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Pre-treatment patient-specific stopping power by combining list-mode proton radiography and X-ray CT
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Download details: IP Address: 207.162.240.147 This content was downloaded on 04/07/2017 at 10:07 Manuscript version: Accepted Manuscript Collins-Fekete et al To cite this article before publication: Collins-Fekete et al, 2017, Phys. Med. Biol., at press: https://doi.org/10.1088/1361-6560/aa7c42 This Accepted Manuscript is: © 2017 Institute of Physics and Engineering in Medicine During the embargo period (the 12 month period from the publication of the Version of Record of this article), the Accepted Manuscript is fully protected by copyright and cannot be reused or reposted elsewhere. As the Version of Record of this article is going to be / has been published on a subscription basis, this Accepted Manuscript is available for reuse under a CC BY-NC-ND 3.0 licence after the 12 month embargo period. After the embargo period, everyone is permitted to copy and redistribute this article for non-commercial purposes only, provided that they adhere to all the terms of the licence https://creativecommons.org/licences/by-nc-nd/3.0 Although reasonable endeavours have been taken to obtain all necessary permissions from third parties to include their copyrighted content within this article, their full citation and copyright line may not be present in this Accepted Manuscript version. Before using any content from this article, please refer to the Version of Record on IOPscience once published for full citation and copyright details, as permission will likely be required. All third party content is fully copyright protected, unless specifically stated otherwise in the figure caption in the Version of Record. When available, you can view the Version of Record for this article at: http://iopscience.iop.org/article/10.1088/1361-6560/aa7c42
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Pre-treatment patient-specific stopping power by combining list-mode proton radiography and X-ray CT Charles-Antoine Collins-Fekete1,2,3 , S´ ebastien Brousmiche4 , David C. Hansen5 , Luc Beaulieu1,2 , Joao Seco3,6,7 1
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D´epartement de physique, de g´enie physique et d’optique et Centre de recherche sur le cancer, Universit´e Laval, Qu´ebec, Canada 2 D´epartement de radio-oncologie et CRCHU de Qu´ebec, CHU de Qu´ebec, QC, Canada 3 Department of Radiation Oncology, Francis H. Burr Proton Therapy Center Massachusetts General Hospital (MGH), Boston, Massachusetts 4 Ion Beams Application - IBA, Louvain-la-Neuve 5 Department of Medical Physics, Aarhus University Hospital, Aarhus 6 Deutsches Krebsforschungszentrum Heidelberg, Baden-W¨ urttemberg, DE 7 University of Heidelberg, Department of Physics and Astronomy Heidelberg, Baden-W¨ urttemberg, DE E-mail: [email protected]
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Abstract. The relative stopping power (RSP) uncertainty is the largest contributor to the range uncertainty in proton therapy. The purpose of this work was to develop a systematic method that yields accurate and patient-specific RSPs by combining 1) pre-treatment X-ray CT and 2) daily proton radiography of the patient. The method was formulated as a penalized least squares optimization problem (argmin(kAx-bk22 )). The parameter A represents the cumulative pathlength crossed by the proton in each material, separated by thresholding on the HU. The material RSPs (water equivalent thickness (WET)/physical thickness) are denoted by x. The parameter b is the list-mode proton radiography produced using Geant4 simulations. The problem was solved using a non-negative linearsolver with x≥0. A was computed by superposing proton trajectories calculated with a cubic or linear spline approach to the CT. The material’s RSP assigned in Geant4 were used for reference while the clinical HU-RSP calibration curve was used for comparison. The Gammex RMI-467 phantom was first investigated. The standard deviation between the estimated material RSP and the calculated RSP is 0.45%. The robustness of the techniques was then assessed as a function
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of the number of projections and initial proton energy. Optimization with two initial projections yields precise RSP (≤1.0%) for 330 MeV protons. 250 MeV protons have shown higher uncertainty (≤2.0%) due to the loss of precision in the path estimate. Anthropomorphic phantoms of the head, pelvis, and lung were subsequently evaluated. Accurate RSP has been obtained for the head (µ=0.21±1.63%), the lung (µ=0.06±0.99%) and the pelvis (µ=0.90±3.87%). The range precision has been optimized using the calibration curves obtained with the algorithm, yielding a mean R80 difference to the reference of 0.11 ± 0.09%, 0.28 ± 0.34% and 0.05 ± 0.06 % in the same order. The solution’s accuracy is limited by the assumed HU/RSP bijection, neglecting inherent degeneracy. The proposed formulation of the problem with prior knowledge X-ray CT demonstrates potential to increase the accuracy of present RSP estimates.
1. Introduction
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Submitted to: Phys. Med. Biol.
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Keywords: list-mode proton radiography, x-ray CT, Monte Carlo, proton range difference
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Proton radiotherapy is a cancer treatment modality that offers several advantages compared to conventional photon radiotherapy. The distal peak of the proton beam, namely the Bragg peak, allows for increased normal tissue sparing and more flexibility in the treatment of severe cancer near critical organs at risk (OARs). To realize the full advantages of proton therapy, a precise calculation of the Bragg peak distal edge fall-off position is critical (Andreo (2009)). A miscalculation of the Bragg peak distal position can lead to severe overdosage of the OARs or under dosage of the tumor zone. The calculation of the Bragg peak range comes from the Bethe-Bloch stopping power with the ICRU corrections (Seltzer and Berger (1982)). This equation relates a material electron density (ρe ) and mean excitation energy (I-value) to the energy loss of a proton traversing the said material. The precision of the range computed from this equation is directly related to the precision of the input information, which cannot be easily extracted from a subject without severe underlying uncertainties. The concept of relative stopping power (henceforth denoted RSP) has been first introduced by Hanson et al. (1981) to minimize the effect of those uncertainties
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when they calculated the proton energy loss ratio to water. The RSP is the ratio of a material stopping power to the stopping power of water. It also relates the physical thickness to the water equivalent thickness (WET), i.e. the water thickness that produces the same energy loss as the material thickness, to the physical thickness. The RSP is a combination of the previous information (ρe and I-value) in one quantity that can then be measured. The usefulness of the RSP is that it is approximately constant with energy. This is valid up to a variation of 0.7% in the 80-300 MeV range (Arbor et al. (2015)). An RSP map of the patient (similar to the Hounsfield Unit (HU) map acquired in photon imaging) is, therefore, the base of proton range calculations in proton therapy treatment planning. As such, the RSP is a quantity of tremendous importance in proton therapy. Its precision is directly related to the proton range calculation accuracy.
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Traditionally, an X-ray computed tomography (CT) was used to estimate the proton RSP map. This method would first require a calibration curve to assign individual HU to RSP. This curve was acquired with either a material by material measurement of both the HU and the RSP or a stoichiometric calibration that separates the mass attenuation coefficient Z-dependence from its relative electronic density dependence (Schneider et al. (1996)). A linear interpolation between the points would then provide a calibration curve on the whole HU range. Nevertheless, these methods are not based on any underlying physics model, and no bijection exists between the mass attenuation coefficient (extracted from the HU) and the RSP. Furthermore, these methods have been shown to introduce uncertainties on the projected RSP between 0.8% (Matsufuji et al. (1998); Chvetsov and Paige (2010)) and 3% if the I-value uncertainty is introduced (Schaffner and Pedroni (1998); Yang et al. (2012)). The uncertainty introduced also varies based on the treatment site. These uncertainties are considered to be the main contributors to the margins required for robust treatment planning in proton therapy (3.5% + 1 mm) (Paganetti (2012)).
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Dual-energy computed tomography (DECT) has been proposed (Yang et al. (2010, 2011); Landry et al. (2013b); H¨ unemohr et al. (2014b); Hansen et al. (2015)) as a more precise alternative to the single energy X-ray CT to acquire RSP maps. In X-ray computed tomography, the attenuation coefficient (µ related to the HU) is both dependent on the Zef f and on the density ρ. With a single measurement,
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the system is under-determined, and it is impossible to extract both pieces of information. Dual-energy CT strength relies on the fact that by using two different photon energy spectrum levels (usually 80 kVp and 140 kVp with a tin filter), two different measurements of the µ are acquired from which it is possible to extract both Zef f and ρ. Yang et al. (2010) found an empirical relation that relates the I-value to the Zef f through a linear interpolation on two regions (low and high Zef f ). With these pieces of information, they have shown that it is then possible to recompute the RSP (using Bethe-Bloch equation) with a particular precision. Nevertheless, the DECT method has yet to be validated using a fully clinical anthropomorphic phantom (H¨ unemohr et al. (2014a)).
