Power spectral analysis of vertebral trabecular bone structure from radiographs: orientation dependence and correlation with bone mineral density and mechanical properties

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.

Density and mechanical properties of vertebral trabecular bone-A review

Being able to predict the mechanical properties of vertebrae in patients with osteoporosis and other relevant pathologies is essential to prevent fractures and to develop the most favorable fracture treatments. Furthermore, a reliable prediction is important for developing more patient- and pathology-specific biomaterials. A plethora of studies correlating bone density to mechanical properties has been reported; however, the results are variable, due to a variety of factors, including anatomical site and methodological differences. The aim of this study was to provide a comprehensive literature review on density and mechanical properties of human vertebral trabecular bone as well as relationships found between these properties. A literature search was performed to include studies, which investigated mechanical properties and bone density of trabecular bone. Only studies on vertebral trabecular bone tissue, reporting bone density or mechanical properties, were kept. A large variation in reported vertebral trabecular bone densities, mechanical properties, and relationships between the two was found, as exemplified by values varying between 0.09 and 0.35 g/cm3 for the wet apparent density and from 0.1 to 976 MPa for the elastic modulus. The differences were found to reflect variations in experimental and analytical processes that had been used, including testing protocol and specimen geometry. The variability in the data decreased in studies where bone tissue testing occurred in a standardized manner (eg, the reported differences in average elastic modulus decreased from 400% to 10%). It is important to take this variability into account when analyzing the predictions found in the literature, for example, to calculate fracture risk, and it is recommended to use the models suggested in the present review to reduce data variability.

Ectopic bone formation in rapidly fabricated acellular injectable dense collagen-Bioglass hybrid scaffolds via gel aspiration-ejection

Gel aspiration-ejection (GAE) has recently been introduced as an effective technique for the rapid production of injectable dense collagen (IDC) gel scaffolds with tunable collagen fibrillar densities (CFDs) and microstructures. Herein, a GAE system was applied for the advanced production and delivery of IDC and IDC-Bioglass(®) (IDC-BG) hybrid gel scaffolds for potential bone tissue engineering applications. The efficacy of GAE in generating mineralizable IDC-BG gels (from an initial 75-25 collagen-BG ratio) produced through needle gauge numbers 8G (3.4 mm diameter and 6 wt% CFD) and 14G (1.6 mm diameter and 14 wt% CFD) was investigated. Second harmonic generation (SHG) imaging of as-made gels revealed an increase in collagen fibril alignment with needle gauge number. In vitro mineralization of IDC-BG gels was confirmed where carbonated hydroxyapatite was detected as early as day 1 in simulated body fluid, which progressively increased up to day 14. In vivo mineralization of, and host response to, acellular IDC and IDC-BG gel scaffolds were further investigated following subcutaneous injection in adult rats. Mineralization, neovascularization and cell infiltration into the scaffolds was enhanced by the addition of BG and at day 21 post injection, there was evidence of remodelling of granulation tissue into woven bone-like tissue in IDC-BG. SHG imaging of explanted scaffolds indicated collagen fibril remodelling through cell infiltration and mineralization over time. In sum, the results suggest that IDC-BG hybrid gels have osteoinductive properties and potentially offer a novel therapeutic approach for procedures requiring the injectable delivery of a malleable and dynamic bone graft that mineralizes under physiological conditions.

Quantifying tumour heterogeneity with CT

Heterogeneity is a key feature of malignancy associated with adverse tumour biology. Quantifying heterogeneity could provide a useful non-invasive imaging biomarker. Heterogeneity on computed tomography (CT) can be quantified using texture analysis which extracts spatial information from CT images (unenhanced, contrast-enhanced and derived images such as CT perfusion) that may not be perceptible to the naked eye. The main components of texture analysis can be categorized into image transformation and quantification. Image transformation filters the conventional image into its basic components (spatial, frequency, etc.) to produce derived subimages. Texture quantification techniques include structural-, model- (fractal dimensions), statistical- and frequency-based methods. The underlying tumour biology that CT texture analysis may reflect includes (but is not limited to) tumour hypoxia and angiogenesis. Emerging studies show that CT texture analysis has the potential to be a useful adjunct in clinical oncologic imaging, providing important information about tumour characterization, prognosis and treatment prediction and response.

Assessment of performance improvement in content-based medical image retrieval schemes using fractal dimension

RATIONALE AND OBJECTIVES

The aim of this study was to investigate whether using a fractal dimension as an objective index (quantitative measure) to assess and control the "visual" or "texture" similarity of reference-image regions selected by a content-based image retrieval (CBIR) scheme would (or would not) affect the performance of the scheme in classification between image regions depicting suspicious breast masses.

