Analysis of translational errors in frame-based and frameless cranial radiosurgery using an anthropomorphic phantom

Abstract Objective: To evaluate three-dimensional translational setup errors and residual errors in image-guided radiosurgery, comparing frameless and frame-based techniques, using an anthropomorphic phantom. Materials and Methods: We initially used specific phantoms for the calibration and quality control of the image-guided system. For the hidden target test, we used an Alderson Radiation Therapy (ART)-210 anthropomorphic head phantom, into which we inserted four 5mm metal balls to simulate target treatment volumes. Computed tomography images were the taken with the head phantom properly positioned for frameless and frame-based radiosurgery. Results: For the frameless technique, the mean error magnitude was 0.22 ± 0.04 mm for setup errors and 0.14 ± 0.02 mm for residual errors, the combined uncertainty being 0.28 mm and 0.16 mm, respectively. For the frame-based technique, the mean error magnitude was 0.73 ± 0.14 mm for setup errors and 0.31 ± 0.04 mm for residual errors, the combined uncertainty being 1.15 mm and 0.63 mm, respectively. Conclusion: The mean values, standard deviations, and combined uncertainties showed no evidence of a significant differences between the two techniques when the head phantom ART-210 was used.

Multiple scales analysis of nonlinear oscillations of a portal frame foundation for several machines

An analytical study of the nonlinear vibrations of a multiple machines portal frame foundation is presented. Two unbalanced rotating machines are considered, none of them resonant with the lower natural frequencies of the supporting structure. Their combined frequencies is set in such a way as to excite, due to nonlinear behavior of the frame, either the first anti-symmetrical mode (sway) or the first symmetrical mode. The physical and geometrical characteristics of the frame are chosen to tune the natural frequencies of these two modes into a 1:2 internal resonance. The problem is reduced to a two degrees of freedom model and its nonlinear equations of motions are derived via a Lagrangian approach. Asymptotic perturbation solutions of these equations are obtained via the Multiple Scales Method.

On non-ideal and non-linear portal frame dynamics analysis using bogoliubov averaging method

We apply the Bogoliubov Averaging Method to the study of the vibrations of an elastic foundation, forced by a Non-ideal energy source. The considered model consists of a portal plane frame with quadratic nonlinearities, with internal resonance 1:2, supporting a direct current motor with limited power. The non-ideal excitation is in primary resonance in the order of one-half with the second mode frequency. The results of the averaging method, plotted in time evolution curve and phase diagrams are compared to those obtained by numerically integrating of the original differential equations. The presence of the saturation phenomenon is verified by analytical procedures.