Analysis of bone X-rays using morphological fractals

Evaluation of cortical and trabecular bone structure of the mandible in patients with ankylosing spondylitis

This study aimed to examine the difference between the fractal dimension (FD) values of the mandibular trabecular bone and the panoramic mandibular index (PMI), mandibular cortical index (MCI) and mandibular cortical thickness (MCW) of patients with ankylosing spondylitis (AS) and healthy control group. A total of 184 individuals (92 cases, 92 controls), were examined in our study. PMI, MCI, and MCW values were calculated on panoramic images of all individuals. For FD values, the region of interest (ROI) was selected with the size of 100 × 100 pixels from the right-left gonial and interdental regions and 50 × 50 pixels from the condylar region. Degenerative changes in the temporomandibular joint (TMJ) region were recorded. PMI, MCI, and MCW values showed statistically significant differences between the groups (p = 0.000, p < 0.001). The radiological signs of mandibular cortical resorption were more severe in the case group than in the control group. PMI and MCW values were found to be lower in the case group than in the control group. It was determined that the number of C3 and C2 values, among the MCI values, was higher in the case group. Only the FD values of the ROI selected from the condyle region were found to be statistically significant and were lower in the case group (p = 0.026, p < 0.05). Degenerative changes in the TMJ region were significantly more frequent in the case groups (p = 0.000, p < 0.001). The fact that the mandibular cortex shows more resorptive features in individuals with AS may require further evaluation in terms of osteoporosis. Because of the low FD values of the condylar regions of these patients and the more frequent degenerative changes, the TMJ region should be followed carefully. Detailed examination of the mandibular cortex and condylar region is beneficial in patients with AS for screening and following osteoporotic changes in these individuals, which is essential for the patient's life quality.

A Detailed Systematic Review on Retinal Image Segmentation Methods

The separation of blood vessels in the retina is a major aspect in detecting ailment and is carried out by segregating the retinal blood vessels from the fundus images. Moreover, it helps to provide earlier therapy for deadly diseases and prevent further impacts due to diabetes and hypertension. Many reviews already exist for this problem, but those reviews have presented the analysis of a single framework. Hence, this article on retinal segmentation review has revealed distinct methodologies with diverse frameworks that are utilized for blood vessel separation. The novelty of this review research lies in finding the best neural network model by comparing its efficiency. For that, machine learning (ML) and deep learning (DL) were compared and have been reported as the best model. Moreover, different datasets were used to segment the retinal blood vessels. The execution of each approach is compared based on the performance metrics such as sensitivity, specificity, and accuracy using publically accessible datasets like STARE, DRIVE, ROSE, REFUGE, and CHASE. This article discloses the implementation capacity of distinct techniques implemented for each segmentation method. Finally, the finest accuracy of 98% and sensitivity of 96% were achieved for the technique of Convolution Neural Network with Ranking Support Vector Machine (CNN-rSVM). Moreover, this technique has utilized public datasets to verify efficiency. Hence, the overall review of this article has revealed a method for earlier diagnosis of diseases to deliver earlier therapy.

Differentiation of osteosarcoma from osteomyelitis using microarchitectural analysis on panoramic radiographs

Diagnosing osteosarcoma (OS) is very challenging and OS is often misdiagnosed as osteomyelitis (OM) due to the nonspecificity of its symptoms upon initial presentation. This study investigated the possibility of detecting OS-induced trabecular bone changes on panoramic radiographs and differentiating OS from OM by analyzing fractal dimensions (FDs) and degrees of anisotropy (DAs). Panoramic radiographs of patients with histopathologically proven OS and OM of the jaw were obtained. A total of 23 patients with OS and 40 patients with OM were enrolled. To investigate whether there was a microarchitectural difference between OS lesions and normal trabecular areas in each patient, two regions of interest (ROIs) were located on the CT images. Three microarchitectural parameters (box-counting FD, fast Fourier transform-based FD, and DA) were calculated. For both OS and OM, significant differences were found for all three microarchitectural parameters. Compared to normal trabecular bone, trabecular bone affected by OS and OM became isotropic and more complex. When comparing OS and OM, a statistically significant difference was found only in DA. Trabecular bones affected by OS became more isotropic than those affected by OM. Microarchitectural analysis, especially DA, could be useful for detecting OS-induced trabecular alterations and differentiating OS from OM.

