Logan graphical analysis with plasma input function. The Logan method applies a transformation to the blood and tissue data, where LoganX(t) = òCi(t)/Ci, and LoganY(t) =  òCp(t)/Ci.  Ci and Cp are the tracer concentrations in blood and tissue respectively.  As the tissue tracer concentration approaches equilibrium, a plot of LoganY(t) vs. LoganX(t) becomes linear with slope equal to the distribution volume (DV=K1/k2*(1+BP)).  The distribution volume in OCC is used as an estimate of K1/k2 then BP is determined from DV/OCC-1.

 

Logan graphical analysis with reference region (OCC) input function. When a tracer achieves a relatively rapid equilibrium, then the tracer concentration in a reference region may be used as an input function.  The data transformations are the same as given above, except OCC is substituted for the plasma concentration Cp.  Again, a plot of LoganY(t) vs. LoganX(t) yields a straight line but now the slope is equal to DV/OCC, and the binding potential (BP) equals the slope-1. These plots clearly become linear in our studies, indicating that it is appropriate to apply this technique.