Quantitative carbon ion beam radiography and tomography with a flat-panel detector

All measurements have been carried out at the Heidelberg Ion–Beam Therapy Center (HIT) in Heidelberg, Germany. The hospital-based ion facility was built in 2005 and started its clinical operation in November 2009. The synchrotron installed at HIT is designed to accelerate charged particles ranging from protons up to oxygen ions. Due to the reduced lateral scattering of carbon ions over protons, this study investigated solely carbon ions for radiographic and tomographic imaging. From the synchrotron the ions are extracted in 'bunches' which are called spills. Each extraction spill with a maximum duration of 5 sec is followed by a break of roughly the same length used for acceleration of new particles. Particle ranges in water from 20–300 mm are provided in 255 energy steps with a step width corresponding to 1 mm range in water for medium energies and 1.5 mm for high energies (Parodi et al 2012). For carbon ions these energy intervals correspond to energies of 89–430 MeV u⁻¹ (Haberer et al 2004). Another distinctive feature of the facility is the beam delivery system. It allows conformal irradiation of the target volume by deflecting the beam laterally and vertically by perpendicular magnets. Depending on the particle type and energy, the pencil beam has a FWHM of 4–20 mm. It's lateral profile is approximately normally distributed in fluence and energy.

The features of the beam delivery system that are most important for particle radiography are the available energies, the energy spread and the angular divergence. The energies available at the HIT facility are sufficiently high to image structures with a WET of up to 30 cm. To reach high resolution in the radiographic images it is beneficial to have a beam with small energy spread after the particles emerge from the beamline. The momentum in a single pulse at HIT is normally distributed with a momentum uncertainty dp/p of 0.1% (FWHM) (Gross and Pavlovic 1998). The beams extracted from accelerators show, in addition to energy spread, angular convergence or divergence. It is desirable to minimize these non-uniformities of the particle beam. At the HIT accelerator, the optics are chosen to have dispersion and its derivative close to zero at the isocenter. In order to have "quasi-parallel" beam scanning, the scanner magnets are located at a distance of about 7 m upstream from the isocenter (Lazarev et al 2011).

The flat-panel detector investigated in this work is an indirect detection device, RID 256-L from PerkinElmer Optoelectronics GmbH & Co. KG (Wiesbaden, Germany). It is designed for kilo- and megavoltage x-ray portal imaging. The detector has an active area consisting of a pixel matrix with a pixel size of 800×800 µm². The scintillator consists of a Lanex fast back phosphor screen bonded to an amorphous silicon layer deposited on a glass substrate. The detector was extensively characterized in photon beams by Partridge et al (2002). First measurements with the detector in ion beams have already been performed by Martis˘íková et al (2010). They showed excellent signal linearity of the integrated signal as a function of beam intensity as long as the dynamic range was not exceeded by the signal. Further, no dose rate effects of the signal were observed. So far radiation damage of the RID 256-L due to ion irradiation has not been observed. The response was found to be stable within ±0.1 % (Martis˘íková et al 2010).

The measured signal in a particular pixel of the flat-panel detector is depending on the energy loss of the particles and thus their energy and type, and the particle fluence rate. Single particle energy depositions cannot be calculated unambiguously from the measured signal.

A detector image is formed by integrating the signal over the time of the lateral scanning irradiation procedure. In the end, the detector response has to be corrected for differences in sensitivity between the pixels of the detector as well as offset drifts of single pixels. To do so, a specific correction routine was implemented (Hartmann et al 2012). Image offset correction is carried out with active dark images using the irradiation free time between single spills of the Heidelberg synchrotron. Dark image, amplifier specific offset shifts, pixel specific short-term response changes and image lag are accounted for in this complex correction routine. Further, the sensitivity of the pixels are corrected with a sensitivity map acquired in homogeneous photon irradiation.

