Quantification of dynamic PET or SPECT data requires an invasive procedure where a series of blood samples are taken to form an input function for kinetic modeling. One of the potential applications of the clustering algorithm presented earlier is in noninvasive quantitative PET. We have proposed a simultaneous estimation approach to estimate the input function and physiological parameters simultaneously with two or more ROIs and our results with in vivo PET data are promising . The method is still limited, however, by the selection of ROIs whose TACs must have distinct kinetics. As the ROIs are drawn manually on the PET images, reproducibility is difficult to achieve. The use of clustering to extract tissue TACs of distinct kinetics has been investigated in three
Table 3.3: Comparison between the estimated input functions obtained using different number of manually drawn ROIs and clustered ROIs, and the measured input functions
Number of ROIs
Manually drawn ROIs
MSE 0.632 0.365 0.431 0.967
AUC (measured = 24.077) 23.796 23.657 24.188 25.138 Linear regression on AUC (n = 19)
Slope 0.967 0.963 0.984 1.022
Intercept 0.493 0.460 0.609 0.712
r value 0.999 0.999 0.999 0.999 Clustered ROIs
MSE 0.100 0.096 0.040 0.066
AUC (measured = 24.077) 20.742 23.721 25.430 23.481 Linear regression on AUC (n = 19)
Slope 0.807 0.953 1.067 0.946
Intercept 0.874 0.575 -0.321 0.481
r value 0.993 0.998 0.999 0.999
MSE = Mean square errors between the estimated and the measured input functions; AUC = area under the blood curve; r = coefficient of correlation; ROI = region of interest.
FDG-PET studies. Table 3.3 summarizes the results for the estimation of the input functions by the proposed modeling approach for both manually drawn ROIs and clustered ROIs. The MSE between the estimated and the measured input functions are tabulated. In addition, results of linear regression analysis on the areas under the curves (AUCs) covered by the measured and the estimated input functions are listed for comparison. Regression lines with slopes close to unity and intercepts close to zero were obtained in all cases for manually drawn ROIs and for clustered ROIs.
Figure 3.16 plots the measured input function and the estimated input functions for manually drawn ROIs and clustered ROIs, respectively. The estimated input functions were obtained by simultaneously fitting with three ROIs of distinct kinetics. There was a very good agreement between the estimated input functions and the measured blood curve, in terms of the shape and the peak time estimation at which the peak occurs, despite the overestimation of the peak value. Thus, cluster analysis may be useful as a preprocessing step before our noninvasive modeling technique.
Alternatively, clustering can be applied to extract input function directly on the dynamic PET/SPECT data if the vascular structures (e.g. left ventricle  and internal carotid artery ) are present in the field of view, providing that partial volume and spillover effects are appropriately corrected. Clustering has also been found useful in analyzing PET/SPECT neuroreceptor kinetics in conjunction with simplified techniques for quantification . In particular, identification of regions that are devoid of specific binding is attractive because the kinetics of these regions can be treated as a noninvasive input function to the simplified approach for parametric imaging of binding potentials and relative delivery [107,108].
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