Reference

The Vt (Logan Plot) model is implemented according to the publication of Logan, et al. [21]. In the abstract, they write:

"A graphical method of analysis applicable to ligands that bind reversibly to receptors or enzymes requiring the simultaneous measurement of plasma and tissue radioactivities for multiple times after the injection of a radiolabeled tracer is presented. It is shown that there is a time t after which a plot of integral of t0ROI(t')dt'/ROI(t) versus integral of t0Cp(t')dt'/ROI(t) (where ROI and Cp are functions of time describing the variation of tissue radioactivity and plasma radioactivity, respectively) is linear with a slope that corresponds to the steady-state space of the ligand plus the plasma volume,.Vp. For a two-compartment model, the slope is given by lambda + Vp, where lambda is the partition coefficient and the intercept is -1/[kappa 2(1 + Vp/lambda)]. For a three-compartment model, the slope is lambda(1 + Bmax/Kd) + Vp and the intercept is -[1 + Bmax/Kd)/k₂ + [koff(1 + Kd/Bmax)]-1) [1 + Vp/lambda(1 + Bmax/Kd)]-1 (where Bmax represents the concentration of ligand binding sites and Kd the equilibrium dissociation constant of the ligand-binding site complex, koff (k₄) the ligand-binding site dissociation constant, and k₂ is the transfer constant from tissue to plasma). This graphical method provides the ratio Bmax/Kd from the slope for comparison with in vitro measures of the same parameter. It also provides an easy, rapid method for comparison of the reproducibility of repeated measures in a single subject, for longitudinal or drug intervention protocols, or for comparing experimental results between subjects. Although the linearity of this plot holds when ROI/Cp is constant, it can be shown that, for many systems, linearity is effectively reached some time before this. This analysis has been applied to data from [N-methyl-¹¹C]-(-)-cocaine (¹¹C cocaine) studies in normal human volunteers and the results are compared to the standard nonlinear least-squares analysis. The calculated value of Bmax/Kd for the high-affinity binding site for cocaine is 0.62 +/- 0.20, in agreement with literature values."