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

Comparison of quantitative radiomorphometric predictors of healthy and MRONJ-affected bone using panoramic radiography and cone-beam CT

OBJECTIVES

To determine the most distinctive quantitative radiomorphometric parameter(s) for the detection of MRONJ-affected bone changes in panoramic radiography (PR) and cone-beam CT (CBCT).

METHODS

PR and sagittal CBCT slices of 24 MRONJ patients and 22 healthy controls were used for the measurements of mandibular cortical thickness (MCT), fractal dimension (FD), lacunarity, mean gray value (MGV), bone area fraction (BA/TA), trabecular thickness (Tb.Th), trabecular separation (Tb.Sp), trabecular number (Tb.N). MCT was measured in the mental foramen region. While FD and lacunarity were measured on mandibular trabecular and cortical regions-of-interest (ROIs), the remaining parameters were measured on trabecular ROIs. The independent samples t-test was used to compare the measurements between the MRONJ and control groups for both imaging modalities (P = .05).

RESULTS

MCT was the only parameter that differentiated MRONJ-affected bone in both PR and CBCT (P < .05). None of the remaining parameters revealed any difference for MRONJ-affected bone in CBCT (P > .05). FD, lacunarity, MGV, BA/TA, and Tb.Sp could distinguish MRONJ-affected trabecular bone in PR (P < .05). The correspondent ROI for both imaging methods that was reliable for detecting MRONJ-affected bone was the trabecular bone distal to the mental foramen above the inferior alveolar canal (ROI-3).

CONCLUSIONS

MCT is a reliable parameter for the discrimination of MRONJ-affected bone in both PR and CBCT images. PR may be used to detect MRONJ-affected trabecular bone using FD, lacunarity, MGV, BA/TA, and Tb.Sp measurements as well.

Relation between mechanical and densimetric properties to fractal dimension in human rib cortical bone

BACKGROUND

Numerous prior studies hypothesized a power-law relationship (E∝ρ^α) between cortical bone Young's modulus (E) and density (ρ) with an exponent 2.3≤α≤3.0, that has not been previously justified in the literature on a theoretical level. Moreover, despite the fact microstructure have been extensively studied, the material correlate of Fractal Dimension (FD) as a descriptor of bone microstructure was not clear in previous studies.

METHODS

This study examined the effect of mineral content and density on the mechanical properties of a large number of human rib cortical bone samples. The mechanical properties were calculated using Digital Image Correlation and uniaxial tensile tests. CT scans were used to calculate the Fractal Dimension (FD) of each specimen. For each specimen, the mineral (f_min), organic (f_org) and water (f_wat) weight fractions were determined. In addition, density was measured after a drying-and-ashing process. Then, Regression Analysis was employed to investigate the relationship between anthropometric variables, weight fractions, density and FD, as well as its impact on the mechanical properties.

FINDINGS

Young's modulus exhibited a power-law relationship with an exponent of α>2.3 when using the conventional density (wet density), but α=2 when using dry density (desecated specimens). In addition, FD increases with decreasing cortical bone density. A significant relationship has been found between FD and density, whereby FD is correlated with the embedding of low density regions in cortical bone.

INTERPRETATION

This study provides a new insight in the exponent value of the power-law relation between Young's Modulus and density, and relates bone behavior with the fragile fracture theory in ceramic materials. Moreover, the results suggest that Fractal Dimension is related to presence of low-density regions.

Prediction of mechanical properties of human rib cortical bone using fractal dimension

A large number of post mortem human subjects was used to investigate the relation between the micro-structure of rib cortical bone and the mechanical properties using Fractal Dimension. Uniaxial tensile tests were performed on coupons of rib cortical bone. Tensile strength, yield stress, Young's Modulus, maximum strain, and work to fracture were determined for each coupon. Fractal dimension was computed using CT images and Digital Image Correlation procedures. A highly significant effect of fractal dimension in the mechanical properties was found. In addition, the variation in mechanical properties was found to be adequately represented by Generalized Extreme Value type distributions.

Effect of ionizing radiation after-therapy interval on bone: histomorphometric and biomechanical characteristics

OBJECTIVES

This study aimed to evaluate the effects of radiotherapy on biomechanical, histomorphometric, and microstructural characteristics of bone, in diverse periods, compared with intact bone tissue.

