Theoretical analysis of the thread effect in helical TomoTherapy

Purpose: The longitudinal dose ripple on the off-axis caused by helical radiation delivery, such as the TomoTherapy system, has been observed, and its relation with respect to pitch has been studied with empirically found optimal pitches, 0.86n, by Kissick Med. Phys. 32, 1414-1423 (2005). This ripple artifact referred to as the thread effect is periodic in nature and is caused by various periodic factors. In this work, the factors that cause the thread effect were unveiled, including jaw profile divergence, the inverse square law, attenuation, and the cone effect, and their impact on the thread effect were studied. Methods: Mathematical formulation for individual and combined factors were set up. Based on theoretical analysis and simulations, optimal pitches that result in local minima of the ripple amplitude with respect to the jaw width and off-axis distance were identified and verified. The effectiveness of optimization in reducing the thread effect were also studied. Results: Analysis and simulation based on the square-shaped jaw profiles well characterize the thread effect. Simulations based on the real jaw profiles show reduced ripples and very good agreement of optimal pitches compared with those based on the square profiles. The optimal pitches were found to have little jaw width dependence, except for the real jaw profile of small width (1.05 cm). The optimal pitches for the real jaw profile of width 1.05 cm are unidentifiable except for the largest ones, due to the relative smoothness of the jaw profile. With optimized intensity modulation, the thread effect can be largely suppressed. For real jaw profiles, the optimal pitches with or without dose optimization do not change much. The numbers 0.86n found by Kissick well approximate the optimal pitches for off-axis distance of 5 cm. However, optimal pitches are not universal for different off-axis distances: they decrease as the off-axis distance increases. Conclusions: The thread effect can be well explained by the proposed model. Optimization can largely reduce the thread effect. However, an optimal pitch reduces the ripple much easier especially when optimization is limited by many constraints. The optimal pitches predicted by the proposed model could be used as a reference for pitch selection regardless the tumor is at large or small off-axis distance.