Implementation of TomoEDGE in the independent dose calculator CheckTomo

Abstract Purpose CheckTomo is an independent dose calculation software for tomotherapy. Recently, Accuray (Accuray Inc., Sunnyvale, CA, USA) released an upgrade of its tomotherapy treatment device, called TomoEDGE Dynamic Jaws, which improves the quality of treatment plans by enhancing the dose delivery with the help of jaws motion. This study describes the upgrade of CheckTomo to that new feature. Methods To account for the varying width and off‐axis shift of dynamic jaws fields, the calculation engine of CheckTomo multiplies the treatment field profile by a penumbral filter and shifts the dose calculation grid. Penumbral filters were obtained by dividing the edge field profiles by that of the corresponding nominal field. They were sampled at widths 1.0, 1.8, and 2.5 cm at isocenter in the edges of the 2.5 and 5 cm treatment field. Results The upgrade of CheckTomo was tested on 30 patient treatments planned with dynamic jaws. The gamma pass rate averaged over 10 abdomen plans was 95.9%, with tolerances of 3 mm/3%. For 10 head and neck plans, the mean pass rate was 95.9% for tolerances of 4 mm/4%. Finally, misplacement and overdosage errors were simulated. In each tested cases, the 2 mm/3% gamma pass rate fell below 95% when a 4 mm shift or 3% dose difference was applied. Conclusions These results are equivalent to what CheckTomo achieves in static jaws cases. So, in terms of dose calculation accuracy and errors detection, the upgraded version of CheckTomo is as reliable for dynamic jaws plans as the former release was for static cases.


| INTRODUCTION
Independent dose verification is considered to be important to ensure patient safety. 1 It can be performed through an independent calculation with commercial softwares for three-dimensional conformal radiation therapy (3DCRT), image-modulated radiation therapy (IMRT), and volume-modulated arc therapy (VMAT) treatments. For tomotherapy, as far as we know, there exists a commercial tool, Mobius 3D (Mobius Medical Systems, Houston, TX, USA), and a single-point dose verification software. 2 Additionally, an open source solution, CheckTomo, was released in 2011. 3 That software independently generates a three-dimensional point-based dose distribution, using patient CT images and delivery plan, and compares it against the dose volume calculated by the tomotherapy treatment planning system (TPS).
Accuray (Accuray Inc., Sunnyvale, CA, USA) released an upgrade of its tomotherapy device called TomoEDGE Dynamic Jaws. 4 The purpose of this upgrade is to reduce the field penumbra along the patient longitudinal (inferior-superior) axis by the mean of jaws motion. The way the dose is delivered is hence modified and the dose calculation engine of CheckTomo needed to be upgraded consequently.
This study aims to present the work done to develop and implement the upgrade of CheckTomo and the tests that were performed to assess that the dose calculation carried out with the upgrade is as reliable as it was with the previous version. It does not suggest any improvement of the core calculation engine.

2.A | TomoEDGE dynamic jaws
In tomotherapy, the field is delimited in the longitudinal (IEC-y) direction by a pair of collimators, called jaws. A non-TomoEDGE direct or helical tomotherapy treatment is delivered with static jaws, i.e., at fixed field width during the whole treatment procedure, either 1, 2.5, or 5 cm at isocenter. This implies that the field penumbra in the longitudinal direction is of approximately the field size on both cranial and caudal sides of the target. To limit the extra dose to organs at risk (OAR) and other healthy tissues, the treatment can be delivered with a smaller field width, but this usually increases the irradiation time.
To overcome this poor trade-off, TomoEDGE introduced jaws motion during treatment delivery. 5 At treatment start, the jaws delimit at isocenter an asymmetrical 1 cm wide field, located off the source axis toward the patient's feet. Then as the couch moves forward, the cranial jaw sweeps toward the patient's head to keep the field edge 5 mm ahead of the planning target volume (PTV), until the jaws delimit a symmetrical field (respectively to the beam axis) of the nominal treatment size, either 2.5 or 5 cm at isocenter. Similarly, the caudal jaw closes behind the PTV as it exits the beam, until the field is 1 cm wide again. 4 In a TomoEDGE treatment, the penumbra on the cranial and caudal sides of the PTV is reduced to 1 cm. See For clarity, the fields will be denominated "nominal" when delimited by symmetrically positioned static jaws and "edge" otherwise.

