Coronal plane segmental flexibility in thoracic adolescent idiopathic scoliosis assessed by fulcrum-bending radiographs

Knowledge about segmental flexibility in adolescent idiopathic scoliosis is crucial for a better biomechanical understanding, particularly for the development of fusionless, growth-guiding techniques. Currently, there is lack of data in this field. The objective of this study was, therefore, to compute segmental flexibility indices (standing angle minus corrected angle/standing angle). We compared segmental disc angles in 76 preoperative sets of standing and fulcrum-bending radiographs of thoracic curves (paired, two-tailed t tests, p < 0.05). The mean standing Cobb angle was 59.7 degrees (range 41.3 degrees -95 degrees ) and the flexibility index of the curve was 48.6\% (range 16.6-78.8\%). The disc angles showed symmetric periapical distribution with significant decrease (all p values <0.0001) for every cephalad (+) and caudad (-) level change. The periapical levels +1 and -1 wedged at 8.3 degrees and 8.7 degrees (range 3.5 degrees -14.8 degrees ), respectively. All angles were significantly smaller on the-bending views (p values <0.0001). We noted mean periapical flexibility indices of 46\% (+1), 49\% (-1), 57\% (+2) and 81\% (-2), which were significantly less (p < 0.001) than for the group of remote levels 105\% (+3), 149\% (-3), 231\% (+4) and 300\% (-4). The discal and bony wedging was 60 and 40\%, respectively, and mean values 35 degrees and 24 degrees (p < 0.0001). Their relationship with the Cobb angle showed a moderate correlation (r = 0.56 and 0.45). Functional, radiographic analysis of idiopathic thoracic scoliosis revealed significant, homogenous segmental tethering confined to four periapical levels. Future research will aim at in vivo segmental measurements in three planes under defined load to provide in-depth data for novel therapeutic strategies.

Uniqueness of minimisers for a Grötzsch-Belinskiĭ type inequality in the Heisenberg group

The modulus method introduced by H. Grötzsch yields bounds for a mean distortion functional of quasiconformal maps between two annuli mapping the respective boundary components onto each other. P. P. Belinskiĭ studied these inequalities in the plane and identified the family of all minimisers. Beyond the Euclidean framework, a Grötzsch-Belinskiĭ-type inequality has been previously considered for quasiconformal maps between annuli in the Heisenberg group whose boundaries are Korányi spheres. In this note we show that--in contrast to the planar situation--the minimiser in this setting is essentially unique.

Tectonic evolution of the Proterozoic Itremo Group metasediments in central Madagascar

The major geologic units of the Itremo region in central Madagascar include: (1) upper amphibolite to granulite facies (higher grade) Precambrian rocks, mainly para- and orthogneisses, and migmatites; (2) the newly defined Itremo Nappes, a fold-and-thrust belt containing the Proterozoic Itremo Group sediments, metamorphosed at greenschist to lower amphibolite facies (lower grade) conditions: (3) Middle Neoproterozoic and Late Neoproterozoic-Cambrian intrusives. The stratigraphic succession of the Itremo Group in the eastern part of the Itremo region is, from bottom to top: quartzites, metapelites, metacarbonates and metapelites overlain by metacarbonates. During D1 the Itremo Group sediments were detached from their continental substratum, deformed into a fold-and-thrust nappe (Itremo Nappes), and transported on top of higher grade rocks that are intruded by Middle Neoproterozoic (c. 797–780 Ma) granites and gabbros. A second phase of deformation shortening (D2) affected both the Itremo Sedimentary Nappes and structurally underlying higher-grade rocksunits, and formed large-scale N-S-trending F2 folds. S1 axial plane foliations in Itremo Group sediments are truncated by Late Neoproterozoic-Cambrian granites (c. 570–540 Ma). The age of the formation of the Itremo Nappes is not well constrained: they formed in Neoproterozoic times between 780 and 570 Ma.