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Single event detection proton computed tomography (pCT) has been presented as the most accurate method to acquire the subject RSP map for proton range calculation (Zygmanski et al. (2000); Schulte et al. (2004)). The pCT reconstruction requires the knowledge of the proton’s directional information obtained from sophisticated single event detectors. This information is then used to reconstruct the proton’s most likely path (MLP) (Schulte et al. (2008)). Subsequently, the pCT can be reconstructed through either an algebraic iterative reconstruction (Hurley et al. (2012)), an adapted filtered back projection (Rit et al. (2013)), or an hybrid method using pre-reconstruction deblurring of the proton radiographs and subsequent filtered back projection (Collins-Fekete et al., 2016). All these methods yield the proton RSP map directly. Although this is acknowledged to be the most precise way of acquiring RSP, it is still both cost and time inefficient due to long acquisition times. Furthermore, most cyclotrons do not provide the proton with sufficient energy to cross thick body regions such as the pelvis or the lung (Wang et al., 2012). Besides, reconstructing a pCT with a subset of the necessary projections would yield poor quality images. Wang et al. (2012) used converted MVCT projections to replace the direction where the proton beam energy was not sufficient to cross the body to obtain a complete sinogram for the pCT reconstruction. However, their acquisition accuracy still relies on acquiring a large number of proton radiographies which makes the whole method slow. This project proposes a novel method to obtain the RSP map from a particular subject. To do so, the patient-specific calibration curve that links the X-ray CT HU numbers to the RSP is extracted from a list-mode proton radiography combined with
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the pre-treatment X-ray CT. The calibration curve stems from the combination of these two data sets. It is then straightforward to map the X-ray CT HU to the RSP to obtain the desired RSP map. A similar idea was investigated by Schneider et al. (2005). In their project, they optimized a calibration curve of a dog patient. To do so, they first acquired a projected digitally reconstructed radiography (from the Xray CT first converted to WET through the calibration curve) and compared it to the proton radiography. They then minimized the chi-squared difference between the two images WET through random modification of the calibration curve. Nevertheless, in their work, no systematic minimization was done, and multiple Coulomb scattering was neglected with the use of linear proton paths. Doolan et al. (2015) have also worked on optimizing the calibration curve by combining proton radiography, X-ray CT, and a systematic minimization algorithm. However, they have used an integrated fluence detector to acquire the proton radiography which prevented them from doing any path estimate. They are therefore obligated to consider bin by bin optimization of a digitally reconstructed radiography (through the X-ray CT), inherently assuming a straight proton path. All those errors are expected to degrade the quality of the extracted calibration curve which may cause a persisting systematic error at certain positions.
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To the best of the author knowledge, no work has been done trying to produce a systematic and consistent method that retrieves the patient specific HU-RSP calibration curve from both the X-ray CT and the list-mode proton radiography using the most up-to-date proton path estimate. In this work, a novel optimization algorithm has been developed for this purpose. It has been tested on a wide variety of phantoms and proved to produce accurate RSP maps that can then be used to reproduce the proton range accurately.
2. Materials and Methods
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Monte Carlo (MC) simulations of 250/330 MeV protons radiographies were done for the Gammex RMI-467 calibration phantom as well as 330 MeV proton radiographies for three anthropomorphic phantoms (lung, pelvis, head). Two different path algorithms were used to estimate the proton trajectory: the cubic spline path (CSP) and the straight line path (SLP). For each phantom and each path estimate, the
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method proposed here allowed to extract an optimized calibration curve. The proton range was investigated for each calibration curve generated from the different path estimates (reference, optimized with CSP/SLP splines and clinical) on each phantom (Gammex, lung, pelvis, head) and compared to the reference proton range. The RSP difference, as well as the range difference, were used as metrics of comparison to assess the performance and the precision of the algorithm proposed here. 2.1. Monte Carlo simulated list-mode proton radiography
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The list-mode proton radiographies were acquired through Monte Carlo simulations. No detector effects were simulated. Proton paths were simulated using the Geant4 (Agostinelli et al. (2003)) code (v4.10.00). The standard processes include energy loss and straggling, multiple Coulomb scattering based on Lewis theory (Goudsmit and Saunderson (1940)) and parameterized proton interactions with nuclei and electrons. In precise term, the following physics lists were enabled: the standard electromagnetic physics option 3 for higher accuracy of electrons, hadrons and ion tracking without a magnetic field, the hadrons elastic model and the binary ion models both for elastic and inelastic collisions. Range cuts below which no secondaries particles are produced were set to 0.1 mm for each particle. The simulations were done with 5x106 330 MeV protons since they have enough range (≈ 60 cm WET) to traverse the thicker part of every anthropomorphic phantom while having an exit energy that is in the constant-RSP domain (> 80 MeV).
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The simulation geometry was based on either a fully parametric definition of the Gammex RMI-467 phantom or a voxelized CT geometry acquired from different anthropomorphic phantom X-ray scan. Geant4 materials require both the mass density and atomic composition to produce precise stopping power tables. The Gammex-RMI 467 insert’s composition and density have been taken from the definition by Landry et al. (2013b). In the anthropomorphic phantoms, the mass density was extracted from the X-ray CT voxel, converted from the relative electron density (ρrel ). The ρrel was initially acquired from a clinical HU-ρrel conversion curve. It was then converted to mass density using Equation 1:
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ρerel · ρwater Ngwater ρ= → Ng
Ng =
X i
Ngi = NA
X w i Zi i
Ai
(1)
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where ρwater is the water density, NA is the Avogadro number, wi represents the fractional mass of every element in the tissue and Zi /Ai is the ratio of the atomic number to the mass number.
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In addition to the density, an atomic composition had to be assigned for each HU. The atomic composition of individual voxel comes from the set of materials detailed in Table 1. This limited number of materials were used as a pivot point to define the broader domain of HU materials. Thereby, for voxels with an HU between two pivots, composite materials were assigned based on a linear interpolation between the pivots materials definition. Thus, for the anthropomorphic voxelized phantom, each HU is assigned to a unique material with a corresponding unique RSP. The chosen method imposes a bijection between the HU and the RSP.
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The Gammex CT images have been produced through the ImaSim software (Landry et al. (2013a)). A perfect computed tomography of the Gammex is acquired using this technique. The phantom is a solid-water cylinder (radius of 16.5 cm) with 16 cylindrical inserts (radius of 1.4 cm) of tissue equivalent plastic material. The three anthropomorphic body sites represent a lung, a pelvis, and a head region. X-ray CT of anthropomorphic phantoms available in our clinic has been acquired for this study. The resolution of their voxelized geometries is (0.68 x 0.68 x 1.25 mm3 ).
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Through these simulations, a list-mode proton radiography of each phantom was produced at multiple angles. The output protons were filtered based on their position, direction and exit energy using the cut suggested in Schulte et al. (2008). Briefly, the standard deviation of the exit energy, lateral deviation and angular deviation for each proton was compiled for each exit pixel. Then, individual protons were filtered out if their lateral/angular deviation or energy loss exceeded the 3σ threshold.
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2.1.1. Water equivalent list-mode proton radiography The quantity of interest in this study was the water equivalent path length (WEPL) rather than the energy lost. The energy loss was converted to WEPL by integrating over the stopping power of water (Talamonti et al. (2010); Plautz et al. (2014)). The stopping power was calculated through the Bethe-Bloch equation (Equation 2) using the ICRU (1993) I-value for water ( Iw = 78 eV) as well as their suggested
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corrections:
H 10.4 11.6 11.2
C 10.6 68.3 51.9
N 3.1 0.2 1.3
O 75.7 19.9 35.6
Ca 0.0 0.0 0.0
P 0.2 0.0 0.0
I [eV] 74.54 63.06 66.14
ρe 0.258 0.933 0.970
ρ 0.26 0.93 0.97
5 40 43 72 100 385
10.5 10.2 10.3 10.1 9.5 7.8
25.6 17.3 14.4 25.2 21.0 31.8
2.7 3.6 3.4 4.6 6.3 3.7
60.2 68.7 71.6 59.9 63.1 44.1
0.0 0.0 0.0 0.0 0.0 8.6
0.2 0.2 0.2 0.1 0.0 4.0
72.3 73.69 74.03 72.25 73.79 81.97
1.016 1.040 1.043 1.0 84 1.103 1.211
1.02 1.05 1.05 1.09 1.12 1.25
538 688 999 1524
7.1 6.3 5.0 3.4
38.1 33.4 21.3 15.6
2.6 2.9 4.0 4.2
34.3 36.3 43.8 43.8
12.2 14.4 17.7 22.6
5.6 6.6 8.1 10.4
85.43 90.24 99.69 111.63
1.279 1.355 1.517 1.781
1.33 1.43 1.61 1.92
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HU -741 -98 -55
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Material Name Lung Deflated Adipose Tissue 3 Adipose Tissue 1 Mean Male soft tissue Muscle Skeletal 1 Muscle Skeletal 2 Skin 1 Connective Tissue Sternum Humerus Spherical Head Femur Total Bone Cranium Cortical Bone
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Table 1: Chemical composition of the materials used as reference for the Monte Carlo simulations (Woodard and White (1986); White et al. (1987)). Materials for HU within the described range are interpolated in between the closest defined materials.