MATERIALS AND METHODS

Eighteen adult male New Zealand rabbits were treated with a single radiation dose of 30 Gy. The animals were randomly divided into six groups: NoIr, control group, no radiation, and five irradiated groups sacrificed after 24 h (Ir24h), 7 (Ir7d), 14 (Ir14d), 21 (Ir21d), and 28 (Ir28d) days. After these periods, the animals were sacrificed and their tibias (n = 6) evaluated using three-point bending test to calculate the ultimate force, work to failure, and bone stiffness. Dynamic indentation test was used to quantify Vickers hardness and elasticity modulus of bone tissue. Micro-CT was used to analyze the cortical volume (CtV), cortical thickness (CtTh), and porosity (Ct.Po). Histomorphometric assessment was based on the lacunarity of bone tissue. Data were analyzed using one-way ANOVA and Kruskal-Wallis tests followed by Tukey, Dunnet, and Dunn's post-tests (P < 0.05).

RESULTS

The ultimate force, work to failure, stiffness, elastic modulus, and Vickers hardness values of irradiated bone were significantly lower that non-irradiated bone. Irradiated bone showed significantly lower CtTh and CtV values and higher CtPo than non-irradiated bone. No significant difference was found for lacunarity between non-irradiated bone and irradiated bone.

CONCLUSIONS

Ionizing radiation decreases normal anisotropy on microarchitecture of cortical bone, and increases bone fragility compared with non-irradiated bone. Further, these changes were seen after longer periods (e.g., 14 and 21 days), and not immediately after radiation therapy.

CLINICAL RELEVANCE

The radiotherapy reduces bone mechanical properties and the normal structure of organic and inorganic bone matrix. For studying the protocols to protect the radiotherapy effect using rabbit model, the use of the sacrificing period between 14 and 21 days is recommended.

Assessment of vertebral wedge strength using cancellous textural properties derived from digital tomosynthesis and density properties from dual energy X-ray absorptiometry and high resolution computed tomography

The purpose of this study was to examine the potential of digital tomosynthesis (DTS) derived cancellous bone textural measures to predict vertebral strength under conditions simulating a wedge fracture. 40 vertebral bodies (T6, T8, T11, and L3 levels) from 5 male and 5 female cadaveric donors were utilized. The specimens were scanned using dual energy X-ray absorptiometry (DXA) and high resolution computed tomography (HRCT) to obtain measures of bone mineral density (BMD) and content (BMC), and DTS to obtain measures of bone texture. Using a custom loading apparatus designed to deliver a nonuniform displacement resulting in a wedge deformity similar to those observed clinically, the specimens were loaded to fracture and their fracture strength was recorded. Mixed model regressions were used to determine the associations between wedge strength and DTS derived textural variables, alone and in the presence of BMD or BMC information. DTS derived fractal, lacunarity and mean intercept length variables correlated with wedge strength, and individually explained up to 53% variability. DTS derived textural variables, notably fractal dimension and lacunarity, contributed to multiple regression models of wedge strength independently from BMC and BMD. The model from a scan orientation transverse to the spine axis and in the anterior-posterior view resulted in highest explanatory capability (R²_adj = 0.91), with a scan orientation parallel to the spine axis and in the lateral view offering an alternative (R²_adj = 0.88). In conclusion, DTS can be used to examine cancellous texture relevant to vertebral wedge strength, and potentially complement BMD in assessment of vertebral fracture risk.

Tug-of-war lacunarity-A novel approach for estimating lacunarity

Modern instrumentation provides us with massive repositories of digital images that will likely only increase in the future. Therefore, it has become increasingly important to automatize the analysis of digital images, e.g., with methods from pattern recognition. These methods aim to quantify the visual appearance of captured textures with quantitative measures. As such, lacunarity is a useful multi-scale measure of texture's heterogeneity but demands high computational efforts. Here we investigate a novel approach based on the tug-of-war algorithm, which estimates lacunarity in a single pass over the image. We computed lacunarity for theoretical and real world sample images, and found that the investigated approach is able to estimate lacunarity with low uncertainties. We conclude that the proposed method combines low computational efforts with high accuracy, and that its application may have utility in the analysis of high-resolution images.

