Direct-current-dependent shift of theta-burst-induced plasticity in the human motor cortex

Animal studies using polarising currents have shown that induction of synaptic long-term potentiation (LTP) and long-term depression (LTD) by bursts of patterned stimulation is affected by the membrane potential of the postsynaptic neurone. The aim of the present experiments was to test whether it is possible to observe similar phenomena in humans with the aim of improving present protocols of inducing synaptic plasticity for therapeutic purposes. We tested whether the LTP/LTD-like after effects of transcranial theta-burst stimulation (TBS) of human motor cortex, an analogue of patterned electrical stimulation in animals, were affected by simultaneous transcranial direct-current stimulation (tDCS), a non-invasive method of polarising cortical neurones in humans. Nine healthy volunteers were investigated in a single-blind, balanced cross-over study; continuous TBS (cTBS) was used to introduce LTD-like after effects, whereas intermittent TBS (iTBS) produced LTP-like effects. Each pattern was coupled with concurrent application of tDCS (<200 s, anodal, cathodal, sham). Cathodal tDCS increased the response to iTBS and abolished the effects of cTBS. Anodal tDCS changed the effects of cTBS towards facilitation, but had no impact on iTBS. Cortical motor thresholds and intracortical inhibitory/facilitatory networks were not altered by any of the stimulation protocols. We conclude that the after effects of TBS can be modulated by concurrent tDCS. We hypothesise that tDCS changes the membrane potential of the apical dendrites of cortical pyramidal neurones and that this changes the response to patterned synaptic input evoked by TBS. The data show that it may be possible to enhance LTP-like plasticity after TBS in the human cortex

Doubly connected minimal surfaces and extremal harmonic mappings

The concept of a conformal deformation has two natural extensions: quasiconformal and harmonic mappings. Both classes do not preserve the conformal type of the domain, however they cannot change it in an arbitrary way. Doubly connected domains are where one first observes nontrivial conformal invariants. Herbert Groetzsch and Johannes C. C. Nitsche addressed this issue for quasiconformal and harmonic mappings, respectively. Combining these concepts we obtain sharp estimates for quasiconformal harmonic mappings between doubly connected domains. We then apply our results to the Cauchy problem for minimal surfaces, also known as the Bjorling problem. Specifically, we obtain a sharp estimate of the modulus of a doubly connected minimal surface that evolves from its inner boundary with a given initial slope.Comment: 35 pages, 2 figures. Minor edits, references adde

Spheres and Prolate and Oblate Ellipsoids from an Analytical Solution of Spontaneous Curvature Fluid Membrane Model

An analytic solution for Helfrich spontaneous curvature membrane model (H. Naito, M.Okuda and Ou-Yang Zhong-Can, Phys. Rev. E {\bf 48}, 2304 (1993); {\bf 54}, 2816 (1996)), which has a conspicuous feature of representing the circular biconcave shape, is studied. Results show that the solution in fact describes a family of shapes, which can be classified as: i) the flat plane (trivial case), ii) the sphere, iii) the prolate ellipsoid, iv) the capped cylinder, v) the oblate ellipsoid, vi) the circular biconcave shape, vii) the self-intersecting inverted circular biconcave shape, and viii) the self-intersecting nodoidlike cylinder. Among the closed shapes (ii)-(vii), a circular biconcave shape is the one with the minimum of local curvature energy.Comment: 11 pages, 11 figures. Phys. Rev. E (to appear in Sept. 1999

Wetting and Minimal Surfaces

We study minimal surfaces which arise in wetting and capillarity phenomena. Using conformal coordinates, we reduce the problem to a set of coupled boundary equations for the contact line of the fluid surface, and then derive simple diagrammatic rules to calculate the non-linear corrections to the Joanny-de Gennes energy. We argue that perturbation theory is quasi-local, i.e. that all geometric length scales of the fluid container decouple from the short-wavelength deformations of the contact line. This is illustrated by a calculation of the linearized interaction between contact lines on two opposite parallel walls. We present a simple algorithm to compute the minimal surface and its energy based on these ideas. We also point out the intriguing singularities that arise in the Legendre transformation from the pure Dirichlet to the mixed Dirichlet-Neumann problem.Comment: 22 page

Induction of cortical plasticity and improved motor performance following unilateral and bilateral transcranial direct current stimulation of the primary motor cortex

