
being the mean of the bins H1… Hn.

In the analysis of distributions, in our case the intensities in the projection domain of straight lines, skewness is a measure of the asymmetry of the distribution under study: positive skewness indicates that the mass of intensity values is concentrated at the smaller end of the scale whereas for a distribution with negative skewness the bulk of intensities is concentrated in the region of larger values.

Kurtosis quantifies the “peakedness” of the intensity distribution with respect to the normal distribution. Distributions with a positive kurtosis tend to have a distinct peak near the mean, decline rapidly, and have heavy tails. Distributions with a negative kurtosis tend to have a flat top near the mean.

Mean absolute deviation is a measure of the variability of values in a distribution, i.e., variability near the center and the variability in the tails of high or low values.

Data analysis

ROC and discriminant analysis

In this study, we employed receiver-operator-characteristic analysis (ROC) to quantify the diagnostic potential of the different parameters with respect to correct prediction of the fracture status. The area-under-the-curve (AUC) of ROC-curves corresponds to the percentage of patients that are correctly categorized and, as such, is a measure of performance for the statistical power of the variable under study. The statistical significance of the difference in AUC-values of ROC-curves of different parameters was obtained by DeLong’s test [26].

We used discriminant-analysis to estimate the predictive potential if a set of two or more parameters was considered simultaneously. Discriminant-analysis is used to model the value of a dependent categorical variable based on its relationship to one or more predictors [27]. It employs Wilks’ lambda tables for assessment of how well each function separates cases into groups. The value of λ is equal to the proportion of the total variance in the discriminant-scores not explained by differences among the groups. A smaller value of Wilks’ λ corresponds to a greater discriminatory ability of the function under study.

Cross validation

We performed a statistical validation of the discrimination results using cross validation (CV) by “leave-one-out” (LOO). For small study populations, LOO allows reliable statistical evaluation and estimates the generalization ability of a statistical classifier [28, 29].

The method calculates standard deviations for two or more parameters, in our case mean AUC of both the bone mineral density and the novel parameters based on the RT. By omission of element i the original data x1, ...xi, ..., xn are partitioned into n disjoint sets (or models) s1, ...si, ...sn containing n-1 elements each. The n-fold cross validation estimate of a given statistic is calculated as the mean of the statistic determined for each of the models.

In this study, LOO is employed to compare the performance of novel, RT-based parameters with densitometric results. If the standard deviations of the mean AUC of both methods are similar, one can conclude that both methods are equally stable or robust.

Statistical tests

Means and standard deviations (SD) of the different parameters were calculated for subjects with and without fracture, the statistical significance of the differences is obtained by the Mann-Whitney U-test at 95% significance level. Correlations between the different parameters were assessed using Pearson’s coefficient of correlation and two-tailed Student’s t-test of significance. All statistical computations were processed using SPSS 10.0.7 (SPSS Inc., Chicago,IL/ USA) and IDL 6.2 software (Research Systems Inc., Boulder,Co, USA). Quantitative processing of image data and visualization of results was accomplished by software composed at our institution under IDL and C ++ (Dev-C ++ Version 4, Bloodshed Software) environments.

Estimation of the precision error

In order to estimate the precision error related to human interaction and positioning, the principal investigator repeatedly evaluated the data of a group of nine patients with hip fracture who had post-operative follow-up examinations after prosthetic joint replacement. RT-based texture analysis of pre- and post-operative X-ray images was conducted for five times.

Results

Patients

In 16 of the cases in the group with fractures of the hip, the left side was affected, in 9 cases the right side. Patients with hip fractures had an average body-mass-index (BMI) of 23.7 ± 3.1 kg/m2, for the controls mean BMI was 24.8 ± 4.0 kg/m2. No statistically significant difference of mean BMI was observed between the two groups (p = .31).