Investigation of mandibular fractal dimension on digital panoramic radiographs in bruxist individuals

OBJECTIVE

This study aimed to evaluate changes in mandibular trabecular bone structure in bruxism using fractal analysis on digital panoramic radiographs obtained with automatic dosing.

STUDY DESIGN

In this prospective study, fractal analysis was performed on radiographs of 126 bruxists and 126 non-bruxists. Eight paired mandibular regions of interest were selected: the bilateral condylar and gonial regions, and the bilateral dentate regions between the apical areas of the first molar and second premolar and between the first premolar and canine. Fractal dimensions (FDs) were calculated at each site.

RESULTS

Mean FD values in the bilateral gonial regions of the bruxists were significantly lower than those of controls (P ≤ .049). In both groups, FD values of the right dentate region anterior to the mental foramen were significantly lower than those on the left side (P ≤ .042). Females exhibited significantly lower FD values in both condylar regions in both groups (P ≤ .039) and in the right dentate regions in the controls (P ≤ .022). Correlations between age and FD in all regions were positive but nonsignificant in both groups (P > .05).

CONCLUSIONS

FD values of mandibular trabecular bone are affected by bruxism in the gonial region and by laterality and sex differences in the condylar and dentate regions.

Evaluation of trabecular bone changes in patients with periodontitis using fractal analysis: A periapical radiography study

BACKGROUND

The present study was aimed to evaluate the trabecular bone changes between healthy individuals and periodontitis patients with fractal dimension analysis on digital periapical radiographs.

METHODS

Data from 35 healthy and 35 individuals with periodontitis were confirmed from the database of our faculty and included in the study. Two regions of interest (ROI) were selected belonging to mesial and distal region of mandibular first molar on periapical radiographs. The mean fractal dimension (FD) values of two regions were calculated with using box-counting method. Student t test was used for the comparison of the FDs.

RESULTS

The mean FD of individuals with periodontitis was 0.97, whereas it was 1.04 for the healthy group. The mean FD values were significantly higher in the healthy group (P < 0.05). In the periodontitis group, as the FD of mesial interdental bone increased, the FD of distal interdental bone increased significantly (P < 0.05).

CONCLUSION

Because of FD numerically showing changes in bone trabeculation, changes in the alveolar bone can be detected quantitatively.

Evaluation of the mandibular trabecular bone in patients with bruxism using fractal analysis

OBJECTIVE

The aims of this study were (1) to investigate the effect of bruxism on the fractal dimension (FD) of the mandibular trabecular bone through digital panoramic radiographs, and (2) to evaluate the effectiveness of fractal analysis as a diagnostic test for bruxism.

METHODS

One hundred and six bruxer and 106 non-bruxer patients were included in the study. Three bilateral regions of interest (ROI) were selected: ROI-1, the mandibular condyle; ROI-2, the mandibular angle; ROI-3, the-area between the apical regions of the mandibular second premolar and the first molar teeth. FD values for the bruxer and non-bruxer groups were compared for each ROI.

RESULTS

Only the FD measurements for the right mandibular condyle (ROI-1) showed a statistically significant difference (p = 0.041) between the bruxer and non-bruxer individuals. FD values measured in the bruxers (1.40 ± 0.09) were lower than in the non-bruxers (1.42 ± 0.08).

CONCLUSION

Fractal analysis may be a useful method for discerning trabecular differences in the condylar areas of bruxer individuals. In future studies, the unilateral mastication habits, the characteristics of dental wear, and the occlusal bite forces of individuals should be documented.