2.B.1 | Software basics
CheckTomo is a software written in MATLAB (The MathWorks Inc., Natick, MA, USA) that computes a three-dimensional point-based dose distribution using CT data and treatment plan on the patient side and independently acquired beam data on the machine side.
Patient data are read from DICOM CT and RT-plan files where beam geometry and patient position during treatment are described.
Beam data are provided with CheckTomo for each nominal treatment field in text files with a homemade structure. They consist of a reference dose point, tissue-phantom ratios (TPRs), output factors (OFs), and off-axis ratios (OARs) measured for various field shapes.
The 5 9 40 cm 2 field at isocenter was taken as the reference one and the dose reference point was measured isocentrically at depth 10 cm. All machine data were independently acquired on a tomotherapy unit using an ionization chamber at different depths in a water tank.
CheckTomo dose distribution is usually calculated on a grid of 15 9 15 9 15 points, with a 1 to 1.5 cm spacing. Grid resolution and size can be adapted if needed. For each sinogram projection (or control point), the dose deposited at a particular location is the F I G . 1. Schematic representation of a TomoEDGE treatment beam at two moments. Dashed lines represent the nominal field width. Edge fields (in red) are represented at treatment start (right) and end (left). At treatment start, the jaws delimit a 1 cm wide field on the negative IEC-y side of the beam axis. During treatment (not represented), as the PTV moves forward, the cranial jaw opens to keep the superior field edge ahead of the PTV superior limit. Then, the caudal jaw closes to keep the inferior field edge behind the PTV inferior limit. Finally, when the treatment ends, the jaws delimit a 1 cm wide field again, but on the positive IEC-y side of the beam axis. product of the projection time, the dose rate, TPR, OF, and OAR.
The fluence is considered to arise from the mean angle of the projection arc, which, regarding the tomotherapy standard of defining 51 control points per gantry rotation, extends over 7.29°. To increase the number of control points and thus improve the dose calculation accuracy, CheckTomo offers the option to split each projection into multiple subprojections. 6 CheckTomo dose distribution can be compared to that calculated by the tomotherapy treatment planning system (TPS) by means of a gamma 7 or box comparison index. 8 Required patient data, beam data collection, dose calculation model, and comparison indices were explained in more detail in the original release paper of CheckTomo. 3

2.B.2 | Beam profile model
In CheckTomo, the longitudinal profile of a nominal field is calculated by multiplying the field OAR, the TPR, and the OF. CheckTomo handles OARs expressed in angular distance respectively to the beam source, instead of Cartesian coordinates. It follows the tomotherapy naming conventions of field size, calling the longitudinal dimension the width and the in-plane dimension the length (width and length are always given at isocenter). Which is more, the OF of the tomotherapy beam, hereafter S cp , is not a function of the equivalent square field size but depends independently on both the field width and length. 3 In CheckTomo, it is therefore considered to be a function S cp;w0 of the field length specific to the nominal field of width w 0 .
Thus, the longitudinal profile at angular coordinate h y and depth d of a nominal field of width w 0 and length L is given by P N ðw 0 ; L; h y ; dÞ ¼ OAR y ðh y ; dÞ Á TPRðA sq ; dÞ Á S cp;wo ðLÞ: (1) A sq is the equivalent square field size.