The WET distribution of an object is measured by detection of the residual energy or residual range of the particles behind the object of interest. The flat-panel detector measures the energy loss of the particles in the active detector layer only. This does not allow to detect the residual energy of the particles. Other detection systems currently investigated for proton and heavy ion imaging (Zygmanski et al 2000, Murashi et al 2007) face the same difficulty. They use passive energy modulation via a range shifter to correlate the signal to energy. The highest detected signal corresponds to an initial beam energy at which the ion's range in water is equal to the WET of the object. In this work in addition to a passive version, the active energy variation of the accelerator was exploited as described in the next section.

2.3.1. Active energy variation

In order to overcome the ambiguous correlation of detector signal to particle energy, a special ion range measurement technique called energy scanning was developed. High energies are used to irradiate through the imaging object, at the back the flat-panel detector is positioned to measure the energy loss of the particles in the active detector layer. Particle energy of the HIT accelerator can be adjusted with high precision in steps of 1 mm WET for medium energies and 1.5 mm WET for high energies. The object is irradiated with a number of rectangular monoenergetic fields with different carbon ion beam energies. This procedure is called energy scanning. This method allows to correlate the measured signal S with the initial beam energy E_init. For each pixel of the detector a dependence of the signal on the initial beam energy is measured, for example see figure 4. The WET of the object is then given by the water equivalent range for the energy at which the maximum signal S_max is detected. This energy corresponds to an energy E_{init, max} at which the particles reach the end of range in the detector.

In order to measure absolute WET of the object, the WET of the flat-panel itself has to be taken into account. It was estimated by measuring a response curve in depth of poly methyl methacrylate (PMMA) (protons, E = 132 MeV) with the flat-panel and comparison of the measured curve to depth-dose data from the HIT base-data (Martis˘íková 2011). The shift of the simulated depth-dose curve to match the measurement determines the WET of the flat-panel. The WET of the flat-panel detector WET_Flat-panel was found to be about 2.3 mm (Martis˘íková 2011) for all applied energies and is assumed to be valid also for carbon ion beams. The final WET_Object is then given by

$$\begin{equation} \mathrm{WET_{Object}}= \mathrm{WET}-\mathrm{WET}_{\mathrm{Flat-panel}}. \end{equation} \tag{ 4 }$$

2.3.2. Passive energy variation

In order to validate the proposed energy scanning technique, the profile of a WET distribution of a cylindrical PMMA phantom equipped with tissue equivalent inserts (Gammex) has been measured (see figure 1). This has the advantage, that the exact geometry and the WEPL of the used materials are known (Jäkel et al 2001). The accuracy of the proposed technique is investigated by comparison of the calculated WET values to values measured by the energy scanning method employing the flat-panel detector. Figure 2 shows a drawing of the radiographed phantom (a) and a profile of the calculated WET values (b). The obtained WET profile is evaluated indicated by the green box in figure 2(b). The setup has been irradiated with carbon ion beams of energies ranging from 244 MeV u⁻¹ to 355 MeV u⁻¹ and a FWHM of 10 mm at three spot positions with a 10 mm spacing as shown in figure 2(a).

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As an extension of the proposed WET measurement technique, the feasibility of carbon ion CT with the flat-panel detector was investigated. Carbon ion CT directly measures the WEPL values of an object by sectional imaging. A carbon ion CT was acquired of the cylindrical PMMA phantom assembled with nine tissue equivalent Gammex rods, see figure 3(a). The WET distributions were measured with passive energy variation by a static PMMA wedge. Therefore, the phantom was placed in a 170×170 mm² PMMA block with a 19.57° PMMA wedge ajar as seen in figure 3(b). The block is used to simplify the geometry and thus minimize the energies needed to measure the WET. Further, the static wedge allows to continuously vary the WET over the phantom. The setup was irradiated with carbon ions of 341 MeV u⁻¹ and a fluence of 5.55× 10⁴ particles mm⁻² for each angle. Inside the PMMA cube rotation of the cylindrical phantom was automatically performed in steps of 2.25° over 180° with a step motor. The single images were evaluated in terms of WET value and than reconstructed with a conventional Ram–Lak filtered backprojection algorithm to obtain a sectional WEPL images.