MATERIALS AND METHODS

An image data set depicting 1500 verified mass regions and 1500 false-positive mass regions was used. Fourteen morphologic and intensity distribution features and a fractal dimension were computed. A CBIR scheme using a k-nearest neighbor classifier was applied, and two experiments were conducted. In the first experiment, the CBIR scheme was evaluated using all 15 features. In the second experiment, the fractal dimension was used as a prescreening feature to guide the CBIR scheme to search for the most similar reference images that had similar measures in the fractal dimension.

RESULTS

The CBIR scheme achieved classification performance with areas under the receiver-operating characteristic curve of 0.857 (95% confidence interval [CI], 0.844-0.870) using 14 features and 0.866 (95% CI, 0.853-0.879) after adding the fractal dimension (P = .005 for both results). After using the fractal dimension as a prescreening feature, the CBIR scheme achieved an area under the receiver-operating characteristic curve of 0.851 (95% CI, 0.837-0.864), without a significant difference from the previous result using the original 14 features (P = .120). The difference of fractal dimension values between the selected similar reference images was reduced by 56.7%, indicating improvement in image texture similarity. In addition, more than half of references were discarded early, without similarity comparisons, indicating improvement in searching efficiency.

CONCLUSIONS

This study demonstrated the feasibility of applying a fractal dimension as an objective (quantitative) and efficient search index to assess and maintain the texture similarity of reference mass regions selected by a CBIR scheme without reducing the scheme's performance in classifying suspicious breast masses.

Advances in osteoporosis imaging

In the assessment of osteoporosis, the measurement of bone mineral density (BMD(a)) obtained from dual energy X-ray absorptiometry (DXA; g/cm(2)) is the most widely used parameter. However, bone strength and fracture risk are also influenced by parameters of bone quality such as micro-architecture and tissue properties. This article reviews the radiological techniques currently available for imaging and quantifying bone structure, as well as advanced techniques to image bone quality. With the recent developments in magnetic resonance (MR) techniques, including the availability of clinical 3T scanners, and advances in computed tomography (CT) technology (e.g. clinical Micro-CT), in-vivo imaging of the trabecular bone architecture is becoming more feasible. Several in-vitro studies have demonstrated that bone architecture, measured by MR or CT, was a BMD-independent determinant of bone strength. In-vivo studies showed that patients with, and without, osteoporotic fractures could better be separated with parameters of bone architecture than with BMD. Parameters of trabecular architecture were more sensitive to treatment effects than BMD. Besides the 3D tomographic techniques, projection radiography has been used in the peripheral skeleton as an additional tool to better predict fracture risk than BMD alone. The quantification of the trabecular architecture included parameters of scale, shape, anisotropy and connectivity. Finite element analyses required highest resolution, but best predicted the biomechanical properties of the bone. MR diffusion and perfusion imaging and MR spectroscopy may provide measures of bone quality beyond trabecular micro-architecture.

Age- and sex-related regional compressive strength characteristics of human lumbar vertebrae in osteoporosis

OBJECTIVE

To obtain the compressive load bearing and energy absorption capacity of lumbar vertebrae of osteoporotic elderly for the everyday medical praxis in terms of the simple diagnostic data, like computed tomography (CT), densitometry, age, and sex.

METHODS

Compressive test of 54 osteoporotic cadaver vertebrae L1 and L2, 16 males and 38 females (age range 43-93, mean age 71.6 ± 13.3 years, mean bone mineral density (BMD) 0.377 ± 0.089 g/cm(2), mean T-score -5.57 ± 0.79, Z-score -4.05 ± 0.77) was investigated. Based on the load-displacement diagrams and the measured geometrical parameters of vertebral bodies, proportional, ultimate and yield stresses and strains, Young's modulus, ductility and energy absorption capacity were determined. Three vertebral regions were distinguished: superior, central and inferior regions, but certain parameters were calculated for the upper/ lower intermediate layers, as well. Cross-sectional areas, and certain bone tissue parameters were determined by image analysis of CT pictures of vertebrae. Sex- and age-related decline functions and trends of strength characteristics were determined.

