Multiple linear analysis methods for the quantification of irreversibly binding radiotracers

Gjedde-Patlak graphical analysis (GPGA) has commonly been used to quantify the net accumulations (K_in) of radioligands that bind or are taken up irreversibly. We suggest an alternative approach (MLAIR: multiple linear analysis for irreversible radiotracers) for the quantification of these types of tracers. Two multiple linear regression model equations were derived from differential equations of the two-tissue compartment model with irreversible binding. Multiple linear analysis for irreversible radiotracer 1 has a desirable feature for ordinary least square estimations because only the dependent variable C_T(t) is noisy. Multiple linear analysis for irreversible radiotracer 2 provides K_in from direct estimates of the coefficients of independent variables without the mediation of a division operation. During computer simulations, MLAIR1 provided less biased K_in estimates than the other linear methods, but showed a high uncertainty level for noisy data, whereas MLAIR2 increased the robustness of estimation in terms of variability, but at the expense of increased bias. For real [¹¹C]MeNTI positron emission tomography data, both methods showed good correlations, with parameters estimated using the standard nonlinear least squares method. Multiple linear analysis for irreversible radiotracer 2 parametric images showed remarkable image quality as compared with GPGA images. It also showed markedly improved statistical power for voxelwise comparisons than GPGA. The two MLAIR approaches examined were found to have several advantages over the conventional GPGA method.