Methods for Random Correction

It has been shown that the noise introduced by random coincidences is an important limiting factor of count-rate performance for PET cameras operating in 3D mode [Bad96, Spi98]. The number of random coincidences may be reduced by altering the camera geometry to restrict the FOV for single events [Spi98] or by reducing the coincidence resolving time of the system. Once these factors have been minimized, the number of random coincidences on a particluar line-of-response (LOR) can be corrected in conventional PET following either the delayed coincidence method or the singles count rates method. The delayed coincidence method is more common in the current generation of cameras. It assumes the measured prompt count rate Cm at a given LOR to be the sum of the true coincidence count rate Ct with the random count rate C_r, provided Cr is stationary in time. Cr is measured at a time signicantly greater than the coincidence resolving time of the detectors and subtracted from Cm for each LOR. In the singles count rates method, singles rates from each individual detector element are collected and used to account for the random count rate of each LOR with the relation

C_r= 2 ∆t C_iC_j, (6.1)

where Ci and Cj are the singles count rates in detectors i and j forming LOR ij and 2 ∆t is the time resolution of the system. The application of both methods to in-beam PET fails because during particle extraction Cr is not constant in time due to the existence of a microstructured beam delivery [Par02b].

6.2.1 The time microstructure of the beam

During beam extraction, a correlation between the moment of arrival of the carbon ions and a given phase of the RF-signal from the accelerator has been found [Par05b]. This correlation is depicted in Fig. 6.1 for a given beam energy and intensity (10⁷ ions/s). During each RF period T_RF the ions arrive within a time window ∆tbunch. The width of ∆tbunch depends on the beam energy and, therefore, on TRF, and is independent from the beam intensity up to the maximum therapy value of 2 × 10⁸ ions/spill, which is orders of magnitude below the incoherent charge space limit of 10¹¹carbon ions/spill of the heavy ion synchrotron SIS¹ at GSI.

At the tumor therapy at GSI, the ¹²C beam energy ranges from 88.83 to 430.10 AMeV, corre-sponding to TRF from 480 down to 250 ns, respectively. The correlation between TRF and the beam relativistic kinetic energy K is given by

T_RF = P_SIS· f (E)

n_SIS· c · K + m_oc²

√K²+ 2Km_oc² , (6.2)

1 Schwerionensynchrotron.

6.2. Methods for Random Correction 113

Figure 6.1: Correlation between the time of particle arrival, illustrated schematically with arrows, and RF-phase (arbitrarily set to π), depicted for a given beam energy and intensity (10⁷ ions/s).

The RF-occupancy occRF in the example displayed is 5, with occRF = I · TRF and I the beam intensity. The letters A and B refer to the time windows outside the microbunch (A) and inside the microbunch with the corresponding high photon yield (B, bunch).

with values and units described in Table 6.1. The particle trajectory factor f(K) arises from the dierent oscillations about the synchrotron perimeter that the particles undergo for a given energy, with f(K) decreasing with increasing energy.

Table 6.1: Parameters correlating beam energy and RF-period.

Name Symbol Value

Perimeter of synchrotron P_SIS 216 m

Particle trajectory factor f (E) 1.091 to 1.008 Number of concomitant bunches nSIS 4

Speed of light in vacuum c 2.998 ×10⁸ m/s

Energy per nucleon E 88.8 to 430.1 AMeV

Total kinetic energy K = 12 · E 1.1 to 5.2 GeV

Rest mass of¹²C m_o 11 178 MeV/c²

The time window ∆tbunch comprises the time slot in which the ions arrive at each RF cycle.

During this time, and shortly after it (∆tbg in Fig. 6.1), a high ux of γ-rays arising from nuclear reactions is emitted [Par05b]. This sub-µs periodic ux constitutes the source of the high, in-beam random rate and any in-beam random suppression method must be able to discard it.

6.2.2 The methods for in-beam PET random correction

Two methods have been proposed which allow for identifying coincident events occuring within the time window ∆tbg [Eng05c] and are depicted in Fig. 6.2. From timing considerations only, and accounting for the accelerator duty factor presently implemented at GSI (∼ 40 % during patient irradiation), an increase in image statistics of up to 65 % is expected if coincidences acquired during the macropulse, but out of the micropulses, can be taken into account. The two methods rely on the synchronization of the γγ-coincidences measured by the positron camera with the time microstructure of the beam, either by using the RF-signal from the accelerator

114 Chapter 6. Suppression of Random Coincidences during Particle Extraction

or the signal of a thin, fast particle detector placed in the beam path immediately in front of the target.

Figure 6.2: Implementation of the methods proposed for in-beam PET random suppression.

Each detected γγ-coincidence is correlated with the incoming ion by using either a fast particle detector or the RF signal from the accelerator.

Using the RF-signal from the accelerator

If each γγ coincidence detected with the positron camera is correlated with the phase of the RF-signal, those events occuring within ∆tbg can either be labeled for posterior elimination or immediately discarded by the acquisition electronics (DAQ). In this rst proof-of-principle ap-proach, the readout of all events was performed with a multi-channel, zero-suppression free, list mode data acquisition (appendix B) that allowed o-line data processing. This was necessary in order to implement a proper timing selection around ∆tbg since coincidence measurements between γγ events and the RF-phase had not been performed before. Furthermore, the width of ∆tbg depends on the time resolution of the scintillation detectors used.

For the detection of a given RF-phase a fast peak detector NIM module (phase-trigger) was developed at FZR [Hei04]. A peak detector was chosen, instead of the leading edge circuit proposed in [Eng05c], because the RF signal delivered to the medical cave where the experiment was performed has about 30 % amplitude variation [For03] depending on the signal frequency.

Although the present experiment was performed at a xed beam energy, the phase trigger was seen to be a good rst solution since the long cabling between the synchrotron and the medical cave introduced low frequency base-line oscillations of ± 10 % of the RF amplitude. A time measurement between RF-periods randomly separated revealed that the phase-trigger used is nearly insensitive to these oscillations with measured deviations being less than 1 % in all cases. Despite its phase detection ability independent of the pulse amplitude, this capacitor-based peak detector introduces frequency dependent delays resulting in a non-constant phase detection when used as a phase-trigger at consecutively changing beam energies, as is the case during therapeutic irradiation by means of the GSI rasterscan beam delivery [Hab93]. A phase-trigger independent of signal amplitude, frequency and base line oscillations, based on the leading edge circuit mentioned but preceeded by a high-pass passive lter and built in zero-crossing mode is proposed in [Eng05c].

Using a fast particle detector

A second method of labeling coincidences arriving during the microbunches makes use of a thin, fast particle detector (FD) placed in the beam path in front of the target. In principle, and for RF-occupancies close to unity, this approach should allow the implementation of narrower