Multi-dimensional reliability assessment of fractal signature analysis in an outpatient sports medicine population

The aim of this study has been to test reproducibility of fractal signature analysis (FSA) in a young, active patient population taking into account several parameters including intra- and inter-reader placement of regions of interest (ROIs) as well as various aspects of projection geometry. In total, 685 patients were included (135 athletes and 550 non-athletes, 18-36 years old). Regions of interest (ROI) were situated beneath the medial tibial plateau. The reproducibility of texture parameters was evaluated using intraclass correlation coefficients (ICC). Multi-dimensional assessment included: (1) anterior-posterior (A.P.) vs. posterior-anterior (P.A.) (Lyon-Schuss technique) views on 102 knees; (2) unilateral (single knee) vs. bilateral (both knees) acquisition on 27 knees (acquisition technique otherwise identical; same A.P. or P.A. view); (3) repetition of the same image acquisition on 46 knees (same A.P. or P.A. view, and same unitlateral or bilateral acquisition); and (4) intra- and inter-reader reliability with repeated placement of the ROIs in the subchondral bone area on 99 randomly chosen knees. ICC values on the reproducibility of texture parameters for A.P. vs. P.A. image acquisitions for horizontal and vertical dimensions combined were 0.72 (95% confidence interval (CI) 0.70-0.74) ranging from 0.47 to 0.81 for the different dimensions. For unilateral vs. bilateral image acquisitions, the ICCs were 0.79 (95% CI 0.76-0.82) ranging from 0.55 to 0.88. For the repetition of the identical view, the ICCs were 0.82 (95% CI 0.80-0.84) ranging from 0.67 to 0.85. Intra-reader reliability was 0.93 (95% CI 0.92-0.94) and inter-observer reliability was 0.96 (95% CI 0.88-0.99). A decrease in reliability was observed with increasing voxel sizes. Our study confirms excellent intra- and inter-reader reliability for FSA, however, results seem to be affected by acquisition technique, which has not been previously recognized.

Characterization of knee osteoarthritis-related changes in trabecular bone using texture parameters at various levels of spatial resolution-a simulation study

Articular cartilage and subchondral bone are the key tissues in osteoarthritis (OA). The role of the cancellous bone increasingly attracts attention in OA research. Because of its fast adaptation to changes in the loading distribution across joints, its quantification is expected to improve the diagnosis and monitoring of OA. In this study, we simulated OA progression-related changes of trabecular structure in a series of digital bone models and then characterized the potential of texture parameters and bone mineral density (BMD) as surrogate measures to quantify trabecular bone structure. Five texture parameters were studied: entropy, global and local inhomogeneity, anisotropy and variogram slope. Their dependence on OA relevant structural changes was investigated for three spatial resolutions typically used in micro computed tomography (CT; 10 μm), high-resolution peripheral quantitative CT (HR-pQCT) (90 μm) and clinical whole-body CT equipment (250 μm). At all resolutions, OA-related changes in trabecular bone architecture can be quantified using a specific (resolution dependent) combination of three texture parameters. BMD alone is inadequate for this purpose but if available reduces the required texture parameter combination to anisotropy and global inhomogeneity. The results are summarized in a comprehensive analysis guide for the detection of structural changes in OA knees. In conclusion, texture parameters can be used to characterize trabecular bone architecture even at spatial resolutions below the dimensions of a single trabecula and are essential for a detailed classification of relevant OA changes that cannot be achieved with a measurement of BMD alone.

Spatial heterogeneity analysis of brain activation in fMRI

In many brain diseases it can be qualitatively observed that spatial patterns in blood oxygenation level dependent (BOLD) activation maps appear more (diffusively) distributed than in healthy controls. However, measures that can quantitatively characterize this spatial distributiveness in individual subjects are lacking. In this study, we propose a number of spatial heterogeneity measures to characterize brain activation maps. The proposed methods focus on different aspects of heterogeneity, including the shape (compactness), complexity in the distribution of activated regions (fractal dimension and co-occurrence matrix), and gappiness between activated regions (lacunarity). To this end, functional MRI derived activation maps of a language and a motor task were obtained in language impaired children with (Rolandic) epilepsy and compared to age-matched healthy controls. Group analysis of the activation maps revealed no significant differences between patients and controls for both tasks. However, for the language task the activation maps in patients appeared more heterogeneous than in controls. Lacunarity was the best measure to discriminate activation patterns of patients from controls (sensitivity 74%, specificity 70%) and illustrates the increased irregularity of gaps between activated regions in patients. The combination of heterogeneity measures and a support vector machine approach yielded further increase in sensitivity and specificity to 78% and 80%, respectively. This illustrates that activation distributions in impaired brains can be complex and more heterogeneous than in normal brains and cannot be captured fully by a single quantity. In conclusion, heterogeneity analysis has potential to robustly characterize the increased distributiveness of brain activation in individual patients.

