Comprehensive evaluation of the high‐resolution diode array for SRS dosimetry

Abstract A high‐resolution diode array has been comprehensively evaluated. It consists of 1013 point diode detectors arranged on the two 7.7 × 7.7 cm2 printed circuit boards (PCBs). The PCBs are aligned face to face in such a way that the active volumes of all diodes are in the same plane. All individual correction factors required for accurate dosimetry have been validated for conventional and flattening filter free (FFF) 6MV beams. That included diode response equalization, linearity, repetition rate dependence, field size dependence, angular dependence at the central axis and off‐axis in the transverse, sagittal, and multiple arbitrary planes. In the end‐to‐end tests the array and radiochromic film dose distributions for SRS‐type multiple‐target plans were compared. In the equalization test (180° rotation), the average percent dose error between the normal and rotated positions for all diodes was 0.01% ± 0.1% (range −0.3 to 0.4%) and −0.01% ± 0.2% (range −0.9 to 0.9%) for 6 MV and 6MV FFF beams, respectively. For the axial angular response, corrected dose stayed within 2% from the ion chamber for all gantry angles, until the beam direction approached the detector plane. In azimuthal direction, the device agreed with the scintillator within 1% for both energies. For multiple combinations of couch and gantry angles, the average percent errors were −0.00% ± 0.6% (range: −2.1% to 1.6%) and −0.1% ± 0.5% (range −1.6% to 2.1%) for the 6MV and 6MV FFF beams, respectively. The measured output factors were largely within 2% of the scintillator, except for the 5 mm 6MV beam showing a 3.2% deviation. The 2%/1 mm gamma analysis of composite SRS measurements produced the 97.2 ± 1.3% (range 95.8‐98.5%) average passing rate against film. Submillimeter (≤0.5 mm) dose profile alignment with film was demonstrated in all cases.


| INTRODUCTION
Small malignant brain lesions are frequently treated with intracranial stereotactic radiosurgery (SRS) to obtain local control. 1,2 Intracranial radiosurgery is a complex, high-precision procedure requiring submillimeter accuracy of the dose placement. That necessitates meticulous commissioning and ongoing quality assurance. 3 Recently, an additional level of complexity was reached with the introduction of the singleisocenter multitarget treatments. [4][5][6][7] Those plans often produce a large number of small multileaf collimator (MLC) apertures, and dosimetric commissioning and ongoing patient-specific end-to-end tests 3 require high-resolution planar or volumetric detectors. Radiochromic film and gel/polymers have the required spatial resolution and have been employed for validation of the SRS techniques. [8][9][10][11] However 3D radiochromic dosimetry is too labor-intensive and expensive for routine patient-specific end-to-end tests. 12 Even radiochromic film has its significant drawbacks, as the readout is delayed and quality dosimetry requires meticulous and time-consuming calibration and readout protocols. [13][14][15] Electronic detector arrays are in many aspects an attractive alternative but historically did not have sufficient spatial resolution for SRS measurements. Among the commercially available instruments, the first high-resolution detector was an array of liquid-filled ionization chambers detectors, with 2.5 mm detector size and pitch. 16 In this work, we introduce a different planar array, designed primarily for SRS measurements in combination with a dedicated phantom. It consists of small diodes (essentially point detectors) with a 2.5 mm pitch and is a high-resolution extension of the Map-CHECK [17][18][19] series of dosimeters (Sun Nuclear Corp., Melbourne, FL). Diode array readings generally exhibit dependence on the multitude of the radiation beam characteristics, and thus require an application of a sophisticated and rigorous calibration and correction formalism tailored to the individual design. 20 We endeavored to validate the array's individual basic calibration and correction parameters, as well as its performance in a series of end-to-end SRS-type tests.

2.A | Radiation sources
For logistical reasons, the measurements were performed on two TrueBeam linear accelerators producing conventional (6MV) and flattening filter free (6MVFFF) radiation beams. The beam energies from both machines were closely matched. Most basic array parameters were measured on the unit equipped with a standard 120-leaf Millennium MLC with the leaves 5 mm wide as projected to isocenter.
The SRS plans were delivered on the machine with the high-definition (HD) MLC (2.5 mm wide leaves at isocenter).