Femoral and lumbar bone mineral density

Mean femoral BMD and T-scores differed significantly between the group of hip fracture patients and controls (p = 0.002 and p < 0.001, respectively). We observed a positive correlation between BMD [T-score] of the hip and spine with r = 0.54 [r = 0.6] (p < 0.001) (Table 1). All patients with hip fracture had pathologically decreased bone mineral density (T-score ≤ 1 SD) at the proximal femur, in 21 of the fracture patients BMD in the lumbar spine was osteoporotic: 20 had femoral T-scores of ≤ -2.5 SD, 14 had lumbar T-scores of ≤ -2.5 SD. In the control population, pathologic femoral [lumbar] BMD of T ≤ -1 SD was found in 22 cases [19 cases], femoral [lumbar] T-scores of ≤ 2.5 SD were measured in 8 subjects [13 subjects]. The area-under-the-curve for correct differentiation between patients with and without fractures by femoral [lumbar] BMD was 0.74 [0.56]. For femoral [lumbar] T-score, AUC was 0.78 [0.56] (Table 2). Standard variation of AUC as tested by LOO was 0.011 for femoral, 0.013 for lumbar densitometric parameters (Table 2). No statistically relevant correlation was found between femoral and lumbar bone density (p = 0.62).
Table 1

Descriptive statistics for fracture patients and controls: densitometric and RT-based parameters

Parameter

Non-fracture n = 25

Fracture n = 25

p

Densitometry

   

Femur

   

  BMD

0.74 ± 0.09

0.67 ± 0.07

0.003

  T-Score

-2.02 ± 1.6

-2.8 ± 0.49

0.001

Lumbar spine

   

  BMD

0.91 ± 0.21

0.89 ± 0.2

0.574

  T-score

-2.16 ± 1.59

-2.34 ± 1.8

0.467

RTA

   

 maxH

2818 ± 414

2386 ± 349

< 0.001

 kurtH

0.4 ± 0.99

-0.28 ± 0.55

0.006

 skewH

1.28 ± 0.32

1.06 ± 0.17

0.006

 madH

1854 ± 297

1636 ± 239

0.001

Table 2

Results of ROC analysis for the densitometric parameters and the texture measures based on the Radon transform with respect to correct identification of hip fractures

Parameter

AUC

SD

Densitometry

  

Femur

  

  BMD

0.75

0.011

  T-score

0.78

0.011

Lumbar spine

  

  BMD

0.55

0.013

  T-score

0.56

0.013

RTA

  

 maxH

0.80

0.009

 kurtH

0.73

0.011

 skewH

0.73

0.010

 madH

0.77

0.011

In this context, standard variation (SD) obtained by cross validation by leave-one-out is a measure of “robustness” for the different classifiers

By discriminant-analysis we could show that femoral T-score identified 80% of fracture cases correctly (λ = 0.733), whereas lumbar densitometry only detected up to 64% of patients with hip fracture (λ ≥ 0.997) (Table 3).
Table 3

Results of discriminant-analysis listed for the densitometric and histogram derived parameters of RT analysis (correct classification results are given as case numbers and percentage for each category (total, fracture patients, and controls)

Parameter

Correct classification

All n = 50

Non-fracture n = 25

Fracture n = 25

Wilks λ

Densitometry

    

Femur

    

  BMD

35 (70%)

16 (64%)

19 (76%)

0.812

  T-score

37 (74%)

17 (68%)

20 (80%)

0.733

 Lumbar spine

    

  BMD

26 (52%)

11 (44%)

15 (60%)

0.998

  T-score

28 (56%)

12 (48%)

16 (64%)

0.997

RTA

    

 maxH

35 (70%)

16 (64%)

19 (76%)

0.751

 kurtH

34 (68%)

14 (56%)

20 (80%)

0.845

 skewH

33 (66%)

13 (52%)

20 (80%)

0.843

 madH

38 (76%)

17 (68%)

21 (84%)

0.855

RTA & densitometry

42 (84%)

20 (80%)

22 (88%)

0.663

Combination of both lumbar and femoral densitometric parameters in a multivariate model did not increase the rate of detection further.

Radon transform analysis

The difference of means of the RT-based parameters between fracture group and controls was statistically significant at a level of p < 0.001 for maxH to p = 0.06 for kurtH and skewH. Standard deviation of AUC-values as tested by LOO ranged from 0.009 for maxH to 0.011 for kurtH and madH (Table 2). No statisticaly significant relationship existed between femoral BMD and the various RT-based parameters (p = 0.05 to p = 0.41). Intercorrelations among the parameters derived from RT ranged from R2 = 0.02 (skewH vs. madH) to R2 = 0.69 (kurtH vs. skewH).

Depending on the RT-based measure, AUC for correct differentiation between patients with and without fractures ranged from 0.73 for kurtH and skewH to 0.8 for maxH.

Differences of AUC values for RT and densitometric parameters was non-significant (p = 0.53 to 0.86).