4πe4 2 Z SP (Iw , E) = ρ z me c2 uβ 2 A
C δ 2me c2 β 2 2 ln − β − ln Iw − − ,(2) (1 − β 2 ) Z 2
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where β represents the particle’s velocity in units of the speed of light c, z is the particles atomic number. Z, A and ρ are the target materials atomic number, mass number, and density respectively. C is the density and δ the shell correction term. me is the electrons mass and e its charge. The WEPL is the integral of the inverse of the stopping power over the energy loss (Equation 3). Z Ein dE W EP L = − (3) Eout SP (Iw , E) 2.2. Optimization algorithm The HU-RSP calibration curve is the link that relates the list-mode proton radiography to the X-ray CT projection. In this work, the WEPL was the quantity
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used to connect both these data sets through the calibration curve.
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W EP Lj =
I X
Li,j · x(si,j )
i=0
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For the j -th proton with a defined path S(t) and differential steps of length Li,j , the WEPL can be defined through the RSP of each voxel and the length spent in it (Equation 4): (4)
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M X
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where i represents the step number within the proton path estimate with i ∈ I, the total number of steps. si,j is the three-dimensional position vector, calculated through the path estimate S(t) and x(si,j ) is the RSP at that position. Since the RSPs are constant with energy, any re-ordering of the materials produces the same WEPL. Let Am,j represents the total length crossed in the m-th material with parameters (RSPm , HUm ), m∈ [0,M], xm (HUm ) represent the RSP of the m-th material with HUm and M is the total number of materials in the phantom. It is possible to rewrite the Equation 4 as a function of the total length Am,j in each material. W EP Lj =
Am,j · xm (HUm )
(5)
m=0
The parameter xm (HUm ) for all materials represents the desired calibration curve. Equation 3 and Equation 5 both yield the WEPL crossed for each proton. The WEPL extracted from each equation will differ only by the precision of the RSP calibration curve. Both equations can be used as part of a cost function as in Equation 6.
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N protons
C(RSP) =
X j=0
"
M X
m=0
Am,j · xm (HUm ) + bj
#
(6)
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where the term bj represents the WEPL extracted from the energy loss acquired in the proton radiography (Equation 3). C(RSP) represents the cost associated with a particular HU-RSP vector solution. It is numerically more convenient to express the last equation in a matrix form (Equation 7). The A-matrix (N x M) is the length crossed in each material for each proton, and the x-vector (length M) denotes the RSP of each material. Finally, the b-vector (length N) indicates the WEPL crossed
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by each proton. The set of RSPs that minimize C is sought.
s.t. xi ≥ 0.
(7)
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argmin kAx − bk22
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2.3. Proton path reconstruction
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Where kui k2 is the l2 norm with the additional constraint that the resulting calibration curve cannot contain negative values. Equation 7 outputs a discrete number of RSPs. However, to increase statistics and decrease noise due to rare materials within the body, the number of reconstructed RSP can be reduced by selecting defined tissue type that represents the chosen body region adequately. The calibration curve is then reproduced by linear interpolation between the extracted points. Equation 7 is solved using a non-negative linear-solver within the Scipy/ Python embedded C/C++ library. In this work, no prior is used for the determination of the RSP vector.
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The proton path reconstruction in the phantom is paramount in proton imaging as well as in the method developed here as it allows when superposed with the X-ray CT, an estimation of the WEPL. The technique usually requires knowledge of the initial and final proton position (x) and direction (p). The most likely path is a probabilistic method of finding the proton given these information (Schneider and Pedroni (1994); Williams (2004); Collins-Fekete et al. (2017)). A Bayesian formalism has been introduced (Schulte et al. (2008); Erdelyi (2009)) that derives a proton path based on a maximal likelihood given the spatial information and Fermi-Eyges moments, at a precise depth and considering little angular deviation. Although this method provides the most likely proton path, it requires a certain amount of computation time. More recently, Collins-Fekete et al. (2015) have developed a phenomenological model of the proton path based on Monte Carlo simulations. The model is based on WET crossed and provides a scaling of the cubic spline path, first introduced by Li et al. (2006). It has demonstrated good accuracy with low computation time and will be used in this study. In this study, the proton path estimate is used to construct the A-matrix. Although an accurate proton path is always desired, it is of interest to investigate cases where
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of the phantom which are poorly modeled by the path estimate. The average error for the head phantom is 0.21± 1.63 %.
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In comparison, the lung phantom (Figure 5-middle) shows great results throughout the whole RSP domain. The relatively small energy loss allows the path estimate to be precise, consequently yielding accurate RSP. The average error for the lung phantom is 0.06 ± 0.99%.
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The anthropomorphic pelvis phantom (Figure 5-bottom) displays sensibly more imprecise RSP, especially below -400 HU. The average error for the pelvis phantom is 0.90 ± 3.87%. However, these HU regions are usually representative of lung material, rarely found in the pelvis area. In this scenario, the proton loses a significant amount of energy while crossing the pelvis phantom. The MLP uncertainty estimation is important and the probability of misregistration increases substantially. Consequently, those path estimate errors lead to a systematic bias that explains the deviation seen here. However, since the probability distribution function of these voxels is small, the impact on the proton beam range is expected to be minimal. This result will be verified in the next section.
3.3. Range difference for a pencil beam in the anthropomorphic phantoms
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The range differences have been computed for each anthropomorphic phantom with the calibration curves extracted from the optimization algorithm. Again, the Amatrix input of the optimization algorithm has been produced using the two different path estimates, SLP and CSP. The clinical HU-RSP calibration curve has also been investigated for comparison purposes. For all these configurations, the list-mode proton radiography was always taken in the lateral direction, from the left-hand side of the figure. For each beam (steps of 45o ), 5x106 330 MeV protons have been simulated. The absolute and relative range error (relative to the total range as shown in Section 2.4) are shown in Table 2. As expected from the previous results, the CSP path estimates provide the HU-RSP calibration curves that have the most precise range prediction. The anthropomorphic head and pelvis phantom show minor variations in between the different path
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Patient specific optimization using combined proton radiography and X-ray CT
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Clinical -0.75 -0.58 -0.49 -0.36 -0.39 0.24 -0.09 -0.69 0.24 -0.39 1.06 -1.25
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Clinical -1.23 -1.20 -1.44 -1.49 -1.22 -0.80 -0.74 0.52 0.52 -0.95 0.84 -1.23
Lung SLP CSP 0.06 -0.07 0.54 0.14 0.14 0.06 -0.04 0.02 0.63 -0.01 0.43 0.11 0.41 0.21 0.12 0.22 0.63 0.22 0.29 0.09 0.80 0.34 0.93 0.28
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0 45 90 135 180 225 270 315 Max.† hXi[mm] σErr [%] hXi[%]
Head SLP CSP 0.13 0.04 0.12 0.05 0.21 0.16 0.22 0.07 0.25 0.04 -0.16 0.03 0.54 0.05 0.62 0.22 0.62 0.22 0.24 0.08 0.32 0.09 0.31 0.11
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Table 2: Range difference between the reference MC simulation and the simulation with RSP extracted from the optimization algorithm through the various path estimate (CSP : Cubic spline path SLP : Straight line path). All three investigated anthropomorphic phantom are presented here with average deviation both in mm (hXi[mm]) and in relative range (hXi [%]). † Maximum absolute error Pelvis SLP 0.07 -0.27 -0.21 -0.24 -0.27 -0.32 -0.13 -0.24 0.07 -0.20 0.07 -0.11
CSP -0.08 0.13 0.14 -0.01 0.26 0.07 0.09 0.04 0.26 0.08 0.06 0.05
Clinical 1.60 1.91 0.87 1.62 2.46 1.29 0.63 0.93 2.46 1.41 0.34 0.80
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This study has demonstrated that it is possible to combine two different forms of imaging, i.e. a list-mode proton radiography and an X-ray CT, to accurately obtain a patient-specific HU-RSP calibration curve. The novel method presented here yields RSPs with 1.0 % maximum error compared to the MC reference using the Gammex RMI-467 calibration phantom with two or more projections. The anthropomorphic phantoms of the head, pelvis, and lung have also shown precise measurement of the RSPs, below 1.0% average error for every phantom.