Utility of the trabecular bone score (TBS) in secondary osteoporosis

Altered bone micro-architecture is an important factor in accounting for fragility fractures. Until recently, it has not been possible to gain information about skeletal microstructure in a way that is clinically feasible. Bone biopsy is essentially a research tool. High-resolution peripheral Quantitative Computed Tomography, while non-invasive, is available only sparsely throughout the world. The trabecular bone score (TBS) is an imaging technology adapted directly from the Dual Energy X-Ray Absorptiometry (DXA) image of the lumbar spine. Thus, it is potentially readily and widely available. In recent years, a large number of studies have demonstrated that TBS is significantly associated with direct measurements of bone micro-architecture, predicts current and future fragility fractures in primary osteoporosis, and may be a useful adjunct to BMD for fracture detection and prediction. In this review, we summarize its potential utility in secondary causes of osteoporosis. In some situations, like glucocorticoid-induced osteoporosis and in diabetes mellitus, the TBS appears to out-perform DXA. It also has apparent value in numerous other disorders associated with diminished bone health, including primary hyperparathyroidism, androgen-deficiency, hormone-receptor positive breast cancer treatment, chronic kidney disease, hemochromatosis, and autoimmune disorders like rheumatoid arthritis. Further research is both needed and warranted to more clearly establish the role of TBS in these and other disorders that adversely affect bone.

Managing osteoporosis in ulcerative colitis: something new?

The authors revise the latest evidence in the literature regarding managing of osteoporosis in ulcerative colitis (UC), paying particular attention to the latest tendency of the research concerning the management of bone damage in the patient affected by UC. It is wise to assess vitamin D status in ulcerative colitis patients to recognize who is predisposed to low levels of vitamin D, whose deficiency has to be treated with oral or parenteral vitamin D supplementation. An adequate dietary calcium intake or supplementation and physical activity, if possible, should be guaranteed. Osteoporotic risk factors, such as smoking and excessive alcohol intake, must be avoided. Steroid has to be prescribed at the lowest possible dosage and for the shortest possible time. Moreover, conditions favoring falling have to been minimized, like carpets, low illumination, sedatives assumption, vitamin D deficiency. It is advisable to assess the fracture risk in all UC patient by the fracture assessment risk tool (FRAX(®) tool), that calculates the ten years risk of fracture for the population aged from 40 to 90 years in many countries of the world. A high risk value could indicate the necessity of treatment, whereas a low risk value suggests a follow-up only. An intermediate risk supports the decision to prescribe bone mineral density (BMD) assessment and a subsequent patient revaluation for treatment. Dual energy X-ray absorptiometry bone densitometry can be used not only for BMD measurement, but also to collect data about bone quality by the means of trabecular bone score and hip structural analysis assessment. These two indices could represent a method of interesting perspectives in evaluating bone status in patients affected by diseases like UC, which may present an impairment of bone quality as well as of bone quantity. In literature there is no strong evidence for instituting pharmacological therapy of bone impairment in UC patients for clinical indications other than those that are also applied to the patients with osteoporosis. Therefore, a reasonable advice is to consider pharmacological treatment for osteoporosis in those UC patients who already present fragility fractures, which bring a high risk of subsequent fractures. Therapy has also to be considered in patients with a high risk of fracture even if it did not yet happen, and particularly when they had long periods of corticosteroid therapy or cumulative high dosages. In patients without fragility fractures or steroid treatment, a medical decision about treatment could be guided by the FRAX tool to determine the intervention threshold. Among drugs for osteoporosis treatment, the bisphosphonates are the most studied ones, with the best and longest evidence of efficacy and safety. Despite this, several questions are still open, such as the duration of treatment, the necessity to discontinue it, the indication of therapy in young patients, particularly in those without previous fractures. Further, it has to be mentioned that a long-term bisphosphonates use in primary osteoporosis has been associated with an increased incidence of dramatic side-effects, even if uncommon, like osteonecrosis of the jaw and atypical sub-trochanteric and diaphyseal femoral fractures. UC is a long-lasting disease and the majority of patients is relatively young. In this scenario primary prevention of fragility fracture is the best cost-effective strategy. Vitamin D supplementation, adequate calcium intake, suitable physical activity (when possible), removing of risk factors for osteoporosis like smoking, and avoiding falling are the best medical acts.