BACKGROUND: Transcranial direct current stimulation (tDCS) is a non-invasive technique that modulates the excitability of neurons within the primary motor cortex (M1). Research shows that anodal-tDCS applied over the non-dominant M1 (i.e. unilateral stimulation) improves motor function of the non-dominant hand. Similarly, previous studies also show that applying cathodal tDCS over the dominant M1 improves motor function of the non-dominant hand, presumably by reducing interhemispheric inhibition. In the present study, one condition involved anodal-tDCS over the non-dominant M1 (unilateral stimulation) whilst a second condition involved applying cathodal-tDCS over the dominant M1 and anodal-tDCS over non-dominant M1 (bilateral stimulation) to determine if unilateral or bilateral stimulation differentially modulates motor function of the non-dominant hand. Using a randomized, cross-over design, 11 right-handed participants underwent three stimulation conditions: 1) unilateral stimulation, that involved anodal-tDCS applied over the non-dominant M1, 2) bilateral stimulation, whereby anodal-tDCS was applied over the non-dominant M1, and cathodal-tDCS over the dominant M1, and 3) sham stimulation. Transcranial magnetic stimulation (TMS) was performed before, immediately after, 30 and 60 minutes after stimulation to elucidate the neural mechanisms underlying any potential after-effects on motor performance. Motor function was evaluated by the Purdue pegboard test. RESULTS: There were significant improvements in motor function following unilateral and bilateral stimulation when compared to sham stimulation at all-time points (all P 0.05). Furthermore, changes in corticomotor plasticity were not related to changes in motor performance. CONCLUSION: These results indicate that tDCS induced behavioural changes in the non-dominant hand as a consequence of mechanisms associated with use-dependant cortical plasticity that is independent of the electrode arrangement

Transcranial direct current stimulation of right dorsolateral prefrontal cortex does not affect model-based or model-free reinforcement learning in humans

There is broad consensus that the prefrontal cortex supports goal-directed, model-based decision-making. Consistent with this, we have recently shown that model-based control can be impaired through transcranial magnetic stimulation of right dorsolateral prefrontal cortex in humans. We hypothesized that an enhancement of model-based control might be achieved by anodal transcranial direct current stimulation of the same region. We tested 22 healthy adult human participants in a within-subject, double-blind design in which participants were given Active or Sham stimulation over two sessions. We show Active stimulation had no effect on model-based control or on model-free ('habitual') control compared to Sham stimulation. These null effects are substantiated by a power analysis, which suggests that our study had at least 60% power to detect a true effect, and by a Bayesian model comparison, which favors a model of the data that assumes stimulation had no effect over models that assume stimulation had an effect on behavioral control. Although we cannot entirely exclude more trivial explanations for our null effect, for example related to (faults in) our experimental setup, these data suggest that anodal transcranial direct current stimulation over right dorsolateral prefrontal cortex does not improve model-based control, despite existing evidence that transcranial magnetic stimulation can disrupt such control in the same brain region

Topology and Signature Changes in Braneworlds

It has been believed that topology and signature change of the universe can only happen accompanied by singularities, in classical, or instantons, in quantum, gravity. In this note, we point out however that in the braneworld context, such an event can be understood as a classical, smooth event. We supply some explicit examples of such cases, starting from the Dirac-Born-Infeld action. Topology change of the brane universe can be realised by allowing self-intersecting branes. Signature change in a braneworld is made possible in an everywhere Lorentzian bulk spacetime. In our examples, the boundary of the signature change is a curvature singularity from the brane point of view, but nevertheless that event can be described in a completely smooth manner from the bulk point of view.Comment: 26 pages, 8 figures, references and comments are added, minor revisions and a number of additional footnotes added, error corrected, minor corrections, to appear in Class. Quant. Gra

Plasticity induced by non-invasive transcranial brain stimulation: A position paper

Several techniques and protocols of non-invasive transcranial brain stimulation (NIBS), including transcranial magnetic and electrical stimuli, have been developed in the past decades. Non-invasive transcranial brain stimulation may modulate cortical excitability outlasting the period of non-invasive transcranial brain stimulation itself from several minutes to more than one hour. Quite a few lines of evidence, including pharmacological, physiological and behavioral studies in humans and animals, suggest that the effects of non-invasive transcranial brain stimulation are produced through effects on synaptic plasticity. However, there is still a need for more direct and conclusive evidence. The fragility and variability of the effects are the major challenges that non-invasive transcranial brain stimulation currently faces. A variety of factors, including biological variation, measurement reproducibility and the neuronal state of the stimulated area, which can be affected by factors such as past and present physical activity, may influence the response to non-invasive transcranial brain stimulation. Work is ongoing to test whether the reliability and consistency of non-invasive transcranial brain stimulation can be improved by controlling or monitoring neuronal state and by optimizing the protocol and timing of stimulation