Journal of Applied Physiology
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J Appl Physiol 88: 1365-1373, 2000;
8750-7587/00 $5.00
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Vol. 88, Issue 4, 1365-1373, April 2000

Low-pass filtering, a new method of fractal analysis: application to PET images of pulmonary blood flow

Jose G. Venegas and Gaetano G. Galletti

Department of Biomedical Engineering, Anesthesiology Services, Massachusetts General Hospital, Harvard Medical School, Boston, Massachusetts 02114

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 R2 = 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 (R2 = 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.

coefficient of variation; digital filtering; fractal dimension; functional imaging; spatial heterogeneity


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