Error analysis on parameter estimates in the ligand - receptor model: application to parameter imaging using PET data

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Abstract
Positron emission tomography and compartmental models allow the in vivo analysis of radioligand binding to receptor sites in the human brain. Benzodiazepine receptor binding was studied using a three-compartmental model and [11C]flumazenil. Four and five parameters were estimated from a single kinetic curve obtained with a multi-injection protocol, and parametric maps of receptor density and of the individual kinetic parameters were created with four-pixel sampling of the experimental images. The coefficient of variation on each estimated model parameter was calculated using the diagonal elements of the covariance matrix. However, these estimates are valid only under some statistical hypotheses which are not always verified with PET data. Thus, in order to verify the validity of the coefficient of variation of each parameter calculated with the covariance matrix, these results have been compared with the more rigorous statistical results provided by a Monte Carlo simulation. The study showed a negligible difference between the results obtained by the two methods for a low noise level in time-concentration curves encountered using large ROIs. However, this bias becomes less negligible when the noise level is high and some estimations of the coefficients of variation were unacceptable (> 100%) with the five-parameter model. Such difficulties did not occur with the four-parameter model which led to parametric images with good quality and acceptable estimates of coefficients of variation (less than 20% in about 75% of the ROIs).

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