The anomalous effect of surface diffusion on the nuclear magnetic resonance signal in restricted geometry

Anisotropy of diffusion properties in a specimen plays a key role in numerous applications of nuclear magnetic resonance (NMR) imaging, like non-invasive tracking of fibers in the central nervous system. We suggest that contrasting fiber structures with certain diameters could be improved if second-order effects are taken into account. We introduce a procedure consisting of two standard diffusion NMR experiments differing in their gradient pulse characteristics. These two echo signals will be called the background and principal signals. We show that the difference obtained by subtracting one echo signal from the other has either typical or anomalous properties. In the typical case, as the duration of the gradient pulse in the second experiment is set to smaller and smaller values, the difference from the background echo signal tends toward its maximum. In contrast, in the anomalous case the difference between the background and the principal signals has a maximum at a certain nonzero duration of the pulse in the second experiment. This critical duration is determined by different characteristics, including the diameters of fibers. For this anomalous effect to take place the fast surface diffusion channel coupled to the surrounding media is required. The diffusion of magnetic molecules along the surface of restricted media and the coupling of the surface and the bulk translational motions can strongly modify the echo attenuation NMR signal. The origin of this strong anomalous effect is the change of the symmetry of the lowest diffusion eigenmode of the system. We illustrate the effect of surface diffusion for a cylindrically symmetric system and describe the experimental conditions under which the anomalous behavior of the echo signals can be observed.

Modeling alternation to synchrony with inhibitory coupling: a neuromorphic VLSI approach

We developed an analog very large-scale integrated system of two mutually inhibitory silicon neurons that display several different stable oscillations. For example, oscillations can be synchronous with weak inhibitory coupling and alternating with relatively strong inhibitory coupling. All oscillations observed experimentally were predicted by bifurcation analysis of a corresponding mathematical model. The synchronous oscillations do not require special synaptic properties and are apparently robust enough to survive the variability and constraints inherent in this physical system. In biological experiments with oscillatory neuronal networks, blockade of inhibitory synaptic coupling can sometimes lead to synchronous oscillations. An example of this phenomenon is the transition from alternating to synchronous bursting in the swimming central pattern generator of lamprey when synaptic inhibition is blocked by strychnine. Our results suggest a simple explanation for the observed oscillatory transitions in the lamprey central pattern generator network: that inhibitory connectivity alone is sufficient to produce the observed transition.

In-phase and antiphase self-oscillations in a model of two electrically coupled pacemakers

The dynamic behavior of a model of two electrically coupled oscillatory neurons was studied while the external polarizing current was varied. It was found that the system with weak coupling can demonstrate one of five stable oscillatory modes: (1) in-phase oscillations with zero phase shift; (2) antiphase oscillations with half-period phase shift; (3) oscillations with any fixed phase shift depending on the value of the external polarizing current; (4) both in-phase and antiphase oscillations for the same current value, where the oscillation type depends on the initial conditions; (5) both in-phase and quasiperiodic oscillations for the same current value. All of these modes were robust, and they persisted despite small variations of the oscillator parameters. We assume that similar regimes, for example antiphase oscillations, can be detected in neurophysiological experiments. Possible applications to central pattern generator models are discussed.