RESULTS

Size-corrected failure load was 15%-25% smaller in women, proportional and ultimate stresses were about 30%-35% smaller for women in any region, and 20%-25% higher in central regions for both sexes. Young's moduli were about 30% smaller in women in any region, and 20%-25% smaller in the central region for both sexes. Small strains were higher in males, large strains were higher in females, namely, proportional strains were about 25% larger in men, yield and ultimate strains were quasi equal for sexes, break strains were 10% higher in women. Ultimate energy absorption capacity was 10%-20% higher in men; the final ductile energy absorption capacity was quasi equal for sexes in all levels. Age-dependence was stronger for men, mainly in central regions (ultimate load, male: r = -0.66, p < 0.01, female: r = -0.52, p < 0.005; ultimate stress, male: r = -0.69, p < 0.01, female: r = -0.50, p < 0.005; Young's modulus, male: r = -0.55, p < 0.05, female: r = -0.52, p < 0.005, ultimate stiffness, male: r = -0.58, p < 0.05, female: r = -0.35, p < 0.03, central ultimate absorbed energy density, male: r = -0.59, p < 0.015, female: r = -0.29, p < 0.08).

CONCLUSIONS

For the strongly osteoporotic population (BMD < 0.4 g/cm(2), T-score < -4) the statical variables (loads, stresses) showed significant correlation; mixed variables (stiffness, Young's modulus, energy) showed moderate correlation; kinematical variables (displacements, strains) showed no correlation with age. The strong correlation of men between BMD and aging (r = -0.82, p < 0.001) and betwen BMD and strength parameters (r = 0.8-0.9, p < 0.001) indicated linear trends in age-related strength loss for men; however, the moderate correlation of women between BMD and aging (r = -0.47, p < 0.005) and between BMD and strength parameters (r = 0.4-0.5, p < 0.005) suggested the need of nonlinear (quadratic) approximation that provided the better fit in age-related strength functions of females modelling postmenopausal disproportionalities.

The distribution of mineral density in the cervical vertebral endplates

Subsidence of various constructs into the vertebral body is a well-known complication in anterior fusion. Information on bone structure is needed, as a basis for improving these procedures. There are, however, no data available on the distribution of mineral density within vertebral endplates. In this study the regional distribution of mineralization within the cervical endplates with respect to endplate orientation (inferior and superior endplate) and level distribution (C3-C7) was examined by means of computed tomographic osteoabsorptiometry (CT-OAM). The distribution of mineralization in 80 cervical endplates of 8 spinal columns (4 male, 4 female, age range 38-62 years) in vertebrae C3-C7 was investigated by CT osteoabsorptiometry (CT-OAM). The subchondral mineralization distribution revealed considerable topographic differences within each endplate, whereby the areas of greatest density were found in the peripheral marginal zones with maxima in the posterolateral surface, whereas mineralization density was much lower in the central areas. The superior endplates showed an additional posteromedial maximum, whereas the inferior endplates showed an additional anterior mineralization maximum. Comparison of the distribution patters of inferior and superior endplates at different levels from C3 to C7 reveals a uniform increase of mineralization in the anterior portions from cranial to caudal. The mineralization distribution showed characteristic reproducible patterns. The maximal values occurred in the posterolateral parts, and can thus be considered a morphological substrate of high long-term loading. This can serve as a basis for improved prosthesis design and the anchorage point for various fusion techniques.

Direct measurement of trabecular bone anisotropy using directional fractal dimension and principal axes of inertia

OBJECTIVE

Precise in vivo measurement of the trabecular bone's mechanical properties is very important for endosseous dental implant treatment and design in clinical practice. The fractal structure of trabecular bone shows directional anisotropy of the architecture, as is shown in most biological fractals. To analyze the anisotropy of the trabecular bone, the fractal geometry technique was applied to 2-dimensional plain radiographs.

STUDY DESIGN

The power spectrum was used to calculate the fractal dimensions (FD) of the trabecular bone. The FDs calculated as a function of orientation yielded the fractal information reflecting the spatial characteristics of the trabecular bone in each direction. A polar plot of directional FDs was defined as an ellipse of inertia. The principal loading direction in a local region of the trabecular bone was determined from the minimum moment of inertia for the ellipse of FDs. The anisotropy was calculated directly as the ratio of the 2 principal moments of inertia from the ellipse.

RESULTS

The anisotropies were measured for radiographs from the angle and incisor region of 21 human mandibles based on the principal axes of inertia and the best-fitting ellipse. The anisotropy of the angle region was significantly greater than that of the incisor region of the mandibles.

CONCLUSION

The method using directional FDs as determined by the principal axis of inertia measures the anisotropy directly, using 2-dimensional plain radiographs. It can quantify the anisotropy of trabecular bone in vivo. The investigation can be applied to the analysis of the relationships between in vivo 2-dimensional parameters and 3-dimensional mechanical properties, which enables us to predict the bone mechanical properties such as strength in vivo in various regions of the mandible.