2.B | Diode array and phantom
SRS MapCHECK (SMC, Sun Nuclear Corp, Melbourne, FL) consists of 1013 point (0.48 × 0.48 mm 2 cross-section, 0.007 mm 3 active volume) diode detectors arranged on the two 7.7 × 7.7 cm 2 printed circuit boards (PCBs). The PCBs are aligned face to face in such a way that the active volumes (p-n junction) of all diodes are in the same plane. The detectors on the main board are facing up in the normal horizontal position. The spacing between the neighboring detectors on each board is 3.5 mm. However, the daughter board is shifted 1.75 mm relative the main board in both X-and Y-axes, resulting in an overall inter-detector spacing of 2.47 mm. The buildup and backscatter to the detectors are provided by 2.2 cm thick poly methyl methacrylate (PMMA) plates. According to the specifications, the device can handle the maximum repetition rate of 3400 MU/min, which exceeds typical values at isocenter for the FFF 6 or 10 MV radiosurgical beams.
StereoPHAN (Sun Nuclear) is specifically designed to accommodate the SMC for the end-to-end dosimetric testing of the SRS treatment plans. It is a cylindrical PMMA phantom with a hemisphereshaped rounded superior end, to mimic the head (Fig. 1). The diameter of both cylindrical and hemispherical parts is 15.24 cm and the total phantom length is 20.87 cm. The phantom has an inner 17.5 × 8.5 × 8.5 cm 3 cavity. With appropriate spacers, this cavity accommodates the SMC as well as other imaging and dosimetric inserts, including those for ion chambers, radiochromic film, and special detectors (scintillator). The film insert houses a square 7.5 × 7.5 cm 2 piece of radiochromic film. There are five embedded titanium fiducials to assist in aligning the phantom with onboard imaging and subsequent spatial registration of the film. The physical depth of the SMC detector active volumes, ion chamber center, and film plane inside the StereoPHAN is 7.62 cm. The distance from the superior spherical end of the phantom to the SMC central detector is the same. When aligned at the accelerator isocenter, the assembly (SMC inserted in the StereoPHAN) provides a means of true composite measurements with gantry and couch rotations. For the noncoplanar beams, the system supports the couch angles of up to ± 45°, to avoid direct irradiation of the array's electronic by the primary beam. The relative array calibration (response equalization) accounts for the inherent differences in the diodes' sensitivity. It generally follows the standard wide field procedure of sequential irradiations in a conventional (flattened) beam with array shifts and rotations. 21,22 However the procedure is somewhat different from the previously described original MapCHECK calibration. 17,18 Because of the two PCB with detectors facing in opposite directions, the sequence is repeated with the array facing towards and away from the beam ("AP and PA" calibrations). This calibration is performed in the manufacturer-supplied PMMA slab phantom. Also, for the optimal measurement accuracy with FFF beams, two additional measurements in the StereoPHAN are required: "AP and PA" 5 × 5 cm 2 fields. In addition to response equalization, the measurements in the parallel-opposed fields help with scaling the angular response function described later.
The effectiveness of the relative calibration is typically verified by a 180°array rotation test. To that end, two identical exposures in a vertical wide field (10 × 10 cm 2 ) were delivered with the SMC electronics facing either the foot or the head of the couch. Percent dose differences for each detector between the standard and rotation orientations were recorded.
Angular dependence is a well-known phenomenon for the diode arrays of this type and must be corrected for in composite-type measurements. 12 The difference in response of nearby diodes on the two PCBs facing towards or away from the beam is appreciable and changes as a function of the beam incidence angle. This change serves as the basis for the incidence angle approximation. The previously measured angular response function, which should be for the most part relatively smooth, is scaled based on the "AP and PA" wide field calibration measurements.
The angular correction efficacy with gantry rotation was verified in the transverse (couch at 0°) and sagittal (couch at 90°) planes, as well as for the various combinations of couch and gantry angles, using standard methodology of measurements against detectors with nearly isotropic response. 12 The phantom with the SMC was placed at the accelerator isocenter. The response was compared at the central axis (CAX) and at the off-axis diodes against the 0.125 cc Semiflex ion chamber (PTW, Freiburg, Germany), and/or a 1 mm diameter, 3 mm long, water-equivalent 23,24 scintillator detector (W1-PSD, Standard Imaging Inc., Middleton, WI). The scintillator was calibrated for Čerenkov radiation discrimination with a minimum/ maximum fiber length exposure in a solid water-equivalent phantom, with the beam perpendicular to the long axis. 25,26 The SMC data were processed with and without applying the angular correction factors to distill the effect of the corrections.
For the transverse plane angular dependence at CAX, the field size was set to 5 × 5 cm 2 and the gantry was rotated in 10°increments, which were progressively reduced to 2°and 1°as the beam direction came closer to the array plane. The SMC response was compared to the ion chamber for both energies. The same SMC data were also verified against the W1-PSD for the 6MVFFF beam.
For sagittal plane angular dependence at CAX measurements, the couch was placed at 90°and the gantry rotated in 30°increments.
The incidence angles where the beam could directly irradiate the electronics were avoided. The SMC results were evaluated against the W1-PSD.
For the combined couch and gantry rotations, the couch angular positions were 0, ±10, ±30, ±50, ±70, and ±90°. At each couch position the gantry was rotated in 30°intervals. The data were again compared to the W1-PSD.
In addition to the diode at the CAX, four off-axis points located at the different locations in the SMC array were selected ( Table 1) The accelerator repetition rate (MU/min) dependence was previously reported for various Sun Nuclear devices 18,20,27 and is corrected for in the SMC software. The correction is applied based on the measured pulse rate during the collection cycle (50 ms). Its  efficiency was investigated for repetition rates ranging from 10 to 600 MU/min for conventional and 400 to 1400 MU/min for FFF 6MV beams. Field size was 5 × 5 cm 2 and 100 MU were delivered at each repetition rate. The data were normalized to the ion chamber readings, which in turn showed negligible collection efficiency difference by the two-voltage technique across the range of repetition rates. The SMC readings were processed with and without the repetition rate correction applied.
Diode sensitivity dependence on field size is also a well-known phenomenon that needs to be accounted for to obtain accurate dosi- in the control software, since for the very small fields the system cannot determine the beam incidence angle and reverts to the average correction, which would have distorted these measurements.
The SMC field size dependence was studied with both "AP and PA" beams.