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Although the RSP precision is crucial when calculating treatment plans, the most relevant piece of information when considering beam precision is the range accuracy. In this work, the mean range prediction has been drastically improved when using the optimized HU-RSP calibration curve. The optimized calibration curve has improved
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the range accuracy in the lung from -1.25% using the clinical curve to 0.28% using the optimized calibration curve, from 0.80% to 0.05% in the pelvis, and from -1.23% to 0.11% in the head phantom. Each difference is expressed as a relative range difference to the Monte Carlo range. Finally, Table 2 demonstrated that even the less precise path estimates (straight-line path) would give better results than the clinical calibration curve.
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It is important to assess the fact that there exists a non-null systematic error in the clinical curve independent of the stochastic error. The clinical curve is obtained by measuring the Gammex materials HU/RSP parameters. The RSP is measured by placing the Gammex inserts in the proton beam, and the HU is obtained from the stoichiometric calibration (Schneider et al., 1996). However, the phantoms were simulated with different tissue-like materials (Table 1). The difference between the materials from which the clinical curve is extracted and the simulated MC tissue is the cause of the observed systematic error. In other words, given another choice of materials for the MC simulation, the absolute difference found here is expected to differ. This difference effectively represents inter-patient tissue variation. Therefore, the relevant information is not to evaluate the clinical curve accuracy for this particular choice of materials but rather to test the reduction of both the systematic and stochastic error when using the method presented here. The relative improvement between the clinical curve and the optimized curve is what can be truly achieved by the algorithm.
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The results shown here compare favorably with the 3.0% limit for RSP accuracy when using the stoichiometric method (Schaffner and Pedroni (1998); Yang et al. (2012)). It is important to note that the imprecise RSP are expected in particular HU regions due to the lack of material such as lung-density tissue in the head or pelvis phantom. Those materials are located in voxels in the vicinity of a high-gradient edge, and a potential misregistration of the path is very likely. However, the range calculations done here proved that their effect is minimal at the Bragg peak. When considering only the effective RSP domain, the results drop below the 1% threshold for the head phantom. DECT has shown promises for investigating accurate RSP in calibration phantoms. In their theoretical study, H¨ unemohr et al. (2014b) have demonstrated that they can
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extract RSPs up to an accuracy of 0.7% based on Monte Carlo DECT simulations. However, the technique they used is both calibrated and used on a single set of data, and the precision is more representative of the artifacts present in the system rather than the technique accuracy. They then provided an experimental validation and obtained values with differences up to 0.6% (H¨ unemohr et al. (2014a)) with reference, within an accuracy of 1.7% and 9.4%. However, the results are not entirely representative of what could be expected of a DECT apparatus as they are acquired on inserts loaded centrally in a smaller diameter (16 cm) phantom, minimizing artifacts from beam hardening and scattering. Yang et al. (2010) demonstrated results with differences up to 1.0% to the reference. Based on the results from both of these studies, 1.0% error is a realistic estimate of the DECT RSP prediction power, slightly higher than what is achieved here. However, no DECT study has been done on real phantoms. The only valid comparison is then with our Gammex RMI-467 phantom. With this phantom, the results demonstrate that the method presented here performs better than the one presented in DECT studies. Hansen et al. (2015) have obtained more accurate results with a root mean square error of 0.5% on the Gammex phantom, but with maximal errors of 1.7%.
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pCT yields the most accurate RSP estimate, as expected. Hurley et al. (2012) achieved 0.5% standard deviation in the RSP extracted in a experimental pCT setup. This is a highly accurate result compared to what we can achieve here (1.0 %) considering the underlying uncertainty detailed before, and can be regarded as the clinically achievable accuracy. Besides, pCT does not suffer from the artifacts present in X-ray CT, such as beam hardening. pCT also has the advantage that it would image the patient directly in the treatment position, which could reduce setup errors. Nevertheless, long acquisition time still prevents the full use of pCT for clinical use. As explained earlier, Wang et al. (2012) proposed to blend converted MVCT projections to proton radiographies to obtain a faster yet accurate pCT reconstruction. When mixing approximately half the MVCT projections with the proton radiographies for the sinogram reconstruction, their algorithm yielded stopping power precision of ±0.86 %, within the same range of what has been found for DECT and here. However, their method accuracy is directly related to the number of proton radiographies projections used and therefore long to acquire. The precision achievable in this project is limited by 1) the number of projections ac-
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quired, 2) the energy requirement, 3) the HU degeneracy and 4) the patient accurate setup and motion. First, the use of a single projection could create some degeneracy problems as seen in the Gammex phantom results (Figure 3a). This problem could be alleviated by using two orthogonal projections which could also be used for prior registration. Second, the current proton center does not have the required proton energy to acquire a proton radiography of the thickest sites examined here. However, with the newest technology (ProTom 330), full proton radiography will become a definite possibility, and this study will be directly applicable clinically. Third, the technique is limited by materials that have identical HU but different RSP. In that scenario, the algorithm would not be able to extract precise RSP for both materials. Using a different prior such as DECT could, however, remove this problem. This problem has been briefly investigated by using the method proposed here on the ICRP adult female phantom (Menzel et al., 2009). The results show an average error of 0.38±0.77% compared to the reference calculated with the Bethe-Bloch formula on the ICRP tissue (Menzel et al., 2009). Further details are shown in the supplementary materials. Fourth, the patient motion could cause a misregistration between the X-ray CT and the acquired list mode proton radiography. Recently, a novel optimization algorithm has been proposed to ameliorate the pRad spatial resolution to perform rigid registration before applying this technique (Collins-Fekete et al., 2016). Furthermore, even though we acknowledge this misregistration to be a cause of error, it has not been the focus of this study as this is a common problem of most techniques and has been thoroughly reviewed elsewhere (Knopf et al. (2011)).
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4.1. Clinical application
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The method described here could be applied in two different ways in a clinical setup. First, it could be part of the pre-treatment planning, by combining the diagnosis X-ray CT with an acquired list-mode proton radiography to have the most accurate treatment plan. By doing so, however, the day-to-day registration advantage brought by the list-mode proton radiography are disregarded. Secondly, it would be possible to acquire a list-mode proton radiography at each fraction, before the treatment, both to position the patient and to obtain the calibration curve specific to this fraction. Subsequently, the patient-specific
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calibration curve could be used as a metric to trigger recalculation based on either the range or RSP difference. The second option could then be combined with another method to acquire RSP such as the DECT as it would position itself as a safeguard step. Either of these options is expected to improve the range calculation and capture the potentially significant difference. However, the second method would seem more suitable to adhere to the busy schedule of a proton therapy center to optimize the patient throughput. 5. Conclusion
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This project aimed to obtain a patient-specific HU-RSP calibration curve by combining information from an X-ray CT and a list-mode proton radiography. For simple phantoms (i.e. Gammex-RMI 467), the RSP accuracy is below 1.0% over the clinical range. For more complicated anthropomorphic phantoms, the RSP prediction accuracy varies as a function of the geometry and the energy loss. The head (σRSP = 1.63%) and lung phantom (σRSP = 0.99%) shows good precision throughout the path, however the pelvis phantom shows higher RSP deviations (σRSP = 3.87%). Nevertheless, the range prediction obtained from these calibration curves shows high accuracy (relative range error of 0.11, 0.28 and 0.05 % against the reference in the head, lung and pelvis phantom) compared to the actual clinical curve (range error of -1.23, -1.25 and 0.80 %) for all phantoms. The optimal technique demonstrated here requires sophisticated single event detectors to reconstruct the proton path throughout the phantom. A straight-line path, requiring a less developed detector, have also been investigated for comparison purposes. The lower precision path estimates have been shown to produce solid HU-RSP calibration curve with smaller range error than the clinical optimization. 6. Acknowledgement
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The authors would like to acknowledge David Craft, Stephen Portillo and Zachary Slepian for the helpful discussion. Charles-Antoine Collins-Fekete is supported by a scholarship from Fonds de Recherche du Qu´ebec – Nature et technologies. CACF acknowledges partial support by the CREATE Medical Physics Research Training Network grant of the Natural Sciences and Engineering Research Council (Grant number: 432290). This work is also supported in part by the National
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REFERENCES
