Investigation of absolute dose calibration accuracy for TomoTherapy using real water

Abstract A systematic bias in TomoTherapy output calibration was reported by the Imaging and Radiation Oncology Core Houston (IROC‐H) after analyzing intensity‐modulated radiation therapy (IMRT) credentialing results from hundreds of TomoTherapy units. Multiple theories were developed to explain this observation. One theory was that the use of a solid water “cheese” phantom instead of real water in the calibration measurement was the culprit. A phantom filled with distilled water was built to investigate whether our TomoTherapy was miscalibrated due to the use of a solid water phantom. A miscalibration of −1.47% was detected on our TomoTherapy unit. It is found that despite following the vendor's updated recommendation on computed tomography (CT) number to density calibration, the cheese phantom was still mapped to a density of 1.028 g/cm3, rather than the 1.01 g/cm3 value reported in literature. When the density of the cheese phantom was modified to 1.01 g/cm3 in the treatment planning system, the measurement also indicated that our TomoTherapy machine was miscalibrated by −1.52%, agreeing with the real water phantom findings. Our single‐institution finding showed that the cheese phantom density assignment can introduce greater than 1% errors in the TomoTherapy absolute dose calibration. It is recommended that the absolute dose calibration for TomoTherapy be performed either in real water or in the cheese phantom with the density in TPS overridden as 1.01 g/cm3.

indicating a good systematic agreement. 6 However, the average dose ratio for TomoTherapy is 0.974, 7 which indicates the existence of systematic errors in the absolute dose calibration.
Multiple theories were developed regarding the source of the systematic error in TomoTherapy absolute dose calibration. Gago-Arias et al. performed experiments to determine the correction factors for the Exradin A1SL thimble ionization chamber, 8 which is standard equipment that comes with TomoTherapy machines. They compared the dose measurements using the Exradin A1SL ionization chamber to the alanine/EPR dosimetry provided by the National Physical Laboratory (NPL, UK) in the machine-specific reference field, the plan-class specific reference field (pcsr), as well as two clinical treatments using their TomoTherapy machine. They found that the A1SL reading was consistently around 2.0% higher, leading to a correction factor of around 0.98. 8 This finding potentially explains why most of the TomoTherapy machines were calibrated at 2% lower (as the IROC-H results have shown), as most people did not apply this correction factor. However, a Monte Carlo study from Sterpin et al. showed that the machine-specific reference field correction factor for the Exradin A1SL chamber is close to 1.00, 9 contradicting the result from Gago-Arias et al.
Although AAPM TG-148 recommends a TG-51-equivalent 3 setup for tomotherapy (static beam, 5 × 10 cm 2 field size, measured in water), 10,11 this measurement does not establish an agreement between the TPS model and the delivered dose to the target. Specifically, the TG-51-like static output calibration (static couch, static gantry) is not the delivery mode for the treatment of patients (moving couch). During the moving couch delivery, the dose to a point in the patient is an integral of the longitudinal profile rather than one point on the longitudinal profile during the static couch delivery. In addition, the patients are not treated with an unmodulated beam.
The modeling of binary MLC, including the leaf behavior as well as small fields formed by the MLC, would create further deviations to the static output calibration. As a result, TG-148 recommends the adoption of a pcsr field approach for absolute dose output calibration. 10 This pcsr calibration of the TomoTherapy machine involves the measurement of the point dose to a solid water phantom using the delivery modes that replicate patient treatment (moving couch, rotating or fixed gantry angle, modulated field, different jaw opening, etc.). 10 The TomoTherapy "cheese" phantom that comes with the machine was recommended for the calibration measurement.
It has been highly recommended 1-3 to perform output calibration in real water (RW) due to its well-known and stable properties (physical density, chemical composition, etc.). Deviations from this practice could lead to increased errors. Recently, Chen 12 proposed that the mis-assignment of the TomoTherapy cheese phantom density for the absolute dose calibration is the major reason behind the systematic miscalibration discovered by IROC-H. In addition, the practice of delivering the same plans over time for absolute dose calibration fails to account for the drift in the machine model (e.g., MLC latency curve). Using a bottle filled with RW as the phantom, they concluded that their TomoTherapy machine was miscalibrated by 2.5%-3.0%.
To date, no further reports from other institutions have confirmed this finding.
The purpose of this study was to investigate the calibration of our TomoTherapy unit following Chen's approach. 12  and a VoLO GPU-based optimizer and dose calculator [14][15][16][17] and delivered to the TomoTherapy cheese phantom (shown in Fig. 1(a)].
The phantom is made with Virtual Water™ material (Med-Cal, Middleton, WI, USA). 18 The cheese phantom was scanned with a Philips Brilliance CT scanner (Philips Company, Netherlands) using "head" protocols. The IVDT was created following vendor-recommended procedures. Specifically, materials that have Hounsfield units (HU) between −100 and 100 were excluded except for water. A cylindrical target, 10 cm in diameter and 10 cm in length, was contoured at the center of the cheese phantom as shown in Fig. 1 Image guidance with mega-voltage CT (MVCT) was performed before the plan delivery to ensure an accurate setup. A calibrated A1SL ionization chamber and Tomo-Electrometer (Standard Image, Madison, WI, USA) were inserted into the "0.5 cm below" hole in the cheese phantom to measure the dose (D measure ) delivered to the target. The planned dose (D plan ) was read from the TPS as the average dose of a small volume around the ionization chamber's sensitive volume. The measurement for each plan was repeated to ensure that the consistency of the measurements is better than 1%.
The dose deviation (Δ) between the planned and measured dose was computed as The same treatment delivery and measurement process used for the Cheese plans were used for the RW plans as well. The dose deviation (Δ) between the planned and measured dose observed with the RW plans was also computed with eq. (1).