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For validation of the energy scan method the WET distribution of a cylindrical PMMA phantom was measured. The signal as a function of the applied beam energy was obtained for each detector pixel. An example of such a curve is shown in figure 4. The obtained peak position corresponds to a certain initial beam energy E_{init, max}. It is translated into its corresponding water equivalent range (WET). The measured WET values are then given by the subtraction of the WET_Flat-panel. They agree well with the expectation from the calculation (see figure 5(a)). The measured WET resolution is limited by the energy steps available from the accelerator. Due to the very different measured peak shapes it is not possible to fit for example a learning base-data set to the obtained signal curve to increase WET resolution. However, a possible way to increased WET resolution is by linear interpolation of the energy-signal curve and evaluation of S₈₀ at which the signal amounts to 80% of the peak value at the steep descending flank of the peak, see figure 4. This idea is based on the fact that the descending flank is very steep and similar for all signal-energy curves. The WET₈₀ value obtained at 80% of the signal increases WET resolution as seen in figure 5(b). However, the measured values are slightly lower than the calculated values. This underestimation can be quantified by investigation of the energy-signal correlation. When passing through matter, an ion experiences deflection caused by the Coulomb field of the nucleus. Neglecting multiple Coulomb scattering in homogeneous material, initial beam energy variation only shifts the Bragg peak in depth while preserving the peak shape. Therefore, the shift between the S_max and S₈₀ value is nearly constant and can be used as a correction factor. Figure 5(b) shows the corrected WET₈₀ values. They agree very well with the calculation. The standard deviations between the calculated and measured WET values are given in figure 6 indicated by the dashed lines. With the interpolation method the standard deviation decreases from 0.61 mm WET to 0.22 mm WET. However in the case of more complex imaging objects, the Bragg peak degrades due to multiple Coulomb scattering at material interfaces (Urie et al 1986). This Bragg peak degradation leads to an increased peak width; see figure 7. As a result the S₈₀ is shifted here towards higher energy values. Correspondingly, the initial beam energy E_{init, 80} is shifted to higher energies, which corresponds to smaller WET₈₀ values. The effect of Bragg peak degradation is strongly correlated to the local inhomogeneity of the imaged object. For the WET measurement of our cylindrical PMMA phantom, minor Bragg peak degradation due to particle scattering and partial volume effect can explain the slight underestimation of measured WET value at the location of around 13 mm, indicated by the red arrow in figure 6.

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Carbon ion CT would in principle allow one to measure distributions of the WEPL of complex imaging objects. In analogy with an x-ray CT, this is done by measuring the WET of the imaging object for many rotation angles, representing single projections. The reconstructed image should yield information about three-dimensional WEPL distribution also for objects where the standard method of x-ray CT transformation tends to be inaccurate.

The cylindrical PMMA phantom equipped with tissue equivalent inserts was radiographed for tomographic imaging with the flat-panel detector. In contrast to the energy scan method for tomographic imaging the setup was modified to accelerate the imaging process. In this modification the phantom symmetry was exploited by embedding the cylindrical phantom in a PMMA cube and placing a static PMMA wedge in front of the detector. This wedge was used to passively modulate the given carbon ion beam energy across the phantom, replacing the energy scanning from the accelerator. Therefore with this setup, a field of x × y (cm²) was irradiated with only one primary energy to measure the WET distribution for each angle. Tomographic imaging was carried out by rotation of the cylindrical head phantom in the reference system of the PMMA cube and wedge (figure 3). Each measured projection (example shown in figure 8(a)) represents in y direction the measured wedge-modulated signal to energy curve for a given position x. The wedge thickness increases from top to bottom forming the characteristic signal curves which were used as replacement for the signal-to-energy curves measured in the previous WET experiments (figure 8(b)). The WET value is given by the position of the maximum signal S_max. The position is calculated by the distance in y direction to the reference position y_ref (air gap) with known wedge thickness d_wedge. To increase the WET resolution, which is given by the slope of the wedge (19.57°), the steep fall-off of the peak dominated by the wedge geometry is used to determine the peak position at 80 % of the peak height.