The parameter madH – as could be demonstrated by discriminant-analysisis—was the over all best parameter for detection of fracture cases with 84% correct predictions. The rate of identification of hip fracture for the other RT-based parameters ranged from 76% to 80% (λ = 0. 0.751 to 0.855).

Combination of two or more RT-based measures in a multivariate model did not increase the rate of detection further.

If both, densitometric and textural information were considered simultaneusly, 84% of all subjects were assigned correctly to either fracture or non-fracture population and proper identification of hip fracture cases rose to 88% (λ = 0.663). By backward elimination discriminant-analysis we were able to identify kurtH, madH, and femoral BMD as the strongest contributors to the discriminative power of our model with p = 0.014, 0.012, and 0.013, respectively.

Precision

By repeated measurements on the pre- and post-operative images of nine patients we were able to estimate the combined effects of patient positioning and manual ROI placement. Precision errors ranged from 2.3% to 3.9% for skewH and kurtH, respectively. From studies on the precision of DXA it is known that patient positioning for assessment of BMD at the proximal femur is associated with a precision error of between 0.6 to 2.6% [30, 31].

Discussion

In this study we have tested the hypothesis that the trabecular texture extracted from clinical X-ray images of the proximal femur can be characterized by parameters based on the Radon transform. We have tested the ability of the new class of parameters with respect to differentiation between patients with and without fracture of the hip.

The hypothesis was confirmed, as we found a significantly higher statistical relationship between the novel measures and the fracture status in our subjects as compared to results obtained by standard densitometry.

The results of our study indicate that texture analysis by RT provides a method to evaluate bone quality in addition to and possibly as an alternative to standard densitometry. To our knowledge, no previous study has assessed the relationship between fracture of the hip and parameters derived from RT. In contrast to bone densitometry, radiographic techniques are ubiquitously available, and it would be highly beneficial if an individuals fracture risk could be estimated from standard radiographs alone, in particular where DXA is regionally unavailable. However, the method will need to be validated in a prospectively designed study involving larger populations.

Study population

Our study population comprised a total of 50 patients, which—in terms of statistics—seems relatively small. In spite of certain limitations related to the size of the population, we could readily demonstrate that the variation in AUC for the RT-based measures and the densitometric paramers is of comparable magnitude using cross validation by LOO. We therefore conclude that our method is as stable and results are as reproducible as the results obtained by the standard procedure of DXA.

The macroscopic shape of bone is determined by a number of factors including size and weight of the patients. It can further be expected, that obesity should have an effect on the image quality which in turn will probably influence the results of textural analysis using the RT. Since in our study population no statistically significant difference existed between the fracture and the non-fracture group with respect to BMI (p = .31) and since there were no extraordinarily obese subjects, no conclusion on how BMI might affect RT results could be drawn.

We consider our study preliminary in the sense that, with our results, we provide evidence for the general feasibility of radiographic texture analysis by RT. This work will prepare the pathway for a larger project benefitting from experience based on the current data set with respect to optimized parameter-setting for image pre-processing steps and choice of RT-derived texture measures. At this stage, due to the retrospective design of the current work we did not focus on investigating in-depth the effects of factors such as patient positioning, BMI, image quality, etc. In a future, prospectively designed project a thorough analysis will need to be conducted.

The “fracture” model

The fundamental assumption of our study was that at the instance of the trauma, mechanical and structural properties of both hips are very similar. Previous work has provided evidence that, under physiological conditions, no significant variation in structure or density is found between right and left hip: Faulkner et al. [32] reported that femoral BMD in opposing femora is highly correlated and hip axis length of both sides is statistically equivalent. Due to circumstances related to the accident, one of the proximal femora fractures. In the case of the fracture patients, we focused on the hip contralateral to the fracture, which in this train of thought is a hip at ultimate risk of fracture.

Since in the case of our study, radiographic imaging and bone densitometry in the fracture population was conducted within a few days of the trauma, our method comes as close as possible to being an ideal model for studying the fragility of the hip in vivo.

Bone densitometry

At present, the assessment of areal bone mineral density is the clinical gold standard for determination of individual fracture risk and follow-up of patients treated for osteoporosis. BMD accounts for 60% to 80% of the variation in bone strength. The remaining 20% to 40% can be attributed to factors other than BMD referred to as the quality of bone [1113] and to trauma-related factors, e.g., the type and direction of fall and the size of impact force [33, 34].

