Fractal analysis of bone X-ray tomographic microscopy projections

A highly generalized classifier for osteoporosis radiography based on multiscale fractal, lacunarity, and entropy distributions

Background: Osteoporosis is a common degenerative disease with high incidence among aging populations. However, in regular radiographic diagnostics, asymptomatic osteoporosis is often overlooked and does not include tests for bone mineral density or bone trabecular condition. Therefore, we proposed a highly generalized classifier for osteoporosis radiography based on the multiscale fractal, lacunarity, and entropy distributions. Methods: We collected a total of 104 radiographs (92 for training and 12 for testing) of lumbar spine L4 and divided them into three groups (normal, osteopenia, and osteoporosis). In parallel, 174 radiographs (116 for training and 58 for testing) of calcaneus from health and osteoporotic fracture groups were collected. The texture feature data of all the radiographs were pulled out and analyzed. The Davies-Bouldin index was applied to optimize hyperparameters of feature counting. Neighborhood component analysis was performed to reduce feature dimension and increase generalization. A support vector machine classifier was trained with only the most effective six features for each binary classification scenario. The accuracy and sensitivity performance were estimated by calculating the area under the curve. Results: Interpretable feature trends of osteoporotic pathological changes were depicted. On the spine test dataset, the accuracy and sensitivity of binary classifiers were 0.851 (95% CI: 0.730-0.922), 0.813 (95% CI: 0.718-0.878), and 0.936 (95% CI: 0.826-1) for osteoporosis diagnosis; 0.721 (95% CI: 0.578-0.824), 0.675 (95% CI: 0.563-0.772), and 0.774 (95% CI: 0.635-0.878) for osteopenia diagnosis; and 0.935 (95% CI: 0.830-0.968), 0.928 (95% CI: 0.863-0.963), and 0.910 (95% CI: 0.746-1) for osteoporosis diagnosis from osteopenia. On the calcaneus test dataset, they were 0.767 (95% CI: 0.629-0.879), 0.672 (95% CI: 0.545-0.793), and 0.790 (95% CI: 0.621-0.923) for osteoporosis diagnosis. Conclusion: This method showed the capacity of resisting disturbance on lateral spine radiographs and high generalization on the calcaneus dataset. Pixel-wise texture features not only helped to understand osteoporosis on radiographs better but also shed new light on computer-aided osteopenia and osteoporosis diagnosis.

Automatic detection of pneumonia in chest X-ray images using textural features

Fast and accurate diagnosis is critical for the triage and management of pneumonia, particularly in the current scenario of a COVID-19 pandemic, where this pathology is a major symptom of the infection. With the objective of providing tools for that purpose, this study assesses the potential of three textural image characterisation methods: radiomics, fractal dimension and the recently developed superpixel-based histon, as biomarkers to be used for training Artificial Intelligence (AI) models in order to detect pneumonia in chest X-ray images. Models generated from three different AI algorithms have been studied: K-Nearest Neighbors, Support Vector Machine and Random Forest. Two open-access image datasets were used in this study. In the first one, a dataset composed of paediatric chest X-ray, the best performing generated models achieved an 83.3% accuracy with 89% sensitivity for radiomics, 89.9% accuracy with 93.6% sensitivity for fractal dimension and 91.3% accuracy with 90.5% sensitivity for superpixels based histon. Second, a dataset derived from an image repository developed primarily as a tool for studying COVID-19 was used. For this dataset, the best performing generated models resulted in a 95.3% accuracy with 99.2% sensitivity for radiomics, 99% accuracy with 100% sensitivity for fractal dimension and 99% accuracy with 98.6% sensitivity for superpixel-based histons. The results confirm the validity of the tested methods as reliable and easy-to-implement automatic diagnostic tools for pneumonia.

