Let X; Y subset of R-2 be topologically equivalent bounded Lipschitz domains. We prove that weak and strong limits of homeomorphisms h: X (onto)-> Y in the Sobolev space W-1,W-p (X, R-2), p >= 2; are the same. As an application, we establish the existence of 2D-traction free minimal deformations for fairly general energy integrals.

Reproducibility of two different methods for quantifying fiber tracts by using a diffusion tensor imaging (DTI) sequence suitable for clinical magnetic resonance imaging (MRI) protocols was evaluated. DTI of 15 subjects was used to analyze intra-rater and inter-rater reproducibility. Another 10 subjects underwent MRI twice for assessment of between-scan reliability. Ten long association tracts were defined by fiber tracking using inclusion and exclusion regions of interest (ROIs). Whole-tract analysis and tractography-based core analysis were performed, and the effect of fractional anisotropy (FA 0.15/0.30) and turning angle threshold (27A degrees/60A degrees) on reproducibility was evaluated. Additionally, ROI measurements were performed in the core of the tracts. For the tract-based methods, intra-rater and inter-rater reliabilities of FA and mean diffusivity (MD) measurements were excellent. Between-scan reproducibility was good or excellent in 127 of 130 of the measurements. There was no systematic difference in the reproducibility of the FA, MD, and volume measurements depending on the FA or turning angle threshold. For the cross-sectional ROI measurements, reliability showed large variation from poor to excellent depending on the tract. Compared with the commonly used cross-sectional core ROI method, the tract-based analyses seem to be a more robust way to identify and measure white matter tracts of interest, and provide a novel reproducible tool to perform core analysis.