Facilitating return to work through early specialist health-based interventions (FRESH): protocol for a feasibility randomised controlled trial

Background Over one million people sustain traumatic brain injury each year in the UK and more than 10 % of these are moderate or severe injuries, resulting in cognitive and psychological problems that affect the ability to work. Returning to work is a primary rehabilitation goal but fewer than half of traumatic brain injury survivors achieve this. Work is a recognised health service outcome, yet UK service provision varies widely and there is little robust evidence to inform rehabilitation practice. A single-centre cohort comparison suggested better work outcomes may be achieved through early occupational therapy targeted at job retention. This study aims to determine whether this intervention can be delivered in three new trauma centres and to conduct a feasibility, randomised controlled trial to determine whether its effects and cost effectiveness can be measured to inform a definitive trial. Methods/design Mixed methods study, including feasibility randomised controlled trial, embedded qualitative studies and feasibility economic evaluation will recruit 102 people with traumatic brain injury and their nominated carers from three English UK National Health Service (NHS) trauma centres. Participants will be randomised to receive either usual NHS rehabilitation or usual rehabilitation plus early specialist traumatic brain injury vocational rehabilitation delivered by an occupational therapist. The primary objective is to assess the feasibility of conducting a definitive trial; secondary objectives include measurement of protocol integrity (inclusion/exclusion criteria, intervention adherence, reasons for non-adherence) recruitment rate, the proportion of eligible patients recruited, reasons for non-recruitment, spectrum of TBI severity, proportion of and reasons for loss to follow-up, completeness of data collection, gains in face-to-face Vs postal data collection and the most appropriate methods of measuring primary outcomes (return to work, retention) to determine the sample size for a larger trial. Discussion To our knowledge, this is the first feasibility randomised controlled trial of a vocational rehabilitation health intervention specific to traumatic brain injury. The results will inform the design of a definitive trial

Fenchel equalities and bilinear minmax equalities

Chief objects here are pairs $(X,F)$ of convex subsets in a Hilbert space, satisfying the bilinear minmax equality 26737 \inf_{x\in X}\sup_{y\in F} \langle x,y\rangle=\sup_{y\in F}\inf_{x\in X} \langle x,y\rangle. 26737 Specializing $F$ to be an affine closed subspace we recover and restate crucial concepts of convex duality, revolving around Fenchel equalities, biconjugation, and inf-convolution. The resulting perspective reinforces the strong links between minmax, set-theoretic, and functional aspects of convex analysis

Fenchel equalities and bilinear minmax equalities

Chief objects here are pairs $(X,F)$ of convex subsets in a Hilbert space, satisfying the bilinear minmax equality 26737 \inf_{x\in X}\sup_{y\in F} \langle x,y\rangle=\sup_{y\in F}\inf_{x\in X} \langle x,y\rangle. 26737 Specializing $F$ to be an affine closed subspace we recover and restate crucial concepts of convex duality, revolving around Fenchel equalities, biconjugation, and inf-convolution. The resulting perspective reinforces the strong links between minmax, set-theoretic, and functional aspects of convex analysis

K+ Conduction and Mg2+ Blockade in a Shaker Kv-Channel Single Point Mutant with an Unusually High Conductance

Vergara-Jaque, A (Vergara-Jaque, Ariela). Univ Talca, Ctr Bioinformat & Simulac Mol, Talca, ChilePotassium channels exhibit a large diversity of single-channel conductances. Shaker is a low-conductance K-channel in which Pro475 -> Asp, a single-point mutation near the internal pore entrance, promotes 6- to 8-fold higher unitary current. To assess the mechanism for this higher conductance, we measured Shaker-P475D single-channel current in a wide range of symmetrical K+ concentrations and voltages. Below 300 mM K+, the current-to-voltage relations (i-V) showed inward rectification that disappeared at 1000 mM K+. Single-channel conductance reached a maximum of similar to 190 pS at saturating [K+], a value 4- to 5-fold larger than that estimated for the native channel. Intracellular Mg2+ blocked this variant with similar to 100-fold higher affinity. Near zero voltage, blockade was competitively antagonized by K+; however, at voltages >100 mV, it was enhanced by K+. This result is consistent with a lock-in effect in a single-file diffusion regime of Mg2+ and K+ along the pore. Molecular-dynamics simulations revealed higher K+ density in the pore, especially near the Asp-475 side chains, as in the high-conductance MthK bacterial channel. The molecular dynamics also showed that K+ ions bound distally can coexist with other K+ or Mg2+ in the cavity, supporting a lock-in mechanism. The maximal K+ transport rate and higher occupancy could be due to a decrease in the electrostatic energy profile for K+ throughout the pore, reducing the energy wells and barriers differentially by similar to 0.7 and similar to 2 kT, respectively