Correlation coefficient constrained parametric images
Multiple-time graphical analyses are fast and generally robust enough methods to be applied to dynamic PET images, producing parametric images of distribution volume, VT, using Logan plot, or net influx rate, Ki, using Patlak plot. There are numerous tools to calculate parametric VT and Ki images from dynamic PET images; Open Source programs imgdv and imgki, with command-line interface, have been developed in Turku PET Centre for these purposes.
Individual time frames in the dynamic image are usually very noisy, and can include large negative pixel values because of scatter correction and image reconstruction artefacts. Especially FBP reconstruction method produces positive/negative streak artefacts that affect not only the background in the image but penetrate also the areas of interest. Pixel-by-pixel calculation of Patlak and Logan plot from the noisy pixel values leads to noisy Ki and VT images, and even though the noise level is lower than in the individual time frame images, it usually is higher than in late-scan SUV images based on a long time frame. In Logan plot, noisy data leads to biased VT (Logan, 2003). In diagnostic studies the noise-induced image artefacts complicate detection of lesions. One solution to this problem is to generate correlation coefficient constrained Patlak parametric images (r-constrained images) from dynamic PET data by zeroing the pixel Ki if the correlation coefficient (r) of the Patlak plot is below a threshold value (Zasadny & Wahl, 1993 and 1996). The appropriate level of correlation coefficient filtering must be empirically determined. This procedure results in marked qualitative improvement in [18F]FDG Ki images (Zasadny & Wahl, 1996). This technique can be adapted in defining the VOIs and calculation of lesion volume and metabolic index (Wu et al., 1996).
In Patlak plot, data is transformed and plotted in a xi,yi graph, and line is fitted to the linear phase of the plot, omitting the non-linear phase in the beginning. The slope of the fitted line represents the Ki of the radioligand. The weighted correlation coefficient (r) can be calculated from equation:
, where i=1 is the first time frame and N is the number of time frames included in the line fit, and wi is the weight for each individual time frame. Zasadny & Wahl (1996) reported that weights were calculated from image pixel concentrations as:
However, variance estimation should not be based on individual image pixel values, but on the number of events collected during the time frame (Mazoyer et al., 1986). Indeed, in later studies the weights have been based on sinogram total events, ci, and time frame lengths, Δti (Karakatsanis et al., 2013 and 2015):
- Image filtering
- Input function
- Model calculations for sinograms
- Tools for processing image data
- Parametric images in presentations and reports
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Karakatsanis NA, Zhou Y, Lodge MA, Casey ME, Wahl RL, Zaidi H, Rahmim A. Generalized whole-body Patlak parametric imaging for enhanced quantification in clinical PET. Phys Med Biol. 2015; 60: 8643-8673. doi: 10.1088/0031-9155/60/22/8643.
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Thiele F, Buchert R. Evaluation of non-uniform weighting in non-linear regression for pharmacokinetic neuroreceptor modelling. Nucl Med Commun. 2008; 29: 179-188. doi: 10.1097/MNM.0b013e3282f28138.
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Updated at: 2018-10-17
Created at: 2018-10-14
Written by: Vesa Oikonen