2012 IEEE Nuclear Science Symposiwn and Medical Imaging Conference Record (NSS/MIC) M22-18

Pile-up Correction Techniques

for Real-Time Dosimetry in Photon Radiotherapy Mojca Miklavec, Student Member, IEEE, Bastian Loher, Deniz Savran, Roman Novak, Member, IEEE,

Simon Sirca, Matjaz Vencelj

Abstract-In radiotherapy, accurate in vivo dose monitoring can improve overall success of treatment. For hadronic therapy, the approach is to measure residual radioactivity after the treatment. In the more widely used, gamma ray radiotherapy under 20 MV, dose monitoring in vivo is far more complicated, since the only way to measure irradiation accuracy is while tinac is operating at extremely high dose rates. Linac's leakage outside the nominal beam can be as high as 1011 photons per cm2s at 1 m, leading to a 2 Gcps event rate even on a small detector crystal (2 x 2 x 20 mm3 LYSO).

One of the prerequisites for real time dose monitoring under such extreme conditions is the ability to handle high count rates as well as measuring the energy of incident photons in highly piled-up regimes. The same techniques can be applied elsewhere, ego to improve results in moderately saturated systems.

The scope of the first part of our study was to determine the count rate dependance of energy resolution, photo peak efficiency and background characteristics for scintillation crystals at high count rates. Pile-up correction of the digitized PMT's output led to both higher efficiency and accuracy than classical methods at high count rates. Thus, we were able to measure energy spectra of incident photons at rates above 107 events per second.

Fast asynchronous digitization and the application of real-time digital pile-up correction techniques enable PET setups to operate at photon ftuence rates almost three orders of magnitude higher than those assumed by [1] and could make dosimetry in gamma ray radiotherapy feasible with significantly less lead shielding.

The engineering problem of handling high data rates and the fundamental question of random coincidences under such regimes remains a subject of further work.

Index Terms-Pile-Up, high count rates, PET.

I. INTRODUCTION

THIS work has been motivated by [1] where a very careful investigation of experimental conditions under medical

linac during radiotherapy has been performed. It has been shown that despite the high background due to Compton scattered events in the patient it could be feasible to see the PET signal originating from positrons generated in pair production during beam irradiation.

Manuscript received November 16,2012. This work was partially supported by Slovenian Research Agency as well as the Slovene Competency Center for Biomedical Engineering, which is co-funded by EU, European Regional Development Fund.

M. Miklavec, R. Novak and M. Vencelj are with the lozef Stefan Institute, Ljubljana, Slovenia (e·mail: mojca.miklavec@ijs.si.matjaz.vencelj@ijs.si).

S. Sirca is with lozef Stefan Institute and University of Ljubljana, Faculty of Mathematics and Physics, Ljubljana, Slovenia

B. Uiher and D. Savran are with ExtreMe Matter Institute EMMI and Research Division, GSI Helmholtzzentrum fUr Schwerionenforschung, Darm­stadt, Germany and Frankfurt Institute for Advanced Studies FIAS, Frankfurt am Main, Germany

While the show stopper turned out to be the extremely high event rate calling for several decimeters of lead shielding, we believe that the progress and price drops in digital electronics could push the limits of manageable event rates by about three orders of magnitude - up to about 107 events per second per crystal - if performing pile-up correction on the digitally sampled pulse as opposed to integration of single events with long dead times and discarding any pile-ups.

Accessibility of fast economical digitizer boards with one FPGA per channel as planned by the OpenPET project [2] could easily enable real-time pile-up reconstruction to work with the algorithm first presented in [3] and [4].

We present the limits of successful energy reconstruction for incident photons on conunonly used LYSO crystal in highly piled-up regimes.

II. EXPERIMENTAL SET-UP

We used a 100 kEq 22Na and a 100 GBq 137Cs as y-ray sources to calibrate energy and determine energy resolution.

We started with small scintillation crystals of two types: LYSO (2x2x20 Imn3) and Pr:LuAG (2x2x 15 Imn3) mounted on classical PMT (Photonis XP2040/pC). At low count rates we were able to achieve 14 % FWHM with LYSO crystals and 8 % FWHM with Pr:LuAG.

Later on we had to switch to larger (10 x 10 x 20 mm3) LYSO crystals to achieve the desired event rates to be able to test the upper limits of pile-up reconstruction with the given radioactive sources.

The signal from the PMT has been digitized with as MS/s and 500 MHz bandwidth 8-bit digitizer (PicoScope 6404 [5]), transferred to PC and analyzed off-line.

