A new method for the construction of bivariate matrix valued rational interpolants (BGIRI) on a rectangular grid is presented in [6]. The rational interpolants are of Thiele-type continued fraction form with scalar de...A new method for the construction of bivariate matrix valued rational interpolants (BGIRI) on a rectangular grid is presented in [6]. The rational interpolants are of Thiele-type continued fraction form with scalar denominator. The generalized inverse introduced by [3]is gen-eralized to rectangular matrix case in this paper. An exact error formula for interpolation is ob-tained, which is an extension in matrix form of bivariate scalar and vector valued rational interpola-tion discussed by Siemaszko[l2] and by Gu Chuangqing [7] respectively. By defining row and col-umn-transformation in the sense of the partial inverted differences for matrices, two type matrix algorithms are established to construct corresponding two different BGIRI, which hold for the vec-tor case and the scalar case.展开更多
This study aims to evaluate inter-fractional set-up errors in patients treated with distinct immobilization equipment (thermoplastic mask, knee-fix and feet-fix, wing board and vac-lok) for four anatomical regions inc...This study aims to evaluate inter-fractional set-up errors in patients treated with distinct immobilization equipment (thermoplastic mask, knee-fix and feet-fix, wing board and vac-lok) for four anatomical regions including brain, head and neck (HN), thorax and pelvis. Data of randomly selected 140 patients who were treated for four anatomical regions were obtained using Hi-Art Helical Tomotherapy (HT) system. Pre-treatment planning was based on automatic registration readings of computed tomography (CT) and mega-voltage computed tomography (MVCT) on a daily basis. Distinct immobilization equipment was used for varying anatomical regions. Individual mean set-up error (M), systematic error (Σ), and random error (σ) values were calculated through daily translational and rotational deviation values. The size of translational, systematic and random error was 1.31 - 4.93 mm for brain, 2.28 - 4.88 mm for HN, 4.04 - 9.90 mm for thorax, and 6.34 - 14.68 mm for pelvis. Rotational values were as follows: 0.06° - 0.73° for brain, 0.42° - 0.6° for HN, 0.48° - 1.14° for thorax and 0.65° - 1.05° for pelvis. The highest translational, systematic and random error value was obtained from the pelvic regional. The highest standard and random error value in pitch and roll was produced in the rotational direction of the pelvis (0.05° and 0.71°), while the highest error value in yaw was (1.14°) produced from thorax. Inter-fractional set-up errors were most commonly produced in the pelvis, followed by thorax. Our study results suggest that the highest systematic and random errors are found for thorax and pelvis. Distinct immobilization equipment was important in these results. Safety margins around the clinical target volume (CTV) are changeable for different anatomical regions. A future work could be developed to new equipment for immobilization because of the reduced margins CTV.展开更多
文摘A new method for the construction of bivariate matrix valued rational interpolants (BGIRI) on a rectangular grid is presented in [6]. The rational interpolants are of Thiele-type continued fraction form with scalar denominator. The generalized inverse introduced by [3]is gen-eralized to rectangular matrix case in this paper. An exact error formula for interpolation is ob-tained, which is an extension in matrix form of bivariate scalar and vector valued rational interpola-tion discussed by Siemaszko[l2] and by Gu Chuangqing [7] respectively. By defining row and col-umn-transformation in the sense of the partial inverted differences for matrices, two type matrix algorithms are established to construct corresponding two different BGIRI, which hold for the vec-tor case and the scalar case.
文摘This study aims to evaluate inter-fractional set-up errors in patients treated with distinct immobilization equipment (thermoplastic mask, knee-fix and feet-fix, wing board and vac-lok) for four anatomical regions including brain, head and neck (HN), thorax and pelvis. Data of randomly selected 140 patients who were treated for four anatomical regions were obtained using Hi-Art Helical Tomotherapy (HT) system. Pre-treatment planning was based on automatic registration readings of computed tomography (CT) and mega-voltage computed tomography (MVCT) on a daily basis. Distinct immobilization equipment was used for varying anatomical regions. Individual mean set-up error (M), systematic error (Σ), and random error (σ) values were calculated through daily translational and rotational deviation values. The size of translational, systematic and random error was 1.31 - 4.93 mm for brain, 2.28 - 4.88 mm for HN, 4.04 - 9.90 mm for thorax, and 6.34 - 14.68 mm for pelvis. Rotational values were as follows: 0.06° - 0.73° for brain, 0.42° - 0.6° for HN, 0.48° - 1.14° for thorax and 0.65° - 1.05° for pelvis. The highest translational, systematic and random error value was obtained from the pelvic regional. The highest standard and random error value in pitch and roll was produced in the rotational direction of the pelvis (0.05° and 0.71°), while the highest error value in yaw was (1.14°) produced from thorax. Inter-fractional set-up errors were most commonly produced in the pelvis, followed by thorax. Our study results suggest that the highest systematic and random errors are found for thorax and pelvis. Distinct immobilization equipment was important in these results. Safety margins around the clinical target volume (CTV) are changeable for different anatomical regions. A future work could be developed to new equipment for immobilization because of the reduced margins CTV.
