PXMOD Implementation

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.

PXMOD Logan Blood Pre-Processing

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.

PXMOD Logan Model Pre-Processing

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.

PXMOD Logan Model Pre-Processing Result

Map Parameters

PXMOD Logan Model Parameters

Vt	Distribution volume = slope of the linear regression to Logan plot from t*.
Intersect	Intercept of the linear regression.

Vt (RE-GP Analysis, Zhou)

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:

The plasma input curve must be mono-exponential. This condition can be verified by fitting a single exponential to the late part of the plasma curve on the Blood tab of PKIN.
The ratio of C_Tissue/C_p is constant. This condition can be verified by switching the KM model to the Tissue/Plasma Ratio model in PKIN.

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 K_s and b_s are obtained from spatially smoothed maps of K and b.