Evaluation of water equivalent thicknesses using the IEM-CSIC scanner prototype

. Proton imaging has been proposed as an alternative low-dose imaging technique for acquiring relative stopping power (RSP) maps and for patient positioning. In proton therapy and hadrontherapy, the water equivalent thickness (WET) of a material represents its radiological thickness, however, its calculation requires computationally intensive methods or approximate solutions. At IEM-CSIC, we have developed a scanner prototype for imaging with protons composed of two double-sided silicon strip detectors (DSSSD) and fast scintillators with high energy resolution, detectors that are commonly used in Experimental Nuclear Physics. Two custom-made samples of aluminum, air, and polymethyl methacrylate (PMMA) were imaged and their proton radiography images (pRads) are presented in terms of WET. Pattern reproduction, spatial resolution, and sensitivity to di ﬀ erent materials were studied. We present pRads of our samples obtained using a rather traditional approach to compute WET values. All three materials of the studied samples, aluminum, PMMA, and air, were well distinguished; the resulting WET values were in good agreement between samples.


Introduction
Proton therapy is a modality in cancer treatment that improves the tumor-to-normal tissue dose ratio in comparison to conventional radiotherapy with X-rays by achieving conformal dose distributions.The proton therapy principle is based on the way protons slow down while traversing matter [1].Protons are interesting for tumor treatment as they allow us to control the deposit of energy at a given depth in the patient by tuning the proton beam energy so that therapeutic doses are applied mostly at a given depth and vanish beyond the tumor.However, uncertainty in the proton range prediction compromises the quality of the treatment plans, as an important fraction of energy might be wrongly deposited in healthy tissue [2,3].The proton range depends on the proton energy and on the stopping power of the materials traversed.In proton therapy, it is very important to achieve precise proton range control, which can be improved with an accurate knowledge of the relative stopping power (RSP) map of the patient in the treatment position [4].
Currently, X-ray computed tomography (xCT) images are used to calculate the RSP maps that are needed for proton therapy treatment planning.This procedure can result in up to 3.5% errors in the determination of RSP, making proton therapy less beneficial as compared to conventional radiotherapy with X-rays [4].Proton computed tomography (pCT) represents a more accurate imaging technique for providing RSP distributions without conversion from Hounsfield units, a measurement of the linear attenuation coefficient of the tissue; while also constituting an advantageous technique in terms of dose delivery when compared to xCT [5].
In proton therapy, the beam penetration range is commonly prescribed in terms of the water equivalent thickness (WET), or the beam penetration depth in liquid water.There are several suggested techniques for calculating WET values, however, they can be easily determined by the range shift related to placing a test object in the proton path [2].
The IEM-CSIC scanner prototype includes two double-sided silicon strip detectors (DSSSDs) as proton trackers.They provide both, spatial and energy-deposited information.Hence, the first DSSSD allows the determination of the initial proton beam energy, whilst the second DSSSD also helps to determine the residual energy of the protons.The residual energy detector of the prototype provides high energy resolution and fast response, which allows us to test it under realistic conditions of proton rates and energy.In this contribution, we present the results obtained from proton radiographs (pRads) using 100 MeV proton beams in terms of WET.The approach we used to determine the WET values is that described by Zhang et al. [6], where we compute proton ranges in liquid water taken from PSTAR database [7] for the initial and residual proton energies.

Proton imaging scanner
The pRads presented in this work were taken at the Cyclotron Centre Bronowice (CCB) facility of the Institute of Nuclear Physics-Polish Academy of Sciences, Krakow, Poland.The proton imaging scanner is described in detail by J.A. Briz et al. [3].It is composed of two tracking planes and a residual energy detector.The experimental setup is shown in Fig. 1.The front and rear tracking planes incorporate a 50×50 mm 2 double-sided silicon strip detector (DSSSD) with a thickness of 1000 μm each.The design of our prototype allows us to obtain the entry and exit position of each proton.
The residual energy detector, the CALIFA Endcap Phoswich Array (CEPA4 detector), is an array of four scintillation units, each of them comprised of two scintillator crystals of LaBr 3 (Ce) and LaCl 3 (Ce) in phoswich configuration with a common photomultiplier tube.Due to its high performance, in terms of energy resolution and fast time response, this detector has proven to be a good tool in proton spectroscopy, making it an ideal instrument for designing our pCT scanner prototype.A full description of the CEPA4 detector can be found in [8].

