A comparison of the texture of computed tomography and projection radiography images of vertebral trabecular bone using fractal signature and lacunarity.

The structural integrity of trabecular bone is an important factor characterizing the biomechanical strength of the vertebra, and is determined by the connectivity of the bone network and the trabeculation pattern. These can be assessed using texture measures such as the fractal signature and lacunarity from a high resolution projection radiograph. Using central sections of lumbar vertebrae we compared the results obtained from high-resolution transverse projection images with those obtained from spatially registered low-resolution images from a conventional clinical CT scanner to determine whether clinical CT data can provide useful structural information. Provided the power spectra of the CT images are corrected for image system blurring, the resulting fractal signature is similar for both modalities. Although the CT images are blurred relative to the projection images, with a consequent reduction in lacunarity, the estimated trabecular separation obtained from the lacunarity plots is similar for both modalities. This suggests that these texture measures contain essential information on trabecular microarchitecture, which is present even in low resolution CT images. Such quantitative texture measurements from CT or MRI images are potentially useful in monitoring bone strength and predicting future fracture risk.     

Use of color texture in determining the nature of melanocytic skin lesions--a qualitative and quantitative approach

Melanocytic nevi are recognized as precursors of melanoma. Aiding in early recognition of melanoma, we estimated color texture parameters, fractal dimension and lacunarity of melanoma and other melanocytic nevi. Digital images of the lesions were processed. Graphic three-dimensional pseudoelevation images of the lesions and surrounding skin were produced to identify irregularities in color texture within the lesions. Estimation of lacunarity and fractal dimension followed in order to produce a numerical estimate of the coarseness of color texture. Clinicians readily perceive the resulting "geographical" images. Irregularity in the anaglyph, which might veil malignancy, is effortlessly identified through these images, and therefore an early excision of a suspect lesion is indicated.     

Lacunarity analysis of spatial pattern in CT images of vertebral trabecular bone for assessing osteoporosis

The structural integrity of vertebral trabecular bone is determined by the continuity of its trabecular network and the size of the holes comprising its marrow space, both of which determine the apparent size of the marrow spaces in a transaxial CT image. A model-independent assessment of the trabeculation pattern was determined from the lacunarity of thresholded CT images. Using test images of lumbar vertebrae from human cadavers, acquired at different slice thicknesses, we determined that both median thresholding and local adaptive thresholding (using a 7 x 7 window) successfully segmented the grey-scale images. Lacunarity analysis indicated a multifractal nature to the images, and a range of marrow space sizes with significant structure around 14-18 mm(2). Preliminary studies of in vivo images from a clinical CT scanner indicate that lacunarity analysis can follow the pattern of bone loss in osteoporosis by monitoring the homogeneity of the marrow spaces, which is related to the connectivity of the trabecular bone network and the marrow space sizes. Although the patient sample was small, derived parameters such as the maximum deviation of the lacunarity from a neutral (fractal) model, and the maximum derivative of this deviation, seem to be sufficiently sensitive to distinguish a range of bone conditions. Our results suggest that these parameters, used with bone mineral density values, may have diagnostic value in characterizing osteoporosis and predicting fracture risk.     

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.     

Fractal-based image texture analysis of trabecular bone architecture

Fractal-based image analysis methods are investigated to extract textural features related to the anisotropic structure of trabecular bone from the X-ray images of cubic bone specimens. Three methods are used to quantify image textural features: power spectrum, Minkowski dimension and mean intercept length. The global fractal dimension is used to describe the overall roughness of the image texture. The anisotropic features formed by the trabeculae are characterised by a fabric ellipse, whose orientation and eccentricity reflect the textural anisotropy of the image. Tests of these methods with synthetic images of known fractal dimension show that the Minkowski dimension provides a more accurate and consistent estimation of global fractal dimension. Tests on bone x-ray (eccentricity range 0.25-0.80) images indicate that the Minkowski dimension is more sensitive to the changes in textural orientation. The results suggest that the Minkowski dimension is a better measure for characterising trabecular bone anisotropy in the x-ray images of thick specimens.     