Comparison of trabecular bone anisotropies based on fractal dimensions and mean intercept length determined by principal axes of inertia

The mechanical quality of trabecular bone depends on both its stiffness and its strength characteristics, which can be predicted indirectly by the combination of bone volume fraction and architectural anisotropy. To analyze the directional anisotropy of the trabecular bone, we applied the fractal geometry technique to plain radiographs. The anisotropy of the bone was quantified from an ellipse, based on the directional fractal dimensions (FD), by the principal axes of inertia. The anisotropies based on the FD were compared with those determined using the common method of mean intercept length (MIL). The directional FD gave the fractal information obtained from a projection along the MIL orientation. For this reason, the spatial variations associated with the bone length in any direction were manifested in a related frequency band of the power spectrum determined along the direction. The directional FD and MIL plots were highly correlated, although they originated from quite different geometries. Of the angle, premolar, and incisor regions of the human mandible, the anisotropies calculated using both FD and MIL showed the highest correlation in the trabecular bone of the angle region. The method using directional FDs as determined by the principal axis of inertia measures the anisotropy directly, using two-dimensional plain radiographs. This kind of method will be a useful to provide better estimates of bone quality in vivo compared with the density measurements alone, especially for the indirect diagnosis of jawbone quality in dental clinics.

Comparative assessment of bone mass and structure using texture-based and histomorphometric analyses

The purpose of this study was to develop a methodology for quantitatively assessing bone quantity and anisotropy based on texture analysis using Gabor wavelets. The wavelet approach has the capability to simultaneously examine the images at low and high resolutions to gain information on both global and detailed local features of the bone image. The program that implemented the texture analysis gave measures of density (M(Density)) and anisotropy (M(Anisotropy)). It also allowed us to examine the texture energy at four orientations (0 degrees , 45 degrees , 90 degrees , 135 degrees) to gain insight about the details of the anisotropy. Analysis of templates of four simulated patterns, which had same number of dots but with differing orientations, demonstrated how the texture-based analysis differentiated between these templates. The measures of M(Anisotropy) discriminated between the four simulated patterns. The M(Density) measures were similar across all patterns. These outcomes matched the design intent of the simulated patterns. We also compared the trabecular bone images obtained from a previous study, in which the right forelimbs of normal female retired breeder beagle dogs (5-7 years old) were cast for 12 months to induce bone loss, using both histomorphometry and texture analysis. Both histomorphometry and the texture analysis detected significant differences in the trabecular bone of the distal metatarsal between the control and disuse groups. Percent trabecular bone (Tb.Ar/T.Ar) and the textural density parameter (M(Density)) were highly correlated (r=0.962). M(Anisotropy) was decreased (3.9%) after the 12-month disuse protocol, but was not significantly different from normal. However, the texture energy values at all orientations (0 degrees , 45 degrees , 90 degrees and 135 degrees) were significantly decreased in the disuse group. Therefore, texture analysis was able to assess anisotropy, which could not be extracted from histomorphometric parameters. We conclude that texture analysis is an effective tool for assessing 2D bone images that yields information regarding the quantity of bone as well as the orientation of the trabecular structure that can augment our ability to discriminate between normal and pathological bone tissue.

Relevance of 2D radiographic texture analysis for the assessment of 3D bone micro-architecture

Although the diagnosis of osteoporosis is mainly based on dual x-ray absorptiometry, it has been shown that trabecular bone micro-architecture is also an important factor in regard to fracture risk. In vivo, techniques based on high-resolution x-ray radiography associated to texture analysis have been proposed to investigate bone micro-architecture, but their relevance for giving pertinent 3D information is unclear. Thirty-three calcaneus and femoral neck bone samples including the cortical shells (diameter: 14 mm, height: 30-40 mm) were imaged using 3D-synchrotron x-ray micro-CT at the ESRF. The 3D reconstructed images with a cubic voxel size of 15 microm were further used for two purposes: (1) quantification of three-dimensional trabecular bone micro-architecture, (2) simulation of realistic x-ray radiographs under different acquisition conditions. The simulated x-ray radiographs were then analyzed using a large variety of texture analysis methods (co-occurrence, spectral density, fractal, morphology, etc.). The range of micro-architecture parameters was in agreement with previous studies and rather large, suggesting that the population was representative. More than 350 texture parameters were tested. A small number of them were selected based on their correlation to micro-architectural morphometric parameters. Using this subset of texture parameters, multiple regression allowed one to predict up to 93% of the variance of micro-architecture parameters using three texture features. 2D texture features predicting 3D micro-architecture parameters other than BV/TV were identified. The methodology proposed for evaluating the relationships between 3D micro-architecture and 2D texture parameters may also be used for optimizing the conditions for radiographic imaging. Further work will include the application of the method to physical radiographs. In the future, this approach could be used in combination with DXA to refine osteoporosis diagnosis.