Prediction of knee osteoarthritis progression using radiological descriptors obtained from bone texture analysis and Siamese neural networks: data from OAI and MOST cohorts

Background

Trabecular bone texture (TBT) analysis has been identified as an imaging biomarker that provides information on trabecular bone changes due to knee osteoarthritis (KOA). In parallel with the improvement in medical imaging technologies, machine learning methods have received growing interest in the scientific osteoarthritis community to potentially provide clinicians with prognostic data from conventional knee X-ray datasets, in particular from the Osteoarthritis Initiative (OAI) and the Multicenter Osteoarthritis Study (MOST) cohorts.

Patients and methods

This study included 1888 patients from OAI and 683 patients from MOST cohorts. Radiographs were automatically segmented to determine 16 regions of interest. Patients with an early stage of OA risk, with Kellgren and Lawrence (KL) grade of 1 < KL < 4, were selected. The definition of OA progression was an increase in the OARSI medial joint space narrowing (mJSN) grades over 48 months in OAI and 60 months in MOST. The performance of the TBT-CNN model was evaluated and compared to well-known prediction models using logistic regression.

Results

The TBT-CNN model was predictive of the JSN progression with an area under the curve (AUC) up to 0.75 in OAI and 0.81 in MOST. The predictive ability of the TBT-CNN model was invariant with respect to the acquisition modality or image quality. The prediction models performed significantly better with estimated KL (KLprob) grades than those provided by radiologists. TBT-based models significantly outperformed KLprob-based models in MOST and provided similar performances in OAI. In addition, the combined model, when trained in one cohort, was able to predict OA progression in the other cohort.

Conclusion

The proposed combined model provides a good performance in the prediction of mJSN over 4 to 6 years in patients with relevant KOA. Furthermore, the current study presents an important contribution in showing that TBT-based OA prediction models can work with different databases.

Multifractal-based lacunarity analysis of trabecular bone in radiography

This study presents textural characterization techniques for effective osteoporosis diagnosis using bone radiograph images. The automatic classification of osteoporosis and healthy (control) cases using bone radiograph images in this work presents a major challenge as the images show no visual differences for both cases. The proposed work utilizes multifractals to characterize the trabecular bone texture in the radiographs. Initially, Holder exponents are computed, then Hausdorff dimensions are determined, which quantify the global regularity of the pixels. Finally, lacunarity is computed from the Hausdorff dimensions. Performance metrics show that estimating lacunarity from the Hausdorff dimensions, rather than the input image, directly helps in achieving better textural characterization of bone radiographs, leading to better performance in osteoporosis classification. The proposed lacunarity-based trabecular bone textural characterization method is compared with other multifractal-based methods for trabecular bone textural characterization, such as box-counting and regularization dimensions. The proposed method is also evaluated with the textural characterization of a bone radiograph challenge dataset to demonstrate its effectiveness compared to the other methods used in the challenge.

Subchondral tibial bone texture predicts the incidence of radiographic knee osteoarthritis: data from the Osteoarthritis Initiative

OBJECTIVES

To evaluate whether trabecular bone texture (TBT) parameters measured on computed radiographs (CR) could predict the onset of radiographic knee osteoarthritis (OA).

MATERIALS AND METHODS

Subjects from the Osteoarthritis Initiative (OAI) with no sign of radiographic OA at baseline were included. Cases that developed either a global radiographic OA defined by the Kellgren-Lawrence (KL) scale, a joint space narrowing (JSN) or tibial osteophytes (TOS) were compared with the controls with no changes after 48 months of follow-up. Baseline bilateral fixed flexion CR were analyzed using a fractal method to characterize the local variations. The prediction was explored using logistic regression models evaluated by the area under the receiver operating characteristic curves (AUC).

RESULTS

From the 344 knees, 79 (23%) developed radiographic OA after 48 months, 44 (13%) developed progressive JSN and 59 (17%) developed osteophytes. Neither age, gender and BMI, nor their combination predicted poorer KL (AUC 0.57), JSN or TOS (AUC 0.59) scores. The inclusion of the TBT parameters in the models improved the global prediction results for KL (AUC 0.69), JSN (AUC 0.73) and TOS (AUC 0.71) scores.