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Sciences and Engineering Council (NSERC) of Canada through grant #4355102013. Computations were made on the supercomputer Colosse from Universit´e Laval, managed by Calcul Qu´ebec and Compute Canada. The operation of this supercomputer is funded by the Canada Foundation for Innovation (CFI), NanoQu´ebec, RMGA and the Fonds de Recherche du Qu´ebec - Nature et Technologies (FRQ-NT). David Hansen is sponsored by the Danish Cancer Society (grant no. A5992). References
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Pre-treatment patient-specific stopping power by combining list-mode proton radiography and X-ray CT
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Download details: IP Address: 207.162.240.147 This content was downloaded on 04/07/2017 at 10:07 Manuscript version: Accepted Manuscript Collins-Fekete et al To cite this article before publication: Collins-Fekete et al, 2017, Phys. Med. Biol., at press: https://doi.org/10.1088/1361-6560/aa7c42 This Accepted Manuscript is: © 2017 Institute of Physics and Engineering in Medicine During the embargo period (the 12 month period from the publication of the Version of Record of this article), the Accepted Manuscript is fully protected by copyright and cannot be reused or reposted elsewhere. As the Version of Record of this article is going to be / has been published on a subscription basis, this Accepted Manuscript is available for reuse under a CC BY-NC-ND 3.0 licence after the 12 month embargo period. After the embargo period, everyone is permitted to copy and redistribute this article for non-commercial purposes only, provided that they adhere to all the terms of the licence https://creativecommons.org/licences/by-nc-nd/3.0 Although reasonable endeavours have been taken to obtain all necessary permissions from third parties to include their copyrighted content within this article, their full citation and copyright line may not be present in this Accepted Manuscript version. Before using any content from this article, please refer to the Version of Record on IOPscience once published for full citation and copyright details, as permission will likely be required. All third party content is fully copyright protected, unless specifically stated otherwise in the figure caption in the Version of Record. When available, you can view the Version of Record for this article at: http://iopscience.iop.org/article/10.1088/1361-6560/aa7c42
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Pre-treatment patient-specific stopping power by combining list-mode proton radiography and X-ray CT Charles-Antoine Collins-Fekete1,2,3 , S´ ebastien Brousmiche4 , David C. Hansen5 , Luc Beaulieu1,2 , Joao Seco3,6,7 1
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D´epartement de physique, de g´enie physique et d’optique et Centre de recherche sur le cancer, Universit´e Laval, Qu´ebec, Canada 2 D´epartement de radio-oncologie et CRCHU de Qu´ebec, CHU de Qu´ebec, QC, Canada 3 Department of Radiation Oncology, Francis H. Burr Proton Therapy Center Massachusetts General Hospital (MGH), Boston, Massachusetts 4 Ion Beams Application - IBA, Louvain-la-Neuve 5 Department of Medical Physics, Aarhus University Hospital, Aarhus 6 Deutsches Krebsforschungszentrum Heidelberg, Baden-W¨ urttemberg, DE 7 University of Heidelberg, Department of Physics and Astronomy Heidelberg, Baden-W¨ urttemberg, DE E-mail: [email protected]
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Abstract. The relative stopping power (RSP) uncertainty is the largest contributor to the range uncertainty in proton therapy. The purpose of this work was to develop a systematic method that yields accurate and patient-specific RSPs by combining 1) pre-treatment X-ray CT and 2) daily proton radiography of the patient. The method was formulated as a penalized least squares optimization problem (argmin(kAx-bk22 )). The parameter A represents the cumulative pathlength crossed by the proton in each material, separated by thresholding on the HU. The material RSPs (water equivalent thickness (WET)/physical thickness) are denoted by x. The parameter b is the list-mode proton radiography produced using Geant4 simulations. The problem was solved using a non-negative linearsolver with x≥0. A was computed by superposing proton trajectories calculated with a cubic or linear spline approach to the CT. The material’s RSP assigned in Geant4 were used for reference while the clinical HU-RSP calibration curve was used for comparison. The Gammex RMI-467 phantom was first investigated. The standard deviation between the estimated material RSP and the calculated RSP is 0.45%. The robustness of the techniques was then assessed as a function
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of the number of projections and initial proton energy. Optimization with two initial projections yields precise RSP (≤1.0%) for 330 MeV protons. 250 MeV protons have shown higher uncertainty (≤2.0%) due to the loss of precision in the path estimate. Anthropomorphic phantoms of the head, pelvis, and lung were subsequently evaluated. Accurate RSP has been obtained for the head (µ=0.21±1.63%), the lung (µ=0.06±0.99%) and the pelvis (µ=0.90±3.87%). The range precision has been optimized using the calibration curves obtained with the algorithm, yielding a mean R80 difference to the reference of 0.11 ± 0.09%, 0.28 ± 0.34% and 0.05 ± 0.06 % in the same order. The solution’s accuracy is limited by the assumed HU/RSP bijection, neglecting inherent degeneracy. The proposed formulation of the problem with prior knowledge X-ray CT demonstrates potential to increase the accuracy of present RSP estimates.
1. Introduction
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Submitted to: Phys. Med. Biol.
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Keywords: list-mode proton radiography, x-ray CT, Monte Carlo, proton range difference
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Proton radiotherapy is a cancer treatment modality that offers several advantages compared to conventional photon radiotherapy. The distal peak of the proton beam, namely the Bragg peak, allows for increased normal tissue sparing and more flexibility in the treatment of severe cancer near critical organs at risk (OARs). To realize the full advantages of proton therapy, a precise calculation of the Bragg peak distal edge fall-off position is critical (Andreo (2009)). A miscalculation of the Bragg peak distal position can lead to severe overdosage of the OARs or under dosage of the tumor zone. The calculation of the Bragg peak range comes from the Bethe-Bloch stopping power with the ICRU corrections (Seltzer and Berger (1982)). This equation relates a material electron density (ρe ) and mean excitation energy (I-value) to the energy loss of a proton traversing the said material. The precision of the range computed from this equation is directly related to the precision of the input information, which cannot be easily extracted from a subject without severe underlying uncertainties. The concept of relative stopping power (henceforth denoted RSP) has been first introduced by Hanson et al. (1981) to minimize the effect of those uncertainties
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when they calculated the proton energy loss ratio to water. The RSP is the ratio of a material stopping power to the stopping power of water. It also relates the physical thickness to the water equivalent thickness (WET), i.e. the water thickness that produces the same energy loss as the material thickness, to the physical thickness. The RSP is a combination of the previous information (ρe and I-value) in one quantity that can then be measured. The usefulness of the RSP is that it is approximately constant with energy. This is valid up to a variation of 0.7% in the 80-300 MeV range (Arbor et al. (2015)). An RSP map of the patient (similar to the Hounsfield Unit (HU) map acquired in photon imaging) is, therefore, the base of proton range calculations in proton therapy treatment planning. As such, the RSP is a quantity of tremendous importance in proton therapy. Its precision is directly related to the proton range calculation accuracy.
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Traditionally, an X-ray computed tomography (CT) was used to estimate the proton RSP map. This method would first require a calibration curve to assign individual HU to RSP. This curve was acquired with either a material by material measurement of both the HU and the RSP or a stoichiometric calibration that separates the mass attenuation coefficient Z-dependence from its relative electronic density dependence (Schneider et al. (1996)). A linear interpolation between the points would then provide a calibration curve on the whole HU range. Nevertheless, these methods are not based on any underlying physics model, and no bijection exists between the mass attenuation coefficient (extracted from the HU) and the RSP. Furthermore, these methods have been shown to introduce uncertainties on the projected RSP between 0.8% (Matsufuji et al. (1998); Chvetsov and Paige (2010)) and 3% if the I-value uncertainty is introduced (Schaffner and Pedroni (1998); Yang et al. (2012)). The uncertainty introduced also varies based on the treatment site. These uncertainties are considered to be the main contributors to the margins required for robust treatment planning in proton therapy (3.5% + 1 mm) (Paganetti (2012)).
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Dual-energy computed tomography (DECT) has been proposed (Yang et al. (2010, 2011); Landry et al. (2013b); H¨ unemohr et al. (2014b); Hansen et al. (2015)) as a more precise alternative to the single energy X-ray CT to acquire RSP maps. In X-ray computed tomography, the attenuation coefficient (µ related to the HU) is both dependent on the Zef f and on the density ρ. With a single measurement,
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the system is under-determined, and it is impossible to extract both pieces of information. Dual-energy CT strength relies on the fact that by using two different photon energy spectrum levels (usually 80 kVp and 140 kVp with a tin filter), two different measurements of the µ are acquired from which it is possible to extract both Zef f and ρ. Yang et al. (2010) found an empirical relation that relates the I-value to the Zef f through a linear interpolation on two regions (low and high Zef f ). With these pieces of information, they have shown that it is then possible to recompute the RSP (using Bethe-Bloch equation) with a particular precision. Nevertheless, the DECT method has yet to be validated using a fully clinical anthropomorphic phantom (H¨ unemohr et al. (2014a)).
