Limitations of bi-linear regression analysis for the determination of receptor occupancy with positron emission tomography

Background and objectives Linear/multilinear regression methods are widely used in quantitative neuroreceptor positron emission tomography. A reference tissue method based on a bi-linear operational equation, the bi-linear reference tissue method, has been introduced in order to overcome the need for arterial blood sampling. The aim of the present paper was to investigate the sensitivity of the bi-linear reference tissue method to statistical noise, with special regard to the assessment of receptor occupancy. In addition, improvement of the bi-linear reference tissue method by regularization using physiological constraints was evaluated. Methods Application of the bi-linear method to dynamic positron emission tomography using the serotonin transporter ligand C-11-(+)McN5652 was considered. Investigations were performed by computer simulations and analysis of 29 patient studies. Results The equilibrium specific-to-non-specific partition coefficient V"(3) was significantly underestimated by the bi-linear reference tissue method. At realistic noise levels the extent of the underestimation ranged from 25% to 75% for partition coefficients ranging from 0.3 to 0.3, respectively. This caused a 15-60% underestimation of changes in receptor occupancy after simulated intervention. The noise dependence of the bias was confirmed in the patient studies. Regularization significantly reduced the underestimation of the occupancy. Conclusions When receptor status or noise level vary substantially, as in receptor occupancy studies, the bias of the bi-linear reference tissue method should be taken into account.