Known samples
The two custom-made samples containing aluminum, air, and polymethyl methacrylate (PMMA) shown in Fig. 2 were studied.Both samples are custom-made plates of PMMA of 10 mm thickness and 76 × 80 mm 2 surface which were placed in between two uniform PMMA plates of equal surface size and 20 mm thickness each.The first sample (A) is a cross pattern sample of aluminum with a uniform thickness of 10 mm, its dimensions are 40 × 40 mm 2 , 54.5 mm diagonal, and 9 mm arm width.The second sample (B) is a regular spatial pattern of 39 × 40 mm 2 surface made of aluminum.On the left side of the pattern, there are holes of 1, 2, 3, and 5 mm diameters and equal separation.While on the right side of it, there are slits of 2, 3, and 5 mm width and separations.This sample was used to evaluate spatial resolution values ranging from 0.1 to 0.5 line pairs per mm.

Proton radiography generation
The position, generated from the Cartesian combination of the vertical and horizontal strips of each DSSSD, and the energy loss of all protons were registered into twodimensional plots of hits and energy loss.These plots represent the number of protons traversing each pixel that deposit energy in each detector and the amount of energy they deposit.Although protons lose energy in a continuous way within the samples, the pRads were generated at  the sample plane, considered to be the central plane of the sample perpendicular to the beam.
To obtain the pRads we assumed a uniform distribution of the hits within the pixel area of each detector to describe the possible trajectories a proton can follow as a straight-line path through the tracking system (Fig. 3) and its corresponding residual energy.The modeling of the uniform distribution of the hits within each detector pixel was done using a random generator between 0 and 1 for the hit position in each DSSSD.This made possible the uniform distribution of the hits within the full area of a detector pixel, using Eq. 1.
x P y P = 1 2 where (x P , y P ) represents the Cartesian coordinates of the proton hit at the image plane considered to be located at the central position of the sample; (x 1 , y 1 ) and (x 2 , y 2 ) are the coordinates of the proton hit on the front and rear DSSSD, respectively, and R i (0, 1) are uniform random values between 0 and 1.The uniform distribution of protons within a detector pixel allowed for an increase in the image granularity beyond the 32 × 32 pixels achievable with the experimental setup, where we used two tracking planes with 16 × 16 pixels each.With the IEM-CSIC scanner prototype, we are capable of determining the residual energy of the proton (E f ) defined as the sum of the energy measured on the second tracker and on the scintillators.The range of protons in water depends on the proton energy (see Fig. 4), hence, Eq. 2 is used to determine the WET of a proton given the initial and residual proton energies (E 0 and E f ) [6].
where R(E) is the range in water of protons with energy E. Proton tracks were stored, and their WET were determined using Eq. 2. Proton ranges were directly obtained from the PSTAR database for protons in liquid water [7].As expected from the Rutherford scattering suffered by the protons on the titanium scattering foil, regions on the rightside of the image showed higher particle counts because they were located closer to the incident beam direction (0 • of polar scattering angle).This effect was compensated by normalizing the images by the number of protons traversing, thus, obtaining the average energy loss per traversing proton.Finally, the pRads were presented as a normalization of the WET values of the imaged objects.

Results
The pRads were obtained following the procedure described in Section 2. Let us remember that the samples were placed in between two PMMA pieces of 20 mm thickness each.Thus, protons passing by the air region traverse 40 mm of PMMA in addition to the 10 mm of air, a similar situation is observed for those protons traversing aluminum or PMMA.