Fractal-based image texture analysis of trabecular bone architecture

Fractal-based image analysis methods are investigated to extract textural features related to the anisotropic structure of trabecular bone from the X-ray images of cubic bone specimens. Three methods are used to quantify image textural features: power spectrum, Minkowski dimension and mean intercept length. The global fractal dimension is used to describe the overall roughness of the image texture. The anisotropic features formed by the trabeculae are characterised by a fabric ellipse, whose orientation and eccentricity reflect the textural anisotropy of the image. Tests of these methods with synthetic images of known fractal dimension show that the Minkowski dimension provides a more accurate and consistent estimation of global fractal dimension. Tests on bone x-ray (eccentricity range 0.25–0.80) images indicate that the Minkowski dimension is more sensitive to the changes in textural orientation. The results suggest that the Minkowski dimension is a better measure for characterising trabecular bone anisotropy in the x-ray images of thick specimens.     

Analysis of texture in macroradiographs of osteoarthritic knees using the fractal signature

Texture of regions of macroradiographs (x5) of six normal and five osteoarthritic knee joints, taken on a high resolution microfocal x-ray unit, are examined using mathematical morphology. Radiographs of bones are two-dimensional projections of attenuation coefficient through the three-dimensional (3D) joint structure. Visible texture represents the summation of the attenuation from numerous thin plates of bone. Where there is no organization in the trabeculae, resultant radiographs approximate a fractal surface. Varying structuring element size in mathematical morphology allows estimation of fractal dimension over a range of resolution. Variation of fractal dimension with resolution, the fractal signature, indicates how images deviate from fractal surfaces. By correct choice of structuring element, a texture analysis method using the fractal signature has been developed, tolerant to changes in image acquisition and digitization. Texture in regions of radiographs of normal tibia approximates a fractal surface with dimension 2.8 as does vertical structure in arthritic patients. In osteoarthritic knee joints, horizontal tibial trabeculae thicken. Horizontal structure in the tibia on radiographs of arthritic patients deviates from the fractal model. This is indicated by peaks in the fractal signature whose height and position match a visual assessment of the degree of arthritic change.     

Fractal analysis of radiographs: assessment of trabecular bone structure and prediction of elastic modulus and strength.

The purpose of this study was to determine whether fractal dimension of radiographs provide measures of trabecular bone structure which correlate with bone mineral density (BMD) and bone biomechanics, and whether these relationships depend on the technique used to calculate the fractal dimension. Eighty seven cubic specimen of human trabecular bone were obtained from the vertebrae and femur. The cubes were radiographed along all three orientations--superior-inferior (SI), medial-lateral (ML), and anterior-posterior (AP), digitized, corrected for background variations, and fractal based techniques were applied to quantify trabecular structure. Three different techniques namely, semivariance, surface area, and power spectral methods were used. The specimens were tested in compression along three orientations and the Young's modulus (YM) was determined. Compressive strength was measured along the SI direction. Quantitative computed tomography was used to measure trabecular BMD. High-resolution magnetic-resonance images were used to obtain three-dimensional measures of trabecular architecture such as the apparent bone volume fraction, trabecular thickness, spacing, and number. The measures of trabecular structure computed in the different directions showed significant differences (p<0.05). The correlation between BMD, YM, strength, and the fractal dimension were direction and technique dependent. The trends of variation of the fractal dimension with BMD and biomechanical properties also depended on the technique and the range of resolutions over which the data was analyzed. The fractal dimension showed varying trends with bone mineral density changes, and these trends also depended on the range of frequencies over which the fractal dimension was measured. For example, using the power spectral method the fractal dimension increased with BMD when computed over a lower range of spatial frequencies and decreased for higher ranges. However, for the surface area technique the fractal dimension increased with increasing BMD. Fractal measures showed better correlation with trabecular spacing and number, compared to trabecular thickness. In a multivariate regression model inclusion of some of the fractal measures in addition to BMD improved the prediction of strength and elastic modulus. Thus, fractal based texture analysis of radiographs are technique dependent, but may be used to quantify trabecular structure and have a potentially valuable impact in the study of osteoporosis.     

Computerized radiographic texture measures for characterizing bone strength: a simulated clinical setup using femoral neck specimens

We are investigating computerized methods to ultimately characterize bone trabecular pattern from clinical skeletal radiographs. In this paper, we present a "phantom" for potential use in the development and evaluation of computerized methods for characterizing radiographic trabecular patterns and ultimately bone strength. Femoral neck specimens were excised during total hip arthroplasties from subjects exhibiting a range of diseases. To mimic the femoral neck in vivo, a "simulated clinical" setup was implemented in which specimens were exposed under conditions that yielded radiographs similar in appearance to standard pelvis radiographs. Fourier-based and fractal-based texture measures were used in the computer analysis; including RMS variation, first moment of the power spectrum, angular-dependent forms of these measures, and fractal dimension. The texture measures obtained from the "simulated clinical" specimen films correlated modestly with those from direct exposure "verification" films of the specimens (r= 0.59-0.69; p<0.0001). From our study, we conclude that the femoral neck specimen "phantoms" may be useful in the development and evaluation of computerized methods for analyzing bone trabecular patterns from skeletal radiographs. The use of a phantom that simulates the clinical radiographic examination allows for repeat exposures without the concern of excessive radiation exposure to a patient.     

