Fractal-based image texture analysis of trabecular bone architecture for assessment of bone health: bone aging in Mexica
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Fractal-based image texture analysis of trabecular bone architecture for assessment of bone health: bone aging in Mexican men M. Navarrete 1, E. Cedillo 1, L. Solís 2, CH Villegas 2, JA Alvarado1, FA Godínez1 1
Instituto de Ingeniería, Universidad Nacional Autónoma de México, Av. Universidad Nº 3000, Universidad Nacional Autónoma de México, C. U., 04510, D. F., México. 2 Instituto Nacional de Rehabilitación; Calzada México Xochimilco No. 289, CP 14389, DF. México. ABSTRACT Two methods based on fractal image analysis were used to extract the architectural features of the anisotropic structure of trabecular bone from scanning electron microscope (SEM) images of sliced bone samples in order to assess the bone's medical condition. Two methods applied were Box-Counting (BC) and Fast Fourier Transform (FFT). Tests with synthetic images of known fractal dimension aided in the interpretation of the fractal dimension (FD) profiles. Samples from L3 vertebrae were removed from Mexican male donors at the time of necropsy and evaluated using computed axial tomography (CAT) scans. Three sliced samples in normal, osteopenic and osteoporotic conditions were identified in order to compare both methods across a range of samples. The three-dimensional projection of the FD profile reflected a multifractal behavior of the trabecular architecture and clearly showed the differences in texture between the three conditions studied: normal, osteopenic and osteoporotic. In addition, the results suggest that the FFT method provides an accurate and consistent estimated for characterizing trabecular bone than the BC method. INTRODUCTION Fractal geometry has gradually grown in importance in image analysis problems especially in medicine. The medical images to be analyzed were obtained from a diverse group of procedures: X-rays, ultrasound, CAT, single photon emission computed tomography, positron emission tomography, magnetic resonance imaging, SEM and charge coupled devices, among others. Numerous publications from the last decade have demonstrated the utility of texture analysis algorithms in extracting diagnostically relevant information from medical images [1]. These include the characterization of trabecular microarchitecture and its evolution in bone diseases. Textured images are examined through a series of structural analysis techniques that provide indirect information on bone microarchitecture. Several techniques are available. Structural texture analysis involves topological characterization of a projection of the trabecular network, in which a threshold is determined and the image is converted to a binary digital image. The threshold is required to determine morphological parameters and can be achieved using a graylevel histogram or other internal calibration [2,3]. In statistical analysis, the differential characteristics of local gray level variations can be described by methods such as co-occurrence matrices or gray level run length [4,5]. Fractal analysis is a statistical method does include nonEuclidean mathematics [5-7]. Analys
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