Nitric oxide suppresses cerebral vasomotion by sGC-independent effects on ryanodine receptors and voltage-gated calcium channels

Background/Aims: In cerebral arteries, nitric oxide (NO) release plays a key role in suppressing vasomotion. Our aim was to establish the pathways affected by NO in rat middle cerebral arteries. Methods: In isolated segments of artery, isometric tension and simultaneous measurements of either smooth muscle membrane potential or intracellular [Ca 2+ ] ([Ca 2+ ] SMC ) changes were recorded. Results: In the absence of L -NAME, asynchronous propagating Ca 2+ waves were recorded that were sensitive to block with ryanodine, but not nifedipine. L -NAME stimulated pronounced vasomotion and synchronous Ca 2+ oscillations with close temporal coupling between membrane potential, tone and [Ca 2+ ] SMC . If nifedipine was applied together with L -NAME, [Ca 2+ ] SMC decreased and synchronous Ca 2+ oscillations were lost, but asynchronous propagating Ca 2+ waves persisted. Vasomotion was similarly evoked by either iberiotoxin, or by ryanodine, and to a lesser extent by ODQ. Exogenous application of NONOate stimulated endothelium-independent hyperpolarization and relaxation of either L -NAME-induced or spontaneous arterial tone. NO-evoked hyperpolarization involved activation of BK Ca channels via ryanodine receptors (RYRs), with little involvement of sGC. Further, in whole cell mode, NO inhibited current through L-type voltage-gated Ca 2+ channels (VGCC), which was independent of both voltage and sGC. Conclusion: NO exerts sGC-independent actions at RYRs and at VGCC, both of which normally suppress cerebral artery myogenic tone.

Evidence both L-type and non-L-type voltage-dependent calcium channels contribute to cerebral artery vasospasm following loss of NO in the rat

We recently found block of NO synthase in rat middle cerebral artery caused spasm, associated with depolarizing oscillations in membrane potential (Em) similar in form but faster in frequency (circa 1 Hz) to vasomotion. T-type voltage-gated Ca2+ channels contribute to cerebral myogenic tone and vasomotion, so we investigated the significance of T-type and other ion channels for membrane potential oscillations underlying arterial spasm. Smooth muscle cell membrane potential (Em) and tension were measured simultaneously in rat middle cerebral artery. NO synthase blockade caused temporally coupled depolarizing oscillations in cerebrovascular Em with associated vasoconstriction. Both events were accentuated by block of smooth muscle BKCa. Block of T-type channels or inhibition of Na+/K+-ATPase abolished the oscillations in Em and reduced vasoconstriction. Oscillations in Em were either attenuated or accentuated by reducing [Ca2+]o or block of KV, respectively. TRAM-34 attenuated oscillations in both Em and tone, apparently independent of effects against KCa3.1. Thus, rapid depolarizing oscillations in Em and tone observed after endothelial function has been disrupted reflect input from T-type calcium channels in addition to L-type channels, while other depolarizing currents appear to be unimportant. These data suggest that combined block of T and L-type channels may represent an effective approach to reverse cerebral vasospasm.

Equivalence of weak formulations of the steady water waves equations

We prove the equivalence of three weak formulations of the steady water waves equations, namely: the velocity formulation, the stream function formulation and the Dubreil-Jacotin formulation, under weak Hölder regularity assumptions on their solutions.

Bistable systems with stochastic noise: virtues and limits of effective one-dimensional Langevin equations

The understanding of the statistical properties and of the dynamics of multistable systems is gaining more and more importance in a vast variety of scientific fields. This is especially relevant for the investigation of the tipping points of complex systems. Sometimes, in order to understand the time series of given observables exhibiting bimodal distributions, simple one-dimensional Langevin models are fitted to reproduce the observed statistical properties, and used to investing-ate the projected dynamics of the observable. This is of great relevance for studying potential catastrophic changes in the properties of the underlying system or resonant behaviours like those related to stochastic resonance-like mechanisms. In this paper, we propose a framework for encasing this kind of studies, using simple box models of the oceanic circulation and choosing as observable the strength of the thermohaline circulation. We study the statistical properties of the transitions between the two modes of operation of the thermohaline circulation under symmetric boundary forcings and test their agreement with simplified one-dimensional phenomenological theories. We extend our analysis to include stochastic resonance-like amplification processes. We conclude that fitted one-dimensional Langevin models, when closely scrutinised, may result to be more ad-hoc than they seem, lacking robustness and/or well-posedness. They should be treated with care, more as an empiric descriptive tool than as methodology with predictive power.

On the Convergence of Two-Stage Iterative Processes for Solving Linear Equations

This paper considers two-stage iterative processes for solving the linear system $Af = b$. The outer iteration is defined by $Mf^{k + 1} = Nf^k + b$, where $M$ is a nonsingular matrix such that $M - N = A$. At each stage $f^{k + 1} $ is computed approximately using an inner iteration process to solve $Mv = Nf^k + b$ for $v$. At the $k$th outer iteration, $p_k $ inner iterations are performed. It is shown that this procedure converges if $p_k \geqq P$ for some $P$ provided that the inner iteration is convergent and that the outer process would converge if $f^{k + 1} $ were determined exactly at every step. Convergence is also proved under more specialized conditions, and for the procedure where $p_k = p$ for all $k$, an estimate for $p$ is obtained which optimizes the convergence rate. Examples are given for systems arising from the numerical solution of elliptic partial differential equations and numerical results are presented.

Stability results for the time-harmonic Maxwell equations with impedance boundary conditions

We consider the time-harmonic Maxwell equations with constant coefficients in a bounded, uniformly star-shaped polyhedron. We prove wavenumber-explicit norm bounds for weak solutions. This result is pivotal for convergence proofs in numerical analysis and may be a tool in the analysis of electromagnetic boundary integral operators.

Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations

In this paper, we extend to the time-harmonic Maxwell equations the p-version analysis technique developed in [R. Hiptmair, A. Moiola and I. Perugia, Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the p-version, SIAM J. Numer. Anal., 49 (2011), 264-284] for Trefftz-discontinuous Galerkin approximations of the Helmholtz problem. While error estimates in a mesh-skeleton norm are derived parallel to the Helmholtz case, the derivation of estimates in a mesh-independent norm requires new twists in the duality argument. The particular case where the local Trefftz approximation spaces are built of vector-valued plane wave functions is considered, and convergence rates are derived.

Comment on “A modified leapfrog scheme for shallow water equations” by Wen-Yih Sun and Oliver M.T. Sun

A recent paper published in this journal considers the numerical integration of the shallow-water equations using the leapfrog time-stepping scheme [Sun Wen-Yih, Sun Oliver MT. A modified leapfrog scheme for shallow water equations. Comput Fluids 2011;52:69–72]. The authors of that paper propose using the time-averaged height in the numerical calculation of the pressure-gradient force, instead of the instantaneous height at the middle time step. The authors show that this modification doubles the maximum Courant number (and hence the maximum time step) at which the integrations are stable, doubling the computational efficiency. Unfortunately, the pressure-averaging technique proposed by the authors is not original. It was devised and published by Shuman [5] and has been widely used in the atmosphere and ocean modelling community for over 40 years.