The time-dependent median values of the input curves stored in the data base were used to calculate a common input curve for the dynamic series (). The maximum SUV of the input curve was 11.78, and was decreasing to 1.91 SUV one hour following FDG injection. The histograms of the compartment parameters for the 1760 patient data sets are shown in . The distribution of the parameters is different for each of the parameters.

Overall, five synthetic studies were obtained, one study for each of the 2-tissue compartment model parameters. Each study was created by varying one compartment parameter from 0.1 to 0.9 in 400 steps while keeping the other parameters constant. Then the linear regression model was applied to these data and the slope values were compared to the corresponding reference data, the 2-tissue compartment parameters, which had been used to generate the time-activity curves. Thus, the impact of each parameter on the slope values was assessed.

The results are shown in . The data demonstrate, that the slope values are primarily dependent on k3, the phosphorylation of the intracellular FDG (). The fractional blood volume, vb, is usually low (90 % of all vb values are equal or less than 0.22) and the impact on the slope is nearby zero (), therefore vb does not have a significant impact on the slope values in clinical routine. The parameters k1 and especially k4 have no major impact on the slope, because the impact values are less than 0.001 for x=0.1 to x=0.9 ( and ). The median of k2 for the 1760 studies in the data base is 0.65, and 90 % of the k2 values are equal or greater than 0.33. Thus, most of the slope data obtained in patient studies will not be altered by k2, because the impact on the slope will be less than 0.001 ().

While the correlation coefficient (r) is a parameter for the degree of relationship between two variables, e.g. the slope and a compartment parameter, the squared correlation coefficient (r^2) reflects the amount of variance in the slope data, which is dependent on a compartment parameter. A very high r^{2} refers to a tight correlation between two variables and a very low random variance of the data. The squared correlation coefficient (r^2) for the slope and k3 is 0.9716, which refers to an explained variance of 97 % of the data. Therefore, only 3 % of the variance is random and in 97 % the slope values are dependent on k3. Thus, the slope values reflect the k3 values of the 2-tissue compartment model for FDG accurately. The slope images may be named as k3 weighted images (k3w) due to the primary dependency on k3.

In an ongoing study we are evaluating the linear regression model with dPET-CT examinations of oncological patients. For this purpose the lower limit for the slope is set to zero to display only voxels with increasing FDG concentrations over time. One general problem of dPET-CT liver examinations is the concentration of non metabolized FDG in the blood as well as in the normal liver tissue. The non metabolized FDG concentrations in the background area can be high, which may prohibit the detection of metastases with a low FDG phosphorylation rate.

shows a CT image of a metastasis from a gastrointestinal stromal tumor (GIST) in the right lateral part of the liver. The patient had received chemotherapeutic treatment with imatinib for some months prior to dPET-CT. The standard PET FDG images (: FDG uptake image; : fused PET-CT image) did not reveal any enhanced FDG uptake in the lesion. However in contrast to the normal FDG uptake image, the slope image ( and ) clearly reflects metabolized FDG in a part of the metastasis. The lesion can be visualized in the slope image due to the removal of non-metabolized FDG in the blood and the normal liver parenchyma.

Besides the improved detection of liver lesions in GIST, the k3w images may be helpful also for other tumor types. shows a regular PET-CT image of a patient with a desmoid. The desmoid was already known and dPET-CT was performed to assess the metabolic activity of the tumor. However, the regular PET-CT image was not helpful to delineate the mass. In contrast, the desmoid can be easily identified in the k3w image (). Two volumes-of-interest (VOIs) were placed over the desmoid and a reference area on the opposite side (). The time-activity curves () demonstrate, that the tracer concentrations are decreasing over time in the reference tissue (green line), while the concentrations are moderately increasing in the desmoid (orange line). Nearly identical tracer concentrations were achieved for both VOIs after one hour, which explains the failure to identify the desmoid in the regular PET-CT uptake image due to missing image contrast. However, the slope, k3w, is negative for the reference VOI and clearly positive for the desmoid. The k3w image is confined to positive slope values, therefore the lesion is visible with high image contrast.