The appended curve technique for deconvolutional analysis —method and validation

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Abstract
Deconvolutional analysis (DCA) is useful in correction of organ time activity curves (response function) for variations in blood activity (input function). Despite enthusiastic reports of applications of DCA in renal and cardiac scintigraphy, routine use has awaited an easily implemented algorithm which is insensitive to statistical noise. The matrix method suffers from the propagation of errors in early data points through the entire curve. Curve fitting or constraint methods require prior knowledge of the expected form of the results. DCA by Fourier transforms (FT) is less influenced by single data points but often suffers from high frequency artifacts which result from the abrupt termination of data acquisition at a nonzero value. To reduce this artifact, we extend the input (i) and response curves to three to five times the initial period of data acquisition (P) by appending a smooth low frequency curve with a gradual taper to zero. Satisfactory results have been obtained using a half cosine curve of length 2-3P. The FTs of the input and response I and R, are computed and R/I determined. The inverse FT is performed and the curve segment corresponding to the initial period of acquisition (P) is retained. We have validated this technique in a dog model by comparing the mean renal transit times of 131I-iodohippuran by direct renal artery injection to that calculated by deconvolution of an intravenous injection. The correlation was excellent (r=0.97, P0.005). The extension of the data curves by appending a low frequency “tail” before DCA reduces the data termination artifact. This method is rapid, simple, and easily implemented on a microcomputer. Excellent results have been obtained with clinical data.