DXA is a widely available, comparatively affordable, and reliable method for bone densitometry. Shepherd et al. [35] reported manufacturer-dependent short-term BMD precision errors of 1.0% to 1.2% in the spine, 0.9% to 1.3% in the total femur, and between 1.5% to 1.9% in the femoral neck. Patient positioning was reportedly associated with a precision error of between 0.6% to 2.6% [30, 31].

X-ray imaging of trabecular bone

In general, X-ray films poorly reflect the mass of the depicted bone structures but provide useful representions of the trabecular texture projected in 2D: the trajectorial pattern visible in the radiograph is the result of superposition of many layers of individual trabeculae. The methodological difficulty with radiography under clinical conditions is that intensity and contrast variations between images may impede or compromise the accurate evaluation of bone structure.

Prior to quantitative evaluation of the image information we introduced a segmentation step to extract the trabecular trajectories in the ROI. Although RT can readily be applied to graylevel image data we propose binarization as a more robust way to obtain comparable results with respect to variable acquisition conditions occurring in clinical practice. However, standard binarization by thresholding is insensitive to the intensity or contrast variations caused by the image acquisition conditions. In order to overcome this problem, we used a local binarization method based on median filtering which effectively eliminated the influence of varying intensity and contrast levels in the images.

Radon transform analysis

The generalised Radon transform is a standard tool extracting parameterised curves from image data. In the case of bone images the trajectorial patterns formed by approximately linearly assembled trabeculae can be analysed using the parameter domain of straight lines. RT-based analysis is optimal for assessing the orientation of peak trajectorial density which combines orientation, length, number and localized mineral density, which according to Odgaard et al. [36] are key features that determine the strength of trabecular bone. Based on this, our hypothesis was that RT-analysis is both anatomically meaningful and objective.

In this study, we have evaluated parameters from the histogram-representation of the Radon transform, that describe the shape of the distribution of intensity values found in the projection domain of straight lines. Intensity values in the projection domain corresponded to the number of pixels that form a straight line in the trabecular pattern of the radiograph. In osteoporotic bone, trabeculae are found to be scarcer and more disrupted than in healthy bone. Figure 4 compares the histogram-representations of the RT intensities for a patient with hip fracture and a control case. Since the peak of the distribution corresponds to the length of the largest group of trajectories a shift to the left signifies a greater proportion of short trajectories, which may be interpreted as the result of structural disruptions due to progressive bone resorption. For the control case we observe an intensity distribution that is shifted towards relatively longer trajectories. Thus, the properties of trabecular bone structure will directly translate to the shape of the corresponding intensity distribution.

Despite the fact that size is a relevant contributor to the mechanical strength of bone, we intentionally chose to extract ROIs with a predefined size in order to control the maximum intensity values in the domain representation of the texture pattern. These intensity values correspond to the number of pixels that form a straight line in the trabecular pattern of the radiograph. In osteoporotic bone, trabeculae are found to be scarcer and more disrupted than in healthy bone. We wanted to assess this state of relative discontinuity rather than absolute length of trabeculae, which in turn would correlate with bone size. Potential confounding factors are that trabecular strands are not necessarily linear which could potentially obscure the RT results. Another issue associated with ROI-positioning is that radiographically overlaid features such as the pelvic rim and the intertrochanteric crest that penetrate the ROI will have an impact on the analysis results.

The aspects of bone-size, ROI-size and ROI-positioning deserve to be analysed further in the future.

Although the results of RT are known to be relatively stable with respect to noise and structural gaps in the image patters under study, it can be argued that susceptibility to noise depends on the SNR of the data to be transformed. Since the current project is primarily aimed at delivering preliminary results the issue of SNR will need to be examined at depth in the context of a separate study in its own right.

We observed highly significant differences for the RT-based parameters between subjects with and without hip fracture (p < 0.001 to p = 0.006). The novel measures identified between 76% and 84% of the fracture patients, which ranged in the same order of magnitude as the densitometric parameters. Cross validation by LOO implied that the novel methodology is as robust as bone densitometry with precision errors ranging from 1.6 to 3.1%.

No statistically relevant correlation existed between the densitometric parameters and the RT-based parameters. It can therefore be assumed that the novel method provides information complementary to BMD. In fact, by combination of both, densitometric and RT-based parameters in a multivariate model the percentage of correctly identified fracture patients rose to 88%.

