A Mathematic Method to Adjust MLC Leaf End Position for Accuracy Dose Calculation in Carbon Ion Beam Radiation Therapy Treatment Planning System

Introduction: We present a mathematic method to adjust the leaf end position for dose calculation correction in carbon ion radiation therapy treatment planning system. Methods and Materials: A struggling range algorism of 400 MeV/n carbon ion beam in nine different multi-leaf collimator (MLC) materials was conducted to calculate the dose 50% point in order to derive the offset corrections in carbon ion treatment planning system (ciPlan). The visualized light field edge position in treatment planning system is denoted as X tang.p and MLC position (X mlc.p ) is defined as the source to leaf end mid-point projection on axis for monitor unit calculation. The virtual source position of an energy at 400 MeV/n and struggling range in MLC at different field sizes were used to calculate the dose 50% position on axis. On-axis MLC offset (correction) could then be obtained from the position corresponding to 50% of the central axis dose minus the X mlc.p MLC position.


Results:
The precise MLC position in carbon ion treatment planning system can be used an offset to do the correction. The offset correction of pure tungsten is the smallest among the others due to its shortest struggling range of carbon ion beam in MLC. The positions of 50% dose of all MLC materials are always located in between X tang.p and X mlc.p under the largest field of 12 cm by 12 cm.

Conclusions:
MLC offset should be adjusted carefully at different field size in treatment planning system especially of its small penumbra characteristic in carbon ion beam. It is necessary to find out the dose 50% position for adjusting MLC leaf edge on-axis location in the treatment planning system to reduce dose calculation error.
A mathematic method to adjust MLC leaf end position for accuracy dose calculation in carbon ion beam radiation therapy treatment planning system

I. INTRODUCTION
In most commercial photon radiation therapy facilities such as linear accelerators, multi-leaf collimator (MLC) systems are used to improve the dose profile of the geometry penumbra and the transmission penumbra [1]. MLC not only used commonly as treatment accessories in photon, but also adopted in heavy charged particles therapy such as carbon ion beam treatment [2]. The coincidence between the 50% dose position and the light field of photon beam cannot be taken for granted with the non-divergent geometry that is found in the curved-leaf linear type of collimator system, the 50% dose position must be verified during MLC system acceptance [3]. Not like the photon, MLC systems utilize designs with rounded leaf ends to improve the coincidence of the radiation 50% point with projected light field edge, the shape of MLC leaf end in charged particle is rectangular [4]. The struggling range of carbon ion beam in MLC saves troubles with the rounded leaf end design caused by photon attenuation in MLC [5]. One of the most important principles of MLC design is to reduce the differences between the dose 50% points and the projected light field edge on axis [6]. The characteristic of the projected light field edge locations and the definition of MLC position as well as the dose 50% points in photon treatment planning system need to be corrected before patients' treatment monitor units are calculated. The MLC position in planning and its relative radiation dose 50% point of the carbon ion MLC are also needed to be corrected and implemented in the computerized treatment planning system for accuracy monitor unit calculation [7]. In this work, we illustrate the specific issues to carry out dose calculation of a rectangular end MLC system with an offset correction in carbon ion beam.

II. Materials and Methods
This work presented here was performed with 400 MeV/n on a carbon ion therapy facility established by the Institute of Modern Physics (IMP), China. The IMP affiliated with the Chinese Academy of Sciences (CAS), was founded in 1957 in Lanzhou, China. In order to take the advantage of full usage of the research facilities at IMP, the National Laboratory of Heavy Ion Accelerator, Lanzhou (NLHIAL) was established at IMP in 1991 [8]. Nine MLC materials including struggling range listed at table 1 were adopted for this study.
The subscript denotes the percentage compositions of each MLC materials. According to IMP previous Monte Carlo simulation, the platform was v8.2/GEANT4-10-05-patch-01 with QGSP_BERT_HP_EMY package of Gate (GEANT4 Application for Tomographic Emission) [9]. The geometric dimensions of WHICH are showed in figure 1. All on-axis profiles were measured with a certain visual light field (nominal light field) at a SAD of 263.3 cm to determine the point receiving 50% of the central axis dose. The projection of the nominal light field at SAD 263.3 cm was adopted as a setup condition for dose profile measurements in water phantom, but the geometry of the tangential interaction on x axis (X tang,p ) was derived from X mlc,p (planning system defined leaf position) in ciPlan treatment planning system; furthermore, the corresponding dose 50% point to the central axis dose of X mlc,p was calculated by mathematical methods in this study. Once dose 50% point was decided, the on-axis correction "offset" could be obtained by subtraction of the point corresponding to 50% of the central axis dose from the position of X mlc.p . beam in this study. The film processing and dose profile measurements followed the international protocols [10]. A pre-exposure technique was used for the calibration curve derivation [ 11 ]. This was performed by giving each film a priming dose of 2 Gy to homogenize the film density using our WHICH facility with a dose of 1 Gy at carbon ion energy of 400 MeV/u. We then measured the dose homogeneity using a densitometer. Graded doses of 5, 10, 15, 40, 60, 80, 100, 150 and 200 cGy were given to the GAF chromic film to obtain the Hurter-Driffield calibration curve (H-D curve).