Quantitative morphologic evaluation of white matter in survivors of childhood medulloblastoma

In survivors of pediatric brain tumors, cranial radiation therapy can cause a debilitating cognitive decline associated with decreased volume in normal-appearing white matter (NAWM). We applied fractal geometry to quantify white matter (WM) integrity in the brain of medulloblastoma survivors. Fractal features of WM were evaluated by indices of fractal dimensions (FDs) of WM intensity and boundary on T1-weighted magnetic resonance images. The FD index of WM intensity was calculated by using a fractional Brownian motion model, and the FD index of WM boundary was calculated by using a box-counting method. Fractal features of WM on 116 magnetic resonance images of 58 patients with medulloblastoma were investigated at the start of therapy (Start TX) and approximately 2 years later (After TX). Patients were assigned to one of two groups based on change in NAWM volumes. Fractal features in patients with decreased NAWM volume were significantly greater After TX, whereas those in patients with increased NAWM volumes were not. Multiple linear regression analysis showed that fractal features were strongly correlated with NAWM volumes After TX in patients with decreased NAWM volume. These results demonstrated significant deficit in NAWM integrity and WM density changes in children treated for medulloblastoma. Multiple regression analysis illustrated that deficits in NAWM integrity in these children may partly explain the decrease in NAWM volume. We conclude that fractal geometry can be used to monitor the morphologic effects of neurotoxicity in brain tumor survivors.

Imaging techniques for evaluating bone microarchitecture

At present, fracture risk prediction in the individual patient relies chiefly on bone mineral density (BMD) measurements. However, many lines of evidence indicate that the decreased bone strength characteristic of osteoporosis is dependent not only on BMD, but also on other factors, most notably bone microarchitecture. Here, we review available tools for characterizing trabecular microarchitecture (in terms of morphology, topology, and texture) and for obtaining 2D and 3D images (using radiography, computed tomography, and magnetic resonance imaging). Bone microarchitecture imaging is a noninvasive method that may improve fracture risk prediction in the individual patient, shed light on the pathophysiology of osteoporosis, and help to monitor the effects of treatments. Among the various methods available to date, magnetic resonance imaging has the advantage of involving no radiation exposure, although its limited availability restricts its usefulness for studying vast populations. Regardless of the methods selected to assess bone microarchitecture, there is a need for validated standardized parameters capable of improving fracture risk prediction in longitudinal studies.

Bone shape, structure, and density as determinants of osteoporotic hip fracture: a pilot study investigating the combination of risk factors

OBJECTIVES

This article compares and combines methods for examining the external shape and the internal structure of the proximal femur with bone mineral density (BMD) to provide a classifier for hip fracture.

MATERIALS AND METHODS

Fifty standard pelvic radiographs were available from age-matched fracture and control groups of postmenopausal women. Femoral shape was measured using an active shape model, the trabecular structure by means of a Fourier transform.

RESULTS

Both the shape and various structure measures were independent of BMD (P=0.16 and >0.50, respectively). Calculating the area under the receiver operator characteristic (ROC) curve (Az), each of shape (Az=0.81), the best structure measure (Az=0.79-0.93), and BMD (Az=0.79), could partially classify the fracture and control groups. However, the combination achieved almost perfect separation (Az=0.99).

CONCLUSIONS

This pilot study shows how bone shape and structure can complement BMD measurements for investigations of fracture risk.

Simulated influence of osteoporosis and disc degeneration on the load transfer in a lumbar functional spinal unit

As life expectancy increases, age-related disorders and the search for related medical care will expand. Osteoporosis is the most frequent skeletal disease in this context with the highest fracture risk existing for vertebrae. The aging process is accompanied by systemic changes, with the earliest degeneration occurring in the intervertebral discs. The influence of various degrees of disc degeneration on the load transfer was examined using the finite element method. The effect of different possible alterations of the bone quality due to osteoporosis was simulated by adjusting the corresponding material properties and their distribution and several loadings were applied. An alteration of the load transfer, characterised by changed compression stiffness and strain distributions as well as magnitudes, due to osteoporotic bone and degenerated discs was found. When osteoporosis was simulated, the stiffness was substantially decreased, larger areas of the cancellous bone were subjected to higher strains and strain maxima were increased. Increasing ratios of transverse isotropy in the osteoporotic bone yielded smaller effects than reduced bone properties. Including a degenerated disc mainly altered the strain distribution. Combining osteoporosis and degenerated discs reduced the areas of cancellous bone subjected to substantial strain. Based on these results, it can be concluded that the definition of a healthy disc in osteoporotic spines might be considered as a worst-case scenario. One attempt to evaluate the progress of osteoporosis can be made by introducing increasing degrees of anisotropy. If several parameters in a model are changed to simulate degeneration, it should be pointed out how each individual definition influences the overall result.