Automated selection of trabecular bone regions in knee radiographs

Osteoarthritic (OA) changes in knee joints can be assessed by analyzing the structure of trabecular bone (TB) in the tibia. This analysis is performed on TB regions selected manually by a human operator on x-ray images. Manual selection is time-consuming, tedious, and expensive. Even if a radiologist expert or highly trained person is available to select regions, high inter- and intraobserver variabilities are still possible. A fully automated image segmentation method was, therefore, developed to select the bone regions for numerical analyses of changes in bone structures. The newly developed method consists of image preprocessing, delineation of cortical bone plates (active shape model), and location of regions of interest (ROI). The method was trained on an independent set of 40 x-ray images. Automatically selected regions were compared to the "gold standard" that contains ROIs selected manually by a radiologist expert on 132 x-ray images. All images were acquired from subjects locked in a standardized standing position using a radiography rig. The size of each ROI is 12.8 x 12.8 mm. The automated method results showed a good agreement with the gold standard [similarity index (SI) = 0.83 (medial) and 0.81 (lateral) and the offset =[-1.78, 1.27]x[-0.65,0.26] mm (medial) and [-2.15, 1.59]x[-0.58, 0.52] mm (lateral)]. Bland and Altman plots were constructed for fractal signatures, and changes of fractal dimensions (FD) to region offsets calculated between the gold standard and automatically selected regions were calculated. The plots showed a random scatter and the 95% confidence intervals were (-0.006, 0.008) and (-0.001, 0.011). The changes of FDs to region offsets were less than 0.035. Previous studies showed that differences in FDs between non-OA and OA bone regions were greater than 0.05. ROIs were also selected by a second radiologist and then evaluated. Results indicated that the newly developed method could replace a human operator and produces bone regions with an accuracy that is sufficient for fractal analyses of bone texture.     

Comparison of radiographic texture analysis from computed radiography and bone densitometry systems

Osteoporosis is a disease that results in an increased risk of bone fracture due to a loss of bone mass and deterioration of bone structure. Bone mineral density (BMD) provides a measure of bone mass and is frequently measured by bone densitometry systems to diagnose osteoporosis. In addition, computerized radiographic texture analysis (RTA) is currently being investigated as a measure of bone structure and as an additional diagnostic predictor of osteoporosis. In this study, we assessed the ability of a peripheral bone densitometry (PD) system to yield images useful for RTA. The benefit of such a system is that it measures BMD by dual-energy x-ray absorptiometry and therefore provides high- and low-energy digital radiographic images. The bone densitometry system investigated was the GE/Lunar PIXI, which provides 512 x 512 digital images of the heel or forearm (0.2 mm pixels). We compared texture features of heel images obtained with this PD system to those obtained on a Fuji computed radiography (CR) system (0.1 mm pixels). Fourier and fractal-based texture features of images from 24 subjects who had both CR and BMD exams were calculated, and correlation between the two systems was analyzed. Fourier-based texture features characterize the magnitude, frequency content, and orientation of the trabecular bone pattern. Good correlation was found between the two modalities for the first moment (FMP) with r=0.71 (p value<0.0001) and for minimum FMP with r=0.52 (p value=0.008). Root-mean-square (RMS) did not correlate with r=0.31 (p value>0.05), while the standard deviation of the RMS did correlate with r=0.79 (p value<0.0001). Good correlation was also found between the two modalities for the fractal-based texture features with r=0.79 (p value<0.0001) for the global Minkowski dimension and r=0.63 (p value=0.0007) for the fractal dimension from a box counting method. The PD system therefore may have the potential for yielding heel images suitable for RTA.     

Fractal analysis of lumbar vertebral cancellous bone architecture.

