High-field MRS studies in brain slices

We are applying multi-nuclear high-field (500 MHz) MR spectroscopy of metabolising whole tissue preparations of the mammalian brain to studies on individual components of convulsions, which include prolonged depolarization, metabolic deprivation, and the effects of excitotoxins. The responses of glial cells and neurones can be partially distinguished by following labelling patterns of metabolic intermediates from ¹³C-labelled glucose or acetate (which enters only glial cells). This approach clearly confirmed our earlier indications that the metabolic response to depolarization (40 mM extracellular K⁺) occurs essentially in glial cells. Some evidence for metabolic shuttling between glia and neurones was obtained from the changes in C3/C4 ratios of glutamate and glutamine, and the C2/C3 of GABA. Mechanisms for metabolic support of neurones by glia may be of importance in neuronal protection under such metabolic stress as occurs in epilepsy. Changes in free intracellular divalent cations ([Ca²⁺]_i and [Zn²⁺]_i) were monitored using the ¹⁹F-MRS indicator, 5FBAPTA. Large increases in [Ca²⁺]_i and decreases in PCr were produced by excitotoxins (glutamate and NMDA), depolarization or ischaemia, but intracellular Zn²⁺ appeared only after exposure to the excitotoxins. The NMDA receptor blocker, MK801, removed all of the responses to NMDA, but only prevented the appearance of Zn²⁺ observed with glutamate. These results indicate that the damage caused to neurones by such insults as convulsions is not due simply to the presence of excessive excitotoxic glutamate.     

Stabilizing the intensity of a wave amplified by a beam of particles

The intensity of an electromagnetic wave interacting self-consistently with a beam of charged particles as in a free electron laser, displays large oscillations due to an aggregate of particles, called the macro-particle. In this article, we propose a strategy to stabilize the intensity by re-shaping the macro-particle. This strategy involves the study of the linear stability (using the residue method) of selected periodic orbits of a mean-field model. As parameters of an additional perturbation are varied, bifurcations occur in the system which have drastic effect on the modification of the self-consistent dynamics, and in particular, of the macro-particle. We show how to obtain an appropriate tuning of the parameters which is able to strongly decrease the oscillations of the intensity without reducing its mean-value.     

A weight-function approach for determining watershed initial conditions for combustion waves

In many generic combustion models, one finds that a combustionwave will develop with a specific wave speed. However, thereare possible initial temperature profiles which do not evolveinto such waves, but rather die out to the ambient temperature.There can exist, in some models, a clear distinction betweenthose initial conditions that do evolve into combustion wavesand those that do not; this is sometimes referred to as thewatershed initial condition. When fuel consumption is consideredto be negligible, analytical methods can be used to obtain theexact watershed. In this paper, we consider the problem of determiningpseudo-watersheds and ascertaining the relationship betweenthese pseudo-watersheds and the exact watersheds. In the processa novel weight-function approach for infinite spatial domainsis developed.     

MRI studies of the neurotoxic effects of L-2-chloropropionic acid on rat brain

L-2-Chloropropionic acid (L-CPA) is selectively toxic to rat cerebellar granule cells; necrosis is first observed about 36 hours after administration of L-CPA (750 mg/kg p.o.) becoming more marked by 48 h. Parallel to the onset of cell death an increase in cerebellar water content and sodium concentration has been reported suggesting an oedematous reaction. In this study T(2)-weighted (T(2)WI) and diffusion weighted (DWI) imaging were used to detect the development of neuronal damage in the cerebellum of rats as a result of exposure to L-CPA. T(2)WI and DWI were not able to detect cerebellar abnormalities at 37 h post-dosing except for a slight swelling of the cerebellum. However, at 48 h post-dosing when cerebellar swelling and granule cell necrosis were marked, T(2)WI and DWI hyperintensities were observed in the cerebellum. Therefore, under the conditions of this study, MRI was not able to detect abnormalities in the cerebellum prior to the onset of the clinical signs of neurotoxicity or at the time of early histological changes. T(2)WI also suggested a marked increase in the amount of fluid in the ventricular system of rats 37 and 48 h after dosing; fluid accumulation was observed in all animals studied whether or not necrosis was detected. The occurrence of T(2)WI hyperintensity in the forebrain lead us to discover a new lesion in the habenular nucleus.     

Analytical results on the magnetization of the Hamiltonian Mean-Field model

The violent relaxation and the metastable states of the Hamiltonian Mean-Field model, a paradigmatic system of long-range interactions, is studied using a Hamiltonian formalism. Rigorous results are derived algebraically for the time evolution of selected macroscopic observables, e.g., the global magnetization. The high- and low-energy limits are investigated and the analytical predictions are compared with direct N-body simulations. The method we use enables us to re-interpret the out-of-equilibrium phase transition separating magnetized and (almost) unmagnetized regimes.