Trabecular bone score: a noninvasive analytical method based upon the DXA image

The trabecular bone score (TBS) is a gray-level textural metric that can be extracted from the two-dimensional lumbar spine dual-energy X-ray absorptiometry (DXA) image. TBS is related to bone microarchitecture and provides skeletal information that is not captured from the standard bone mineral density (BMD) measurement. Based on experimental variograms of the projected DXA image, TBS has the potential to discern differences between DXA scans that show similar BMD measurements. An elevated TBS value correlates with better skeletal microstructure; a low TBS value correlates with weaker skeletal microstructure. Lumbar spine TBS has been evaluated in cross-sectional and longitudinal studies. The following conclusions are based upon publications reviewed in this article: 1) TBS gives lower values in postmenopausal women and in men with previous fragility fractures than their nonfractured counterparts; 2) TBS is complementary to data available by lumbar spine DXA measurements; 3) TBS results are lower in women who have sustained a fragility fracture but in whom DXA does not indicate osteoporosis or even osteopenia; 4) TBS predicts fracture risk as well as lumbar spine BMD measurements in postmenopausal women; 5) efficacious therapies for osteoporosis differ in the extent to which they influence the TBS; 6) TBS is associated with fracture risk in individuals with conditions related to reduced bone mass or bone quality. Based on these data, lumbar spine TBS holds promise as an emerging technology that could well become a valuable clinical tool in the diagnosis of osteoporosis and in fracture risk assessment.

Improving osteoporosis diagnosis in children using image texture analysis

Bone mineral density (BMD) is used in clinical medicine as an indirect indicator of osteoporosis and fracture risk. From a technical point of view Quantitative Computed Tomography (QCT) should be the gold standard in bone densitometry. On the other hand, it is known that a greater percentage increase in skin dose is needed as the patient size is increased: positive results and side effect of long-term steroid treatment as obesity have been found for Duchenne muscular dystrophy (DMD), characterized by a progressive muscle degeneration and substitution with fat. The present work is an effort to improve osteoporosis diagnostic efficacy in children by analyzing the trabecular bone texture in CT L3 vertebra by two methods which are independent of image intensity: fractal dimension with power spectrum and wavelet packets. As results, comparing healthy children (44 children both sexes) with osteoporotic subjects (13 adult women, aged 52-87 years) great differences were noticed in all image texture indicators (p<0.0146). For DMD children (7 boys, not overweight) classified by z-score as osteoporotic because of their low BMD, texture image analysis did not exhibited high spatial frequencies as in the osteoporotic group; the probability that these two groups were similar was weak (p<0.0059), suggesting a more similar bone condition to normal or osteopenia. None of the pediatric groups exhibited as high spatial frequencies as did the osteoporotic women group. These analyses could help to determine osteoporosis in children, where it is often a diagnostic challenge.

Correlations between trabecular bone score, measured using anteroposterior dual-energy X-ray absorptiometry acquisition, and 3-dimensional parameters of bone microarchitecture: an experimental study on human cadaver vertebrae