III. THE ALGORITHM FOR SIGNAL ANALYSIS AND PILE-UP CORRECTION

The signal analysis consisted of the following steps:

1) Extraction of the average signal shape and baseline correction.

2) Triggering: recognition of pulses. 3) Integration with a moving window. 4) Pile-Up correction. 5) Evaluation of reconstruction quality: RMS error.

A. Average signal shape and baseline correction

The average signal shape has been determined by averaging 100 signals sampled at low count rates. Each signal had to reach at least 20% of digitizer's dynamic range. A trace of

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4000 samples has been taken for each and checked against pile-up to make sure that no degenerate signal would be included. The signals have been aligned in time in the same way as described for the triggering phase.

o 100 200 300 400 500

t [ns]

Fig. 1. A set of 20 (scaled) signals and their average.

Since there was no observable baseline drift and because determining the baseline at high count rates would be less accurate if at all possible, a single value for the baseline has been extracted from the same low count rate data and used throughout the experiment for baseline correction.

It might be worth noting that while we were sampling with a relatively fast digitizer, sub-sample alignment in time and some interpolation might help with better reconstruction when working with a slow digitizer (compared to decay constant of the crystal). This could however significantly change the real­time requirements of the DAQ system.

B. Triggering

Implementing an efficient and accurate trigger is a key step of the whole algorithm, as well as the main contributor to errors in reconstruction in case of poor performance.

Implementation of an optimal trigger also strongly depends on digitizer speed, noise and pulse shape. The strategy that worked best for our setup was to find the steepest part of the leading edge. This has been implemented by searching for local maxima of the derivative calculated with a finite impulse response (FIR) filter as depicted on Figure 2.

/ /If\ I , \ \ .. /,

.. '

o 100 200 300

signal -­

differential (for triggering) ------­

integral (calorimetric signal) ------­

shifted calorimetric signal·······

+-- FIR filter shape: difrerential

� FIR filter shape: integral

400 500 600 700 800

t [ns]

Fig. 2. A sample signal from digitizer, the shape of two FIR filters that were used for triggering on signals and for integrating, and signal shape after applying the filter. For the differentiating filter we took a convolution of three boxes (widths 20, 40, 80 samples) with bipolar differentiator (60 units apart). The integrator consisted of a convolution of two boxes of width 40 and 500.

-- signal @ 10 Mcps • trigger

o 500 1000 1500 2000

I [ns]

Fig. 3. Triggering on a longer trace at 10 million events per second.

C. Integration with a moving window

In order to get the energy of a single event one usually integrates over a pulse duration. In case of pile-up we cannot avoid integrating over multiple events at once, but the good news is that linearity is kept which enables us to reconstruct individual energies.

The size of integrating window must be long enough to get sufficient energy resolution for a single pulse, but on the other hand one still needs to keep it reasonable short in order not to integrate over too many events.

The signal integration has been done with a trapezoidal FIR filter as shown on Figure 2 and shifted to the left to make the peak coincide with the trigger.

The result of integration over a longer trace is shown on Figure 4.

-- signal -- integral

o 500

Fig. 4. Integration of the signal.

D. Pile-Up correction

1000 1500 2000

t [ns]

Calorimetric pile-up correction has been performed in the sense first described in [3], [4] and further analyzed in [6].

The key is in assuming a constant pulse shape, up to the multiplicative amplitude factor that codes the event energy. Under this assumption, and using any linear smoothing filter for high frequency noise management, the measured apex heights of piled-up pulses are a linear combination of the true pulse heights. The degree of such inter-pulse mixing depends on the filtered pulse shapes and on the temporal distribution of neighboring pulses' timestamps.

This turns out to be a well-behaved diagonally dominant linear problem. The inverse is analytical for modest pile­up, while entering the more intensely piled-up regime, must

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be tackled numerically. Even so, [4] have shown it to be manageable in real time within 4 % of the chip resources of a yesteryear FPGA.

The practical limit of the approach is in the stochastic nature of scintillation bursts that make each scintillation unique. However at the energies of the order of 1 MeV, some 1500 scintillation photons are typically detectable as photoelectrons, keeping the Poisson noise of the pulse shape sufficiently low for spectroscopy work.

The method is necessarily sensitive to reliable triggering, hence some sort of list mode validation is in order.