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A number of spatial heterogeneity measures of activation maps were explored in children with Rolandic epilepsy and language impairment

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Proposed measures capture the complexity, shape and distribution of brain activation patterns

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For a language task all proposed measures revealed that patients exhibit more heterogeneous activation patterns than controls, whereas for a motor task no differences appeared

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Spatial heterogeneity of activation patterns is a complex feature that cannot be captured by one single measure, but shape and lacunarity represented the best descriptive measures

Quantitative characterization of mineralized silk film remodeling during long-term osteoblast-osteoclast co-culture

The goal of this study was to explore quantitative assessments of mineralized silk protein biomaterial films by co-cultures of human mesenchymal stem cell-derived osteoblasts and human acute monocytic leukemia cell line-derived osteoclasts during long-term culture (8-32 weeks). The remodeled films were quantitatively assessed using three different techniques during this extended cultivation to provide more comprehensive insight into the impact of co-cultures on surface remodeling. Scanning electron microscopy (SEM) with three dimensional surface reconstructions was used to quantitatively determine various surface morphological features and measures of roughness indicative of remodeling by the cells. Additionally, reconstructed surfaces were converted to depth images for Fourier analysis to quantify the potential fractal organization of biomineralization. The long-term remodeled films were also imaged using confocal reflectance microscopy and micro-computed tomography (micro-CT) to further quantify morphological changes. Films remodeled in co-culture demonstrated increased roughness parameters, fractal organization, and volume compared to films remodeled by osteoblasts alone. The combination of these techniques to quantify remodeling of mineralized protein films shows promise for quantifying processes related to mineralized surfaces.

COMPARISON OF ICTAL AND INTERICTAL EEG SIGNALS USING FRACTAL FEATURES

The feature analysis of epileptic EEG is very significant in diagnosis of epilepsy. This paper introduces two nonlinear features derived from fractal geometry for epileptic EEG analysis. The features of blanket dimension and fractal intercept are extracted to characterize behavior of EEG activities, and then their discriminatory power for ictal and interictal EEGs are compared by means of statistical methods. It is found that there is significant difference of the blanket dimension and fractal intercept between interictal and ictal EEGs, and the difference of the fractal intercept feature between interictal and ictal EEGs is more noticeable than the blanket dimension feature. Furthermore, these two fractal features at multi-scales are combined with support vector machine (SVM) to achieve accuracies of 97.58% for ictal and interictal EEG classification and 97.13% for normal, ictal and interictal EEG classification.

Atomic force microscopy characterization of the external cortical bone surface in young and elderly women: potential nanostructural traces of periosteal bone apposition during aging

On the basis of the suggestion that bone nanostructure bears “tissue age” information and may reflect surface deposition/modification processes, we performed nanoscale characterization of the external cortical bone surface at the femoral neck in women using atomic force microscopy (AFM). The specific aims were to assess age-related differences in bone nanostructure and explore the existence of nanostructural traces of potential bone apposition at this surface. Our findings revealed that the external cortical surface represents a continuous phase composed of densely packed mineral grains. Although the grains varied in size and shape, there was a domination of small grains indicative of freshly deposited bone (mean grain size: young, 35 nm; old, 37 nm; p > 0.05). Advanced quantitative analysis of surface morphological patterns revealed comparable roughness and complexity of the surface, suggesting a similar rate of mineral particle deposition at the surface in both groups. Calcium/phosphorus ratio, a measure of bone tissue age, was within the same range in both groups. In summary, our AFM analyses showed consistent nanostructural and compositional bone features, suggesting existence of new bone at the periosteal bone surface in both young and elderly women. Considering observed age-related increase in the neck diameter, AFM findings may support the theory of continuous bone apposition at the periosteal surface.