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The measured WET for a certain position in x is then given by:

$$\begin{equation} \fl \mathrm{WET}(x)=\mathrm{WET}(E_{\mathrm{init}})-\tan (19.57^\circ )\cdot (d_{\mathrm{wedge}}-(y_{\mathrm{ref}}-y_{\mathrm{80}})\cdot 0.8)\cdot \mathrm{WEPL}_{\mathrm{PMMA}} \end{equation} \tag{ 5 }$$

with WET(E_init) being the water equivalent range of the particles of initial energy E_init, WEPL_PMMA the WEPL of PMMA, and 0.8 the conversion factor from the detector pixel size to mm.

The resulting WET distribution for the measurement at 0° is shown in blue in figure 9. Further, the known geometry of the PMMA cube with a side length of d_block and a cutout the size of the cylindrical phantom d_cylinder(x) allows to recalculate the WET distribution of the cylindrical PMMA phantom:

$$\begin{equation} \mathrm{WET}_{\mathrm{corr}}(x)=\mathrm{WET}(x)-(d_{\mathrm{block}}-d_{\mathrm{cylinder}}(x))\cdot \mathrm{WEPL}_{\mathrm{PMMA}}. \end{equation} \tag{ 6 }$$

The final WET distribution WET_corr(x) with the characteristic steep gradient on the left and right side, which is due to the shape of the cylindrical object, is indicated in red in figure 9.

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The setup was imaged for 80 angles in steps of 2.25° over 180°. Calculation of the WET_corr distribution for each rotation angle forms the columns of the sinogram (figure 9(b)). It is used as an input parameter for the filtered back-projection algorithm.

Figure 10 shows the resulting reconstructed WEPL image of the cylindrical PMMA head phantom (a) and the known insert WEPL values (Jäkelet al 2001) in known phantom geometry (b). The overall reconstructed phantom shape with the inserts is in excellent agreement with the given geometry. Due to the reconstruction with a limited number of angles, streaking artifacts can be seen. To some extent image quality could be improved by filtering of raw image data. The quantitatively measured WEPL values were analyzed by averaging the WEPL values of the tissue equivalent inserts over an area of 1.6 cm in diameter. The measured WEPL values from the reconstructed image were plotted against the known WEPL values as shown in figure 11. The obtained data was linearly fitted (red) and shows in comparison to the expected values (black line) a systematic shift in WEPL of −0.007. The measured WEPL values seem to be lower than the known WEPL values.

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The Ram–Lak filter used in the back projection algorithm is designed to cut-off high frequencies above a set threshold. This filtering process can lead to decreased values in the position space. To account for this, scaling of the obtained data is necessary. In x-ray CT imaging this is performed by applying a linear transformation called Hounsfield scale. Here, for the reconstruction in carbon ion CT, a scaling factor was obtained by comparison of the measured WET values of a single projection with the WET values obtained from the reconstructed image. In figure 12(a) the measured WET distribution for one projection is compared to the calculation from the reconstructed image. Clearly the noise originating from the reconstruction process can be seen. The reconstructed image underestimates the measured values. By multiplication with an estimated correction factor, both distributions agree well. This correction factor was found to be valid for all measured projections and WET distributions. Applying this correction factor to the obtained reconstructed WEPL values (figure 12(b)), the reconstructed and expected WEPL values agree within one standard deviation.

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The resolution of the reconstructed WEPL image is given by the standard deviation of the WEPL values shown in figure 12 (vertical bars). The resolvable difference in the WEPL image corresponds to twice the standard deviation given by the fit. The WEPL resolution in the reconstructed carbon ion CT image is better than 0.01 WEPL.