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.

Fluctuation-driven mechanotransduction regulates mitochondrial-network structure and function

“…The D f of actin were computed from both RFP-labelled and phalloidin-labelled actin images by using an established low-pass filtering technique 45 , because thresholding these images did not always produce proper binary images. Images were filtered with progressively larger circular moving-average low-pass filters, and the slope of the linear regression of variance versus filter size following logarithmic transformation of both variables was used to compute the fractal dimension.…”

Topographical distribution of pulmonary perfusion and ventilation, assessed by PET in supine and prone humans

“…To assess regional lung function, we used the 13 N2-saline bolus infusion technique (9,14,29,32). Simultaneously with the start of a 13 N2-saline bolus infusion, the collection of a PET scan of the thorax was initiated.…”

“…The theoretical basis for the measurement of Q from the 13 N2 concentration during apnea was provided in detail by Mijailovich et al (14). Because of the low solubility of 13 N2 in blood and tissues (partition coefficient water/air ϭ 0.015 at 37°C), on arrival into the pulmonary capillaries, virtually all the tracer diffuses into the alveolar air space at first pass (23,24,30), and regional tracer content during apnea is proportional to regional Q (14,32). Mean-normalized regional Q could thus be expressed as the ratio between tracer concentration in each voxel and mean tracer concentration of all voxels in the imaged lung field, measured during the plateau phase of the apnea.…”

Perfusion heterogeneity in human skeletal muscle: fractal analysis of PET data

“…In principle, by using fractal analysis it is possible to obtain information regarding physiological parameters beyond the physical resolution of the imaging technique. Previous promising reports of PET data and fractal scaling have been focussed on the effects of image processing methods [18] and, recently, on the application of a lowpass filtering technique to PET images of pulmonary blood flow [19].…”