CONCLUSIONS

Several differences were found between the models predictive of three different outcomes (KL, JSN and TOS), indicating different underlying mechanisms. These results suggest that TBT parameters assessed when radiographic signs are not yet apparent on radiographs may be useful in predicting the onset of radiological tibiofemoral OA as well as identifying at-risk patients for future clinical trials.

Anisotropic Discrete Dual-Tree Wavelet Transform for Improved Classification of Trabecular Bone

This paper deals with a new anisotropic discrete dual-tree wavelet transform (ADDTWT) to characterize the anisotropy of bone texture. More specifically, we propose to extend the conventional discrete dual-tree wavelet transform (DDTWT) by using the anisotropic basis functions associated with the hyperbolic wavelet transform instead of isotropic spectrum supports. A texture classification framework is adopted to assess the performance of the proposed transform. The generalized Gaussian distribution is used to model the distribution of the sub-band coefficients. The estimated vector of parameters for each image is then used as input for the support vector machine classifier. Experiments were conducted on synthesized anisotropic fractional Brownian motion fields and on a real database composed of osteoporotic patients and control cases. Results show that the ADDTWT outperforms most of the competing anisotropic transforms with an area under curve rate of 93%.

Fractional Brownian Motion and Rao Geodesic Distance for Bone X-Ray Image Characterization

Osteoporosis diagnosis has attracted particular attention in recent decades. Textured images from the microarchitecture of osteoporotic and healthy subjects show a high degree of similarity, increasing the difficulty of classifying such textures. Thus, the evaluation of osteoporosis from the bone X-ray images presents a major challenge for pattern recognition and medical applications. The purpose of this paper is to use the fractional Brownian motion (fBm) model and the probability density function of its increments to compute a similarity measure with the Rao geodesic distance to classify trabecular bone X-ray images. When evaluated on synthetic fBm images (test vectors) with the well-known Hurst parameter H, the proposed method met our expectations in which a good classification of the synthetic images was achieved. A clinical study was conducted on textured bone X-ray images from two different female populations of osteoporotic patients (fracture cases) and control subjects. Using the proposed method, an area under curve rate of 97% was achieved.

Bone texture characterization for osteoporosis diagnosis using digital radiography

We introduce texture classification techniques to effectively diagnose osteoporosis in bone radiography data. Osteoporosis is an age-related systemic bone skeletal disorder characterized by low bone mass and bone structure deterioriation that results in increased bone fragility and higher fracture risk. Therefore, early diagnosis can effectively predict fracture risk and prevent the disease. Automated diagnosis from digital radiographs is very challenging since the scans of healthy and osteoporotic subjects show little or no visual differences, and their density histograms mostly overlap. We designed a system to separate healthy from osteoporotic subjects using high-dimensional textural feature representations computed from radiographs. These features were then reduced using feature selection to obtain the more discriminant subset that was finally classified by our methods. The top performing approach yields 79.3% accuracy and 81% area under the ROC over 116 bone radiographs.

Fracture discrimination by combined bone mineral density (BMD) and microarchitectural texture analysis

The use of bone mineral density (BMD) for fracture discrimination may be improved by considering bone microarchitecture. Texture parameters such as trabecular bone score (TBS) or mean Hurst parameter (H) could help to find women who are at high risk of fracture in the non-osteoporotic group. The purpose of this study was to combine BMD and microarchitectural texture parameters (spine TBS and calcaneus H) for the detection of osteoporotic fractures. Two hundred and fifty five women had a lumbar spine (LS), total hip (TH), and femoral neck (FN) DXA. Additionally, texture analyses were performed with TBS on spine DXA and with H on calcaneus radiographs. Seventy-nine women had prevalent fragility fractures. The association with fracture was evaluated by multivariate logistic regressions. The diagnostic value of each parameter alone and together was evaluated by odds ratios (OR). The area under curve (AUC) of the receiver operating characteristics (ROC) were assessed in models including BMD, H, and TBS. Women were also classified above and under the lowest tertile of H or TBS according to their BMD status. Women with prevalent fracture were older and had lower TBS, H, LS-BMD, and TH-BMD than women without fracture. Age-adjusted ORs were 1.66, 1.70, and 1.93 for LS, FN, and TH-BMD, respectively. Both TBS and H remained significantly associated with fracture after adjustment for age and TH-BMD: OR 2.07 [1.43; 3.05] and 1.47 [1.04; 2.11], respectively. The addition of texture parameters in the multivariate models didn't show a significant improvement of the ROC-AUC. However, women with normal or osteopenic BMD in the lowest range of TBS or H had significantly more fractures than women above the TBS or the H threshold. We have shown the potential interest of texture parameters such as TBS and H in addition to BMD to discriminate patients with or without osteoporotic fractures. However, their clinical added values should be evaluated relative to other risk factors.