In the non-fracture group, densitometry in combination with RT identified four additional cases with low femoral BMD (0.64 ± 0.03 g/cm2). One of the cases with comparatively high BMD (0.82 g/cm2) was moved from correct classification to misclassification by including the RT parameters. In this particular case the trabecular pattern within the femoral neck ROI appeared thinned whereas the cortical structures seemed strong, thus resulting in a normal BMD. In the fracture group, RT in combination with the densitometric parameters correctly identified four additional cases. On the other hand, two cases that were initially correctly classified based on densitometry were ultimately misclassified. The four newly found cases had high BMD values despite being fractured, the ones that were wrongly removed as a result of adding information based on RT parameters had low BMD values (0.63 and 0.64 g/cm2) but the radiograph showed a normal trabecular pattern within the ROI placed in the femoral neck.

Although not validated in prospective studies involving larger populations, our data imply that radiographic texture analysis and clinical DXA of the femur appear to have a comparable statistical potential with respect to discriminate between patients with hip fracture and controls. As far as radiation exposure is concerned, DXA of the spine or hip involves less than 60 µSv whereas diagnostic radiography of the pelvis is quoted to be associated with exposure levels of 0.7 mSv [3739]. On the other hand—in contrast to densitometry—radiographic techniques are ubiquitously available, and it would be a great advantage if qualitative information on skeletal morphology as well as quantitative assessment of fracture risk could be obtained from a single imaging procedure, i.e., standard radiography, in particular where DXA is regionally unavailable.

It remains to be evaluated, whether or not prediction of fragility by radiographic texture evaluation is ethically justified and whether it may supplement or replace screening for osteoporosis.

Comparison with similar studies

Several previous studies have advocated the analysis of X-ray images for measuring bone structure [3941]. Singh et al. [17] have introduced an index describing the degree of osteoporosis by assessing changes in the trabecular pattern of the proximal femur. A strong correlation was found between radiological and histological assessment of osteoporosis.

A number of papers focused on radiographic texture analysis of the os calcis [4244]. Benhamou et al. [42] suggested that fracture risk evaluation can be improved by fractal analysis of calcaneal texture depicted by film radiography. They found that a parameter derived from fractal dimension was capable of differentiating between populations with and without vertebral and femoral fractures.

Pulkkinen et al. [19] analysed radiographic projections of cadaveric femoral specimens and observe a close correlation with ultimate compression strength. Gregory et al. [18] successfully distinguished between hip fracture patients and controls by Fourier analysis of radiographs depicting the trabecular structure of the proximal femur with AUC values of 0.84 to 0.93.

Recently, a combination of both, densitometry and density-pattern analysis has been suggested by our group [45]. Topological analysis of the gray-level distribution in densitometer-generated images in conjunction with femoral bone density identified a significantly larger number of patients with hip fracture than standard evaluation of femoral BMD alone.

All the studies mentioned above imply, that textural features of trabecular bone can readily be obtained from projective imaging modalities and novel analysis techniques exist with performance equal to or better than clinical bone densitometry.

At a rate of up to 84% correctly identified cases of fracture patients, RT-derived measures range in the same order of magnitude as the fractal- or Fourier-based parameters [18, 42]. In our view the latter do not have the same intuitive interpretation as RT-analysis but still application to bone structure may well be justified for these methods. It will definitely be worth comparing performance of the different approaches on the same set of data. At this stage we suggest that RT is a potentially valuable stand-alone or supplemental solution for differentiation between hip-fracture cases and non-fractured controls.

Conclusion

In this paper we have presented a novel method for structural analysis of trabecular bone from clinical radiographs. We have demonstrated that parameters derived from the Radon transform can be used to describe structural properties in images which may be related to fracture, and which provide information independent of BMD. At this stage, we have limited our study to a relatively small number of the datasets. Further analysis is needed to validate our findings. The advantage of the proposed method is twofold: (a) identification of patients at high risk of hip fracture seems to be comparable to clinical densitometry, and (b) the method can be applied to standard radiographs.

In contrast to densitometry, radiographic techniques are widely available throughout the world, and it would be highly beneficial if qualitative information on skeletal morphology as well as quantitative assessment of fracture risk could be obtained during the same imaging procedure, i.e., standard radiography, in particular where DXA is regionally unavailable.

Since X-ray imaging of the hip is associated with exposure levels significantly higher than that of DXA the question has to be asked whether or not radiological texture analysis may supplement or replace screening for osteoporosis.

Conflicts of interest

None.

Copyright information

© International Osteoporosis Foundation and National Osteoporosis Foundation 2008