Developing a novel technique for the efficient, noninvasive clinical evaluation of bone microarchitecture remains both crucial and challenging. The trabecular bone score (TBS) is a new gray-level texture measurement that is applicable to dual-energy X-ray absorptiometry (DXA) images. Significant correlations between TBS and standard 3-dimensional (3D) parameters of bone microarchitecture have been obtained using a numerical simulation approach. The main objective of this study was to empirically evaluate such correlations in anteroposterior spine DXA images. Thirty dried human cadaver vertebrae were evaluated. Micro-computed tomography acquisitions of the bone pieces were obtained at an isotropic resolution of 93μm. Standard parameters of bone microarchitecture were evaluated in a defined region within the vertebral body, excluding cortical bone. The bone pieces were measured on a Prodigy DXA system (GE Medical-Lunar, Madison, WI), using a custom-made positioning device and experimental setup. Significant correlations were detected between TBS and 3D parameters of bone microarchitecture, mostly independent of any correlation between TBS and bone mineral density (BMD). The greatest correlation was between TBS and connectivity density, with TBS explaining roughly 67.2% of the variance. Based on multivariate linear regression modeling, we have established a model to allow for the interpretation of the relationship between TBS and 3D bone microarchitecture parameters. This model indicates that TBS adds greater value and power of differentiation between samples with similar BMDs but different bone microarchitectures. It has been shown that it is possible to estimate bone microarchitecture status derived from DXA imaging using TBS.

Evaluation of the potential use of trabecular bone score to complement bone mineral density in the diagnosis of osteoporosis: a preliminary spine BMD-matched, case-control study

The trabecular bone score (TBS) is a new parameter that is determined from gray-level analysis of dual-energy X-ray absorptiometry (DXA) images. It relies on the mean thickness and volume fraction of trabecular bone microarchitecture. This was a preliminary case-control study to evaluate the potential diagnostic value of TBS as a complement to bone mineral density (BMD), by comparing postmenopausal women with and without fractures. The sample consisted of 45 women with osteoporotic fractures (5 hip fractures, 20 vertebral fractures, and 20 other types of fracture) and 155 women without a fracture. Stratification was performed, taking into account each type of fracture (except hip), and women with and without fractures were matched for age and spine BMD. BMD and TBS were measured at the total spine. TBS measured at the total spine revealed a significant difference between the fracture and age- and spine BMD-matched nonfracture group, when considering all types of fractures and vertebral fractures. In these cases, the diagnostic value of the combination of BMD and TBS likely will be higher compared with that of BMD alone. TBS, as evaluated from standard DXA scans directly, potentially complements BMD in the detection of osteoporotic fractures. Prospective studies are necessary to fully evaluate the potential role of TBS as a complementary risk factor for fracture.

Correlations between grey-level variations in 2D projection images (TBS) and 3D microarchitecture: applications in the study of human trabecular bone microarchitecture

X-ray imaging remains a very cost-effective technique, with many applications in both medical and material science. However, the physical process of X-ray imaging transforms (e.g. projects) the 3-dimensional (3D) microarchitecture of the object or tissue being studied into a complex 2D grey-level texture. The 3D/2D projection process continues to be a difficult mathematical problem, and neither demonstrations nor well-established correlations have positioned 2D texture analysis-based measurement as a valid indirect evaluation of 3D microarchitecture. The trabecular bone score (TBS) is a new grey-level texture measurement which utilizes experimental variograms of 2D projection images. The aim of the present study was to determine the level of correlation between the 3D characteristics of trabecular bone microarchitecture, as evaluated using muCT reconstruction, and TBS, as evaluated using 2D projection images derived directly from 3D muCT reconstruction. Analyses were performed using sets of human cadaver bone samples from different anatomical sites (lumbar spine, femoral neck, and distal radius). Significant correlations were established via standard multiple regression analysis, and via the use of a generic mathematical 3D/2D relationship. In both instances, the correlations established a significant relationship between TBS and two 3D characteristics of bone microarchitecture: bone volume fraction and mean bone thickness. In particular, it appears that TBS permits to accurately differentiate between two 3D microarchitectures that exhibit the same amount of bone, but different trabecular characteristics. These results demonstrate the existence of a robust and generic relationship, taking into consideration a simplified model of a 2D projection image. Ultimately, this may lead to using TBS measurements directly on DXA images obtained in routine clinical practice.