Microarchitecture parameters describe bone structure and its strength better than BMD

Introduction and Hypothesis. Some papers have shown that bone mineral density (BMD) may not be accurate in predicting fracture risk. Recently microarchitecture parameters have been reported to give information on bone characteristics. The aim of this study was to find out if the values of volume, fractal dimension, and bone mineral density are correlated with bone strength. Methods. Forty-two human bone samples harvested during total hip replacement surgery were cut to cylindrical samples. The geometrical mesh of layers of bone mass obtained from microCT investigation and the volumes of each layer and fractal dimension were calculated. The finite element method was applied to calculate the compression force F causing ε = 0.8% strain. Results. There were stronger correlations for microarchitecture parameters with strength than those for bone mineral density. The values of determination coefficient R² for mean volume and force were 0.88 and 0.90 for mean fractal dimension and force, while for BMD and force the value was 0.53. The samples with bigger mean bone volume of layers and bigger mean fractal dimension of layers (more complex structure) presented higher strength. Conclusion. The volumetric and fractal dimension parameters better describe bone structure and strength than BMD.

Modelling of chromatin morphologies in breast cancer cells undergoing apoptosis using generalized Cauchy field

Chromatin morphologies in human breast cancer cells treated with an anti-cancer agent are analyzed at their early stage of programmed cell death or apoptosis. The gray-level images of nuclear chromatin are modelled as random fields. We used two-dimensional isotropic generalized Cauchy field to characterize local self-similarity and global long-range dependence behaviors in the image spatial data. Generalized Cauchy field allows the description of fractal behavior inferred from fractal dimension and the long-range dependence inferred from correlation exponent to be carried out independently. We demonstrated the usefulness of locally self-similar random fields with long-range dependence for modelling chromatin condensation.

Clinical interest of bone texture analysis in osteoporosis: a case control multicenter study

We demonstrate the clinical interest of bone texture analysis with a new high resolution X-ray device. We have found that the combination of BMD and texture parameter values provided a better assessment of the fracture risk than that obtainable solely by BMD measurement.

INTRODUCTION

Osteoporosis is characterized by BMD and trabecular bone microarchitecture. We have developed a new high-resolution X-ray device with direct digitization. The aim of this study was to demonstrate in a multicenter case control study the clinical interest of bone texture analysis with this new device.

METHODS

In this cross-sectional multicenter case-control population study in post-menopausal women, 159 osteoporotic fractures were compared with 219 control cases. Images were obtained on calcaneus with a direct digital X-ray device (BMA, D3A Medical Systems). Co-occurrence, run-length matrices and the fractal parameter Hmean were evaluated. BMD was measured at the lumbar spine (LS), femoral neck (FN) and total hip (TH) by DXA.

RESULTS

The three texture parameters were significantly lower in osteoporotic fracture cases than in control cases. These differences persisted after adjustment for TH BMD. Receiver operating characteristic curves were used to compare the discriminant capacity of texture parameters and BMD measurements for fracture. The highest areas under curve (AUC) were 0.721 for TH BMD and 0.706 for Hmean (AUC THBMD vs. AUC Hmean, p = NS). We determined the threshold between high and low Hmean parameter values and then the odds ratios (OR) of fracture for low Hmean, for BMD < or =2.5 SD in the T-score and for combinations of both parameters. The OR of fracture for low H was 2.72 (95% CI, 1.36-5.4). For a FN BMD < or = -2.5 SD, the OR of 4.78 (2.19-10.43) shifted to 14.06 (4.41-44.85) adding H.