Improved Fourier-based characterization of intracellular fractal features

A novel Fourier-based image analysis method for measuring fractal features is presented which can significantly reduce artifacts due to non-fractal edge effects. The technique is broadly applicable to the quantitative characterization of internal morphology (texture) of image features with well-defined borders. In this study, we explore the capacity of this method for quantitative assessment of intracellular fractal morphology of mitochondrial networks in images of normal and diseased (precancerous) epithelial tissues. Using a combination of simulated fractal images and endogenous two-photon excited fluorescence (TPEF) microscopy, our method is shown to more accurately characterize the exponent of the high-frequency power spectral density (PSD) of these images in the presence of artifacts that arise due to cellular and nuclear borders.

Age-dependence of power spectral density and fractal dimension of bone mineralized matrix in atomic force microscope topography images: potential correlates of bone tissue age and bone fragility in female femoral neck trabeculae

There is an increasing interest in bone nano-structure, the ultimate goal being to reveal the basis of age-related bone fragility. In this study, power spectral density (PSD) data and fractal dimensions of the mineralized bone matrix were extracted from atomic force microscope topography images of the femoral neck trabeculae. The aim was to evaluate age-dependent differences in the mineralized matrix of human bone and to consider whether these advanced nano-descriptors might be linked to decreased bone remodeling observed by some authors and age-related decline in bone mechanical competence. The investigated bone specimens belonged to a group of young adult women (n = 5, age: 20-40 years) and a group of elderly women (n = 5, age: 70-95 years) without bone diseases. PSD graphs showed the roughness density distribution in relation to spatial frequency. In all cases, there was a fairly linear decrease in magnitude of the power spectra with increasing spatial frequencies. The PSD slope was steeper in elderly individuals (-2.374 vs. -2.066), suggesting the dominance of larger surface morphological features. Fractal dimension of the mineralized bone matrix showed a significant negative trend with advanced age, declining from 2.467 in young individuals to 2.313 in the elderly (r = 0.65, P = 0.04). Higher fractal dimension in young women reflects domination of smaller mineral grains, which is compatible with the more freshly remodeled structure. In contrast, the surface patterns in elderly individuals were indicative of older tissue age. Lower roughness and reduced structural complexity (decreased fractal dimension) of the interfibrillar bone matrix in the elderly suggest a decline in bone toughness, which explains why aged bone is more brittle and prone to fractures.

Peri-implant bone tissue assessment by comparing the outcome of intra-oral radiograph and cone beam computed tomography analyses to the histological standard

OBJECTIVES

The present study aims to identify radiographic methods revealing data that are most representative for the true peri-implant bone as assessed by histology.

MATERIALS AND METHODS

Eighty implants were placed in 10 minipigs. To assess matching between different image modalities, measurements conducted on intra-oral digital radiographs (IO), cone beam computer tomography (CBCT) and histological images were correlated using Spearman's correlation. Paired tests (Wilcoxon test) were used to determine changes in the bone parameters after 2 and 3 months of healing.

RESULTS

Significant correlations between bone defect depth on IO and histological slices (r= + 0.7, P<0.01), as well as on CBCT images and histological slices (r= + 0.61, P<0.01), were found. CBCT and IO images deviate, respectively, 1.20 and 1.17 mm from the histology regarding bone defects. No significant correlations were detected between fractal analysis on CBCT, intra-oral radiography and histology. For bone density assessment, significant but weaker correlations (r= + 0.5, P<0.01) were found for intra-oral radiography vs. histology. Significant marginal bone-level changes could be observed after 3 months of healing using intra-oral radiography.

CONCLUSIONS

This study allowed linking radiographic bone defect depth to the histological observations of the peri-implant bone. Minute bone changes during a short-term period can be followed up using digital intra-oral radiography. Radiographic fractal analysis did not seem to match histological fractal analysis. CBCT was not found to be reliable for bone density measures, but might hold potential with regard to the structural analysis of the trabecular bone.