Technical factors in fractal analysis of periapical radiographs

OBJECTIVES

Fractal analysis quantifies complex geometric structures by generating a fractal dimension, which can measure trabecular bone density. The use of non-standardized radiographic techniques potentially limits the reliability of fractal analysis. The objective of this study was to determine how variations in radiographic technique affect fractal dimension.

METHODS

Periapical radiographs of maxillary incisors taken on eight dry human skulls at varying angulation, tube potential and impulse settings were subjected to Fourier transform fractal analysis.

RESULTS

A significant (p < 0.05) difference in fractal dimension, ranging from 2.5 to 2.9, was found between the skulls, potentially reflecting variations in bone trabeculation. However, variations in angulation, tube potential or impulse did not have a statistically significant effect (p > 0.05) on fractal dimension, with the standard deviation of the fractal dimension ranging from +/- 0.005 to +/- 0.062 at various radiographic machine settings.

CONCLUSIONS

This study indicates that non-standardized periapical radiographs may provide a reliable method for determining fractal dimensions, which could be useful in analysing changes in alveolar bone density in various bone disorders.

Morphology-based multifractal estimation for texture segmentation

Multifractal analysis is becoming more and more popular in image segmentation community, in which the box-counting based multifractal dimension estimations are most commonly used. However, in spite of its computational efficiency, the regular partition scheme used by various box-counting methods intrinsically produces less accurate results. In this paper, a novel multifractal estimation algorithm based on mathematical morphology is proposed and a set of new multifractal descriptors, namely the local morphological multifractal exponents is defined to characterize the local scaling properties of textures. A series of cubic structure elements and an iterative dilation scheme are utilized so that the computational complexity of the morphological operations can be tremendously reduced. Both the proposed algorithm and the box-counting based methods have been applied to the segmentation of texture mosaics and real images. The comparison results demonstrate that the morphological multifractal estimation can differentiate texture images more effectively and provide more robust segmentations.

Fractal and Fourier analysis of the hepatic sinusoidal network in normal and cirrhotic rat liver

The organization of the hepatic microvascular network has been widely studied in recent years, especially with regard to cirrhosis. This research has enabled us to recognize the distinctive vascular patterns in the cirrhotic liver, compared with the normal liver, which may explain the cause of liver dysfunction and failure. The aim of this study was to compare normal and cirrhotic rat livers by means of a quantitative mathematical approach based on fractal and Fourier analyses performed on photomicrographs and therefore on discriminant analysis. Vascular corrosion casts of livers belonging to the following three experimental groups were studied by scanning electron microscopy: normal rats, CCl(4)-induced cirrhotic rats and cirrhotic rats after ligation of the bile duct. Photomicrographs were taken at a standard magnification; these images were used for the mathematical analysis. Our experimental design found that use of these different analyses reaches an efficiency of over 94%. Our analyses demonstrated a higher complexity of the normal hepatic sinusoidal network in comparison with the cirrhotic network. In particular, the morphological changes were more marked in the animals with bile duct-ligation cirrhosis compared with animals with CCl(4)-induced cirrhosis. The present findings based on fractal and Fourier analysis could increase our understanding of the pathophysiological alterations of the liver, and may have a diagnostic value in future clinical research.

Fractal dimension and lacunarity analysis of dental radiographs

OBJECTIVE

As the occlusal forces transmitted to the jaw bones during mastication might be different in dentate and edentulous regions, there might be different radiographical trabecular bone texture in these regions. Image analysis procedures are promising techniques which are used to detect structural changes of bone texture on radiographs. In this study, the differences of fractal dimension (FD) and lacunarity measurements of radiographical trabecular bone between dentate and edentulous regions were investigated.

METHODS

Direct digital radiographs of premolar-molar region were taken from 51 patients who were included in our study. Two rectangular regions of interest (ROIs) with the same dimensions (37x119 pixels) were created on these radiographs; one in the edentulous region and the other one in the dentate region. The ROIs were segmented as black and white areas. Box-counting fractal dimension and lacunarity of these regions were calculated.