II.A. Geometry specifications
All exposed films of depth dose curve were then scanned with an Epson Expression 11000XL scanner in the 48-bit RGB mode (16 bits per color), and the data were saved as tagged image file format (TIFF) and analyzed by the VariSoft imaging procession software. A red filter was placed on top of the GAF films before scanning to increase the slope of the H-D curve, thereby raising the resolution of the dose-OD curves [12 ].
The field size derived from dose 50% of the dose profile at isocenter was then compared to an upstream and downstream films with a gap of -15 cm and +15 cm for determining the virtual source position.
A.7. The 50% dose position: X 50% The radiation field size is defined as the lateral distance between the 50% isodose line (X 50% ) at a reference depth. In photon beam, the dose 50% of the central axis dose is determined by the attenuation of radiation in MLC, while in carbon ion beam, the struggling range dominate the position of X 50% . When the MLC moves near to or away from the central axis (Fig. 2), the X 50% position might locate at point n (right to X mlc.p ) or point k (left to X mlc.p ), respectively. This depends on the struggling range in MLC (denoted as ̅̅̅̅ or ̅̅̅̅ in Fig. 2).

A.8. Determination of dose 50% by struggling range of carbon ion beam in MLC
The number of beam nuclei that survive passage through the MLC, N can be determined from the total number of carbon ion particles interaction events in MLC. This particles number is compared with the total number of incident nuclei, N B , as determined from the total number of events in the collision history [13].   The on-axis offset (the 50% dose position minus the planned leaf position) is used for accurate monitor unit calculation. Figure 2 shows X tang,p , X mlc,p , and the on-axis position receiving 50% of the central axis dose (point k or n). In photon beams, when MLC leaf travels close to the central axis, owing to gain enough attenuation the 50% dose position must project outside X mlc,p ( right to X mlc,p ) on point n. As the MLC leaf travels away from the central axis, the 50% dose projection position move inside X mlc,p ( left to to X mlc,p ) to point k for less attenuation in figure 2. Not like photons, the carbon ion X 50% are always located in between X tang,p , X mlc,p regardless the field size due to the struggling range is enough for 50% dose attenuation. This offset adjustment can be of importance in clinical situations of split fields to avoid calculating over-dosage or under-dosage at treatment.

N = N B
The maximum field size of our institute carbon ion beam is 12 cm x 12 cm, the corresponding offset and light-radiation agreement of half field size of 6 cm in table 2 were -0.3689 mm and -0.59767 mm, respectively. The minus sign means the X 50% located in-between X tang,p and X mlc,p. For photon beams, the design of rounded leaf end structure reduce the distance of X 50% to X tang,p and X mlc,p , while in carbon ion beams, the rectangular leaf end have the same effect with rounded leaf end due to the struggling range of heavy charged particle in MLC.

V. Conclusions
In this study, we illustrate that the accumulated and planned radiation doses may not always be in agreement for MLC treatment fields at a carbon ion beam treatment planning system unless the offset is carefully adjusted.
It is necessary to find out the dose 50% position for adjusting MLC leaf edge on-axis location in the treatment planning system to reduce dose calculation error.
We should keep in mind that patient treatment monitor unit calculations at extremely settings such as split field in carbon ion beam could result in significant uncorrectable under-dosage or over-dosage in treatment planning calculation.
The physical dimensions of carbon ion facility at WHICH.

Figure2.
The definition of MLC nominal light field (visualized light field) edge, X tang.p , the intersection of a line from the source to the leaf tip with an angle of θ', X mlc.p , and the dose 50% position X 50% ( straggling range) of tungsten in treatment planning system. Nine MLC materials including the percentage compositions of each MLC materials denoted as subscript symbols with struggling range were listed for this study. Table2.
The tungsten MLC leaf end offset correction of 400 MeV/n carbon ion beam at different fields.
Table3. Figure 1 The physical dimensions of carbon ion facility at WHICH.

Figure 2
The de nition of MLC nominal light eld (visualized light eld) edge, Xtang.p, the intersection of a line from the source to the leaf tip with an angle of θ', Xmlc.p, and the dose 50% position X50%( straggling range) of tungsten in treatment planning system.

Figure 3
Schematic demonstrates the offset corrections of different material for MLC. The offset correction is increased because of the composition of different metal increased leading to the increasement of struggling ranges.

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