3D dosimetry of proton beams and influences on response

Proton beams offer the ability to conform dose distributions exquisitely to target volumes, allowing radiation oncologists to avoid exceeding tolerance doses to sensitive normal tissues. Several volumetric dosimeters have shown potential in conventional radiotherapy modalities, but suffer from dose under-responding, or signal quenching, in proton therapy. This reduced response has been seen with gels as well as with radiochromic plastics and may result from dependences on dose rate and linear energy transfer (LET). Investigations have shown that the under-response is affected by the chemical concentration of the active components of PRESAGE®, and changes to the composition have been shown to reduce quenching. It is not clear if similar changes can be made to gels. This report reviews studies into the impact of formulation changes on signal quenching, and the degree to which mathematical corrections might still be needed to achieve accurate dosimetry.


Frequency of errors in radiation therapy
Errors in radiation therapy occur relatively infrequently, but when they do occur, they can be disastrous.The likelihood and impact of errors in radiation therapy were highlighted in a series of articles in the New York Times, beginning in 2010 [1].The articles indicated that the errors that make the headlines may be the most severe, but probably underestimate the total number of misadministrations as some may not be reported, and many may go undetected.The recognition that errors can occur at each stage of the treatment process: prescription, simulation, treatment planning, and delivery, as well as during quality assurance procedures and machine basic calibration, underscores the critical need for a comprehensive quality assurance program.
The frequency of errors in radiation therapy has been investigated by the Imaging and Radiation Oncology Core (IROC-Houston, formerly the Radiological Physics Center.)Participants in some clinical trials sponsored by the US National Cancer Institute are required to irradiate a phantom provided by IROC using the technique specified by the trial and achieve acceptable results.According to IROC, after 1,139 irradiations of a head-and-neck phantom between 2001 and 2011, performed at 763 institutions, the passing rate was 82% [2].Passing was defined as delivering a dose within 7% and 4 mm distance-to-agreement, when compared with the institution's own treatment plan for the phantom.The irradiations were all delivered using IMRT techniques, with a variety of treatment planning and delivery equipment at the different institutions.The results indicate that, even when performed under ideal conditions, one out of 5 institutions failed to deliver the dose distribution prescribed by their own treatment plan, to within quite generous criteria.IROC determined that the causes for the failures included the use of incorrect data entered into the treatment planning system, inexact beam modeling, and software and hardware failures.These results suggest that improvements to institutional quality assurance programs might be warranted.

Benefits of 3D dosimetry in proton therapy
Proton therapy carries with it additional demands for quality assurance.Treatment with particle beams is attractive for some diseases because the particles penetrate tissue to a depth that is predicted by the energy at the entrance surface.Beyond that depth, the dose is much lower, and in the case of protons, is essentially zero.As shown in Figure 1, at the maximum depth of penetration, the distal edge of a proton beam falls rapidly from the dose in the peak to zero.The advantage of the rapid distal falloff is evident; tissues beyond that depth are spared while the tissue within the peak (known as the Bragg peak) receives a large dose.The goal in proton therapy is to position the Bragg peak within the target volume with the distal edge at the deepest margin of the target volume.This sometimes allows for the escalation of target dose while maintaining low normal tissue doses, resulting in improved therapeutic gain and better treatment outcomes.An example of the improvement achievable over photon treatment is shown in Figure 2.

