Model-based measurements of MLC leaf-offset and transmission factors for IMRT dose calculations Yoichi Watanabe, Xiaoyang Fu and Gerald J Kutcher Radiation Oncology, Columbia University, New York, NY ABSTRACT Absorbed dose calculations for IMRT require an incident photon intensity distribution. The leaf transmission factor, ε, and the effective leaf offset, δ, are required to accurately compute the incident fluence distribution from leaf motion data. Currently, ε and δ are independently measured. We present a method to obtain these, simultaneously. As opposed to a linear equation used by other investigators, we found that a non-linear equation best represents the relation between the delivered point dose and the leaf parameters, i.e., the width of leaf opening of the sliding window and the total travel length of the leaves in addition to ε and δ. We considered the delivery of uniform dose over a 10x10 cm2 field. The absorbed dose was measured with cylindrical ionization chambers at the depth of dose maximum in a phantom for 6 and 10 MV photon beams of Varian 21EX with a standard 80 leave MLC and 6 and 18 MV beams of Varian 2100C with a Millennium 120 leaf MLC. The values of ε and δ were estimated by applying a non-linear regression analysis method to the measured data. The measured transmission factors are 2.62, 2.70, 2.32, and 2.47 % for 6MVX (21EX), 10MVX, 6MVX (2100C), 18MVX, respectively. The effective leaf offsets are 0.91, 0.95, 0.76, and 0.83 mm, respectively. The non-linear equation fits the experimental data very well. This suggests the validity of our model. The measured data are being used with our in-house point dose calculation program for IMRT plan check. Bibliography Y. Watanabe, “Point dose calculations using an analytical pencil beam kernel for IMRT plan checking,” Phys Med Biol 46 (4), 1031-8. (2001). T. LoSasso, C. S. Chui, and C. C. Ling, “Physical and dosimetric aspects of a multileaf collimation system used in the dynamic mode for implementing intensity modulated radiotherapy,” Med Phys 25 (10), 1919- 27 (1998). M. R. Arnfield, J. V. Siebers, J. O. Kim, Q. Wu, P. J. Keall, and R. Mohan, “A method for determining multileaf collimator transmission and scatter for dynamic intensity modulated radiotherapy,” Med Phys 27 (10), 2231- 41. (2000). Figure 1: Relative dose vs. window width for 6MV photon beam of 21EX. Our model shows non-linear dependence of dose on the widow width. The measured data can be fitted very well with the non-linear equation. The estimated values agree with those published in the literature. We plan to use the measured data with our in-house point dose calculation program for IMRT plan check. Figure 1 shows the relative dose as a function of window width for 6MV photon beam of 21EX. The travel length of leaves L were 5 cm and 10 cm. The solid curve for L=10cm and the dashed curve for L=5 cm are obtained from Eq.(1) by substituting the estimated parameters. The data show clearly the non-linear dependence of the dose to W. The data are fitted very well using Eq.(1) The estimated parameters are given in Table I for in-phantom measurements. Only the data for L = 10 cm are shown. Comparison of Table I with the data for in-air measurements shows that ε and δ are almost independent of the measurement medium (phantom or air). Table I shows that ε is about 2.5% for all machines and energy. These values are larger than those by independent transmission factor measurements by approximately 1 %. The values of δ are slightly larger for higher energy. Our values ranges from 0.76 to 0.95 mm and agree with those found in literature. Estimation of diffusion coefficient According to Figs. 2 and 3, the diffusion takes place in the spatial dimension, y, of 4.0. This corresponds to 1.0 cm in the actual scale (see Fig. 1); hence, the value of h can be estimated by I. INTRODUCTION II. MODEL III. RESULTS AND DISCUSSION IV. CONCLUSIONS Fast independent point dose calculations are desirable for IMRT treatment plan check. Previously we developed a simple method using analytical pencil beam kernel1. The dose at a point is calculated for a given MU value and DMLC leaf motion data. The calculations require the calculation of incident fluence profile. The fluence calculation, in turn, needs the leaf transmission factor, ε, and the effective leaf-end offset, δ. In this paper we discuss a self-consistent method to measure δ and ε for multileaf collimators used for IMRT with a sliding window technique. We formulate an equation that represents a relation between the delivered dose at the isocenter and the delivery parameters of DMLC. The DMLC parameters are the width of leaf opening of sliding window, W, and the total travel length of the leaves, L, in addition to ε and δ. We consider a delivery of uniform fluence over a 10x10 cm2 field. Using the graphical representation of the leave motion as a function of time (or accumulated MU), we can derive an equation for the dose at d-max on the central axis. The absorbed dose at the measurement point is a sum of the primary, phantom scattered, and leaf-leakage photons. By representing the scatter contribution relative to the primary component by η, the dose D is given by (1) where C is a constant and includes the total monitor unit. By taking a ratio of D for arbitrary W to D for W=L, one can eliminate the unknown constant C. Note that Eq.(1) shows a non-linear dependence on the window width W as opposed to the accepted notion that indicates the linearity2,3. The linear relation is in fact widely used to estimate δ by extrapolating W to zero. It is easy to show that Eq.(1) is a linear function of δ when W << L. MLC leaf motion files were manually created. The leaf stopping positions correspond to the physical leaf-end. The MCLTABLE.TXT data file on the MLC control system of Varian accelerators will shift those positions by a small amount for the radiation field edge. We use the maximum leaf travel length of 10 cm. The shift for leaf position between -5 cm to 5 cm is less than 0.2 mm. Furthermore, the shift at the CAX, where we made the dose measurement, is zero. The absorbed dose was measured using Capintec 6.4 mm-diameter cylindrical ionization chambers. The chambers were placed at the depth of dose maximum in a phantom and in-air with appropriate build-up cap for 6MV and 10 MV photon beams of Varian 21EX and 6MV and 18MV photon beams of Varian 2100C. 21EX is equipped with a standard 80 leave MLC. 2100C is equipped with a Millennium 120 leaf MLC. The values of ε, δ and η are estimated by applying the non-linear regression analyses to the measured relative dose data. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0 1 2 3 4 5 6 7 8 9 10 Window Width, W [cm] Relative dose L=10cm L=5cm Fitted to L=10 Fitted to L=5 Table I: Estimated parameters: In-phantom measurements Machine 21EX 2100C Energy 6X 10X 6X 18X ε [%] 2.62 2.70 2.32 2.47 δ [mm] 0.907 0.947 0.758 0.835 η 1.33e-5 3.54e-6 1.73e-13 2.46e-7