CONCLUSIONS

These data confirmed the clinical interest of the combination of BMD and texture parameters to improve the assessment of the risk of fracture other that obtainable by the sole BMD measurement.

Fractal dimension of 40 MHz intravascular ultrasound radio frequency signals

OBJECTIVE

Fully automatic tissue characterization in intravascular ultrasound systems is still a challenge for the researchers. The present work aims to evaluate the feasibility of using the Higuchi fractal dimension of intravascular ultrasound radio frequency signals as a feature for tissue characterization.

METHODS

Fractal dimension images are generated based on the radio frequency signals obtained using mechanically rotating 40 MHz intravascular ultrasound catheter (Atlantis SR Plus, Boston Scientific, USA) and compared with the corresponding correlation images.

CONCLUSION

An inverse relation between the fractal dimension images and the correlation images was revealed indicating that the hard or slow moving tissues in the correlation image usually have low fractal dimension and vice-versa. Thus, the present study suggests that fractal dimension images may be used as a feature for intravascular ultrasound tissue characterization and present better resolution then the correlation images.

Automatic detection of malignant tumors in mammograms

Detection of malignant tumors at an early stage is an important first step in diagnosis of the cancerous regions in mammograms. Although many detection schemes have been presented, they are still not adequate to safely eliminate all risks. In this paper we propose classification schemes of unknown test mammograms using fractal analysis and spatial moments distributions as image processing techniques. Two classifiers will be used in conjunction with these techniques: a backpropagation neural network and a self-organizing map. Investigation of the histograms of the spatial moments at low orders shows that discrete image spatial moments cannot distinguish between benign and malignant mammograms. The two-stage backpropagation neural network and the one-stage self-organizing map both give detection rates of 70% and low false positive rates. With further preprocessing and optimization, the performance of these classifiers may be further improved.

Estimation of the 3D self-similarity parameter of trabecular bone from its 2D projection

It has been shown that the analysis of two dimensional (2D) bone X-ray images based on the fractional Brownian motion (fBm) model is a good indicator for quantifying alterations in the three dimensional (3D) bone micro-architecture. However, this 2D measurement is not a direct assessment of the 3D bone properties. In this paper, we first show that S(3D), the self-similarity parameter of 3D fBm, is linked to S(2D), that of its 2D projection, by S(3D)=S(2D)-0.5. In the light of this theoretical result, we have experimentally examined whether this relation holds for trabecular bone. Twenty one specimens of trabecular bone were derived from frozen human femoral heads. They were digitized using a high resolution mu-CT. Their projections were simulated numerically by summing the data in the three orthogonal directions and both 3D and 2D self-similarity parameters were measured. Results show that the self-similarity of the 3D bone volumes and that of their projections are linked by the previous equation. This demonstrates that a simple projection provides 3D information about the bone structure. This information can be a valuable adjunct to the bone mineral density for the early diagnosis of osteoporosis.

Self-similar random field models in discrete space

Self-similar random fields are of interest in various areas of image processing since they fit certain types of natural patterns and textures. Current treatments of self-similarity in continuous two-dimensional (2-D) space use a definition that is a direct extension of the one-dimensional definition, which requires invariance of the statistics of a random process to time scaling. Current discrete-space 2-D approaches do not consider scaling, but, instead, are based on ad hoc formulations, such as digitizing continuous random fields. In this paper, we show that the current statistical self-similarity definition in continuous space is restrictive and provide an alternative, more general definition. We also provide a formalism for discrete-space statistical self-similarity that relies on a new scaling operator for discrete images. Within the new framework, it is possible to synthesize a wider class of discrete-space self-similar random fields and texture images.