Figure 1.
A pristine, or monoenergetic proton beam with a sharp Bragg peak is compared with a spreadout Bragg peak and an 18 MV x-ray beam [3].
A pristine proton beam as shown in Figure 1 is often a pencil beam, having transverse dimensions of 1 cm or less.Consequently, it must be broadened in the transverse direction to treat a typical target volume effectively.In addition, the width of the Bragg peak in the axial dimension is determined by the energy spectrum at that depth and generally is too narrow to be useful for treatment without modification.To broaden the peak in both the transverse and axial directions to a width comparable to the dimensions of a target volume, several options are available.The first, and simplest technique for transverse broadening is to insert a scattering foil into the beam.This is called passive scattering.The scattering foil broadens the beam considerably, and then collimation is required (comparable to a photon beam) to limit the transverse dimensions of the field as needed.
To broaden the beam in the axial direction requires that proton beams of several different energies be superimposed as shown in Figure 1.Creating such a spread-out Bragg peak (SOBP) has two effects: it broadens the high-dose region to the dimensions of the target volume in the axial direction, but it also raises the dose in the plateau upstream from the Bragg peak.As is clear from Figure 1, however, when compared to a photon beam, a proton beam provides a greater dose differential between the target volume and tissues both upstream and downstream.There are several techniques available to spread the Bragg peak in the axial direction.The first is typically employed when passive scattering is used and involves modulating the beam energy during treatment.This can be accomplished using filters of different thicknesses that can be inserted into the beam, with each thickness chosen to decrease the penetration of the beam in increments on the order of 1 cm.A range modulator wheel is generally used to rapidly modify the beam penetration during treatment.
A second method, which today is considered standard therapy, is to deliver the treatment through many pristine pencil beams, modulating the energy and position of each beam to build up the dose throughout the target volume.This technique, called spot scanning, allows the dose distribution to be tailored to the target volume in three dimensions.When spot scanning is used from multiple beam directions, and the dose deposited by each spot is adjusted to optimize the dose distribution, the technique is called intensity-modulated proton therapy (IMPT).As shown in Figure 2, calculated dose distributions using IMPT show substantially lower doses to normal tissues when compared with stateof-the-art photon therapy.
The range of the protons depends critically on not only the incident energy but also on the narrowness of the energy spectrum, and on the relative stopping powers of the tissues through which the beam passes.The incident energy spectrum can be controlled and accounted for in treatment planning, but the tissue stopping powers must be determined from CT scans of the patient.As shown in Figure 3, protons undergo several types of interactions with the atoms composing human tissue, including inelastic coulombic interactions with atomic electrons, elastic coulombic interactions with nuclei, and nuclear collisions.Proton interactions depend far more on the atomic composition of tissues than do photon interactions, and consequently there is not a direct relationship between Hounsfield Units and proton stopping powers as there is between HU and mass energy absorption coefficients.This leads to greater uncertainties in the effects of tissue characteristics on proton energy spectrum, depth of penetration, and lateral scattering.Furthermore, the treatment plans used in contemporary proton therapy are considerably more complex than suggested above, with complex optimization algorithms used to develop spot-scanned, intensity-modulated treatment plans using multiple beam angles.Assessing the quality of such complex plans using conventional point detectors or planar arrays is inadequate.Three-dimensional dosimetry systems such as gels and radiochromic plastics are ideal to evaluate the quality of such treatments.