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Single event detection proton computed tomography (pCT) has been presented as the most accurate method to acquire the subject RSP map for proton range calculation (Zygmanski et al. (2000); Schulte et al. (2004)). The pCT reconstruction requires the knowledge of the proton’s directional information obtained from sophisticated single event detectors. This information is then used to reconstruct the proton’s most likely path (MLP) (Schulte et al. (2008)). Subsequently, the pCT can be reconstructed through either an algebraic iterative reconstruction (Hurley et al. (2012)), an adapted filtered back projection (Rit et al. (2013)), or an hybrid method using pre-reconstruction deblurring of the proton radiographs and subsequent filtered back projection (Collins-Fekete et al., 2016). All these methods yield the proton RSP map directly. Although this is acknowledged to be the most precise way of acquiring RSP, it is still both cost and time inefficient due to long acquisition times. Furthermore, most cyclotrons do not provide the proton with sufficient energy to cross thick body regions such as the pelvis or the lung (Wang et al., 2012). Besides, reconstructing a pCT with a subset of the necessary projections would yield poor quality images. Wang et al. (2012) used converted MVCT projections to replace the direction where the proton beam energy was not sufficient to cross the body to obtain a complete sinogram for the pCT reconstruction. However, their acquisition accuracy still relies on acquiring a large number of proton radiographies which makes the whole method slow. This project proposes a novel method to obtain the RSP map from a particular subject. To do so, the patient-specific calibration curve that links the X-ray CT HU numbers to the RSP is extracted from a list-mode proton radiography combined with
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the pre-treatment X-ray CT. The calibration curve stems from the combination of these two data sets. It is then straightforward to map the X-ray CT HU to the RSP to obtain the desired RSP map. A similar idea was investigated by Schneider et al. (2005). In their project, they optimized a calibration curve of a dog patient. To do so, they first acquired a projected digitally reconstructed radiography (from the Xray CT first converted to WET through the calibration curve) and compared it to the proton radiography. They then minimized the chi-squared difference between the two images WET through random modification of the calibration curve. Nevertheless, in their work, no systematic minimization was done, and multiple Coulomb scattering was neglected with the use of linear proton paths. Doolan et al. (2015) have also worked on optimizing the calibration curve by combining proton radiography, X-ray CT, and a systematic minimization algorithm. However, they have used an integrated fluence detector to acquire the proton radiography which prevented them from doing any path estimate. They are therefore obligated to consider bin by bin optimization of a digitally reconstructed radiography (through the X-ray CT), inherently assuming a straight proton path. All those errors are expected to degrade the quality of the extracted calibration curve which may cause a persisting systematic error at certain positions.
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To the best of the author knowledge, no work has been done trying to produce a systematic and consistent method that retrieves the patient specific HU-RSP calibration curve from both the X-ray CT and the list-mode proton radiography using the most up-to-date proton path estimate. In this work, a novel optimization algorithm has been developed for this purpose. It has been tested on a wide variety of phantoms and proved to produce accurate RSP maps that can then be used to reproduce the proton range accurately.
2. Materials and Methods
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Monte Carlo (MC) simulations of 250/330 MeV protons radiographies were done for the Gammex RMI-467 calibration phantom as well as 330 MeV proton radiographies for three anthropomorphic phantoms (lung, pelvis, head). Two different path algorithms were used to estimate the proton trajectory: the cubic spline path (CSP) and the straight line path (SLP). For each phantom and each path estimate, the
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method proposed here allowed to extract an optimized calibration curve. The proton range was investigated for each calibration curve generated from the different path estimates (reference, optimized with CSP/SLP splines and clinical) on each phantom (Gammex, lung, pelvis, head) and compared to the reference proton range. The RSP difference, as well as the range difference, were used as metrics of comparison to assess the performance and the precision of the algorithm proposed here. 2.1. Monte Carlo simulated list-mode proton radiography
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The list-mode proton radiographies were acquired through Monte Carlo simulations. No detector effects were simulated. Proton paths were simulated using the Geant4 (Agostinelli et al. (2003)) code (v4.10.00). The standard processes include energy loss and straggling, multiple Coulomb scattering based on Lewis theory (Goudsmit and Saunderson (1940)) and parameterized proton interactions with nuclei and electrons. In precise term, the following physics lists were enabled: the standard electromagnetic physics option 3 for higher accuracy of electrons, hadrons and ion tracking without a magnetic field, the hadrons elastic model and the binary ion models both for elastic and inelastic collisions. Range cuts below which no secondaries particles are produced were set to 0.1 mm for each particle. The simulations were done with 5x106 330 MeV protons since they have enough range (≈ 60 cm WET) to traverse the thicker part of every anthropomorphic phantom while having an exit energy that is in the constant-RSP domain (> 80 MeV).
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The simulation geometry was based on either a fully parametric definition of the Gammex RMI-467 phantom or a voxelized CT geometry acquired from different anthropomorphic phantom X-ray scan. Geant4 materials require both the mass density and atomic composition to produce precise stopping power tables. The Gammex-RMI 467 insert’s composition and density have been taken from the definition by Landry et al. (2013b). In the anthropomorphic phantoms, the mass density was extracted from the X-ray CT voxel, converted from the relative electron density (ρrel ). The ρrel was initially acquired from a clinical HU-ρrel conversion curve. It was then converted to mass density using Equation 1:
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ρerel · ρwater Ngwater ρ= → Ng
Ng =
X i
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X w i Zi i
Ai
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where ρwater is the water density, NA is the Avogadro number, wi represents the fractional mass of every element in the tissue and Zi /Ai is the ratio of the atomic number to the mass number.
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In addition to the density, an atomic composition had to be assigned for each HU. The atomic composition of individual voxel comes from the set of materials detailed in Table 1. This limited number of materials were used as a pivot point to define the broader domain of HU materials. Thereby, for voxels with an HU between two pivots, composite materials were assigned based on a linear interpolation between the pivots materials definition. Thus, for the anthropomorphic voxelized phantom, each HU is assigned to a unique material with a corresponding unique RSP. The chosen method imposes a bijection between the HU and the RSP.
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The Gammex CT images have been produced through the ImaSim software (Landry et al. (2013a)). A perfect computed tomography of the Gammex is acquired using this technique. The phantom is a solid-water cylinder (radius of 16.5 cm) with 16 cylindrical inserts (radius of 1.4 cm) of tissue equivalent plastic material. The three anthropomorphic body sites represent a lung, a pelvis, and a head region. X-ray CT of anthropomorphic phantoms available in our clinic has been acquired for this study. The resolution of their voxelized geometries is (0.68 x 0.68 x 1.25 mm3 ).
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Through these simulations, a list-mode proton radiography of each phantom was produced at multiple angles. The output protons were filtered based on their position, direction and exit energy using the cut suggested in Schulte et al. (2008). Briefly, the standard deviation of the exit energy, lateral deviation and angular deviation for each proton was compiled for each exit pixel. Then, individual protons were filtered out if their lateral/angular deviation or energy loss exceeded the 3σ threshold.
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2.1.1. Water equivalent list-mode proton radiography The quantity of interest in this study was the water equivalent path length (WEPL) rather than the energy lost. The energy loss was converted to WEPL by integrating over the stopping power of water (Talamonti et al. (2010); Plautz et al. (2014)). The stopping power was calculated through the Bethe-Bloch equation (Equation 2) using the ICRU (1993) I-value for water ( Iw = 78 eV) as well as their suggested
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corrections:
H 10.4 11.6 11.2
C 10.6 68.3 51.9
N 3.1 0.2 1.3
O 75.7 19.9 35.6
Ca 0.0 0.0 0.0
P 0.2 0.0 0.0
I [eV] 74.54 63.06 66.14
ρe 0.258 0.933 0.970
ρ 0.26 0.93 0.97
5 40 43 72 100 385
10.5 10.2 10.3 10.1 9.5 7.8
25.6 17.3 14.4 25.2 21.0 31.8
2.7 3.6 3.4 4.6 6.3 3.7
60.2 68.7 71.6 59.9 63.1 44.1
0.0 0.0 0.0 0.0 0.0 8.6
0.2 0.2 0.2 0.1 0.0 4.0
72.3 73.69 74.03 72.25 73.79 81.97
1.016 1.040 1.043 1.0 84 1.103 1.211
1.02 1.05 1.05 1.09 1.12 1.25
538 688 999 1524
7.1 6.3 5.0 3.4
38.1 33.4 21.3 15.6
2.6 2.9 4.0 4.2
34.3 36.3 43.8 43.8
12.2 14.4 17.7 22.6
5.6 6.6 8.1 10.4
85.43 90.24 99.69 111.63
1.279 1.355 1.517 1.781
1.33 1.43 1.61 1.92
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HU -741 -98 -55
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Material Name Lung Deflated Adipose Tissue 3 Adipose Tissue 1 Mean Male soft tissue Muscle Skeletal 1 Muscle Skeletal 2 Skin 1 Connective Tissue Sternum Humerus Spherical Head Femur Total Bone Cranium Cortical Bone
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Table 1: Chemical composition of the materials used as reference for the Monte Carlo simulations (Woodard and White (1986); White et al. (1987)). Materials for HU within the described range are interpolated in between the closest defined materials.