2.C. | Implementation of a dynamic jaws beam profile model in CheckTomo
Jaws motion induces changes in the field shape and OF that have to be accounted for in the profile model. Theoretically, the longitudinal profile of an edge field is obtained by multiplying Eq. (1) by a jaw penumbral filter and by correcting the OF. But as mentioned in section 2.B.2, the OF function S cp was not designed to account for a varying field width. To overcome this limitation, the relative jaw penumbral filter (RJPF) was introduced, defined as the ratio of the edge and nominal longitudinal profiles P E and P N , Here P E is the edge field profile given in angular coordinates respectively to the beam source. The transformation consists in first applying a coordinates shift along the longitudinal axis so that the field maximum is at IECÀy = 0. Then, the shifted Cartesian coordinates are converted in angular distances.
The edge field profile equation is obtained by inverting relation (2) and replacing P N with equation (1), namely P E ðw; w 0 ; L; h y ; dÞ ¼ OAR y ðh y ; dÞ Á TPRðA sq;d Þ Á S cp;w0 ðLÞ Á RJPFðw; w 0 ; h y ; dÞ: Note that it yields a profile originating at the source axis. To account for the edge field off-axis nature, the dose calculation grid is shifted longitudinallytoward head or feet depending on the edge sideby half the field width.
In practice, P E and P N were sampled at field widths and depths specified in section 2.D, normalized, respectively, to P N peak maxima and converted into angular coordinates. RJPFs were then calculated from Eq. (2) by interpolating P E and P N over for a set of arbitrary points. These data were stored in new text files shrinking or extending the original target volume. Plans were calculated for the 2.5 cm field on these three PTVs and for the 5 cm field on the 6 cm and 10 cm PTVs. All plans were calculated in dynamic jaw mode. The PTVs were centered on the machine isocenter, the prescription dose was of 2 Gy and the pitch was 0.287. To force some field modulation, a constraint was applied on a structure of the same size as the target located 2 cm beneath it.
All five plans were calculated in CheckTomo with a 2.5 mm longitudinal spacing and global 2 mm/3% and 3 mm/4% gamma indices were calculated. Additionally, the dose profiles along the longitudinal axis in the isocenter plane were extracted from both the CheckTomo and tomotherapy TPS dose volume so that they could be compared visually.

2.E.2 | Dose verification in real patient cases
The  Though, as can be seen in Fig. 2 (3), the spatial coordinate is the angular distance at the source, but that the field profiles are represented in Fig. 2 in Cartesian coordinates. T A B L E 5 Number of successes to the gamma comparison test (N c>95% , i.e., pass rate above 95%) and mean gamma pass rate ( c) for various tolerances for the three different regions investigated. Ten treatment plans were tested in each region. Points within the 50% isodose and at least 5 mm depth were considered in the calculation of the gamma index. 3.B | Dose calculation gamma pass rate

3.B.1 | Gradient verification
Gamma index pass rates for all five plans calculated in the Tomo-Phant are given in Table 1. With the 2.5 cm field, the pass rate is high (99.8%) for the 6 cm and 10 cm target. For the 2 cm target, the index tolerance must be increased to 3 mm/4%. Note that this case was designed for testing purposes. In clinical practice, it would not make sense to try to cover a 2 cm long PTV with the 2.5 cm wide field and the 1 cm field would have been used instead.
The gamma pass rates of the plans calculated with the 5 cm field are lower, below 90% for the 2 mm/3% tolerance. As can be seen in Fig. 4 (b), the dose calculation is perturbed over 5 cm by the approximation of the varying field width profile. Though, this figure also shows that calculation of the field gradient by CheckTomo matches well that of the TPS both in space and dose.   Performing an independent dose calculation with CheckTomo is not as comprehensive as actually measuring it during a QA procedure, in that sense that it performs no control on the machine side.

3.B.2 | Real patient cases and errors detection
Though, CheckTomo successfully detected simulated errors exceeding tolerances. In other words, it is conservative of the quality assurance, thus can provide a good indicator of the accuracy of the dose calculation. Nonetheless, the way CheckTomo could be used in practice (e.g., replace a patient QA measurements) remains the responsibility of the local medical physicist.

3.C | Occasional edge dose calculation error
In some cases, the dose is over or under estimated in the target volume edges, as shown in Fig. 5 left-hand side. The occurrence of such errors seems random and is caused by rounding mistakes in the calculation of the dose grid coordinates. Even a submillimetric registration error between the CheckTomo and tomotherapy TPS dose distributions could lead to a dose miscalculation of several Gy within the high gradient region. Though, such a problem can be easily addressed by shifting longitudinally the TPS dose volume, using a manual registration tool included in CheckTomo since the first version. As it happens, the error appearing in Fig. 5