Candidate 3D dosimeters for proton beams
As has been reported elsewhere, gel dosimeters offer the ability to measure and display 3D dose distributions [4][5][6].Two broad classes of gel dosimeters are quite widely used: polymer gels and Fricke gels.Polymer gels record a dose distribution by converting local acrylic monomers to polymer clusters and chains.The polymers absorb and scatter light and a measurement of the optical density change can be related to the absorbed dose.Some polymer gels also change their paramagnetic characteristics and yield a signal on magnetic resonance imaging (MRI).The conversion of monomers to polymers raises the physical density of the gel matrix slightly, allowing a measurement by x-ray CT [7].
Fricke gels take advantage of the phenomenon first reported by Fricke and Morse and act by converting ferrous (Fe 2+ ) ions to ferric (Fe 3+ ) ions [8].The ferrous sulfate is mixed with gelatin or another stabilizing agent, although some migration of the ferrous and ferric ions has been observed.The ferric ion concentration can be determined by optical methods, especially if a coloring agent such as xylenol orange is used, although MRI is often used [9].A novel demonstration of the use of Fricke gels was shown by Lee et al, who used an MR-linac to image a gel as it was being irradiated, measuring the dose as it was being deposited [10].
Radiochromic plastics cannot be imaged with MRI and optical methods must be used instead.An example of a polyurethane matrix containing a radiochromic dose reporting system was described by Adamovics et al [11].This dosimeter is available as a commercial product called Presage®.In this system, a dye, leuco malachite green, which is colorless, is converted to malachite green, which exhibits a green color.The converted dye absorbs light, particularly red light, and the resulting linear optical density coefficient (e.g., ∆OD/cm) exhibits a dose dependence.The mechanism requires an activator or radical initiator, for which chloroform or a similar compound can be used.Radiochromic plastics exhibit no oxygen sensitivity, as is the case with polymer gels, which simplifies their handling [12].As the dose-reporting compounds are bound to the plastic, the signal is not reduced by diffusion, as is the case with ferric ions migrating through gelatin.Because the dosimeter is a solid, no container is required.And the dosimeter can be molded or machined into any desired shape or size.Disadvantages of radiochromic plastics include the complexity of manufacturing, which must be done in a fume hood and requires that the polyurethane be cured while under elevated atmospheric pressure.As mentioned above, optical imaging must be used for readout.
A fourth class of 3D dosimeter with the potential to demonstrate proton dose distributions has been described by Beddar et al [13].This is a liquid scintillator solution that emits light when irradiated with a proton beam.The light is captured by video cameras that view a tank of the scintillator solution through mirrors, from different angles, and generate a 3D image from the multiple views.A quantitative relationship between the image and the absorbed dose has not yet been described.

Proton dosimetry with 3D dosimeters
Proton beams introduce several challenges not seen with photon and electron beams.First, there appear to be several mechanisms of signal loss that have to do with greater density of dose-deposition interactions.Jirasek and Duzenli evaluated a polyacrylamide gel system and showed through Fourier transform observations and track structure calculations that the high doses deposited close to the proton tracks saturated activation sites in the gel, reducing the sensitivity of the gel [14].Gustavsson et al investigated a normoxic polymer gel and postulated that in regions of high linear energy transfer (LET), recombination of the radicals produced by ionization reduced the response of the gel [15].
Efforts have been undertaken to improve the agreement between 3D dosimeters and conventional dosimetry systems.Zeidan et al reported good agreement with treatment planning data in one of several polymer gels whose formulation had been modified to include larger or smaller amounts of the radical initiator [16].Our own measurements in a formulation of Presage® intended for proton measurements demonstrated a broadening of the distal edge of a SOBP, suggesting both an under-response in the high dose, high LET region, and a small over-response in the low-dose, high-LET region [17].This is shown in Figure 4.
The decrease in signal resulting from chemical physical processes is called quenching and is observed in nearly all chemical dosimeters [18].In proton beams, it is attributed to the density of ionizations along the tracks of the protons.For Presage® dosimeters, and in regions of high LET, quenching can reduce the signal by 20 % or more.

Measurements in modified formulations of polyurethane radiochromic dosimeters
Polyurethane dosimeters of several different formulations were prepared and were irradiated with proton beams to selected doses to evaluate their sensitivity and linearity of response.The results are shown in Figure 5.The data indicate that greater concentrations of the radical initiators chloroform and bromoform both increase the sensitivity of the dosimeter, and that for comparable concentrations of the initiator, dosimeters containing bromoform are considerably more sensitive.All four preparations showed excellent linearity.On the basis of the data in Figure 5, the more sensitive bromoform-based formulation was selected for further modification to evaluate the effect on quenching.Figure 6 summarizes the results obtained when the bromoform concentration was varied between 1% and 27.5%, and the concentration of the dose reporting compound, leuco malachite green, was varied between 0.5% and 4%.The figure shows that bromoform concentrations between 10% and 15%, and LMG concentrations between 2.0% and 2.5% were successful in reducing the quenching observed in the high LET region to less than 5%.
The data shown in Figure 6 further indicate that quenching is most likely a result of saturation of the radical initiator.Quenching decreases as the concentration of the initiator is increased, suggesting that the availability of more initiators reduces the competition for interaction sites.

