Canonical description of incompressible fluid -- Dirac brackets approach

We present a novel canonical description of the incompressible fluid dynamics. This description uses the dynamical constraints, in our case reflecting "incompressibility" assumption, and leads to replacement of usual hydrodynamical Poisson brackets for density and velocity fields with Dirac brackets. The resulting equations are then known nonlinear, and non-local in space, equations for incompressible fluid velocity.Comment: 7 pages, late

MPTP-induced degeneration: interference with glutamatergic toxicity

Parkinson's disease (PD) is characterised by the progressive degeneration of nigrostriatal dopamine (DA) neurons resulting in the major symptoms of akinesia and rigidity. Although the primary cause of PD is still not known some features make this disorder a model for neurodegenerative diseases in general. It has been known for some time that symptomatic PD can be attributed to insults with symptoms occurring many years later such as post-encephalitic PD or PD following manganese poisoning. More recently, MPTP (1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine) has been identified as a neurotoxin selective for melanin-containing dopaminergic neurons in humans and non-human primates. The specificity of this neurotoxin and the striking clinical similarities to idiopathic PD, seen in primates, make MPTP-induced parkinsonism the most useful animal model of a neurological disease. There are numerous theoretical possibilities to interfere with both MPTP-induced neurotoxicity and the symptomatology of PD. In recent years excitatory amino acids have gained considerable interest since they can cause excitotoxic lesion of neurons under a number of pathological conditions (Olney et al., 1989; Choi, 1988). Here we summarise the present data and provide new experimental evidence indicating that MPTP-induced degeneration of dopaminergic neurons does involve glutamate-mediated toxicity. It is concluded that glutamate-mediated excitotoxicity results in the destruction of DAergic somata in the substantia nigra. Non-competitive or competitive NMDA antagonists protect nigral neurons from MPTP-induced degeneration whereas their striatal terminals still seem to degenerate