A multilinear reference tissue approach has been widely used recently for the assessment of neuroreceptor-ligand interactions with positron emission tomography. The authors analyzed this "multilinear method" with respect to its sensitivity to statistical noise, and propose regularization procedures that reduce the effects of statistical noise. Computer simulations and singular value decomposition of its operational equation were used to investigate the sensitivity of the multilinear method to statistical noise. Regularization was performed by truncated singular value decomposition, Tikhonov-Phillips regularization, and by imposing boundary constraints on the rate constants. There was a significant underestimation of distribution volume ratios. Singular value decomposition showed that the bias was caused by statistical noise. The regularization procedures significantly increased the test-retest stability. The bias could be reduced by applying linear constraints on the rate constants based on their normal range. Underestimation of distribution volume ratios by the multilinear method is caused by its sensitivity to statistical noise. Statistical power in the discrimination of different groups of subjects can be significantly improved by regularization procedures without introducing additional bias. Correct distribution volume ratios can be obtained by imposing physiologic constraints on the rate constants.
