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Abstract  This note reports and briefly discusses some of the numerous reasons for bad convergence in linear buckling optimisation. Above all, it highlights that erratic convergence history can be avoided when the design optimisation problem includes enough buckling modes (and not only the first ones as it is the usual case), which keep the whole structure sensitive to the design restriction. This strategy is illustrated with an example and shows that possible significant improvement in the convergence speed can also be achieved by simply considering a large number of buckling modes in the optimisation problem. The selection of a suitable approximation scheme is also discussed. [ABSTRACT FROM AUTHOR]

: PurposeA CT-based three-dimensional (3D) method was used to analyze the intra- and interfraction reproducibility of lung immobilization during moderate deep inspiration breath hold (mDIBH), defined as 75% of the maximal inspiration using an active breathing control (ABC) apparatus.: Methods and materialsThe ABC apparatus was used to immobilize the breathing motion with a computer-controlled valve. Immobilization of the lungs in breast cancer patients was used as a model to evaluate the reproducibility of mDIBH using the ABC apparatus. CT scans were acquired twice at mDIBH in the same session for 30 breast cancer patients. Twenty-three of them were immobilized with an α-cradle, of which 14 had a repeat scan at mDIBH 1–4 weeks later. Twelve of those patients received intensity-modulated radiotherapy to the left breast at mDIBH to displace the heart from the beam. The remaining patients were treated at free breathing, with either intensity-modulated irradiation to the whole breast or conformal partial breast irradiation. To remove the component of setup error, mDIBH scans were registered with respect to the vertebrae. The lungs and carina were auto-contoured to form 3D surfaces for each data set. The closest distance-to-agreement (DTA) for each point between the 3D surfaces of the corresponding CT scans was displayed on a 3D surface map. For analysis, each lung was divided along its inferior to superior extent into six regions, from the basal 10%, the next four consecutive 20% sections in height, to the last apical 10%. Likewise, the carina was divided into regions of the trachea and bifurcation. The mean and standard deviation (SD) of the DTA for each of these regions was computed.: ResultsWith the patient positioned in an α-cradle, the mean ± SD intrafraction DTA was 1.5 ± 1.4 mm for the left lung and 1.0 ± 1.4 mm for the right lung. The corresponding values without the use of an α-cradle were significantly greater, with 1.9 ± 2.1 mm and 2.2 ± 2.2 mm for the left and right lung, respectively (p <0.005 for the SD of the left lung and p <0.0003 for the SD of the right lung). The interfraction DTA for the left and right lungs was 1.4 ± 1.7 mm and 1.4 ± 1.6 mm, respectively. The regional analysis demonstrated better immobilization for the upper two-thirds of the chest wall compared with that for the lung base. The DTA values obtained for the tracheal bifurcation were 0.9 ± 0.8 mm for intrafraction and 1.4 ± 1.0 mm for interfraction.: ConclusionThe ABC device can be used to reduce respiratory motion at mDIBH in breast cancer patients or those patients who can perform the maneuver. This device demonstrated excellent intra- and interfraction reproducibility of chest wall and carina immobilization, especially when combined with α-cradle immobilization. Internal margins for suspended breathing can be extrapolated from these data for various anatomic regions within the lung and chest wall. [Copyright &y& Elsevier]