RESULTS

Paired samples t-test and Pearson correlation coefficients were calculated. It was found that there were differences between dentate and edentulous regions for FD and lacunarity (P=0.000). There is a negative correlation between FD and lacunarity (-0.643, P<0.01), positive correlation between dentate and edentulous regions and FD (0.819, P<0.01), and a negative correlation between lacunarity and dentate and edentulous regions (-0.541, P<0.01).

CONCLUSIONS

The differences of occlusal forces generated in dentate and edentulous regions during mastication cause some alterations in trabecular bone structure, and fractal dimension and lacunarity can reveal these alterations quantitatively.

Fractal analysis of mandibular bony healing after orthognathic surgery

OBJECTIVES

We evaluated the radiographic changes to the operational sites after orthognathic surgery by using fractal analysis.

STUDY DESIGN

Panoramic radiographs from 35 patients who underwent orthognathic surgery on the mandible without any complications during the osseous healing process were selected. The radiographs taken before the operation (stage 0) and 1 or 2 days (stage 1), 1 month (stage 2), 6 months (stage 3), and 12 months (stage 4) after the operation were digitized at 600 dpi with 256 gray levels. The fractal dimension was calculated by means of a tile-counting method in the region of interest centered on the operational site and was statistically analyzed according to its stages.

RESULTS

The fractal dimension was decreased immediately after the operation and increased gradually according to the time lapse (P <.05). The fractal dimension in the region of interest 12 months postoperatively was similar to that preoperatively.

CONCLUSION

This result suggests that fractal dimension can be used to evaluate the bony healing process after orthognathic surgery.

Fractal dimension of trabecular bone projection texture is related to three-dimensional microarchitecture

The purpose of this work was to understand how fractal dimension of two-dimensional (2D) trabecular bone projection images could be related to three-dimensional (3D) trabecular bone properties such as porosity or connectivity. Two alteration processes were applied to trabecular bone images obtained by magnetic resonance imaging: a trabeculae dilation process and a trabeculae removal process. The trabeculae dilation process was applied from the 3D skeleton graph to the 3D initial structure with constant connectivity. The trabeculae removal process was applied from the initial structure to an altered structure having 99% of porosity, in which both porosity and connectivity were modified during this second process. Gray-level projection images of each of the altered structures were simply obtained by summation of voxels, and fractal dimension (Df) was calculated. Porosity (phi) and connectivity per unit volume (Cv) were calculated from the 3D structure. Significant relationships were found between Df, phi, and Cv. Df values increased when porosity increased (dilation and removal processes) and when connectivity decreased (only removal process). These variations were in accordance with all previous clinical studies, suggesting that fractal evaluation of trabecular bone projection has real meaning in terms of porosity and connectivity of the 3D architecture. Furthermore, there was a statistically significant linear dependence between Df and Cv when phi remained constant. Porosity is directly related to bone mineral density and fractal dimension can be easily evaluated in clinical routine. These two parameters could be associated to evaluate the connectivity of the structure.

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 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.

Texture analysis in radiographs: the influence of modulation transfer function and noise on the discriminative ability of texture features

Tissue structures, represented by textures in radiographs, can be quantified using texture analysis methods. Different texture analysis methods have been used to discriminate between different aspects of various diseases in primarily x rays of chest, bone, and breasts. However, most of these methods have not specifically been developed for use on radiographs. Certain characteristics of the radiographic process, e.g., noise and blurring, influence the visible texture. In order for a texture analysis method to be able to discriminate between different underlying textures, it should not be too sensitive for such processes as image noise and blur. In this study, we investigated the sensitivity of four different texture analysis methods for image noise and blur. First, a baseline measurement was performed of the discriminative performance of the Spatial Gray-Level Dependence method, the Fourier Power Spectrum, the Fractal Dimension, and the Morphological Gradient Method on images, which were not affected by radiographic noise and blur. Two types of images were used: fractal and Brodatz. Whereas the Brodatz images represent very different textures, the differences between the fractal images are more gradual. We assume that the behavior of the different texture analysis methods on the fractal images is representative for their performance on radiologic textures. On these types of images we simulated the effect of four different noise levels and the effect of two different modulation transfer functions, corresponding with different screenfilm combinations. The influence on the discriminative performance of the four texture analysis methods was evaluated. The influence of noise on the discriminative performance is, as expected, dependent on the image type used; the discrimination of more gradually different images, such as the fractal images, is already lowered for relatively low noise levels. In contrast, when the images are more different, only high noise levels decrease the discriminative performance. The discriminative power of the Morphological Gradient Method is least affected by image blur. We conclude that the discriminative performance of the Morphological Gradient Method is superior to that of other methods in circumstances which mimic the conditions prevailing in radiographs.