Bone imaging: traditional techniques and their interpretation

Patients with osteoporosis have to be diagnosed at an early stage to prevent fractures, the worst complication of this disease. Currently, measurements of bone mineral density (BMD) are used most frequently in the diagnosis of osteoporosis. According to the World Health Organization, osteoporosis is defined on the basis of BMD measurements that are compared with those of a healthy, young, female population. The best established techniques to measure BMD are dual x-ray absorptiometry of the lumbar spine and proximal femur and quantitative computed tomography of the lumbar spine. Conventional radiographs are not suited to assess bone mass, but they are important in the diagnosis and differential diagnosis of osteoporotic fractures. Quantitative ultrasound and structure analysis, based on high-resolution magnetic resonance imaging and computed tomography, are newer techniques in the diagnosis of osteoporosis that also focus on the assessment of bone structure.

Bone fractal analysis

Fractal analysis is a quantitative method used to evaluate complex anatomic findings in their elementary component. Its application to biologic images, particularly to cancellous bones, has been well practiced within the past few years. The aims of these applications are to assess changes in bone and the loss of spongious architecture, indicate bone fragility, and to show the increased risk for fracture in primary or secondary osteoporosis. The applications are very promising to help complete the studies that can define bone density (bone mineral density by dual energy x-ray absorptiometry or quantitative computed tomography), and also have the capacity to distinguish the patients with a high or low risk for fracture. Their extension to the clinical fields, to define a test for fracture risk, is still limited by difficult application to the medical quantitative imaging of bones, between correct application at superficial bones and unreliable application to deep bones. The future evolution and validity do not depend upon fractal methods but upon well-detailed imaging of the bones in clinical conditions.

The importance of the endplate for interbody cages in the lumbar spine

Intervertebral cages in the lumbar spine represent an advancement in spinal fusion to relieve low back pain. Different implant designs require different endplate preparations, but the question of to what extent preservation of the bony endplate might be necessary remains unanswered. In this study the effects of endplate properties and their distribution on stresses in a lumbar functional spinal unit were investigated using finite-element analyses. Three-dimensional finite-element models of L2-L3 with and without a cage were used. An anterior approach for a monobloc, box-shaped cage was modelled. The results showed that inserting a cage increased the maximum von Mises stress and changed the load distribution in the adjacent structures. A harder endplate led to increased concentration of the stress peaks and high stresses were propagated further into the vertebral body, into areas that would usually not experience such stresses. This may cause structural changes and provide an explanation for the damage occurring to the underlying bone, as well as for the subsequent subsidence of the cage. Stress distributions were similar for the two endplate preparation techniques of complete endplate preservation and partial endplate removal from the centre. It can be concluded that cages should be designed such that they rely on the strong peripheral part of the endplate for support and offer a large volume for the graft. Furthermore, the adjacent vertebrae should be assessed to ensure that they show sufficient density in the peripheral regions to tolerate the altered load transfer following cage insertion until an adequate adaptation to the new loading situation is produced by the remodelling process.

Current technologies in the evaluation of bone architecture

In the context of osteoporosis, bone quality (which encompasses trabecular bone and cortical bone architecture), bone mineralization, turnover, and microdamage are all important, as are bone density and total content. Noninvasive assessment of bone quality has recently received considerable attention because bone density alone is not a surrogate for fracture prevalence and occurrence, and does not completely explain the therapeutic efficacy of emerging treatments. This paper focuses on the assessment of trabecular bone architecture, one of the factors that governs bone strength and may be categorized as a contributor to bone quality. The methodologies described include micro-computed tomography, magnetic resonance imaging, and computerized analysis of radiographic patterns of trabecular bone.

Osteoporosis imaging

Because osteoporotic fractures may be prevented, diagnostic techniques are essential in the assessment of osteoporosis. Conventional radiographs of the spine are not suited for diagnosing early osteoporosis, but they show fractures that may have no clinical symptoms. The radiologist should be aware of the enormous significance of these fractures for future osteoporotic fractures. Bone mass measurements are standard techniques in the diagnosis of osteoporosis, which are the basis of the WHO definition of osteoporosis. In this article the authors presented these standard techniques and newer diagnostic techniques that provide insights in the structure of trabecular bone.

