The graphical analysis method, which transforms multiple time measurements
of plasma and tissue uptake data into a linear plot, is a useful tool for r
apidly obtaining information about the binding of radioligands used in PET
studies. The strength of the method is that it does not require a particula
r model structure. However, a bias is introduced in the case of noisy data
resulting in the underestimation of the distribution volume (DV), the slope
obtained from the graphical method. To remove the bias, a modification of
the method developed by Feng et al. (1993), the generalized linear least sq
uares (GLLS) method, which provides unbiased estimates for compartment mode
ls was used. The one compartment GLLS method has a relatively simple form,
which was used to estimate the DV directly and as a smoothing technique for
more general classes of model structures. In the latter case, the GLLS met
hod was applied to the data in two parts, that is, one set of parameters wa
s determined for times 0 to T-1 and a second set from T-1 to the end time.
The curve generated from these two sets of parameters then was used as inpu
t to the graphical method. This has been tested using simulations of data s
imilar to that of the PET ligand [C-11]-d-threo-methylphenidate (MP, DV = 3
5 mL/mL) and C-11 raclopride (RAC, DV = 1.92 mL/mL) and compared with two e
xamples from image data with the same tracers. The noise model was based on
counting statistics through the half-life of the isotope and the scanning
time. Five hundred data sets at each noise level were analyzed. Results (DV
) for the graphical analysis (DV,), the nonlinear least squares (NLS) metho
d (DV,,,), the one-tissue compartment GLLS method (DV,), and the two part G
LLS followed by graphical analysis (DV,,) were compared. DV,, was found to
increase somewhat with increasing noise and in some data sets at high noise
levels no estimate could be obtained. However, at intermediate levels it p
rovided a good estimation of the true DV. This method was extended to use a
reference tissue in place of the input function to generate the distributi
on volume ratio (DVR) to the reference region. A linearized form of the sim
plified reference tissue method of Lammertsma and Hume (1996) was used. The
DVR generated directly from the model (DVRFL) was compared with DVRFG (det
ermined from a "smoothed" uptake curve as for DVFG) using the graphical met
hod.