Image Processing Techniques in Emission Tomography - Correction Techniques in Emission Tomography - page 141

Recovery coecient
The recovery coecient (RC) is a multiplicative factor that is applied to a
specified region-of-interest (ROI), e.g., a tumor or lesion, to correct the inten-
sity values in this area. This factor has to be calculated for a structure that
approximately equals the ROI in shape and size. The RC depends on the PET
system and on the respective position within the field of view. It is calculated
according to

Measured sphere activity Measured background activity
Known sphere activity Known background activity

RC = : (7.26)

Computation of the RC is done by measuring the extent of the PSF for known
signals of different sizes. This is compared to the ideal values of the ROIs. For
spherical ROIs this leads to a function depending on the sphere size and the
sphere-to-background contrast [63]. There are also ways to calculate the RC
for non-spherical ROIs [62].
All RC algorithms are based on a compartment model with only two dif-
ferent tissue types, e.g., a tumor and the region near it. The RC algorithms
can be divided into two groups: First, algorithms assuming the ROI is a hot
spot in front of a cold background. Second, algorithms generalizing this as-
sumption and allowing ROIs to be surrounded by regions with significant SUV
values [63].
The use of RCs is rather limited for observing tumor metabolism following
cancer therapy. This is due to the assumption of uniform uptake in the region-
of-interest, which is not correct for tumors with necrotic tissue parts and can
lead to biases in quantification [62].
Commonly, a tumor is assumed to be approximately spheric and its di-
ameter can be well estimated from CT data. For this simple scenario clinical
feasibility studies have been discussed recently [19].

Geometric transfer matrix
The geometric transfer matrix (GTM) is a generalization of the RC and ex-
pands the compartment model by using more than two different tissues. Yet,
it is assuming homogeneous uptake for each region as well. The compartments
have to be delineated either manually or automatically. Subsequently, each of
the n compartments in the image is blurred by convolution with the system's
PSF to simulate the spill-over eect to the remaining n 1 compartments.
This yields a nn matrix, called the geometric transfer matrix, composed of
transfer coecients W ij . The coecients W ij give the signal spill-over from
compartment i to compartment j. The PVC problem can be restated as a
linear equation system of n unknowns and n equations:

W · u = m ; (7.27)

+ is the vector of signal intensities for the n compartments
and where u 2R

where m 2R

+ denotes the unknown vector of partial volume corrected