E. Evaluation of reconstruction quality

The most reliable method of evaluating the algorithm's success is to compare the original or integrated signal with reconstructed signal based on extracted timestamps, resolved energies and average pulse shape. By calculating the RMS error under individual signals we can detect misaligned or missing events and either attempt to do some basic correction or reject the ones with the error above a certain threshold.

IV. RESULTS

Figure 5 shows the reconstructed energy spectrum of 137 Cs at different count rates with the photopeak at 66l.7 keY. With increasing count rates when the current was constantly flowing through the PMT we experienced a moderate voltage drop on the PMT which made it necessary to do a separate energy calibration for each distance from the radioactive source.

a 200 400 600 sao

S.6Meps --

3.6 Meps --

2.2 Meps -­

l.OMeps --

1000 1200

E [keV]

Fig. 5. Energy spectrum of 137 Cs at different count rates.

V. CONCLUSION

In conclusion, we find that we were able to successfully use our setup to perform spectroscopy at count rates exceeding lO Mcps in a single LYSO crystal. For the given scintillator crystal size of 2 x 2 x 20 mm3, this corresponds to roughly one thousand times the maximal photon fluence considered by Konnol et al. [1]. This has important enabling consequences for the mechanical design limitations for the shielding within the discussed scenario. Significant further work is envisioned regarding the spectral qualities of the scattered photon field in the geometrical shadow of the shielding.

The use of SiPM based readout is in our experience still seriously hindered by the binomial saturation of the SiPM at

such high count rates, and is the subject of a separate ongoing study within our group. Glass photomultipliers also have to be optimized for the high current regime, with rather robust voltage dividers and typically operated at slightly lower HV bias than the usual setting that is optimized for high timing accuracy.

An interesting new scintillation material candidate Pr:LuAG has been identified and is to be tested. With its fast decay time around 20 ns [7], while still being non-hygroscopic, as opposed to LaBr, this could well be the ideal material for the device discussed.

We did not study the effect of radiation damage on detectors and the rest of the equipment. During most of our experiments the detectors were only irradiated for a few seconds, however when dealing with extremely high count rates for prolonged time this might become a concern, given the inevitably signif­icant unit-level costs of the hypothetical device.

Performing pile-up correction in real time requires one digitizer and up to one FPGA per channel. For systems with (tens of) thousands of channels the cost of such a system might still be prohibitively high. On the other hand the digitizer boards developed by OpenPET [2] could already enable data acquisition and processing with a couple of boards with 32 channels per board.

We did not discuss the potentially problematic issue of the search for coincidences at lO Mcps: with 120 Mbit/s data per channel and 20,000 channels, the coincidence board would have to deal with approximately 2.4 Tbit/s of data. This poses an obvious technological problem as well as a fundamental one. The latter is in the polynomially increasing probability for chance coincidences in the regime of extremely high singles rates. At some point, the reconstructed image becomes useless by the extreme levels of Poisson noise. This remains a subject of further work within this study.

REFERENCES

[l] T. Kormoll, D. Kunath, and W. Enghardt, "3d in-vivo dosimetry for photon radiotherapy based on pair production," in 2009 IEEE Nuclear Science Symposium Con! Rec. (NSS/MIC). Orlando, FL: IEEE, Oct. 2009, pp. 2969-2975.

[2] OpenPET, General Purpose Readout Electronics for Radionuclide Imaging, Lawrence Berkeley National Laboratory. [Online]. Available: http:(!openpet.lbl.gov

[3] M. Vencelj, K. Bucar, R. Novak, and H. Wortche, "Event by event pile­up compensation in digital timestamped calorimetry," NIM A, vol. 607, no. 3, pp. 581-586, Aug. 2009.

[4] R. Novak and M. Vencelj, "Gauss-seidel iterative method as a real-time pile-up solver of scintillation pulses," IEEE Trans. Nuc!. Sci., vol. 56, pp. 3680-3687, Dec. 2009.

[5] PicoScope 6404, Pico Technology. [6] B. Uiher, D. Savran, E. Fiori, M. Miklavec, N. Pietralla, and M. Vencelj,

"High count rate spectroscopy with LaBr3:Ce scintillation detectors," NIM A, vol. 686, pp. 1-6, Sep. 2012.

[7] H. Ogino, A. Yoshikawa, M. Nikl, A. Krasnikov, K. Kamada, and T. Fukuda, "Growth and scintillation properties of Pr-doped LU3Als012 crystals," Journal of Crystal Growth, vol. 287, no. 2, pp. 335-338, Jan. 2006.

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