Modulus method and radial stretch map in the Heisenberg group

We develop a modulus method for surface families inside a domain in the Heisenberg group and we prove that the stretch map between two Heisenberg spherical rings is a minimiser for the mean distortion among the class of contact quasiconformal maps between these rings which satisfy certain boundary conditions.

Ligament origins are preserved in distal radial intraarticular two-part fractures: a computed tomography-based study

Background Operative fixation of intraarticular distal radius fractures is increasingly common. A greater understanding of fracture patterns will aid surgical fixation strategy. Previous studies have suggested that ligamentous insertions may less commonly be involved, but these have included heterogeneous groups of fractures and have not addressed Lister's tubercle. Purpose We hypothesize that fracture lines of distal radial intraarticular 2-part fractures have reproducible patterns. They propagate through the cortical bone between ligament origins and do not involve Lister's tubercle. Methods Axial CT scans of two-part intraarticular distal radius fractures were assessed independently by two examiners. The fractures were mapped onto a grid and the cortical breaches expressed as a percentile of the total radial width or length. The cortical breaches were compared with the ligamentous insertions on the distal and Lister's tubercle. Associated injuries were also documented. Results The cortical breaches occurred between the ligamentous insertions in 85%. Lister's tubercle was not involved in 95% of the fractures. Three major fracture patterns emerged: radial styloid, dorsal, and volar. Each major pattern had two subtypes. Associated injuries were common. Scapholunate dissociation was associated with all types, not just the radial styloid fracture pattern. Conclusions The fracture patterns of two-part intraarticular fractures mostly involved the interligamentous zones. Three major groups were identified: dorsal, volar, and radial styloid. Lister's tubercle was preserved with fractures tending to propagate radial or ulnar to this structure. We suggest conceptualizing fracture fragments as osseo-ligamentous units to aid prediction of fracture patterns and associated injury. Study Design Diagnostic III Level of Evidence 3.

Intra-annual dynamics of non-structural carbohydrates in the cambium of mature conifer trees reflects radial growth demands

The presence of soluble carbohydrates in the cambial zone, either from sugars recently produced during photosynthesis or from starch remobilized from storage organs, is necessary for radial tree growth. However, considerable uncertainties on carbohydrate dynamics and the consequences on tree productivity exist. This study aims to better understand the variation in different carbon pools at intra-annual resolution by quantifying how cambial zone sugar and starch concentrations fluctuate over the season and in relation to cambial phenology. A comparison between two physiologically different species growing at the same site, i.e., the evergreen Picea abies Karst. and the deciduous Larix decidua Mill., and between L. decidua from two contrasting elevations, is presented to identify mechanisms of growth limitation. Results indicate that the annual cycle of sugar concentration within the cambial zone is coupled to the process of wood formation. The highest sugar concentration is observed when the number of cells in secondary wall formation and lignification stages is at a maximum, subsequent to most radial growth. Starch disappears in winter, while other freeze-resistant non-structural carbohydrates (NSCs) increase. Slight differences in NSC concentration between species are consistent with the differing climate sensitivity of the evergreen and deciduous species investigated. The general absence of differences between elevations suggests that the cambial activity of trees growing at the treeline was not limited by the availability of carbohydrates at the cambial zone but instead by environmental controls on the growing season duration.