Osteoporosis is characterized by bone mineral density (BMD) decreasing and spongy bone rearrangement with consequent loss of elasticity and increased bone fragility. Quantitative computed tomography (QCT) quantifies bone mineral content but does not describe spongy architecture. Analysis of trabecular pattern may provide additional information to evaluate osteoporosis. The aim of this study was to determine whether the fractal analysis of the microradiography of lumbar vertebrae provides a reliable assessment of bone texture, which correlates with the BMD. The lumbar segment of the spine was removed from 22 cadavers with no history of back pain and examined with standard x-ray, traditional tomography, and quantitative computed tomography to measure BMD. The fractal dimension, which quantifies the image fractal complexity, was calculated on microradiographs of axial sections of the fourth lumbar vertebra to determine its characteristic spongy network. The relationship between the values of the BMD and those of the fractal dimension was evaluated by linear regression and a statistically significant correlation (R = 0.96) was found. These findings suggest that the application of fractal analysis to radiological analyses can provide valuable information on the trabecular pattern of vertebrae. Thus, fractal dimensions of trabecular bone structure should be considered as a supplement to BMD evaluation in the assessment of osteoporosis.     

A quantitative approach to scar analysis

Analysis of collagen architecture is essential to wound healing research. However, to date no consistent methodologies exist for quantitatively assessing dermal collagen architecture in scars. In this study, we developed a standardized approach for quantitative analysis of scar collagen morphology by confocal microscopy using fractal dimension and lacunarity analysis. Full-thickness wounds were created on adult mice, closed by primary intention, and harvested at 14 days after wounding for morphometrics and standard Fourier transform-based scar analysis as well as fractal dimension and lacunarity analysis. In addition, transmission electron microscopy was used to evaluate collagen ultrastructure. We demonstrated that fractal dimension and lacunarity analysis were superior to Fourier transform analysis in discriminating scar versus unwounded tissue in a wild-type mouse model. To fully test the robustness of this scar analysis approach, a fibromodulin-null mouse model that heals with increased scar was also used. Fractal dimension and lacunarity analysis effectively discriminated unwounded fibromodulin-null versus wild-type skin as well as healing fibromodulin-null versus wild-type wounds, whereas Fourier transform analysis failed to do so. Furthermore, fractal dimension and lacunarity data also correlated well with transmission electron microscopy collagen ultrastructure analysis, adding to their validity. These results demonstrate that fractal dimension and lacunarity are more sensitive than Fourier transform analysis for quantification of scar morphology.     

Trabecular bone does not have a fractal structure on light microscopic examination

The fractal dimension of the boundary of trabecular bone in 62 biopsies was measured on histological sections using a box-counting method implemented on a microcomputer image analysis system. The calculated fractal dimension had a mean value of 0.99 with a normal distribution. Since this value is not greater than the topological dimension (1), trabecular bone, when examined by light microscopy, does not have a fractal structure. Conventional Euclidean dimensions will continue to be the most useful measurements in bone histomorphometry.     

In vivo assessment of trabecular bone structure using fractal analysis of distal radius radiographs

Our purpose in this study was (i) to measure trabecular bone structure using fractal analysis of distal radius radiographs in subjects with and without osteoporotic hip fractures, and (ii) to compare these measures with bone mineral density (BMD) as well as with measures of trabecular bone structure derived from high resolution magnetic resonance (MR) images. Distal radius radiographs were obtained using semi-industrial films (55 kVp, 400 mAs) in 30 postmenopausal patients, who had suffered osteoporotic hip fractures (74.8+/-8.2 years) in the last 24 months and 27 postmenopausal age-matched (74.6+/-6.6 yr) normal volunteers. Radiographs were digitized at 50 microm. A Fourier power spectrum-based fractal dimension (FD) characterizing the trabecular pattern was measured in a region of interest proximal to the joint line. The fractal dimension was calculated over two spatial frequency (f) ranges: FD1 was calculated over 0.5相似文献   

Fractal properties of postural sway during quiet stance with changed visual and proprioceptive inputs

We studied the fractal dynamics of postural sway during quiet stance with changed visual and/or proprioceptive information. Radius-vector length and angle of rotation of center of foot pressure (COP) displacements were used as parameters of postural sway. The experiments were performed on 24 healthy volunteers of both sexes aged 20–30 years. Using a battery of nonlinearity tests, differences in the degree of fractality of both parameters during stance were found. We found that the behavior of radius-vector was similar to fractional Brownian motion, while that of angle of rotation was similar to flicker noise. Quantitative parameters that can be used to characterize the changes in radius-vector length and angle of rotation include self-similarity intervals and fractal dimension. In healthy subjects, the process of postural control maintains its fractal structure independently of altered sensory information. We believe that this analysis provides information about new methods for evaluating postural sway behavior during quiet stance.