The 6-minute walk test and other endpoints in Duchenne muscular dystrophy: longitudinal natural history observations over 48 weeks from a multicenter study.

IntroductionDuchenne muscular dystrophy (DMD) subjects ≥5 years with nonsense mutations were followed for 48 weeks in a multicenter, randomized, double-blind, placebo-controlled trial of ataluren. Placebo arm data (N = 57) provided insight into the natural history of the 6-minute walk test (6MWT) and other endpoints.MethodsEvaluations performed every 6 weeks included the 6-minute walk distance (6MWD), timed function tests (TFTs), and quantitative strength using hand-held myometry.ResultsBaseline age (≥7 years), 6MWD, and selected TFT performance are strong predictors of decline in ambulation (Δ6MWD) and time to 10% worsening in 6MWD. A baseline 6MWD of <350 meters was associated with greater functional decline, and loss of ambulation was only seen in those with baseline 6MWD <325 meters. Only 1 of 42 (2.3%) subjects able to stand from supine lost ambulation.ConclusionFindings confirm the clinical meaningfulness of the 6MWD as the most accepted primary clinical endpoint in ambulatory DMD trials

Representations and classification of traveling wave solutions to Sinh-G{\"o}rdon equation

Two concepts named atom solution and combinatory solution are defined. The classification of all single traveling wave atom solutions to Sinh-G{\"o}rdon equation is obtained, and qualitative properties of solutions are discussed. In particular, we point out that some qualitative properties derived intuitively from dynamic system method aren't true. In final, we prove that our solutions to Sinh-G{\"o}rdon equation include all solutions obtained in the paper[Fu Z T et al, Commu. in Theor. Phys.(Beijing) 2006 45 55]. Through an example, we show how to give some new identities on Jacobian elliptic functions.Comment: 12 pages. accepted by Communications in theoretical physics (Beijing

A compactness theorem for complete Ricci shrinkers

We prove precompactness in an orbifold Cheeger-Gromov sense of complete gradient Ricci shrinkers with a lower bound on their entropy and a local integral Riemann bound. We do not need any pointwise curvature assumptions, volume or diameter bounds. In dimension four, under a technical assumption, we can replace the local integral Riemann bound by an upper bound for the Euler characteristic. The proof relies on a Gauss-Bonnet with cutoff argument.Comment: 28 pages, final version, to appear in GAF

Dirichlet sigma models and mean curvature flow

The mean curvature flow describes the parabolic deformation of embedded branes in Riemannian geometry driven by their extrinsic mean curvature vector, which is typically associated to surface tension forces. It is the gradient flow of the area functional, and, as such, it is naturally identified with the boundary renormalization group equation of Dirichlet sigma models away from conformality, to lowest order in perturbation theory. D-branes appear as fixed points of this flow having conformally invariant boundary conditions. Simple running solutions include the paper-clip and the hair-pin (or grim-reaper) models on the plane, as well as scaling solutions associated to rational (p, q) closed curves and the decay of two intersecting lines. Stability analysis is performed in several cases while searching for transitions among different brane configurations. The combination of Ricci with the mean curvature flow is examined in detail together with several explicit examples of deforming curves on curved backgrounds. Some general aspects of the mean curvature flow in higher dimensional ambient spaces are also discussed and obtain consistent truncations to lower dimensional systems. Selected physical applications are mentioned in the text, including tachyon condensation in open string theory and the resistive diffusion of force-free fields in magneto-hydrodynamics.Comment: 77 pages, 21 figure

Living with muscular dystrophy: health related quality of life consequences for children and adults

<p>Abstract</p> <p>Background</p> <p>Muscular dystrophies are chronic diseases manifesting with progressive muscle weakness leading to decreasing activities and participation. To understand the impact on daily life, it is important to determine patients' quality of life.</p> <p>Objective</p> <p>To investigate Health Related Quality of Life (HRQoL) of children and adults with muscular dystrophy (MD), and to study the influence of type and severity of MD on HRQoL in adult patients.</p> <p>Methods</p> <p>Age-related HRQoL questionnaires were administered to 40 children (8–17 years), and 67 adult patients with muscular dystrophies.</p> <p>Results</p> <p>Significant differences in HRQoL were found in children and adults with MD compared to healthy controls. Patients with Becker muscular dystrophy reported a better HRQoL on the several scales compared to patients with other MDs. Severity was associated with worse fine motor functioning and social functioning in adult patients.</p> <p>Conclusion</p> <p>This is one of the first studies describing HRQoL of patients with MD using validated instruments in different age groups. The results indicate that having MD negatively influences the HRQoL on several domains.</p

