This correction is based on the assumption that the imaging volume can be separated into tissue volumes (VOIs) with homogeneous uptake. If the resolution of the PET scanner is known, the mutual signal contaminations across the VOIs can be calculated and corrected for. This method is known as the GTM (Geometric Transfer Matrix) method and was introduced by Rousset et al. [1].
The relation of the measured average PET values in the VOIs (affected by the partial-volume effect) to the true PET values is given by the matrix equation
with the following notations:
Ctrue |
Vector of the true average activity concentration in the different VOIs of interest. The vector length n equals the number of object VOIs. |
Cmeasured |
Actually measured average activity concentration in the different VOIs. Each VOI is assumed to have a homogeneous concentration. |
GTM |
Geometric Transfer Matrix which describes the spill-over among all the VOIs. The matrix is square with nxn weighting elements wi,j which express the fraction of true activity spilled over from VOIi into VOIj. In practice, wi,j is calculated as follows: A binary map is created with 1 in all pixels of VOIi and 0 elsewhere. The map is convolved with the imaging Point-Spread Function (PSF), and in the resulting spillover map the weighted average of all VOIj pixels calculated. |
The GTM equation above represents a system of linear equations. Once the weights have been calculated, the system can be solved for the true average concentration values Ctrue in all VOIs by matrix inversion.
Recommendations
According to Rousset et al. [2,3], the accuracy of the GTM method depends primarily on the proper identification of the tissues which have different functional properties. If this is the case, the GTM algorithm is capable of accurately correcting the regional concentration within small structures such as the human basal ganglia. Furthermore, the propagation of statistical noise during partial-volume correction was found to be easily predictable and suitable for the application in dynamic PET.