Cross pattern sample
The image shown in Fig. 5 was obtained when using the sample shown in Fig. 2(A) in between two PMMA uniform slices 20 mm thick each.Three main regions are clearly distinguished, each one being consistent with the materials of the cross pattern sample.WET values are presented in millimeters.In Fig. 5, the black zones (WET≈ 58 mm) correspond to the air regions of the sample; the grey zone (WET≈ 66 mm) is the region where the PMMA is located, i.e. the square frame around the cross pattern; and the zone of the cross pattern made of aluminum appears in white (WET≈ 73 mm).Notice that the grey gradient (WET≈ 61 mm) observed between the black and white zones corresponds to the air-aluminum interface.region.In the same figure, the mean WET values and the regions corresponding to σ, 2σ, and 3σ for each material are shown in degraded colors.Looking back into the sample, it must be said that it was placed between two slices 20-mm thick of PMMA each.Hence, for protons of 100 MeV, a water thickness of 57.8 mm is equivalent to 40 mm of PMMA, 66.6 mm of water is equivalent to 50 mm of PMMA, and 72.7 mm of water is equivalent to a combination of 40 mm of PMMA and 10 mm of aluminum.

Regular spatial pattern sample
The image shown in Fig. 7 was obtained for the sample pattern shown in Fig. 2(B).The statistical study of the averaged WET values showed that, for protons of 100 MeV, WET values of the PMMA and aluminum regions were 66.8(6) mm and 72.8( 6) mm, respectively.The WET values of PMMA and aluminum regions were consistent with the ones obtained for the cross-pattern sample.The larger air regions (3-and 5-mm) provided WET values in agreement with those obtained in Section 3.1.

Conclusion
The first steps in the performance tests of our proton imaging device have been completed by obtaining proton radiographs (pRads) of simple samples with known geometries and known materials.We presented a fast and functional, but at the same time useful, process to generate a pRad in terms of water equivalent thickness (WET) values.An important step in the WET calibration as a function of the initial and residual beam energy was introduced.The WET histogram of the cross-pattern sample indicated that the device has enough sensitivity to distinguish bulk structures of aluminum, PMMA, and air.As for the regular spatial pattern sample, the WET value results PMMA, aluminum, and the larger air regions were compatible between samples.We have made significant progress in the WET value determination, however, there is work to be done for the implementation of more sophisticated analysis methods, a more realistic description of the proton paths, and the improvement of the data acquisition rate to reduce scanning times, so that it would be possible to get closer to a preclinical stage with the IEM-CSIC prototype used as a proton radiography scanner.

Figure 1 .
Figure 1.Experimental setup used to obtain the proton radiographs at the CCB facility.The proton-scanner prototype is formed by two DSSSDs, for proton tracking, and the CEPA4 scintillation detector, as residual energy detector.The sample under study is placed in between the DSSSDs.

Figure 2 .
Figure 2. Pictures of the studied samples with the aluminum patterns and their dimensions.(A) Cross pattern, (B) Regular spatial pattern, from top to bottom: diameter and spacing size of the regions with circles of 1 mm, 2 mm, 3 mm, 5 mm; and bar width and separation width of 2 mm, 3 mm, 5 mm.

Figure 3 .
Figure 3. Possible proton trajectories through two pixels of the detection system.

Figure 4 .
Figure 4. Scheme of the range in water for protons with initial energy E 0 , after traversing (A) no material, (B) material with thickness t m and density ρ m , and (C) equivalent water thickness t w , reproducing the same exit energy (E f ), therefore the same range in water R(E f ).

Figure 5 .
Figure 5. Experimental pRad obtained with the cross-shaped pattern sample.The image is a 2D map of the WET values in mm.The position on the image plane was obtained using the hit positions on DSSSD1 and DSSSD2, as described in Section 2.3.

Figure 6 .
Figure 6.Histogram of the WET values obtained from the image pixels of the pRad of the cross pattern sample.The vertical axis represents the number of pixels shown in Fig. 5 with the same WET value (±0.1 mm).Three main peaks corresponding to the air (red), PMMA (blue), and aluminum (pink) regions are observed.The mean WET values and the regions corresponding to σ, 2σ, and 3σ are displayed in degraded colors.

Figure 7 .
Figure 7. Experimental pRad obtained with the regular spatial pattern sample.The image is a 2D map of the WET values in mm.The position on the image plane was obtained using the hit positions on DSSSD1 and DSSSD2, as described in Section 2.3.The spatial resolution of the IEM-CSIC scanner prototype was determined to be better than 2 mm in[3].