Intrinsic optical biomarkers associated with the invasive potential of tumor cells in engineered tissue models

This report assesses the ability of intrinsic two-photon excited fluorescence (TPEF) and second harmonic generation (SHG) imaging to characterize features associated with the motility and invasive potential of epithelial tumor cells engineered in tissues. Distinct patterns of organization are found both within the cells and the matrix that depend on the adhesive properties of the cells as well as factors attributed to adjacent fibroblasts. TPEF images are analyzed using automated algorithms that reveal unique features in subcellular organization and cell spacing that correlate with the invasive potential. We expect that such features have significant diagnostic potential for basic in vitro studies that aim to improve our understanding of cancer development or response to treatments, and, ultimately can be applied in prognostic evaluation.

Image analysis in medical imaging: recent advances in selected examples

Medical imaging has developed into one of the most important fields within scientific imaging due to the rapid and continuing progress in computerised medical image visualisation and advances in analysis methods and computer-aided diagnosis. Several research applications are selected to illustrate the advances in image analysis algorithms and visualisation. Recent results, including previously unpublished data, are presented to illustrate the challenges and ongoing developments.

A quantitative assessment of carbon nanotube dispersion in polymer matrices

Quantifying the nature and extent of the dispersion of nanomaterials in polymer matrices is the important first step in understanding the relationship between the nanoscale structure and the bulk scale functional performance of nanocomposites. We present here a methodology for using scanning electron microscope images of nanocomposites taken under high accelerating voltages to quantify four parameters that relate to the dispersion of the nanomaterial. This image analysis methodology is general and applicable to images from other microscopes as well. The analysis performed here was done on representative local areas of six samples to determine the effects of processing conditions, matrix chemistry, and carbon nanotube composition on the level of dispersion. Future work will involve expanding this analysis to rapidly cover larger areas and reducing the data in a manner that is similar to the approach of small angle scattering studies.

Progression of emphysema in a 12-month hyperpolarized 3He-MRI study: lacunarity analysis provided a more sensitive measure than standard ADC analysis

RATIONALE AND OBJECTIVES

Inhaled hyperpolarized (3)He magnetic resonance (MR) imaging has been used to measure alveolar size in patients with emphysema. The aim of this study was to test the hypothesis that (3)He MR images could be used to develop a biomarker of emphysema progression.

MATERIALS AND METHODS

Twelve healthy controls and 18 patients with emphysema (eight current smokers, 10 ex-smokers) were imaged at baseline and 6 and 12 months. An additional nine subjects with alpha-1 antitrypsin deficiency (four with emphysema, six without symptoms) were also imaged at baseline and at 6 months. Each subject was imaged at two lung volumes: functional residual capacity (FRC) and FRC plus 15% of total lung capacity. Means and standard deviations of apparent diffusion coefficients (ADCs) were calculated from coronal images of the entire lung and correlated with pulmonary function test results. The lacunarity hypothesis was tested and calculated from the data using a range of 2 x 2 x 2 to 6 x 6 x 6 voxels, and the average was calculated.

RESULTS

There was no change in the mean ADC at either lung volume in any subject over the 6- or 12-month period. FRC and residual volume increased over the 12 months, suggesting air trapping. The lacunarity of images collected at FRC increased at 6 and 12 months in smokers only (P = .063 and P = .023, respectively).

CONCLUSIONS

The mean ADC calculated from MR images of the lungs with helium was not sufficiently sensitive to detect changes over a 12-month period. However, lacunarity captured more of the spatial information in the images and detected emphysema progress in the smokers.

Optical characterization of the nanoscale organization of mineral deposits on silk films

The alignment of deposited minerals in tissues such as bone and teeth plays a critical role in the mechanical properties of these tissues. Therefore, assessment of features that are characteristic of aligned biominerals could aid in the development of novel biomaterials and engineered tissues that can be used to replace damaged or defective human tissues. In this study, we demonstrate that light scattering spectroscopy can serve as a useful tool for the noninvasive characterization of mineralization on aligned organic substrates. Specifically, we used silk films with oriented and nonoriented secondary structures as a protein matrix for control of mineralization. The mineral deposits displayed self-affine fractal morphologies with the oriented films yielding a significantly higher Hurst parameter, which in turn suggests higher levels of fractal organization. In addition, the value of the upper bound of fractal correlation lengths was significantly smaller for the oriented than for the nonoriented films and correlated well with the size of the corresponding nanocrystalline mineral beads identified by scanning electron microscope imaging.

