Effects of tumor motion in GRID therapy
The reference GRID geometry: the isocenter-projected hole diameter is , and the minimum center-to-center hole separation is . The unit hexagon around the central hole is shown. The sides of the highlighted equilateral triangle of the unit hexagon define the GRID orientation, with aligned with the vertical side for convenience. The vector is perpendicular to . The interhole separation in the direction is .
(a) Waveforms for the isocenter displacement with respect to the static isocenter, and (b) the corresponding cumulative distribution function (CDF). The displacement axis is in units of , the amplitude of motion.
Single hole dose profiles (SHPs) at a depth of in a moving water phantom for the central hole (solid curves) and the two neighboring holes (dotted curves) along the direction. The phantom is irradiated with a beam via the reference GRID. The motion is in the direction with the isocenter displacement waveform given by: (a) , and (b) , with values of as indicated. The gray regions correspond to the shielded areas of the phantom irradiated with the full GRID when there is no motion. As varies, the overlap of the adjacent profiles also varies, which explains several features of the full GRID dose profiles shown in Fig. 4.
Full GRID dose profiles (FGPs) at a depth for (a) , and (b) , with the values of as indicated. is the peak static dose. (See Fig. 3 for correspondence with the single hole profiles.)
Gray-scale representation of the dose distribution from which the profiles in Fig. 4 are extracted. Motion is in the direction with the isocenter displacement (a) and (b) . Values of are indicated.
Peak and valley doses vs. motion amplitude for the three types of waveforms in Fig. 2 with motion in the direction. Changing changes the relative time a point spends under the open and blocked regions of the GRID, causing the peak and valleys dose to vary periodically with . The local extrema are related to , the hole separation in the direction.
Gray-scale representation of the dose distribution at depth for motion in the direction with the isocenter displacement varying as (a) and (b) .
Peak and valley doses vs. motion amplitude for the three types of waveforms in Fig. 2, with motion in the direction. The amplitude at the the local extrema is related to , the hole separation in the direction.
Peak and valley dose vs. motion amplitude for sinusoidal motion in the direction for hexagonal GRID designs with the following combinations of hole diameter and separation: (a) and (reference GRID), (b) and ( reduced by 23%), and (c) and ( and both reduced by 23%).
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