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

The Clifford torus as a self-shrinker for the Lagrangian mean curvature flow

We provide several rigidity results for the Clifford torus in the class of compact self-shrinkers for Lagrangian mean curvature flow.Comment: 10 page

Manifolds with 1/4-pinched flag curvature

We say that a nonnegatively curved manifold $(M,g)$ has quarter pinched flag curvature if for any two planes which intersect in a line the ratio of their sectional curvature is bounded above by 4. We show that these manifolds have nonnegative complex sectional curvature. By combining with a theorem of Brendle and Schoen it follows that any positively curved manifold with strictly quarter pinched flag curvature must be a space form. This in turn generalizes a result of Andrews and Nguyen in dimension 4. For odd dimensional manifolds we obtain results for the case that the flag curvature is pinched with some constant below one quarter, one of which generalizes a recent work of Petersen and Tao

Reachable workspace and performance of upper limb (PUL) in duchenne muscular dystrophy

IntroductionThe Kinect-based reachable workspace relative surface area (RSA) is compared with the performance of upper limb (PUL) assessment in Duchenne muscular dystrophy (DMD).Methods29 individuals with DMD (ages: 7-23; Brooke: 1-5) underwent both Kinect-based reachable workspace RSA and PUL assessments. RSAs were also collected from 24 age-matched controls. Total and quadrant RSAs were compared with the PUL total, shoulder-, middle-, and distal-dimension scores.ResultsThe total reachable workspace RSA correlated well with the total PUL score (Spearman ρ = -0.602; P < 0.001), and with each of the PUL dimensional scores: shoulder (ρ = -0.624; P < 0.001), middle (ρ = -0.564; P = 0.001), and distal (ρ = -0.630; P < 0.001). With quadrant RSA, reachability in a particular quadrant was closely associated with respective PUL dimensional-level function (lateral-upper quadrant for shoulder-, lateral-upper/lower quadrants for middle-, and lateral-lower quadrant for distal-level function).ConclusionsThis study demonstrates concurrent validity of the reachable workspace outcome measure (RSA) with the DMD-specific upper extremity outcome measure (PUL)

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

Parabolic stable surfaces with constant mean curvature

We prove that if u is a bounded smooth function in the kernel of a nonnegative Schrodinger operator $-L=-(\Delta +q)$ on a parabolic Riemannian manifold M, then u is either identically zero or it has no zeros on M, and the linear space of such functions is 1-dimensional. We obtain consequences for orientable, complete stable surfaces with constant mean curvature $H\in\mathbb{R}$ in homogeneous spaces $\mathbb{E}(\kappa,\tau)$ with four dimensional isometry group. For instance, if M is an orientable, parabolic, complete immersed surface with constant mean curvature H in $\mathbb{H}^2\times\mathbb{R}$, then $|H|\leq 1/2$ and if equality holds, then M is either an entire graph or a vertical horocylinder.Comment: 15 pages, 1 figure. Minor changes have been incorporated (exchange finite capacity by parabolicity, and simplify the proof of Theorem 1)

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

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