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Optimum Fourier Filtering of Cardiac Data: A Minimum-Error Method: Concise Communication

National Institutes of Health, Bethesda, Maryland

Correspondence: For reprints contact: Stephen L. Bacharach, Nuclear Medicine Dept., Building 10, Room 1C401, National Institutes of Health, Bethesda, MD 20205.

ABSTRACT

Random fluctuations limit the accuracy of quantities derived from cardiac time-activity curves (TACs). To overcome this problem, TACs are often fitted with a truncated Fourier series giving rise to two sources of error: (a) the truncated series may not adequately describe the TAC shape, causing errors in parameters calculated from the fit: and (b) successive TACs acquired from the same subject under identical circumstances will fluctuate due to limited counts, causing the Fourier fits (and parameters derived from them) to fluctuate. These two errors, respectively, decrease and increase as the number of harmonics increases, suggesting the existence of a minimum in total error. This number of harmonics for minimum error (NHME) was calculated for each of six common parameters used to described LV TACs. The "true" value of each parameter was determined from TACs of very high statistical precision. Poisson noise was added to simulate lower count rates. For low-count TACs, use of either a smaller or a larger number of harmonics resulted in significantly greater error. NHME was found to occur at two harmonics for the systolic parameters studied, regardless of the noise level present in the TAC. For diastolic parameters, however, NHME was a strong function of the noise present in the TAC, varying from three harmonics for noise levels typical of regional TACs, to five or six harmonics for high-count global TACs.

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