Deficient correlation between motion and PET data

The occurrence of blurred β⁺-activity distributions is not solely an indication for an inac-curate motion mitigation. Physiological processes like the biological washout that might be another possible origin for an additional smearing of the β⁺-activity should also be neglected in the following examination. An incorrect consideration of the intra-fractional target motion might also have a strong influence on the blurring in the reconstructed image. There are two main tasks to be fulfilled prior to the actual 4D IBT-PET data reconstruction to realize a successful motion handling:

- the extraction of the real, complex motion patterns and the related creation of the cor-responding transformation matrices and attenuation corrections from the 4D planning CT image and

- the assignment of the PET listmode data to the correct motion phases by means of a suitable surrogate signal.

For the first task there exist several commercial and open source software packages which enable a suitable handling of 4D patient CT images. The second task demands a time correlation between both data streams. At the experimental in-beam PET facility at GSI, there does not exist any dedicated hardware module for the combination of both data streams.

Instead, the synchronisation had to be done manually as described in appendix D. As shown below, a slight delay in one signal branch, which might also occur at a commercial system, can seriously influence the image quality.

1 0 1 1 1 2 1 3 1 4

Figure 5.9: Section of the cos² (left) and cos⁴ (right) motion signal of the moving point source and its shifting ∆t by up to 300 ms in time to induce a slightly incorrect correlation with the listmode PET data.

Systematic point source experiment

The consequences of a deficient correlation between the motion information and the listmode PET data stream was systematically analysed by means of a moving ²²Na point source of 945 kBq. Its 1D motion pattern was either of cos² and cos⁴ shape with a peak-to-peak ampli-tude of 20 mm and a period time of 4 s. The listmode PET data and the motion information had been recorded simultaneously by the different data acquisition systems and both data streams were synchronized afterwards. The motion information was artificially shifted by multiples of 50 ms to induce a delay ∆t relative to the original data stream as it is illus-trated in figure 5.9. The PET listmode data have been divided into 9 amplitude-sorted and time-sorted motion phases, each according to the time-shifted motion information and were reconstructed by the 4D MLEM algorithm. The results from the amplitude-sorted listmode data are visualized in figure 5.10. The blurring of the β⁺-activity distributions parallel to the motion direction increases with rising time delay ∆t while delays with up to 100 ms seem to be tolerable. The specific influence of the asymmetric cos⁴ motion becomes already vis-ible in the reconstructed β⁺-activity distribution for ∆t ≥ 250 ms which corresponds to a period fraction of 6.25%. The blurring effect is quantified in table 5.3 by the ratio of the FWTM values, similar as it was introduced in section 3.2.2. For measurements including the asymmetric cos⁴ motion with the larger gradients in the motion curve, the β⁺-activity distributions are more affected by the incorrect correlation than those from the cos² motion.

If time-sorted motion phases are used, an incorrect correlation between the motion and the PET data by about 100 ms (2.5% of the motion period) will already lead to a FWTM ratio above 1.1, since there remains even for the correct correlation an increased motion influence after the reconstruction in comparison to the amplitude-sorted motion phases (cp. figure 3.14 and 3.15).

Discussion

For the temporal correlation between the motion and PET data, it is not reasonable to state a tolerable inaccuracy in terms of an absolute time offset. The influence of an deficient correlation onto the final β⁺-activity distribution depends on several motion parameters

0 ms

Figure 5.10: Reconstructed β⁺-activity distributions of the ²²Na point source performing a cos² -(top) or cos⁴-shaped (bottom) motion. An increasing (from left to right) time offset of 0 ms to 300 ms was added to the corresponding motion signal before sorting the listmode data into the 9 amplitude-sorted motion phases. The according blurring in the motion direction (y) is quantified by the ratio of the FWTM values of the distribution (FWTMy/FWTMx) which is given in the lower right corner.

like the peak-to-peak amplitude, the period time and the exact motion pattern with all irregularities. These parameters determine the gradients in the motion curve and thus the absolute deviation in elongation for a certain time delay. The amount of coincidences that is sorted into wrong motion phases and the absolute difference in the transformation vectors for the correct and wrong motion phase determine the blurring in the final image. Also the

Table 5.3: FWTM ratios (FWTM_y/FWTMx) for β⁺-activity distributions of the point source that have been reconstructed with 9 amplitude- or time-sorted motion phases. Listmode PET data were assigned to these phases according to the cos²- or cos⁴-shaped motion signal which was delayed relative to the exact synchronized motion signal by ∆t.

∆t: 0 ms 50 ms 100 ms 150 ms 200 ms 250 ms 300 ms

9 amplitude-sorted motion phases

cos² motion: 1.02 1.03 1.04 1.12 1.24 1.49 1.68

cos⁴ motion: 1.06 1.08 1.10 1.22 1.50 1.71 1.92

9 time-sorted motion phases

cos² motion: 1.05 1.06 1.11 1.17 1.29 1.41 1.62

cos⁴ motion: 1.07 1.08 1.12 1.25 1.36 1.54 1.79

inaccurate attenuation correction for coincidences that are sorted into a wrong motion phase influence the result but should be of minor importance.

The examined tolerance for a wrong temporal correlation between the PET and motion data of more than 50 ms seems to be fairly high. However, the limited accuracy for real-time tumour motion detection and the related unavoidable mis-sorting of coincidences into motion phases strengthen clearly the aim to aspire the best achievable accuracy in signal correlation. The verification of the correct correlation is desired when evaluating 4D IBT-PET data of patients. A quite simple and effective method would be the attachment of a point source with low β⁺-activity to the moving body surface. The source activity can only be reproduced as a circular-shaped β⁺-activity in the reconstructed image if there is a correct motion correlation. Otherwise, a data reconstruction in small intervals of a few ten milliseconds and the subsequent fit of the source position could be used to extract the immanent motion signal. However, such a usage of a radioactive source is debatable due to the additional radiation exposure to the patient. The correct correlation between the PET and motion acquisition systems should at least be verified with the presented point source method as one part of the daily routine checks.