2.C.2 | Response linearity with monitor units
For completeness, dose response linearity with monitor units was investigated. The monitor units for a 6MV beam varied from 1 to 100, and the SMC response was compared to the ion chamber. The diode readings were averaged between five centrally located detectors (e.g., within a 3.5 × 3.5 mm 2 square).

2.D.1 | Treatment planning
The device is intended to be used for the true composite (e.g., with planned gantry and table angles) 28 Fig. 2 provides an example of the target arrangement around the isocenter. The plans were optimized to deliver conformal high dose to each target while minimizing dose to the remainder of the volume, using a single-isocenter VMAT technique.
The details of the plans are provided in Table 2. The VMAT optimization employed two full coplanar and two partial (130°or 90°s pan) noncoplanar arcs. The last two columns in Table 2 provide the details of the couch and gantry angles for each plan. Each target was planned to receive 24 Gy.
In addition to the three targets, a 2 cm diameter spherical structure was drawn at the isocenter and was included in the optimization to achieve a low-gradient 18 Gy dose region across the 0.125 cc chamber. This allowed us to more accurately convert film density to dose by applying an ion chamber-derived scaling factor in addition to the calibration curve.

3.C | Angular dependence in the sagittal plane
The response characteristics with the couch at 90°are presented in Fig. 4. The device agrees with the scintillator to within 1% for both energies.

3.D | Angular response with gantry and couch angle combinations for diodes at central and off-axis locations
The angular dependence of SMC response was further sampled for a range of combinations of gantry and couch angles. Fig. 5 shows the heat map of percent errors for uncorrected and corrected central diode response against the W1-PSD for the 6MV beam. The uncorrected measurement data show deviations as large as 8% at the large gantry and/or couch angles. The corrected response, however, agrees with the W1 scintillator detector within 1% for all gantry and couch angles studied in this section, except for gantry angles at ±90°where the device was found under-responding by~3%. A similar behavior was observed for the 6MVFFF beam (Table 3). F I G . 5. A heat map of SMC readings percent errors compared to the scintillator in a 6MV beam, for different combinations of gantry and couch angles. Table 3 lists the descriptive statistics for the percent errors for the diodes both at the CAX and off-axis locations for both energies.

3.E | Repetition rate dependence
The repetition rate dependence is presented in Fig. 7. The SMC response with repetition correction applied agrees with the ion chamber to within 1% for 6MV and 0.5% for 6MVFFF for the repetition rate range studied. The maximum deviation of 2.5% was observed for 6MV beam at 10 MU/min.

3.G | Response linearity with monitor units
The SMC response relative to the ion chamber is plotted in Fig. 9. The difference is less than 2% upwards of 6 MU. After the sensitivity curve reaches a plateau, the higher monitor units are not a concern since the readout electrometers are reset after each 50 ms collection cycle. Table 4 shows the gamma analysis passing rates for SMC measurements against film.

3.H.1 | SMC vs Film gamma analysis
T A B L E 3 Descriptive statistics of percent dose errors of diode located at the central axis and off-axis locations vs W1 scintillator for all combinations of gantry and couch rotations in this section.
F I G . 6. Percent errors for SMC off-axis diodes r response (at points P0-P4 in Table 1) against the W1-PSD. The upper graph shows the data for the 6MV and the lower one for the 6MVFF beam.   treatments. During the commissioning, the artificial targets can be fairly easily moved around to coincide with the active area. The device is well suited for single-target patient-specific end-to-end testing recommended for SRS treatments. 3 Its application can be logistically more challenging for single-isocenter multiple-target plans. To sample all the targets, multiple measurements at different array angular orientations might be necessary. In addition, some targets could be farther away from the isocenter than the extent of the active area. As an alternative, supplementing/replacing direct measurements with semiempirical 3D dose reconstruction could be considered for such cases. 10

| CONCLUSIONS
The SRS MapCHECK diode array in the StereoPHAN phantom has sufficient dosimetric accuracy and spatial resolution to be a useful tool for SRS commissioning and quality assurance, including singleisocenter multiple-met modulated plans. The limitations of the device for some cases might be the size of the active area and inability to sample certain beams at their planned angles.

ACKNOWLEDGMENTS
This work was supported in part by a grant from Sun Nuclear Corp.

CONF LICT OF I NTEREST
SA is a graduate student supported by an SNC grant and VF is the PI on the project.