4πe4 2 Z SP (Iw , E) = ρ z me c2 uβ 2 A
C δ 2me c2 β 2 2 ln − β − ln Iw − − ,(2) (1 − β 2 ) Z 2
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where β represents the particle’s velocity in units of the speed of light c, z is the particles atomic number. Z, A and ρ are the target materials atomic number, mass number, and density respectively. C is the density and δ the shell correction term. me is the electrons mass and e its charge. The WEPL is the integral of the inverse of the stopping power over the energy loss (Equation 3). Z Ein dE W EP L = − (3) Eout SP (Iw , E) 2.2. Optimization algorithm The HU-RSP calibration curve is the link that relates the list-mode proton radiography to the X-ray CT projection. In this work, the WEPL was the quantity
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used to connect both these data sets through the calibration curve.
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W EP Lj =
I X
Li,j · x(si,j )
i=0
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For the j -th proton with a defined path S(t) and differential steps of length Li,j , the WEPL can be defined through the RSP of each voxel and the length spent in it (Equation 4): (4)
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where i represents the step number within the proton path estimate with i ∈ I, the total number of steps. si,j is the three-dimensional position vector, calculated through the path estimate S(t) and x(si,j ) is the RSP at that position. Since the RSPs are constant with energy, any re-ordering of the materials produces the same WEPL. Let Am,j represents the total length crossed in the m-th material with parameters (RSPm , HUm ), m∈ [0,M], xm (HUm ) represent the RSP of the m-th material with HUm and M is the total number of materials in the phantom. It is possible to rewrite the Equation 4 as a function of the total length Am,j in each material. W EP Lj =
Am,j · xm (HUm )
(5)
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The parameter xm (HUm ) for all materials represents the desired calibration curve. Equation 3 and Equation 5 both yield the WEPL crossed for each proton. The WEPL extracted from each equation will differ only by the precision of the RSP calibration curve. Both equations can be used as part of a cost function as in Equation 6.
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N protons
C(RSP) =
X j=0
"
M X
m=0
Am,j · xm (HUm ) + bj
#
(6)
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where the term bj represents the WEPL extracted from the energy loss acquired in the proton radiography (Equation 3). C(RSP) represents the cost associated with a particular HU-RSP vector solution. It is numerically more convenient to express the last equation in a matrix form (Equation 7). The A-matrix (N x M) is the length crossed in each material for each proton, and the x-vector (length M) denotes the RSP of each material. Finally, the b-vector (length N) indicates the WEPL crossed
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by each proton. The set of RSPs that minimize C is sought.
s.t. xi ≥ 0.
(7)
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argmin kAx − bk22
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2.3. Proton path reconstruction
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Where kui k2 is the l2 norm with the additional constraint that the resulting calibration curve cannot contain negative values. Equation 7 outputs a discrete number of RSPs. However, to increase statistics and decrease noise due to rare materials within the body, the number of reconstructed RSP can be reduced by selecting defined tissue type that represents the chosen body region adequately. The calibration curve is then reproduced by linear interpolation between the extracted points. Equation 7 is solved using a non-negative linear-solver within the Scipy/ Python embedded C/C++ library. In this work, no prior is used for the determination of the RSP vector.
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The proton path reconstruction in the phantom is paramount in proton imaging as well as in the method developed here as it allows when superposed with the X-ray CT, an estimation of the WEPL. The technique usually requires knowledge of the initial and final proton position (x) and direction (p). The most likely path is a probabilistic method of finding the proton given these information (Schneider and Pedroni (1994); Williams (2004); Collins-Fekete et al. (2017)). A Bayesian formalism has been introduced (Schulte et al. (2008); Erdelyi (2009)) that derives a proton path based on a maximal likelihood given the spatial information and Fermi-Eyges moments, at a precise depth and considering little angular deviation. Although this method provides the most likely proton path, it requires a certain amount of computation time. More recently, Collins-Fekete et al. (2015) have developed a phenomenological model of the proton path based on Monte Carlo simulations. The model is based on WET crossed and provides a scaling of the cubic spline path, first introduced by Li et al. (2006). It has demonstrated good accuracy with low computation time and will be used in this study. In this study, the proton path estimate is used to construct the A-matrix. Although an accurate proton path is always desired, it is of interest to investigate cases where
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of the phantom which are poorly modeled by the path estimate. The average error for the head phantom is 0.21± 1.63 %.
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In comparison, the lung phantom (Figure 5-middle) shows great results throughout the whole RSP domain. The relatively small energy loss allows the path estimate to be precise, consequently yielding accurate RSP. The average error for the lung phantom is 0.06 ± 0.99%.
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The anthropomorphic pelvis phantom (Figure 5-bottom) displays sensibly more imprecise RSP, especially below -400 HU. The average error for the pelvis phantom is 0.90 ± 3.87%. However, these HU regions are usually representative of lung material, rarely found in the pelvis area. In this scenario, the proton loses a significant amount of energy while crossing the pelvis phantom. The MLP uncertainty estimation is important and the probability of misregistration increases substantially. Consequently, those path estimate errors lead to a systematic bias that explains the deviation seen here. However, since the probability distribution function of these voxels is small, the impact on the proton beam range is expected to be minimal. This result will be verified in the next section.
3.3. Range difference for a pencil beam in the anthropomorphic phantoms
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The range differences have been computed for each anthropomorphic phantom with the calibration curves extracted from the optimization algorithm. Again, the Amatrix input of the optimization algorithm has been produced using the two different path estimates, SLP and CSP. The clinical HU-RSP calibration curve has also been investigated for comparison purposes. For all these configurations, the list-mode proton radiography was always taken in the lateral direction, from the left-hand side of the figure. For each beam (steps of 45o ), 5x106 330 MeV protons have been simulated. The absolute and relative range error (relative to the total range as shown in Section 2.4) are shown in Table 2. As expected from the previous results, the CSP path estimates provide the HU-RSP calibration curves that have the most precise range prediction. The anthropomorphic head and pelvis phantom show minor variations in between the different path
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4. Discussion
Clinical -0.75 -0.58 -0.49 -0.36 -0.39 0.24 -0.09 -0.69 0.24 -0.39 1.06 -1.25
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Clinical -1.23 -1.20 -1.44 -1.49 -1.22 -0.80 -0.74 0.52 0.52 -0.95 0.84 -1.23
Lung SLP CSP 0.06 -0.07 0.54 0.14 0.14 0.06 -0.04 0.02 0.63 -0.01 0.43 0.11 0.41 0.21 0.12 0.22 0.63 0.22 0.29 0.09 0.80 0.34 0.93 0.28
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0 45 90 135 180 225 270 315 Max.† hXi[mm] σErr [%] hXi[%]
Head SLP CSP 0.13 0.04 0.12 0.05 0.21 0.16 0.22 0.07 0.25 0.04 -0.16 0.03 0.54 0.05 0.62 0.22 0.62 0.22 0.24 0.08 0.32 0.09 0.31 0.11
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Table 2: Range difference between the reference MC simulation and the simulation with RSP extracted from the optimization algorithm through the various path estimate (CSP : Cubic spline path SLP : Straight line path). All three investigated anthropomorphic phantom are presented here with average deviation both in mm (hXi[mm]) and in relative range (hXi [%]). † Maximum absolute error Pelvis SLP 0.07 -0.27 -0.21 -0.24 -0.27 -0.32 -0.13 -0.24 0.07 -0.20 0.07 -0.11
CSP -0.08 0.13 0.14 -0.01 0.26 0.07 0.09 0.04 0.26 0.08 0.06 0.05
Clinical 1.60 1.91 0.87 1.62 2.46 1.29 0.63 0.93 2.46 1.41 0.34 0.80
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This study has demonstrated that it is possible to combine two different forms of imaging, i.e. a list-mode proton radiography and an X-ray CT, to accurately obtain a patient-specific HU-RSP calibration curve. The novel method presented here yields RSPs with 1.0 % maximum error compared to the MC reference using the Gammex RMI-467 calibration phantom with two or more projections. The anthropomorphic phantoms of the head, pelvis, and lung have also shown precise measurement of the RSPs, below 1.0% average error for every phantom.
