Blood Flow Heterogeneity Versus Cerebral Hypoperfusion Revealed by Fractal Analysis on ^99mTc-HMPAO SPECT

TO THE EDITOR:

A recent article published in The Journal of Nuclear Medicine reported findings on the “heterogeneity” of cerebral blood flow (CBF) in patients showing vascular dementia with small-vessel disease (1). The study applied 3-dimensional fractal analysis to images obtained with ^99mTc-hexamethylpropyleneamine oxime (HMPAO) SPECT, using an intensity-cutoff algorithm previously documented for Alzheimer’s disease (2). The results suggested that the CBF heterogeneity could readily be assessed by calculating the fractal dimension and that the fractal dimension was abnormally increased in vascular dementia patients, compared with age-matched healthy control subjects (1). In both articles (1,2), the fractal dimension derived from the image data was claimed to indicate the degree of CBF heterogeneity, with a larger fractal dimension standing for increased heterogeneity.

My colleagues and I have emphasized many times that fractal dimension, as defined using the intensity-cutoff approach, is an index representing solely the percentage volume of reduced radioactivity (3–5), independent of the anatomy examined and the imaging modality used. This point has been proven using more than a hundred sets of nuclear medicine image data, randomly chosen by combining SPECT images and projection scintigrams of the lungs, the livers, and the brains from 28 patients, to yield a Pearson correlation coefficient as high as 0.999 (3). The relationship between the intensity-cutoff fractal dimension and the percentage volume of low radioactivity was not only strong but almost a one-to-one association. As a natural consequence, it is not surprising that increased fractal dimensions were reported for diseases that are already known to exhibit impaired CBF, in particular vascular dementia (1) and Alzheimer’s disease (2). In fact, if the scientific community were in favor of the intensity-cutoff fractal analysis approach, we would predict that all patients with physiologic and pathologic situations showing hypoperfusion on ^99mTc-HMPAO SPECT, such as normal aging, cerebral ischemia, or cocaine abuse, would also exhibit significantly increased intensity-cutoff fractal dimensions. Likewise, for other diseases that manifest by focally reduced radioactivity in nuclear medicine examinations, such as impaired glucose uptake in epileptic seizure foci demonstrated on ¹⁸F-FDG PET scans, an increase in the intensity-cutoff fractal dimension could also be anticipated. As long as the percentage volume of reduced radioactivity reaches statistical significance between patients and healthy control subjects, the intensity-cutoff fractal dimension will reach a similar level of statistical significance because of the modality-independent one-to-one association.

Fractal analysis is of contemporary interest to the scientific community, in that it may be an effective approach toward objective quantification of morphologically complex systems. But that is not to say that the fractal dimension can be arbitrarily defined. Parameters such as the fractal dimension defined in different manners will convey different physical meanings, even if named identically. The fractal dimension calculated from relative dispersion at different sizes of regions of interest indicates spatial heterogeneity of radioisotope distribution, whereas the fractal dimension computed by pixel counting at different cutoff intensities does not reveal equivalent information. In the case of the intensity-cutoff fractal dimension, whether fractal dimension is the appropriate term is not the most relevant issue. Rather, the essential point lies in the fact that, other than representing the percentage volume of low radioactivity (which can be obtained through simple, traditional methods of image analysis), the intensity-cutoff fractal dimension does not provide any new diagnostic or prognostic insights despite its methodologic origin.

We strongly suggest further nuclear medicine studies of the intensity-cutoff fractal analysis algorithm to include a scatter plot showing the fractal dimension versus the percentage volume of reduced radioactivity. Such a plot would provide direct evidence on whether the intensity-cutoff fractal dimension indeed offers additional information other than the existence of reduced radioactivity or, in the case of ^99mTc-HMPAO SPECT, impaired CBF. Proof that the intensity-cutoff fractal dimension indicates “heterogeneity” requires at least that the variable of deterministic value in clinical diagnosis (i.e., the percentage volume of hypoperfusion) be controlled.