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Fractal analysis of radiographs: assessment of trabecular bone structure and prediction of elastic modulus and strength. 1999

S Majumdar, and J Lin, and T Link, and J Millard, and P Augat, and X Ouyang, and D Newitt, and R Gould, and M Kothari, and H Genant
Magnetic Resonance Science Center, Department of Radiology, University of California, San Francisco 94143, USA. majumdar@mrsc.ucsf.edu

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

UI MeSH Term Description Entries
D011859 Radiography Examination of any part of the body for diagnostic purposes by means of X-RAYS or GAMMA RAYS, recording the image on a sensitized surface (such as photographic film). Radiology, Diagnostic X-Ray,Roentgenography,X-Ray, Diagnostic,Diagnostic X-Ray,Diagnostic X-Ray Radiology,X-Ray Radiology, Diagnostic,Diagnostic X Ray,Diagnostic X Ray Radiology,Diagnostic X-Rays,Radiology, Diagnostic X Ray,X Ray Radiology, Diagnostic,X Ray, Diagnostic,X-Rays, Diagnostic
D012044 Regression Analysis Procedures for finding the mathematical function which best describes the relationship between a dependent variable and one or more independent variables. In linear regression (see LINEAR MODELS) the relationship is constrained to be a straight line and LEAST-SQUARES ANALYSIS is used to determine the best fit. In logistic regression (see LOGISTIC MODELS) the dependent variable is qualitative rather than continuously variable and LIKELIHOOD FUNCTIONS are used to find the best relationship. In multiple regression, the dependent variable is considered to depend on more than a single independent variable. Regression Diagnostics,Statistical Regression,Analysis, Regression,Analyses, Regression,Diagnostics, Regression,Regression Analyses,Regression, Statistical,Regressions, Statistical,Statistical Regressions
D001842 Bone and Bones A specialized CONNECTIVE TISSUE that is the main constituent of the SKELETON. The principal cellular component of bone is comprised of OSTEOBLASTS; OSTEOCYTES; and OSTEOCLASTS, while FIBRILLAR COLLAGENS and hydroxyapatite crystals form the BONE MATRIX. Bone Tissue,Bone and Bone,Bone,Bones,Bones and Bone,Bones and Bone Tissue,Bony Apophyses,Bony Apophysis,Condyle,Apophyses, Bony,Apophysis, Bony,Bone Tissues,Condyles,Tissue, Bone,Tissues, Bone
D004548 Elasticity Resistance and recovery from distortion of shape.
D005583 Fourier Analysis Analysis based on the mathematical function first formulated by Jean-Baptiste-Joseph Fourier in 1807. The function, known as the Fourier transform, describes the sinusoidal pattern of any fluctuating pattern in the physical world in terms of its amplitude and its phase. It has broad applications in biomedicine, e.g., analysis of the x-ray crystallography data pivotal in identifying the double helical nature of DNA and in analysis of other molecules, including viruses, and the modified back-projection algorithm universally used in computerized tomography imaging, etc. (From Segen, The Dictionary of Modern Medicine, 1992) Fourier Series,Fourier Transform,Analysis, Cyclic,Analysis, Fourier,Cyclic Analysis,Analyses, Cyclic,Cyclic Analyses,Series, Fourier,Transform, Fourier
D006801 Humans Members of the species Homo sapiens. Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
D001696 Biomechanical Phenomena The properties, processes, and behavior of biological systems under the action of mechanical forces. Biomechanics,Kinematics,Biomechanic Phenomena,Mechanobiological Phenomena,Biomechanic,Biomechanic Phenomenas,Phenomena, Biomechanic,Phenomena, Biomechanical,Phenomena, Mechanobiological,Phenomenas, Biomechanic
D013718 Tensile Strength The maximum stress a material subjected to a stretching load can withstand without tearing. (McGraw-Hill Dictionary of Scientific and Technical Terms, 5th ed, p2001) Strength, Tensile,Strengths, Tensile,Tensile Strengths
D015519 Bone Density The amount of mineral per square centimeter of BONE. This is the definition used in clinical practice. Actual bone density would be expressed in grams per milliliter. It is most frequently measured by X-RAY ABSORPTIOMETRY or TOMOGRAPHY, X RAY COMPUTED. Bone density is an important predictor for OSTEOPOROSIS. Bone Mineral Content,Bone Mineral Density,Bone Densities,Bone Mineral Contents,Bone Mineral Densities,Density, Bone,Density, Bone Mineral
D017709 Fractals Patterns (real or mathematical) which look similar at different scales, for example the network of airways in the lung which shows similar branching patterns at progressively higher magnifications. Natural fractals are self-similar across a finite range of scales while mathematical fractals are the same across an infinite range. Many natural, including biological, structures are fractal (or fractal-like). Fractals are related to "chaos" (see NONLINEAR DYNAMICS) in that chaotic processes can produce fractal structures in nature, and appropriate representations of chaotic processes usually reveal self-similarity over time. Fractal

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