title: Low-pass filtering, a new method of fractal analysis: application to PET images of pulmonary blood flow.
abstract: The pattern of a spatial structure that repeats itself independently of the scale of magnification or resolution is often characterized by a fractal dimension (D). Two-dimensional low-pass filtering, which may serve as a method to assess D, was applied to functional images of pulmonary perfusion measured by positron emission tomography. The corner frequency of a low-pass filter is inversely proportional to the resolution scale. The method was applied to three types of images: random noise images, synthetic fractal images, and positron emission tomographic images of pulmonary perfusion. Images were processed with two-dimensional low-pass filters of decreasing corner frequencies, and a spatial heterogeneity index, the coefficient of variation, was calculated for each low-pass-filtered image. The natural logarithm of the coefficient of variation scaled linearly with the natural logarithm of the resolution scale for the PET images studied (average R(2) = 0.99). D ranged from 1.25 to 1.36 for the residual distribution of pulmonary perfusion after vertical gradients were removed by linear regression. D of the same data without removal of vertical gradients ranged from 1.11 to 1.14, but the fractal plots had systematic deviations from linearity and a lower linear correlation coefficient (R(2) = 0. 96). The method includes all data in the lung field and is insensitive to the effects of misregistration. We conclude that low-pass filtering offers new insights into the interpretation of D of two-dimensional functional images as a measure of the frequency content of spatial heterogeneity.
authors.affiliation: Department of Biomedical Engineering, Anesthesiology Services, Massachusetts General Hospital, Harvard Medical School, Boston, MA 02114, USA. jvenegas@vqpet.mgh.harvard.edu
authors.forename: J G
authors.initials: JG
authors.lastname: Venegas
authors.forename: G G
authors.initials: GG
authors.lastname: Galletti
mesh_terms: D017709:Fractals; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008168:Lung / Q000098:blood supply; D011652:Pulmonary Circulation; D012039:Regional Blood Flow; D014055:Tomography, Emission-Computed / Q000379:methods*