jlogan @bnl.gov * Introduction Graphical analysis refers to the transformation of multiple time measurements of plasma and tissue uptake data into a linear plot, the slope of which is related to the number of available tracer binding sites. This type of analysis allows easy comparisons among experiments. No particular model structure is assumed, however it is assumed that the tracer is given by bo}us injeetion and that both tissue uptake' and the plasma concentration of unchanged tracer are monitored following tracer injection. The requirement of plasma measurements can be eliminated in some cases when a reference region is available. There are two categories of graphical methods which apply to two general types of ligands -those which bind reversibl y during the scanning procedure [1] and those which are irreversible or trapped during the time of the scanning procedure [2, 34,5].
GraphieaI analysis of reversible IigandsFor reversible systems the form of the graphical analysis equation can be derived from a general set of compartmental equations [2]
de -= m+ E,cp(t) dt(1)Where~is the column vector of concentrations (radioactivities) for each compartment at time t, is the matrix of transfer constants between compartments, and~1 is the vector describing transfer from plasma to tissue (generally there is only nonzero component, Kl), C'pis the plasma concentration of the unchanged tracer. Using ROl(t) = U. T~+ Vp =~Ci(t) + Vp Cp, that is, i ROI is the sum of radioactivities from all compartments in a given region of interest (ROI) plus a con&bution from the regional blood volume Vp, (Unis a column vector of 1's), Eq(l) can be rearranged into a linear form (when the second term on the righthand side of Eq(2) is constant).The individual points are defined by the scanning times t Nonspecific binding is also included in k2.The condition for linearity of Eq (2) The distribution volume, which is related to the number of tracer binding sites, has been, found to be estimated with much higher accuracy than individual model parameters [6].Furthermore comparisons between DV'S obtained from a nonlinear least squares (NLLSQ) fit to . a particular model and the DV'S determined graphically have been found to be in good ' agreement, for example data from [1lC]raclopride PET studies in humans using region of interest (ROI) [7]. Koeppe et al compared the graphical analysis to compartmental analysis for (+)-cY-[llC]-dihydrotetrabenazine (DTBZ) which binds to the vesicular monoamine transporter, finding, agreement within 5% for ROI data [8]. They also found that images constm~ted using the graphical method and the weighted integral method were essentially equivalent.The total distribution volume contains within it effects of plasma protein binding (Kl) nonspecific binding [7]. The kinetic constants for nonspecific binding are assumed to be sufficiently rapid that it is always in a steady state [9] and is implicitly included in model and parameters. By taking the ratio of the DV from a ROI with a significant number of binding ...