2.C | Analysis of the observed discrepancy between the water and cheese phantoms
The means and standard deviations (SDs) of dose deviations for RW and Cheese group plans were calculated, respectively. A paired t test was performed to test the similarity of the dose deviation between the two groups with a P < 0.05 indicating the statistical significance.

2.D |
Corrected density mapping for the cheese phantom To confirm that the discrepancy between the dose deviation observed in the water and cheese phantoms originated from the mis-assignment of the cheese phantom density, the density of the cheese phantom was "corrected." To achieve this correction, the average CT HU of the Cheese Phantom CT images scanned in the study were measured, and a new IVDT was created by adding a point that maps the average cheese phantom HU to 1.01 (as shown in Fig. 3), which is the density The calibration of our TomoTherapy HDA machine was first checked in the vendor-provided cheese phantom using the IVDT created fol-

3.B | Calibration check with water cube phantom
Dose measurements in the water cube phantom are shown in

3.C | Density correction for the cheese phantom
The average CT value of the cheese phantom scanned on our CT scanner is 35 HU. Using the IVDT created following the vendor's recommendation, this maps to a density of 1.028 g/cm 3 . Since McEwen et al. 18 reported a density (range) scaling factor of 1.01 for Virtual Water™, a new point was added to the IVDT to map the cheese phantom to a corrected density of 1.01 g/cm 3 . The plans created with the corrected cheese phantom density were delivered and measured; the results of which are listed in their machine. Because TomoTherapy's IVDT calibration procedure requires the physical density of the material be used, one likely practice is to associate the physical density of 1.047 g/cm 3 of Virtual Water™ to the cheese phantom HU in the IVDT curve 18 . However, due to the composition difference between solid water and RW phantoms, the behavior under radiation is more accurately described by the electron density rather than the physical density. 18,[23][24][25][26][27][28][29] The contrast under the kV beam (and thus, the HU value in the CT) has a stronger contribution from the photo-electric effect, which has a Z 3 dependence. However, the mass-attenuation coefficient under MV is primarily from Compton interactions, which depend on Z/A. 27 The Z/A for Virtual Water™ is only 97% that of the RW (0.538 vs. 0.556). 26 Because the linear attenuation coefficient is the product of the mass-attenuation coefficient and the physical density, the attenuation coefficient for Virtual Water™ is much closer to water than the physical density indicates. Measurements showed the density (range) scaling factor should be 1.01. 18 Therefore, the machine miscalibration from the clinics that use 1.047 g/cm 3 for the cheese phantom will be greater than what our clinic observed.
The vendor has noticed this problem and issued a memo (T-PPA-605-0710C) as well as updated the user manuals 13 to address this, their recommendation was to remove the materials that have a CT number between −100 and +100 HU except for RW. However, because this recommendation is unique to TomoTherapy, physicists who were mainly trained for Linac may not be aware of this practice.
Further, this practice will not fully correct the error. According to the vendor, this approach should lead to the density assignment of around 1.023 g/cm 3 for the cheese phantom, which is similar to our finding (1.028 g/cm 3 ), rather than the value of 1.01 g/cm 3 . Therefore, the absolute dose calibration for TomoTherapy will still contain a systematic error in measurement media properties. As the goal of the absolute dose calibration of a medical Linac is to reach an accuracy of within 1%, 1-3,10,30 care must be taken to reduce this systematic error.
Multiple calibration protocols for conventional Linac advocate 1-3 the use of RW for calibration measurement. For conventional Linac, this is achieved with a water tank for static measurement. We believe that the absolute dose calibration for TomoTherapy should also be performed in RW. However, in the absence of a suitable phantom filled with RW, our study showed that overriding the cheese phantom density to 1.01 g/cm 3 is an acceptable alternative.
Note that the corrected IVDT curve is only used for the TomoTherapy cheese phantom to correct the assigned density for the phantom. The IVDT for patient dose calculation is not affected.
T A B L E 2 Comparison between the planned and measured dose in the water cube phantom.
Plan number Delivery mode Jaw wide/mode D plan (Gy) D measure (Gy) Δ (%) The limitation of this study is that our result is still a singleinstitution finding. While we have demonstrated that the issue of the cheese phantom density still exists even if the vendor's new recommendation on IVDT creation is followed, it is difficult to know the exact practice and errors at other TomoTherapy centers. Therefore, we are unable to assert whether the phantom density is the sole contributor of the observed systematic bias in TomoTherapy calibration. Regardless, the finding on our TomoTherapy unit demonstrates that it is at least one of the major factors. The identification of this factor has helped to improve the calibration accuracy of TomoTherapy in our clinic.

| CONCLUSIONS
Our investigation confirms that the improper density assignment for the cheese phantom used during the TomoTherapy absolute dose calibration would lead to a lower output calibration. It is recommended that the absolute dose calibration for TomoTherapy be performed in RW, or in the vendor-supplied cheese phantom, but with the density in TPS overridden as 1.01 g/cm 3 .

CONF LICT OF I NTEREST
No conflicts of interest.

D A T A A V A I L A B I L I T Y S T A T E M E N T
The data that support the findings of this study are available from the corresponding author upon reasonable request.