A novel two-stage iterative vessel tracking algorithm for determining an image derived input function for PET

Objectives In dynamic PET a plasma arterial input function (AIF) is required to quantify data with a compartment model. As this is cumbersome to acquire and causes discomfort to the subject, alternative methods based on an image derived input function (IDIF) have been explored. We report here a semi-automatic 2 stage algorithm for extracting the IDIF directly from dynamic PET images, without the need for a coregistered anatomical image.

Methods Stage I Given a seed region R, find a sphere of diameter D adjacent to R with the highest peak value of its time activity curve (TAC). Stage II (vessel tracking): Take a step size S in either direction along a set of discretized lines passing through center of the current sphere Si and construct the next sphere Si+1 of diameter D. Select the direction that produces a TAC with the closest match to Si . Continue until the specified maximum length is reached or tracking fails. The algorithm was implemented in the software FireVoxel (wp.nyu.edu/FireVoxel) and applied to FDG PET (Siemens HR+) data for n=9 subjects for which a direct invasive measure of AIF was available (see below). Parameter estimates of K1, k2, k3 and KI for the FDG model were made using the IDIF as it was derived and using a linear correction technique (for partial volume and whole blood to plasma) (Zhou et al, 2011) that requires a few measured plasma samples. An exponential fit to the IDIF was used for smoothing and the ratios of the IDIF to measured samples at 3 points were fit to a straight line after 10 minutes. The IDIF was corrected using this linear function to form IDIFcorr. Results are reported for the average (over subjects and 7 brain ROIs) of K1, K1/k2, k3 and KI, the influx constant using AIF (plasma from left radial artery collected on the Ole-Dich blood sampler with 5 sec samples around the peak, 6mCi dose), IDIF and IDIFcorr. To assess the ability of the two IDIFs to correctly rank subjects, differences in rank position of the 9 subjects between invasively sampled AIF and the IDIFs were calculated for each ROI.

Results A typical AIF, IDIF and IDIFcorr are shown in the figure. Average model parameters were K1: 0.099 ± 0.013 (AIF), 0.16 ± 0.078 (IDIFcorr),0.284 ± .077 (IDIF);K1/k2: 0.58 ± 0.15 (AIF), 0.50 ± 0.14 (IDIFcorr), 1.40 ± 0.32 (IDIF); k3: .069 ± .013 (AIF), 0.074 ± 0.017 (IDIFcorr), 0.039 ± 0.007 (IDIF); KI: 0.0276 ± 0.005 (AIF), 0.0284 ± 0.0049 (IDIFcorr), 0.044 ± 0.0088 (IDIF). KI AIF vs KI IDIFcorr slope 1.05, int=-.005 and correlation .989 (ICC=0.97). KI AIF vs IDIF slope 1.4, int .0053 and correlation 0.73 (ICC=-.32). Average displacements from AIF rank among 9 subjects were using IDIFcorr K1 1.41, k3 1.62, KI 0.44 and using IDIF K1 2.63 k3 1.52 KI 2.02.

Conclusions Good agreement was found for KI for AIF and IDIFcorr. However due to underestimation of the AIF peak by the IDIF and IDIFcorr, K1 is higher for both. The underestimation of the peak is due to 30 second temporal sampling (compared to 5 sec for AIF) for first 5 min and low (with respect to vessel) spatial resolution of the HR+ PET camera which could not adequately capture AIF shape . However more important is the ability to correctly rank subjects and this is achieved using IDIFcorr for KI. For the IDIF the ranking was not as good. Better temporal sampling and spatial resolution will help in this respect. The combination of the automated IDIF and a calibration based on few venous plasma samples promises an adequate input function for dynamic FDG PET studies and may work for other PET tracers as well.

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