Helicoidal surfaces rotating/translating under the mean curvature flow

We describe all possible self-similar motions of immersed hypersurfaces in Euclidean space under the mean curvature flow and derive the corresponding hypersurface equations. Then we present a new two-parameter family of immersed helicoidal surfaces that rotate/translate with constant velocity under the flow. We look at their limiting behaviour as the pitch of the helicoidal motion goes to 0 and compare it with the limiting behaviour of the classical helicoidal minimal surfaces. Finally, we give a classification of the immersed cylinders in the family of constant mean curvature helicoidal surfaces.Comment: 21 pages, 22 figures, final versio

The Abresch-Gromoll inequality in a non-smooth setting

We prove that the Abresch-Gromoll inequality holds on infinitesimally Hilbertian CD(K,N) spaces in the same form as the one available on smooth Riemannian manifolds

Critical behavior of collapsing surfaces

We consider the mean curvature evolution of rotationally symmetric surfaces. Using numerical methods, we detect critical behavior at the threshold of singularity formation resembling the one of gravitational collapse. In particular, the mean curvature simulation of a one-parameter family of initial data reveals the existence of a critical initial surface that develops a degenerate neckpinch. The limiting flow of the Type II singularity is accurately modeled by the rotationally symmetric translating soliton.Comment: 23 pages, 10 figure

Discrete conformal maps: boundary value problems, circle domains, Fuchsian and Schottky uniformization

We discuss several extensions and applications of the theory of discretely conformally equivalent triangle meshes (two meshes are considered conformally equivalent if corresponding edge lengths are related by scale factors attached to the vertices). We extend the fundamental definitions and variational principles from triangulations to polyhedral surfaces with cyclic faces. The case of quadrilateral meshes is equivalent to the cross ratio system, which provides a link to the theory of integrable systems. The extension to cyclic polygons also brings discrete conformal maps to circle domains within the scope of the theory. We provide results of numerical experiments suggesting that discrete conformal maps converge to smooth conformal maps, with convergence rates depending on the mesh quality. We consider the Fuchsian uniformization of Riemann surfaces represented in different forms: as immersed surfaces in \mathbb {R}^{3}, as hyperelliptic curves, and as \mathbb {CP}^{1} modulo a classical Schottky group, i.e., we convert Schottky to Fuchsian uniformization. Extended examples also demonstrate a geometric characterization of hyperelliptic surfaces due to Schmutz Schaller

Health status in non-dystrophic myotonias: close relation with pain and fatigue

To determine self-reported health status in non-dystrophic myotonias (NDM) and its relationship to painful myotonia and fatigue. In a cross-sectional study, 32 NDM patients with chloride and 30 with sodium channelopathies, all off treatment, completed a standardised interview, the fatigue assessment scale (FAS), and the 36-item Short-Form Health Survey (SF-36). Beside formal assessment of pain, assessment of painful or painless myotonia was determined. The domain scores of the SF-36 were compared with Dutch community scores. Apart from the relationship among SF-36 scores and (1) painful myotonia and (2) fatigue, regression analyses in both NDM groups were conducted to determine the strongest determinants of the SF-36 domains general health perception, physical component (PCS) and mental component summary (MCS). All physically oriented SF-36 domains in both NDM groups (P ≤ 0.01) and social functioning in the patients with sodium channelopathies (P = 0.048) were substantially lower relative to the Dutch community scores. The patients with painful myotonia (41.9%) scored substantially (P < 0.05) lower on most SF-36 domains than the patients without painful myotonia (58.1%). Fatigued patients (53.2%) scored substantially lower (P ≤ 0.01) on all SF-36 domains than their non-fatigued counterparts (46.8%). The regression analysis showed that fatigue was the strongest predictor for the general-health perception and painful myotonia for the physical-component summary. None of the patients showed below-norm scores on the domain mental-component summary. The impact of NDM on the physical domains of patients’ health status is substantial, and particularly painful myotonia and fatigue tend to impede their physical functioning