Binary Local Fractal Dimension: a Precise Structure Parameter for 3D High Resolution Computed Tomography Images of the Human Spongiosa

We present the Binary Local Fractal Dimension (LFD) to analyze osteoporosis induced fracture risk with clinical 3D high resolution quantitative computed tomographic (HRCT) images of human vertebrae. We test if LFD parameters provide precise additional information besides bone mineral density (BMD) and standard descriptors of bone quality, for example bone surface ratio (BS/BV). We define a weighted LFD (wLFD) using the ¯R2 of the H¨older exponents. We compare the LFD with standard methods (distance transform, direct secant method and run-length method) on 5 vertebrae × 8 volumes of interest and 5 repeated scans. The wLFD contains the highest direct and BMD-independent precision (R2 = 0.985 and R2 = 0.949), followed by BS/BV (R2 = 0.977 and R2 = 0.920) including low correlation with BMD (wLFD: R2 = 0.704, BS/BV: R2 = 0.814). LFD improves the translation from reference μCT- to clinical HRCT-resolution. In conclusion, LFD provides a strong diagnostic tool to characterize bone quality to predict osteoporosis induced fracture risk.Sociedad Argentina de Informática e Investigación Operativ

Binary Local Fractal Dimension: a Precise Structure Parameter for 3D High Resolution Computed Tomography Images of the Human Spongiosa

We present the Binary Local Fractal Dimension (LFD) to analyze osteoporosis induced fracture risk with clinical 3D high resolution quantitative computed tomographic (HRCT) images of human vertebrae. We test if LFD parameters provide precise additional information besides bone mineral density (BMD) and standard descriptors of bone quality, for example bone surface ratio (BS/BV). We define a weighted LFD (wLFD) using the ¯R2 of the H¨older exponents. We compare the LFD with standard methods (distance transform, direct secant method and run-length method) on 5 vertebrae × 8 volumes of interest and 5 repeated scans. The wLFD contains the highest direct and BMD-independent precision (R2 = 0.985 and R2 = 0.949), followed by BS/BV (R2 = 0.977 and R2 = 0.920) including low correlation with BMD (wLFD: R2 = 0.704, BS/BV: R2 = 0.814). LFD improves the translation from reference μCT- to clinical HRCT-resolution. In conclusion, LFD provides a strong diagnostic tool to characterize bone quality to predict osteoporosis induced fracture risk.Sociedad Argentina de Informática e Investigación Operativ

Binary Local Fractal Dimension: a Precise Structure Parameter for 3D High Resolution Computed Tomography Images of the Human Spongiosa

We present the Binary Local Fractal Dimension (LFD) to analyze osteoporosis induced fracture risk with clinical 3D high resolution quantitative computed tomographic (HRCT) images of human vertebrae. We test if LFD parameters provide precise additional information besides bone mineral density (BMD) and standard descriptors of bone quality, for example bone surface ratio (BS/BV). We define a weighted LFD (wLFD) using the ¯R2 of the H¨older exponents. We compare the LFD with standard methods (distance transform, direct secant method and run-length method) on 5 vertebrae × 8 volumes of interest and 5 repeated scans. The wLFD contains the highest direct and BMD-independent precision (R2 = 0.985 and R2 = 0.949), followed by BS/BV (R2 = 0.977 and R2 = 0.920) including low correlation with BMD (wLFD: R2 = 0.704, BS/BV: R2 = 0.814). LFD improves the translation from reference μCT- to clinical HRCT-resolution. In conclusion, LFD provides a strong diagnostic tool to characterize bone quality to predict osteoporosis induced fracture risk.Sociedad Argentina de Informática e Investigación Operativ

Estimation of Trabecular Thickness in Gray-Scale Images Through Granulometric Analysis

This paper extends to gray-scale the method proposed by Hildebrand and Ru ̈egsegger for estimating thickness of trabecular bone, which is the most used in trabecular bone research, where local thickness at a point is defined as the diameter of the maximum inscribed ball that includes that point. The proposed extension takes advantage of the equivalence between this method and the opening function computed for the granulometry generated by the opening operation of mathematical morphology with ball-shaped structuring elements of different radii. The proposed extension (a) uses gray-scale instead of binary mathematical morphology, (b) uses all values of the pattern spectrum of the granulometry instead of the maximum peak as used for binary images, (c) corrects bias on local thickness estimations generated by partial volume effects, and (d) uses the gray-scale as a weighting function for global thickness estimation. The proposed extension becomes equivalent to the original method when it is applied to binary images. A new non-flat structuring element is also proposed in order to reduce the discretization errors generated by traditional flat structuring elements. Translation invariance can be attained by up-sampling the images through interpolation by a factor of two. Results for synthetic and real images show that the quality of the measurements obtained through the original method strongly depend on the binarization process, whereas the measurements obtained through the proposed extension does not. Consequently, the proposed extension is more appropriate for images with limited resolution where binarization is not trivial.

Estimation of Trabecular Thickness in Gray-Scale Images Through Granulometric Analysis

This paper extends to gray-scale the method proposed by Hildebrand and Rüegsegger for estimating thickness of trabecular bone, which is the most used in trabecular bone research, where local thickness at a point is defined as the diameter of the maximum inscribed ball that includes that point. The proposed extension takes advantage of the equivalence between this method and the opening function computed for the granulometry generated by the opening operation of mathematical morphology with ball-shaped structuring elements of different diameter. The proposed extension (a) uses gray-scale instead of binary mathematical morphology, (b) uses all values of the pattern spectrum of the granulometry instead of the maximum peak as used for binary images, (c) corrects bias on local thickness estimations generated by partial volume effects, and (d) uses the gray-scale as a weighting function for global thickness estimation. The proposed extension becomes equivalent to the original method when it is applied to binary images. A new non-flat structuring element is also proposed in order to reduce the discretization errors generated by traditional flat structuring elements. Translation invariance can be attained by up-sampling the images through interpolation by a factor of two. Results for synthetic and real images show that the quality of the measurements obtained through the original method strongly depends on the binarization process, whereas the measurements obtained through the proposed extension do not. Consequently, the proposed extension is more appropriate for images with limited resolution where binarization is not trivial