Anisotropy changes in post-menopausal osteoporosis: characterization by a new index applied to trabecular bone radiographic images

Bone intrinsic strength is conditioned by several factors, including material property and trabecular micro-architecture. Bone mineral density (BMD) is a good surrogate for material property. Architectural anisotropy is of special interest in mechanics-architecture relations and characterizes the degree of directional organization of a material. We have developed anisotropy indices from the Fast Fourier Transform (FFT) on bone radiographs. We have validated these indices in a cross-sectional uni-center case-control study including 39 postmenopausal women with vertebral fracture and 70 age-matched control cases. BMD was measured at the lumbar spine and femoral neck. A fractal analysis of texture was performed on calcaneus radiographs at three regions of interest (ROIs), and the result was expressed as the H parameter (fractal dimension =H-2). The anisotropy evaluation was based on the FFT spectrum of these three ROIs extracted on calcaneus radiographs. On the FFT spectrum, we have measured the spreading angle of the longitudinal trabeculae called the dispersion longitudinal index (DLI) and the spreading angle of the transversal trabeculae called the dispersion transversal index (DTI). From the measured parameters, an anisotropy index was derived, and the degree of anisotropy (DA) calculated with DLI and DTI. We have compared the results from the vertebral fracture cases and control cases. The best distinction was obtained for the largest ROI located in the great tuberosity of the calcaneus for all parameters ( P <10(-4)).( )The DA parameter showed a higher value in vertebral fracture cases (1.746+/-0.169) than in control cases (1.548+/-0.136); P <10(-4), and the difference persisted after removal of the subjects with hormonal replacement therapy. The analysis of the receiver operating characteristics (ROC) has shown the best results with DA and Hmean: areas under curves (AUCs) respectively of 0.765 and 0.683, while AUCs associated to LS-BMD and FN-BMD were 0.614 and 0.591 lower, respectively. We determined the odds ratios (OR) by uni- and multivariate analysis. Crude ORs were respectively 3.91 (95% CI: 2.22-6.87) and 3.08 (95% CI: 1.72-5.52) for DA and Hmean. Crude ORs were respectively 1.71 (95% CI: 1.15-2.56) and 1.56 (95% CI: 1.05-2.31) for LS-BMD and FN-BMD. All ORs were statistically significant, and those associated to Hmean and anisotropy indices were higher than those of BMD measurements. From a multivariate analysis including anisotropy indices, Hmean, age and FN-BMD, the remaining significant ORs were respectively 6.33 (95% CI: 2.80-14.30) and 3.08 (95% CI: 1.48-6.37) for DA and Hmean. These data have shown that anisotropy indices on calcaneus radiographs can distinguish vertebral fracture cases from control cases. This analysis provides complementary information concerning the BMD and fractal parameter. These data suggest that we can improve the fracture risk evaluation by adding information related to the directional organization of trabecular bone derived from the FFT spectrum on conventional radiographic images.

Analysis of trabecular bone texture by modified Hurst orientation transform method

There is a growing need for noninvasive and inexpensive methods that can effectively be used on a large scale, to detect an onset of early osteoarthritis in human knee joints. Of many possible options, fractal analysis of two-dimensional projection x-ray images of trabecular bone (TB) texture, appears as one of the best approaches. However, there are some problems associated with the characterization of the roughness and anisotropy of the bone texture. To resolve these problems, a modified Hurst orientation transform (HOT) method, previously developed by the authors, has been used in this study. The advantages of the HOT method over other techniques used to analyze bone texture, are that it calculates a two-dimensional fractal dimension in all possible directions and also provides a measure of anisotropy for both surfaces exhibiting strong anisotropy and surfaces exhibiting weak anisotropy. In this study, the accuracy of the HOT method in measuring the bone texture roughness and anisotropy; together with the effects of image noise, blur, exposure, magnification, and projection angle on its performance were investigated. Computer-generated images of fractal surfaces and x-ray images obtained for a human tibia head were used. Results obtained show that the HOT method can effectively be used to characterize the roughness and anisotropy (isotropy) of TB texture.