Purpose To investigate the spatial correlation between high uptake regions of 2-deoxy-2-[18F]-fluoro-D-glucose positron emission tomography (18F-FDG PET) before and after therapy in recurrent lung cancer. Methods and Materials We enrolled 106 patients with inoperable lung cancer into a prospective study whose primary objectives were to determine first, the earliest time point when the maximum decrease in FDG uptake representing the maximum metabolic response (MMR) is attainable and second, the optimum cutoff value of MMR based on its predicted tumor control probability, sensitivity, and specificity. Of those patients, 61 completed the required 4 serial 18F-FDG PET examinations after therapy. Nineteen of 61 patients experienced local recurrence at the primary tumor and underwent analysis. The volumes of interest (VOI) on pretherapy FDG-PET were defined by use of an isocontour at ≥50% of maximum standard uptake value (SUVmax) (≥50% of SUVmax) with correction for heterogeneity. The VOI on posttherapy images were defined at ≥80% of SUVmax. The VOI of pretherapy and posttherapy 18F-FDG PET images were correlated for the extent of overlap. Results The size of VOI at pretherapy images was on average 25.7% (range, 8.8%-56.3%) of the pretherapy primary gross tumor volume (GTV), and their overlap fractions were 0.8 (95% confidence interval [CI]: 0.7-0.9), 0.63 (95% CI: 0.49-0.77), and 0.38 (95% CI: 0.19-0.57) of VOI of posttherapy FDG PET images at 10 days, 3 months, and 6 months, respectively. The residual uptake originated from the pretherapy VOI in 15 of 17 cases. Conclusions VOI defined by the SUVmax- ≥50% isocontour may be a biological target volume for escalated radiation dose.

Abstract. Minimal surfaces with planar curvature lines are classical geometric objects, having been studied since the late 19th century. In this paper, we revisit the subject from a different point of view. After calculating their metric functions using an analytical method, we recover the Weierstrass data, and give clean parametrizations for these surfaces. Then, using these parametrizations, we show that there exists a single continuous deformation between all minimal surfaces with planar curvature lines. In the process, we establish the existence of axial directions for these surfaces.

Minimal surfaces with planar curvature lines in the Euclidean space have been studied since the late 19th century. On the other hand, the classification of maximal surfaces with planar curvature lines in the Lorentz-Minkowski space has only recently been given. In this paper, we use an alternative method not only to refine the classification of maximal surfaces with planar curvature lines, but also to show that there exists a deformation consisting exactly of all such surfaces. Furthermore, we investigate the types of singularities that occur on maximal surfaces with planar curvature lines. Finally, by considering the conjugate of maximal surfaces with planar curvature lines, we obtain analogous results for maximal surfaces that are also affine minimal surfaces.• catenoid of second kind, with Weierstrass data 1−e z 1+e z , −1 − cosh z dz , or • one surface in the Bonnet family, with Weierstrass data {(e z + t, e −z dz), t > 0} up to isometries and homotheties of R 2,1 .

This report provides some statistical information based on clinical data gathered on low vision patients who attended the low vision clinic of the Hong Kong Society for the Blind in the first three years of its operation. In this period, low vision devices were prescribed for 393 patients (46.5 per cent of the sample). The most commonly prescribed aids were simple magnifiers and distance telescopes. Cataract was the major cause of low vision.