Acquisition and Data Requirements
Image Data |
A dynamic PET data set. |
Blood Data |
Blood activity sampled at a peripheral artery from the time of injection until the end of the acquisition. |
Tissue TAC |
A regional time-activity curve from a representative brain region. It is presented as a Logan plot and can be used to define the linear segment where regression analysis should be done. |
Blood Preprocessing
Decay correction is the only blood correction option.
Model Preprocessing
The Logan graphical plot is performed with the TAC from a tissue VOI (TAC1) and presented to the user. In this plot, the TAC should become linear after an equilibration time. The slope of the linear segment equals the total distribution volume. The user must decide on the beginning of the linear segment and specify this time in the model configuration. An alternative is to apply an automatic criterion for determining this start time.
t* |
The linear regression estimation should be restricted to a range after an equilibration time. t* marks the beginning of the range used in the multi-linear regression analysis. It can be fitted based on the Max. Err. criterion. Note that the t* is in acquisition time. |
Max. Err. |
Maximum relative error ( (measured-predicted)/predicted ) allowed between the linear regression and the Logan-transformed measurements in the segment starting from t*. |
Threshold |
Discrimination threshold for background masking. |
Vt |
Distribution volume = slope of the linear regression to the Logan plot. |
Intersect |
Intercept of the linear regression line. |
Start |
Time corresponding to t* in the Logan plot. |
The Logan plot is shown in the preprocessing Result. The user should consult this plot in order to check whether the Start time is adequate.
Map Parameters
Vt |
Distribution volume = slope of the linear regression to Logan plot from t*. |
Intersect |
Intercept of the linear regression. |
In 2009 Zhou et al. introduced a new graphical method [41]. It can be applied with a plasma input curve for the calculation of the distribution volume, and with a reference tissue curve for the calculation of the binding potential. The equation of the graphical plot called "RE plot" (for Relative Equilibrium) is given by
For the RE plot to be applicable there must exist a time t* after which two conditions are fulfilled:
Under these conditions the tracer in all tissue compartments reaches equilibrium relative to plasma. Note that the conditions must be verified explicitly, because the linear appearance of the RE plot is not a sufficient criterion.
It was shown with Raclopride data and with simulations, that unlike the Logan plot the RE plot is not suffering from bias due to high noise levels. As a consequence, the results obtained with VOI-averaged TACs is consistent to the results obtained in pixel-wise applications. However, it was found that violation of the relative equilibrium condition did introduce bias. To compensate this bias Zhou et al [42] combined the RE plot with the Patlak plot in the following bi-graphical manner.
The same data is analyzed with the RE plot above and the Patlak plot,
using the same t* for fitting two respective lines. A consistent and unbiased distribution volume is then obtained by combining the slopes and intercepts of the two plots:
For the pixel-wise application of the RE-GP Analysis the results of the Patlak plot are smoothed, so that the calculation turns into
where Ks and bs are obtained from spatially smoothed maps of K and b.