Small Animal Imaging Resource Program @ Johns Hopkins

JHU/JHMI SAIRP

Logan graphical analysis

**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=*K*1/*k*2*(1+BP)). The distribution volume in OCC is used as an estimate of *K*1/*k*2 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.