Three-dimensional kinematic analysis of upper and lower limb motion during gait of post-stroke patients

The aim of this study was to analyze the alterations of arm and leg movements of patients during stroke gait. Joint angles of upper and lower limbs and spatiotemporal variables were evaluated in two groups: hemiparetic group (HG, 14 hemiparetic men, 53 ± 10 years) and control group (CG, 7 able-bodied men, 50 ± 4 years). The statistical analysis was based on the following comparisons (P ≤ 0.05): 1) right versus left sides of CG; 2) affected (AF) versus unaffected (UF) sides of HG; 3) CG versus both the affected and unaffected sides of HG, and 4) an intracycle comparison of the kinematic continuous angular variables between HG and CG. This study showed that the affected upper limb motion in stroke gait was characterized by a decreased range of motion of the glenohumeral (HG: 6.3 ± 4.5, CG: 20.1 ± 8.2) and elbow joints (AF: 8.4 ± 4.4, UF: 15.6 ± 7.6) on the sagittal plane and elbow joint flexion throughout the cycle (AF: 68.2 ± 0.4, CG: 46.8 ± 2.7). The glenohumeral joint presented a higher abduction angle (AF: 14.2 ± 1.6, CG: 11.5 ± 4.0) and a lower external rotation throughout the cycle (AF: 4.6 ± 1.2, CG: 22.0 ± 3.0). The lower limbs showed typical alterations of the stroke gait patterns. Thus, the changes in upper and lower limb motion of stroke gait were identified. The description of upper limb motion in stroke gait is new and complements gait analysis.53754

Infinitesimal and local convexity of a hypersurface in a semi-Riemannian manifold

Given a Riemannian manifold M and a hypersurface H in M, it is well known that infinitesimal convexity on a neighborhood of a point in H implies local convexity. We show in this note that the same result holds in a semi-Riemannian manifold. We make some remarks for the case when only timelike, null or spacelike geodesics are involved. The notion of geometric convexity is also reviewed and some applications to geodesic connectedness of an open subset of a Lorentzian manifold are given.Comment: 14 pages, AMSLaTex, 2 figures. v2: typos fixed, added one reference and several comments, statement of last proposition correcte

Convex domains of Finsler and Riemannian manifolds

A detailed study of the notions of convexity for a hypersurface in a Finsler manifold is carried out. In particular, the infinitesimal and local notions of convexity are shown to be equivalent. Our approach differs from Bishop's one in his classical result (Bishop, Indiana Univ Math J 24:169-172, 1974) for the Riemannian case. Ours not only can be extended to the Finsler setting but it also reduces the typical requirements of differentiability for the metric and it yields consequences on the multiplicity of connecting geodesics in the convex domain defined by the hypersurface.Comment: 22 pages, AMSLaTex. Typos corrected, references update

Rotational Surfaces in L3\mathbb{L}^3 and Solutions in the Nonlinear Sigma Model

The Gauss map of non-degenerate surfaces in the three-dimensional Minkowski space are viewed as dynamical fields of the two-dimensional O(2,1) Nonlinear Sigma Model. In this setting, the moduli space of solutions with rotational symmetry is completely determined. Essentially, the solutions are warped products of orbits of the 1-dimensional groups of isometries and elastic curves in either a de Sitter plane, a hyperbolic plane or an anti de Sitter plane. The main tools are the equivalence of the two-dimensional O(2,1) Nonlinear Sigma Model and the Willmore problem, and the description of the surfaces with rotational symmetry. A complete classification of such surfaces is obtained in this paper. Indeed, a huge new family of Lorentzian rotational surfaces with a space-like axis is presented. The description of this new class of surfaces is based on a technique of surgery and a gluing process, which is illustrated by an algorithm.Comment: PACS: 11.10.Lm; 11.10.Ef; 11.15.-q; 11.30.-j; 02.30.-f; 02.40.-k. 45 pages, 11 figure