Proton Track Reconstruction in a Digital Tracking Calorimeter for Proton Computed Tomography
HELSE BERGEN
Haukeland University Hospital
H. E. S. Pettersen1,2,3 , I. Meric3 , O. H. Odland1 , H. Shafiee3 , J. R. Sølie3 , D. Röhrich2 1
Department of Oncology and Medical Physics, Haukeland University Hospital, Bergen, Norway 2 Department of Physics and Technology, University of Bergen, Norway 3 Department of Electrical Engineering, Western Norway University of Applied Sciences, Norway Corresponding author:
[email protected]
The Digital Tracking Calorimeter
The Proton Beam
Reconstruction CPU Time
A Digital Tracking Calorimeter (DTC) is currently under development as a detector for a proton Computed Tomography (CT) system [1].
The simulated proton beam is a mono-energetic pencil beam with energy 250 MeV. The beam is Gaussian distributed in the lateral dimensions.
A clinical version of a proton CT applying a DTC requires that the data acquisition, the track reconstruction and, finally, the image reconstruction are performed within a time frame compatible with clinical constraints.
Water phantom to modulate protons to lower energies
Proton beam line
Sensor layers + energy absorbers with variable thickness
Phantom
The beam energy is degraded by a 16 cm water phantom, so that (approximately) clinically realistic energy spectra and spatial distributions are generated.
CPU time / proton [ms]
Figure 1: A Digital Tracking Calorimeter setup.
Incoming protons traverse through a water phantom (or patient) and then into the DTC. A track reconstruction algorithm calculates the initial vector and the range of each proton, from 10–1000 concurrent tracks. An image reconstruction algorithm should then be applied to estimate the volumetric stopping power map of the traversed target, for use in proton therapy dose planning. The DTC is planned to consist of ∼40 layers of stacked “ALPIDE” pixel sensor chips [2]: each layer is separated by an energy degrading layer of 3.5 mm aluminum.
Figure 3: Lateral profile of a beam with spot size σxy = (4 mm, 2 mm) (2σxy value shown as red ellipse).
Results The reconstruction procedure must take into account the effects of multiple Coulomb scattering (many small angle deflections) and of nuclear interactions (few large angle deflections).
Track Reconstruction Algorithm The track reconstruction algorithm is based on the winning contribution to the 2017 CtD Hackathon (hyperbelle_tree_6 [3]), and follows the steps:
Even for low proton densities, a 100% reconstruction efficiency is not achieved. Both fake tracks (unmatched MC history IDs) and unused data are present: most of the fake tracks are in the pencil beam core.
1. Identify all seed pairs in the first two layers, accounting for large incoming angles. 2. Find the total angular change for each seed qP n 2 pair: Sn = (∆θ ) layer layer
With a σxy = 3 mm pencil beam, an 80% reconstruction efficiency is achieved with 61 concurrent protons in the reconstruction frame.
Layer 2
Layer 4
Layer 6
𝚫𝜽𝟎 𝚫𝜽𝟐 𝚫𝜽𝟑,𝟏 𝚫𝜽𝟑,𝟎
All tracks (58)
Unused data (11%)
12 10 8 6 4 2 30
100
200 1000 2000 Protons per reconstruction frame
Figure 6: The CPU time spent on proton track reconstruction. Below 100 protons per reconstructionframe, the (constant) time spent on reconstruction overhead becomes a large fraction of the total time.
Conclusion The track reconstruction algorithm as applied here is sufficient for the proof-of-concept of the DTC prototype. The obtained results, representing the theoretical limits of the current algorithm, reflect the high amounts of scattering inherent in a proton beam at therapeutic energies and spatial distributions.
The degradation of image resolution due to fake tracks needs to be further explored in order to find the best possible achievable proton intensity capacity.
Acknowledgements This project has been supported by Helse Vest RHF grant [911933] and Bergen Research Foundation grant [BFS2015PAR03].
100% 90% 80% 70%
References
60% 50% 40%
5 mm 3 mm 2 mm
30% 20% 2 3 45
Figure 2: Example of the track reconstruction: Here ∆θ3,0 ∆θ3,1 and the former is chosen at the next track segment.
Fake tracks (20%)
Figure 4: Examples of several reconstructed tracks (σxy = 3 mm): separated into all tracks, fake tracks and unused hits. Correctly reconstructed tracks
Layer 0
14
For a proton CT applying a DTC to enter into the clinic, a better performing reconstruction algorithm is required, both in terms of accuracy and reconstruction time.
3. For each seed pair, identify hits in the next layer where Sn+1 < Smax . If several hits are identified, the best is chosen as the next track segment. Both are chosen if two hits yield similar Sn+1 values: too many track forkings lead to a very slow reconstruction! 4. Repeat the above step. The final track with the lowest score is kept, and its hits are removed from the pool. Smax values of 200–300 mrad yield satisfactory results. The value should be adjusted based on the expected density of the proton tracks (smaller Smax with higher track density).
The time necessary for the track reconstruction, as it has been implemented here, is 2–14 ms per proton, depending on the track density.
10
20 100 200 1000 Protons per reconstruction frame
0% 5: Fraction of correctly reconstructed tracks Figure in three pencil beams with different circular spot sizes (σxy = 2–5 mm).
[1] H. E. S. Pettersen et al., Proton tracking in a highgranularity Digital Tracking Calorimeter for proton CT purposes. Nucl. Instrum. and Meth. in Phys. Res. A. 860, 51–61 (2017) [2] G. A. Rinella, The ALPIDE pixel sensor chip for the upgrade of the ALICE Inner Tracking System, Nucl. Instr. and Meth. in Phys. Res. A. 845, 583–587 (2016) [3] S. Amrouche et al., Track reconstruction at LHC as a collaborative data challenge use case with RAMP, EPJ Web Conf., 150.
