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Fractal Analysis of Nuclear Medicine Images for the Diagnosis of Pulmonary Emphysema

Interpretations, Implications, and Limitations

Hsiao-Wen Chung1 and Yih-Hwen Huang1,2

1 Department of Electrical Engineering, Rm. 238, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei, Taiwan 10764, R. O. C.
2 Department of Nuclear Medicine, National Taiwan University Hospital, Taipei, Taiwan, R. O. C.



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  		Fig. 1A. —54-year-old man with pulmonary embolism. Lung perfusion scintigram shows typical technetium-99m uptake in lungs.

 


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  		Fig. 1B. —54-year-old man with pulmonary embolism. Corresponding intensity histogram shows five thresholds marked out as dashed lines. Note total numbers of pixels on right side of dashed lines, M({epsilon}). M = measure. {epsilon} = scale.

 


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  		Fig. 1C. —54-year-old man with pulmonary embolism. Graph shows calculation of fractal dimension D. Calculation of D using five values of M({epsilon}) requires use of information in B only. Fractal dimension, absolute slope of hypotenuse of right triangle, is equal to h / w. h = height, w = width.

 


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  		Fig. 2. —Ln-ln plot of M({epsilon}) versus {epsilon} shows large range of thresholds (5-60% of maximal pixel intensity with 5% increments) for three typical sets of images. All curves are highly nonlinear, leading to ambiguous determination of fractal dimension. In contrast, data within small range of 15-35% thresholds are highly linear as shown by dotted lines. + = patient 7, o = patient 12, x = patient 14. M = measure, {epsilon} = scale.

 


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  		Fig. 3. —Graph shows fractal dimension computed using five threshold values and plotted versus logarithm of ratio of apparent tissue areas segmented at 15% and 35% of maximal pixel intensity. Note high correlation coefficient of r = 0.999 regardless of imaging technique or anatomy examined. Also note regression equation shows that fractal dimension and logarithm of area ratio are linearly related with proportionality constant at 1.181, which is only 0.06% deviation from theoretic predicted value of 1.180 plus negligible intercept of -0.0082. y = 1.181x-0.0082, n = 108, y = fractal dimension, x = ln (area ratio).

 


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  		Fig. 4. —Graph shows Bland-Altman [10] analysis plotting percentage of disagreement in D computed using two methods versus their average. Note that disagreement at two standard deviations (dashed lines) is only 5.13% (average of D ranging from 0.2 to 1.9), indicating that fractal dimension as defined in work of Nagao et al. [1] is effectively equivalent to area ratio.

 


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  		Fig. 5A. —47-year-old man with suspected pulmonary embolism. Lung perfusion scintigram shows typical technetium-99m uptake in lungs.

 


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  		Fig. 5B. —47-year-old man with suspected pulmonary embolism. Corresponding postprocessed image obtained with dual-threshold segmentation at 15% and 35% of maximal pixel intensity shows three gray levels only. Diagnostic information provided by fractal dimension alone, which can be derived solely from image in B, may not be sufficient for monitoring pulmonary emphysema.

 

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