High (20-Hz) and low (1-Hz) frequency transcranial magnetic stimulation as adjuvant treatment in medication-resistant depression.

Studies of repetitive transcranial magnetic stimulation (rTMS) in depression have found antidepressant effects when high frequency stimulation (HF-rTMS; >1 Hz) is applied over the left prefrontal cortex (LPF). A few studies have also reported success with low frequency stimulation (LF-rTMS) to the right prefrontal cortex (RPF). Both HF-rTMS and LF-rTMS have been reported to work better in areas with cerebral hypometabolism or hypermetabolism, respectively. Thirty medication-resistant patients with major depression were randomized into three groups. The first group received sham rTMS and the second group received active rTMS (20-Hz rTMS to the LPF and 1-Hz rTMS to the RPF). The third group, however, received active rTMS that was focused on different regions of the brain after examination with single photon emission computed tomography (20-Hz rTMS to an area of relatively low activity and 1-Hz rTMS to an area showing relatively high activation). Patients and raters were blind to the treatment condition. Comparison of the sham rTMS group with the overall group that received active rTMS revealed statistically significant changes on the Hamilton Rating Scale for Depression after 10 sessions. This study demonstrated that combined 20+1-Hz rTMS was effective, but no additional advantages were obtained by focusing rTMS on areas identified by single photon emission tomography as showing high versus low levels of functional activity.

Stochastic approach to diffusion inside the chaotic layer of a resonance.

We model chaotic diffusion in a symplectic four-dimensional (4D) map by using the result of a theorem that was developed for stochastically perturbed integrable Hamiltonian systems. We explicitly consider a map defined by a free rotator (FR) coupled to a standard map (SM). We focus on the diffusion process in the action I of the FR, obtaining a seminumerical method to compute the diffusion coefficient. We study two cases corresponding to a thick and a thin chaotic layer in the SM phase space and we discuss a related conjecture stated in the past. In the first case, the numerically computed probability density function for the action I is well interpolated by the solution of a Fokker-Planck (FP) equation, whereas it presents a nonconstant time shift with respect to the concomitant FP solution in the second case suggesting the presence of an anomalous diffusion time scale. The explicit calculation of a diffusion coefficient for a 4D symplectic map can be useful to understand the slow diffusion observed in celestial mechanics and accelerator physics.