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Although the RSP precision is crucial when calculating treatment plans, the most relevant piece of information when considering beam precision is the range accuracy. In this work, the mean range prediction has been drastically improved when using the optimized HU-RSP calibration curve. The optimized calibration curve has improved
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the range accuracy in the lung from -1.25% using the clinical curve to 0.28% using the optimized calibration curve, from 0.80% to 0.05% in the pelvis, and from -1.23% to 0.11% in the head phantom. Each difference is expressed as a relative range difference to the Monte Carlo range. Finally, Table 2 demonstrated that even the less precise path estimates (straight-line path) would give better results than the clinical calibration curve.
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It is important to assess the fact that there exists a non-null systematic error in the clinical curve independent of the stochastic error. The clinical curve is obtained by measuring the Gammex materials HU/RSP parameters. The RSP is measured by placing the Gammex inserts in the proton beam, and the HU is obtained from the stoichiometric calibration (Schneider et al., 1996). However, the phantoms were simulated with different tissue-like materials (Table 1). The difference between the materials from which the clinical curve is extracted and the simulated MC tissue is the cause of the observed systematic error. In other words, given another choice of materials for the MC simulation, the absolute difference found here is expected to differ. This difference effectively represents inter-patient tissue variation. Therefore, the relevant information is not to evaluate the clinical curve accuracy for this particular choice of materials but rather to test the reduction of both the systematic and stochastic error when using the method presented here. The relative improvement between the clinical curve and the optimized curve is what can be truly achieved by the algorithm.
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The results shown here compare favorably with the 3.0% limit for RSP accuracy when using the stoichiometric method (Schaffner and Pedroni (1998); Yang et al. (2012)). It is important to note that the imprecise RSP are expected in particular HU regions due to the lack of material such as lung-density tissue in the head or pelvis phantom. Those materials are located in voxels in the vicinity of a high-gradient edge, and a potential misregistration of the path is very likely. However, the range calculations done here proved that their effect is minimal at the Bragg peak. When considering only the effective RSP domain, the results drop below the 1% threshold for the head phantom. DECT has shown promises for investigating accurate RSP in calibration phantoms. In their theoretical study, H¨ unemohr et al. (2014b) have demonstrated that they can
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extract RSPs up to an accuracy of 0.7% based on Monte Carlo DECT simulations. However, the technique they used is both calibrated and used on a single set of data, and the precision is more representative of the artifacts present in the system rather than the technique accuracy. They then provided an experimental validation and obtained values with differences up to 0.6% (H¨ unemohr et al. (2014a)) with reference, within an accuracy of 1.7% and 9.4%. However, the results are not entirely representative of what could be expected of a DECT apparatus as they are acquired on inserts loaded centrally in a smaller diameter (16 cm) phantom, minimizing artifacts from beam hardening and scattering. Yang et al. (2010) demonstrated results with differences up to 1.0% to the reference. Based on the results from both of these studies, 1.0% error is a realistic estimate of the DECT RSP prediction power, slightly higher than what is achieved here. However, no DECT study has been done on real phantoms. The only valid comparison is then with our Gammex RMI-467 phantom. With this phantom, the results demonstrate that the method presented here performs better than the one presented in DECT studies. Hansen et al. (2015) have obtained more accurate results with a root mean square error of 0.5% on the Gammex phantom, but with maximal errors of 1.7%.
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pCT yields the most accurate RSP estimate, as expected. Hurley et al. (2012) achieved 0.5% standard deviation in the RSP extracted in a experimental pCT setup. This is a highly accurate result compared to what we can achieve here (1.0 %) considering the underlying uncertainty detailed before, and can be regarded as the clinically achievable accuracy. Besides, pCT does not suffer from the artifacts present in X-ray CT, such as beam hardening. pCT also has the advantage that it would image the patient directly in the treatment position, which could reduce setup errors. Nevertheless, long acquisition time still prevents the full use of pCT for clinical use. As explained earlier, Wang et al. (2012) proposed to blend converted MVCT projections to proton radiographies to obtain a faster yet accurate pCT reconstruction. When mixing approximately half the MVCT projections with the proton radiographies for the sinogram reconstruction, their algorithm yielded stopping power precision of ±0.86 %, within the same range of what has been found for DECT and here. However, their method accuracy is directly related to the number of proton radiographies projections used and therefore long to acquire. The precision achievable in this project is limited by 1) the number of projections ac-
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quired, 2) the energy requirement, 3) the HU degeneracy and 4) the patient accurate setup and motion. First, the use of a single projection could create some degeneracy problems as seen in the Gammex phantom results (Figure 3a). This problem could be alleviated by using two orthogonal projections which could also be used for prior registration. Second, the current proton center does not have the required proton energy to acquire a proton radiography of the thickest sites examined here. However, with the newest technology (ProTom 330), full proton radiography will become a definite possibility, and this study will be directly applicable clinically. Third, the technique is limited by materials that have identical HU but different RSP. In that scenario, the algorithm would not be able to extract precise RSP for both materials. Using a different prior such as DECT could, however, remove this problem. This problem has been briefly investigated by using the method proposed here on the ICRP adult female phantom (Menzel et al., 2009). The results show an average error of 0.38±0.77% compared to the reference calculated with the Bethe-Bloch formula on the ICRP tissue (Menzel et al., 2009). Further details are shown in the supplementary materials. Fourth, the patient motion could cause a misregistration between the X-ray CT and the acquired list mode proton radiography. Recently, a novel optimization algorithm has been proposed to ameliorate the pRad spatial resolution to perform rigid registration before applying this technique (Collins-Fekete et al., 2016). Furthermore, even though we acknowledge this misregistration to be a cause of error, it has not been the focus of this study as this is a common problem of most techniques and has been thoroughly reviewed elsewhere (Knopf et al. (2011)).
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4.1. Clinical application
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The method described here could be applied in two different ways in a clinical setup. First, it could be part of the pre-treatment planning, by combining the diagnosis X-ray CT with an acquired list-mode proton radiography to have the most accurate treatment plan. By doing so, however, the day-to-day registration advantage brought by the list-mode proton radiography are disregarded. Secondly, it would be possible to acquire a list-mode proton radiography at each fraction, before the treatment, both to position the patient and to obtain the calibration curve specific to this fraction. Subsequently, the patient-specific
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Patient specific optimization using combined proton radiography and X-ray CT
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calibration curve could be used as a metric to trigger recalculation based on either the range or RSP difference. The second option could then be combined with another method to acquire RSP such as the DECT as it would position itself as a safeguard step. Either of these options is expected to improve the range calculation and capture the potentially significant difference. However, the second method would seem more suitable to adhere to the busy schedule of a proton therapy center to optimize the patient throughput. 5. Conclusion
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This project aimed to obtain a patient-specific HU-RSP calibration curve by combining information from an X-ray CT and a list-mode proton radiography. For simple phantoms (i.e. Gammex-RMI 467), the RSP accuracy is below 1.0% over the clinical range. For more complicated anthropomorphic phantoms, the RSP prediction accuracy varies as a function of the geometry and the energy loss. The head (σRSP = 1.63%) and lung phantom (σRSP = 0.99%) shows good precision throughout the path, however the pelvis phantom shows higher RSP deviations (σRSP = 3.87%). Nevertheless, the range prediction obtained from these calibration curves shows high accuracy (relative range error of 0.11, 0.28 and 0.05 % against the reference in the head, lung and pelvis phantom) compared to the actual clinical curve (range error of -1.23, -1.25 and 0.80 %) for all phantoms. The optimal technique demonstrated here requires sophisticated single event detectors to reconstruct the proton path throughout the phantom. A straight-line path, requiring a less developed detector, have also been investigated for comparison purposes. The lower precision path estimates have been shown to produce solid HU-RSP calibration curve with smaller range error than the clinical optimization. 6. Acknowledgement
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The authors would like to acknowledge David Craft, Stephen Portillo and Zachary Slepian for the helpful discussion. Charles-Antoine Collins-Fekete is supported by a scholarship from Fonds de Recherche du Qu´ebec – Nature et technologies. CACF acknowledges partial support by the CREATE Medical Physics Research Training Network grant of the Natural Sciences and Engineering Research Council (Grant number: 432290). This work is also supported in part by the National
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REFERENCES
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Sciences and Engineering Council (NSERC) of Canada through grant #4355102013. Computations were made on the supercomputer Colosse from Universit´e Laval, managed by Calcul Qu´ebec and Compute Canada. The operation of this supercomputer is funded by the Canada Foundation for Innovation (CFI), NanoQu´ebec, RMGA and the Fonds de Recherche du Qu´ebec - Nature et Technologies (FRQ-NT). David Hansen is sponsored by the Danish Cancer Society (grant no. A5992). References
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