Determination of empirical correction factor
To improve the accuracy of the selected formulation of polyurethane dosimeter, the data in Figure 6 were used to determine a Quenching Correction Factor.First, the correlation between polyurethane dosimeter response and the dose determined by ion chamber readings was determined along the depthdose curve of a pristine proton beam: Eq. 1 where    is the normalized ionization chamber measurements,   is the polyurethane dosimeter signal, and    is the calibration factor of the dosimeter signal.The Quenching Correction Factor is therefore the reciprocal of the correlation above: Because the QCF is a function of depth and incident energy, the application of a single model to another irradiation configuration becomes unrealistic.Consequently, an empirical correlation of QCF as a function of LET was made by fitting the calculated QCF from Eq. 2 with the voxel-averaged LETφ.The QCF-LET relationship was obtained and QCF as a function of LET (henceforth referred to as QCF(LETφ)) was derived allowing the application of the function to other irradiation configurations with LETφ similarly modeled using Monte Carlo.The derived QCF(LETφ) is shown in Figure 7 and was applied to subsequent measurements of proton depth dose obtained with the low-quenching formulation of polyurethane dosimeter.The low-quenching formulation of polyurethane dosimeter was employed to measure the depth dose of a passively-scattered 140 MeV proton beam with a 4 cm spread-out Bragg peak.The dosimeter results demonstrated disagreement with ion chamber measurements, as shown in Figure 8.However, after application of the QCF(LETφ) determined previously, much improved agreement with ion chamber measurements was seen.The corrected results are shown in Figure 8, and with expanded coordinates in Figure 9.   7 showing the effect of applying the QCF(LETφ).

Conclusions
3D dosimeters offer many benefits beyond conventional dosimeters for evaluation of proton beams, both through remote audits and as a supplemental device in the clinic.These include more comprehensive dose analysis, and the potential to use time and resources more effectively.In addition to the demonstrated benefit with proton beams, 3D dosimeters have been shown to have applications in nearly all other facets of radiotherapy: IMRT, SRS, HDR Brachy, and MRgRT.

Figure 2 .
Figure 2. Treatment plans for a head-and-neck tumor are shown.The panel on the left is a calculated dose distribution prepared for intensity-modulated proton therapy; the center panel shows a treatment plan created for intensity-modulated photon beams; and the right-hand panel shows the difference, reflecting the additional dose delivered by photons to healthy tissues.

Figure 3 .
Figure 3. Protons interact with the atoms that make up human tissues through three general mechanisms: (a) inelastic coulombic interactions with electrons, (b) elastic coulombic interactions with nuclei, and (c) nuclear collisions [3].

Figure 4 .
Figure 4. Relative depth dose comparison in a 225-MeV proton beam with 10 cm SOBP as measured by multi-layer ion chamber (blue), large volume Presage® formulated for proton beams (red), and cuvettes of Presage® (orange points).The agreement between large volume and cuvette measurements is shown (black line).

Figure 5 .
Figure 5.The sensitivities and linearities exhibited by four formulations of radiochromic polyurethane dosimeter.

Figure 6 .
Figure 6.The percent of signal quenching measured at the distal-most point in the proton SOBP for several formulations using bromoform as the radical initiator.Error bars represent the standard deviation of three intrabatch cuvette comparisons.

12th 8 Figure 7 .
Figure 7.The Quenching Correction Factor as a function of LET.A polynomial fit to the data is provided to demonstrate the smooth variation of the function, and is the QCF(LETφ).

Figure 8 .
Figure 8.A comparison between ion chamber readings, the dose measured with the low-quenching formulation of polyurethane dosimeter, and the QCF(LETφ)-corrected dosimeter measurements.

12th 9 Figure 9 .
Figure 9.An expanded view of the data in Figure7showing the effect of applying the QCF(LETφ).