Noninvasive assessment of bone structure

Bone fragility is determined by bone mass and trabecular structure. While bone mass can be readily measured as bone density, bone trabecular structure cannot be easily assessed by currently available methods. The realization of the importance of bone structure in determining fracture risk has led to the development of several imaging modalities aimed at evaluating the contribution of bone quality to its biomechanical strength and fragility. High-resolution magnetic resonance imaging and computed tomography have limited spatial resolution and high cost but have a potential to generate true three-dimensional images of trabecular structure in vivo. Bone radiographs subjected to various forms of texture analysis have higher resolution and lower cost but provide only a two-dimensional representation of bone structure. Both two- and three-dimensional methods have been shown to predict biomechanical strength in vitro and to differentiate between subjects with and without fractures in vivo. Therefore, all of these methods deserve closer evaluation and also need further technical improvements before they can be considered for use in clinical practice.

Fourier and fractal analysis of maxillary alveolar ridge repair using platelet rich plasma (PRP) and inorganic bovine bone

This report concerns the regeneration of the maxillary alveolar process in a 17-year-old patient who had lost the upper central incisors together with alveolar bone as a result of a car accident. Three months later, GBR (guided bone regeneration) was started with the use of autogenic platelet rich plasma (PRP) and inorganic bovine bone. The regenerated bone was analysed after 10 months and compared with intact bone using Fourier analysis of radiograms. The radial and spatial distribution of Fourier transforms showed that the original trabecular pattern existing in the intact bone on both sides of the defect was replicated in an evident way in the regenerated bone. Fractal analysis of intact and regenerated bone showed a higher fractal dimension for intact bone in comparison with regenerated bone, confirming a lower complexity of the newly formed trabecular structures. Replication of the original trabecular pattern in regenerated bone allows us to conclude that genetic mechanisms are influencing the organization of the trabecular pattern of regenerated bone tissue, probably under the influence of the growth factors contained in autologous PRP.

Hierarchical structure of bone and micro-computed tomography

Bone is highly complex, with multiple hierarchical levels of structure. Micro-CT has been able to provide much information about the properties of bone at several of these levels at the mid-range of bone's hierarchical structure, and it will continue to provide a valuable tool for further characterizing bone in various conditions and explaining mechanisms of bone failure.

An investigation of thoracic and lumbar cancellous vertebral architecture using power-spectral analysis of plain radiographs

The internal architecture of the vertebral bodies spanning the levels T1 to L5 in seven male columns was studied using mammographic-resolution radiographs of 2.5-mm-thick planar parasagittal slices. The overlapping radiographic shadows of vertebral trabeculae combined in the image to form a series of 'elements', broadly representative of the cancellous structure. The orientations and sizes of these elements were analysed by applying the Fast Fourier transform (FFT) to the digitized radiographic images. Elements aligned in the 'vertical' orientation, along the long axis of the column, were the most prominent for all vertebral levels. The relative prominence of horizontal to vertical elements was generally constant along the column below T5. In contrast, the relative prominence of oblique to vertical elements declined in the cranio-caudal direction, particularly in individuals aged > or = 60 years. The ratio of 'large' (x > 0.3 mm) to 'small' (0.15 mm < or = x < or = 0.3 mm) elements was unchanged cranio-caudally in specimens < 60 years. However, in individuals > or = 60 years, large elements increased in relative prominence in the caudal direction. These results suggest that a basic orthogonal pattern of trabeculae is found along the male human spine, regardless of differences in vertebral body size. Power-spectral analysis is shown to yield information summarizing the predominant orientations and sizes of radiographically rendered architectural elements of vertebral cancellous bone, to define the effects of ageing on architecture, and to identify broad structural differences between vertebral levels in the adult male spine.

Fractal dimension analysis of weight-bearing bones of rats during skeletal unloading

Fractal analysis was used to quantify changes in trabecular bone induced through the use of a rat tail-suspension model to simulate microgravity-induced osteopenia. Fractal dimensions were estimated from digitized radiographs obtained from tail-suspended and ambulatory rats. Fifty 4-month-old male Sprague-Dawley rats were divided into groups of 24 ambulatory (control) and 26 suspended (test) animals. Rats of both groups were killed after periods of 1, 4, and 8 weeks. Femurs and tibiae were removed and radiographed with standard intraoral films and digitized using a flatbed scanner. Square regions of interest were cropped at proximal, middle, and distal areas of each bone. Fractal dimensions were estimated from slopes of regression lines fitted to circularly averaged plots of log power vs. log spatial frequency. The results showed that the computed fractal dimensions were significantly greater for images of trabecular bones from tail-suspended groups than for ambulatory groups (p < 0.01) at 1 week. Periods between 1 and 4 weeks likewise yielded significantly different estimates (p < 0.05), consistent with an increase in bone loss. In the tibiae, the proximal regions of the suspended group produced significantly greater fractal dimensions than other regions (p < 0.05), which suggests they were more susceptible to unloading. The data are consistent with other studies demonstrating osteopenia in microgravity environments and the regional response to skeletal unloading. Thus, fractal analysis could be a useful technique to evaluate the structural changes of bone.