Time and space results of dynamic texture feature extraction in MR and CT image analysis

Texture feature extraction is a fundamental part of texture image analysis. Therefore, the reduction of its computational time and storage requirements should be an aim of continuous research. The Spatial Grey Level Dependence Method (SGLDM) is one of the most important statistical texture description methods, especially in medical image analysis. Co-occurrence matrices are employed for the implementation of this method; however, they are inefficient in terms of computational time and memory space, due to their dependency on the number of gray levels (gray-level range) in the entire image. Since texture is usually measured in a small image region, a large amount of memory is wasted while the computational time of the texture feature extraction operations is unnecessarily raised. Their inefficiency puts up barriers to the wider utilization of SGLDM in a real application environment, such as a clinical environment. In this paper, the memory space and time efficiency of a dynamic approach to texture feature extraction in SGLDM is investigated through a pilot application in the analysis of magnetic resonance (MR) and computed tomography (CT) images.

Estimating fractal dimension with fractal interpolation function models

Fractal dimension (fd) is a feature which is widely used to characterize medical images. Previously, researchers have shown that fd separates important classes of images and provides distinctive information about texture. We analyze limitations of two principal methods of estimating fd: box-counting (BC) and power spectrum (PS). BC is ineffective when applied to data-limited, low-resolution images; PS is based on a fractional Brownian motion (fBm) model-a model which is not universally applicable. We also present background information on the use of fractal interpolation function (FIF) models to estimate fd of data which can be represented in the form of a function. We present a new method of estimating fd in which multiple FIF models are constructed. The mean of the fd's of the FIF models is taken as the estimate of the fd of the original data. The standard deviation of the fd's of the FIF models is used as a confidence measure of the estimate. We demonstrate how the new method can be used to characterize fractal texture of medical images. In a pilot study, we generated plots of curvature values around the perimeters of images of red blood cells from normal and sickle cell subjects. The new method showed improved separation of the image classes when compared to BC and PS methods.

Spatial distribution of femoral bone mineral in dual energy X-ray absorptiometry images: a possible technique to improve discrimination between normal and osteoporotic patients

The measurement of bone mineral density (BMD) using dual energy X-ray absorptiometry (DXA) provides an indicator of subsequent risk of hip fracture, but because of the significant overlap of measurements obtained from osteoporotic and control groups its predictive power is limited. The radiographic technique of Singh grading for the assessment of femoral osteoporosis utilizes information about the distribution of trabecular bundles, but the morphological information available in the DXA image has not previously been analysed. In this study of DXA images from 64 individuals (32 controls and 32 classified as osteoporotic) a subjective grading technique analogous to Singh grading is proposed, and quantitative measurements are made of image features corresponding to two of the categories. Discrimination was assessed using receiver operating characteristic (ROC) curves: the best discrimination was by spinal BMD (Az = 0.85 +/- 0.05) a performance equalled by one of the new parameters; the subjective grading method (Az = 0.79 +/- 0.07) performed as well as measurements of BMD in the femur. These results suggest that although the alternative measures do not improve on the discrimination possible using spinal BMD, morphological information from the hip itself may in the future have a place in the assessment of bone quality.