Non-invasive optical characterization of biomaterial mineralization

Current approaches to study biomaterial mineralization are invasive and prevent dynamic characterization of this process within the same sample. Polarized light scattering spectroscopy (LSS) may offer a non-invasive alternative for assessing the levels of mineralization as well as some aspects of the organization of the mineral deposits. Specifically, we used LSS to characterize the formation of hydroxyapatite deposits on three types of silk films (water-annealed, methanol-treated and polyaspartic acid (PAA)-mixed) following 1, 3, 5 and 7 cycles of mineralization. We found that the total light scattering intensity provided a quantitative measure of the degree of mineralization as confirmed by thermal gravimetric analysis (TGA). The PAA-mixed silk films yielded the highest level of mineral deposition and the water-annealed ones the least, consistent with the beta sheet content of the films prior to the onset of mineralization. The wavelength dependence of the singly backscattered light was consistent with a self-affine fractal morphology of the deposited films within scales in the range of 150-300nm; this was confirmed by Fourier analysis of scanning electron microscopy (SEM) images of the corresponding films. The deposits of minerals in the water-annealed films were predominantly flake-like, with positively correlated density fluctuations (Hurst parameter, H>0.5), whereas methanol-treated and PAA-mixed silk films resulted in densely-packed, bulk mineral deposits with negatively correlated density fluctuations (H<0.5). Therefore, LSS could serve as a valuable tool for understanding the role of biomaterial properties in mineral formation, and, ultimately, for optimizing biomaterial designs that yield mineral deposits with the desired organization.

Nuclear fractal dimension as a prognostic factor in oral squamous cell carcinoma

Strong theoretical reasons exist for using fractal geometry in measurements of natural objects, including most objects studied in pathology. Indeed, fractal dimension provides a more precise and theoretically more appropriate approximation of their structure properties and especially their shape complexity. The aim of our study was to evaluate the nuclear fractal dimension (FD) in tissue specimens from patients with oral cavity carcinomas in order to assess its potential value as prognostic factor. Relationships between FD and other factors including clinicopathologic characteristics were also investigated. Histological sections from 48 oral squamous cell carcinomas as well as from 17 non-malignant mucosa specimens were stained with Hematoxylin-Eosin for pathological examination and with Feulgen for nuclear complexity evaluation. The sections were evaluated by image analysis using fractal analysis software to quantify nuclear FD by the box-counting method. Carcinomas presented higher mean values of FD compared to normal mucosa. Well differentiated neoplasms had lower FD values than poorly differentiated ones. FD was significantly correlated with the nuclear size. Patients with FD lower than the median value of the sample had statistically significant higher survival rates. Within the sample of patients studied, FD was proved to be an independent prognostic factor of survival in oral cancer patients. In addition this study provides evidence that there are several statistically significant correlations between FD and other morphometric characteristics or clinicopathologic factors in oral squamous cell carcinomas.

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.

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

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

Leaf shape analysis using the multiscale Minkowski fractal dimension, a new morphometric method: a study with Passiflora (Passifloraceae)

A new method is proposed for the extraction of morphometric characteristics of plant leaf structures. A sample of 10 species of the genus Passiflora (P. coriacea Juss., P. foetida L., P. miersii Mast., P. organensis Gardner, P. pohlii Mast., P. suberosa L., P. amethystina J.C. Mikan, P. caerulea L., P. gibertii N.E.Br., P. maliformis L.) was used in an experiment to test the method. This genus shows a wide range of leaf forms, but there are some species pairs or groups whose morphological similarity makes their correct identification difficult. The multiscale function of the Minkowski fractal dimension was applied to digital images of leaves to generate complexity measures of their internal (veins) and external (leaf outline) form. The results of the leaf characteristic extraction method, as well as its potential as the basis for an identification mechanism, are discussed for the 10 species. The method was very accurate in correctly differentiating among species, since no leaf was erroneously identified. A small number of leaves per species was sufficient for establishing a characteristic pattern for each of them, which constitutes an important advantage of the method in the recognition and classification procedure.Key words: image processing, fractal dimension, plant taxonomy, morphometry, Passiflora.

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.

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

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