Fractal signature and lacunarity in the measurement of the texture of trabecular bone in clinical CT images

Fractal analysis is a method of characterizing complex shapes such as the trabecular structure of bone. Numerous algorithms for estimating fractal dimension have been described, but the Fourier power spectrum method is particularly applicable to self-affine fractals, and facilitates corrections for the effects of noise and blurring in an image. We found that it provided accurate estimates of fractal dimension for synthesized fractal images. For natural texture images fractality is limited to a range of scales, and the fractal dimension as a function of spatial frequency presents as a fractal signature. We found that the fractal signature was more successful at discriminating between these textures than either the global fractal dimension or other metrics such as the mean width and root-mean-square width of the spectral density plots. Different natural textures were also readily distinguishable using lacunarity plots, which explicitly characterize the average size and spatial organization of structural sub-units within an image. The fractal signatures of small regions of interest (32x32 pixels), computed in the frequency domain after corrections for imaging system noise and MTF, were able to characterize the texture of vertebral trabecular bone in CT images. Even small differences in texture due to acquisition slice thickness resulted in measurably different fractal signatures. These differences were also readily apparent in lacunarity plots, which indicated that a slice thickness of 1 mm or less is necessary if essential architectural information is not to be lost. Since lacunarity measures gap size and is not predicated on fractality, it may be particularly useful for characterizing the texture of trabecular bone.

Future methods in the assessment of bone mass and structure

There have been major advances in the diagnosis of osteoporosis over the last few decades not only in the definitions that are now used but also in the technology that is available. The future will see further development of the techniques currently in common clinical use, such us dual energy X-ray absorptiometry and quantitative ultrasound. In addition new techniques for assessing bone structure, including MRI and fractal analysis of X-rays, may add significantly to our understanding of the pathophysiology of osteoporosis and to the prediction of fracture risk.

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.

Optical processing of radiographic trabecular pattern versus bone mineral density of proximal femur as measures of bone strength

The purpose of the present study was to evaluate a noninvasive method that utilizes optical processing to analyze the trabecular pattern on bone radiographs. The trabecular network on proximal femur radiographs of 17 intact cadaveric femora was analyzed by optical Fourier transform, yielding a trabecular bone index (TBI) at several locations. The bone mineral density (BMD) of the proximal femur was measured by dual X-ray absorptiometry. Dimensions of the proximal femur were obtained from the radiograph. The bones were fractured in a "fall configuration" to yield the fracture load. A multiple regression model, combining only radiograph- derived parameters-bone dimensions and the TBI at the intertrochanteric region and at the greater trochanter-yielded a correlation of 0.938 with the fracture load. A model combining the BMD at the greater trochanter and at the neck yielded a correlation of 0.928 with the fracture load. When all the variables were introduced into a combined analysis, the correlation with the fracture load was 0.973. The TBI obtained by optical processing of the trabecular bone pattern on femoral radiographs together with bone dimensions derived from these radiographs may serve as an effective estimate for hip fracture risk.

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<log(f)<l.0, FD2 over the higher range 1.0<log(f)<1.5. Trabecular BMD in the radius was obtained using peripheral quantitative computed tomography (pQCT) (Stratec GmbH, Germany). In addition BMD of the proximal femur was determined using dual x-ray absorptiometry (DXA) (QDR 2000, Hologic, MA). In a subset of patients (16 controls and 18 with hip fractures), high resolution MR imaging of the distal radius (spatial resolution of 156 x 156 x 500 microm) was used to obtain measures analogous to bone histomorphometry. There were significant differences (p<0.05) between the fracture and nonfracture groups in the total femur BMD (13%), trabecular BMD in the distal radius (4%), and the fractal dimension in the radiographs (FD2) (3%). The correlations between FD2 and the total femur BMD as well as trabecular bone BMD in the distal radius were -0.48 (p<0.006) and -0.22 (p<0.33); respectively; FD1 increased with BMD and showed lower correlations. FD2 showed good correlations with App. Tb.N (-0.71) and App. Tb.Sp (0.69) (p<0.01), moderate correlation with App BV/TV (-0.53) (p<0.05), and no significant correlation with App. Tb.Th. The correlations between structural measures and FD1 showed the inverse trend and were typically lower. The odds ratios for a hip fracture were 2.44 for total femur BMD, 1.5 for trabecular BMD (radius), and 1.5 for FD2, respectively. In summary, the fractal measures derived from radiographs of the radius show differences between subjects with and without hip fractures, the predictive power of measures in the distal radius are comparable to radial trabecular BMD but lower than that of total hip BMD.