Glutathione and glutamate in schizophrenia: a 7T MRS study

In schizophrenia, abnormal neural metabolite concentrations may arise from cortical damage following neuroinflammatory processes implicated in acute episodes. Inflammation is associated with increased glutamate, whereas the antioxidant glutathione may protect against inflammation-induced oxidative stress. We hypothesized that patients with stable schizophrenia would exhibit a reduction in glutathione, glutamate and/or glutamine in the cerebral cortex, consistent with a postinflammatory response, and that this reduction would be most marked in patients with residual schizophrenia an early stage with positive psychotic symptoms has progressed to a late stage characterised by long-term negative symptoms and impairments. We recruited 28 patients with stable schizophrenia and 45 healthy participants matched for age, gender and parental socio-economic status. We measured glutathione, glutamate and glutamine concentrations in the anterior cingulate cortex (ACC), left insula, and visual cortex using 7T proton Magnetic Resonance Spectroscopy (MRS). Glutathione and glutamate were significantly correlated in all three voxels. Glutamine concentrations across the three voxels were significantly correlated with each other. Principal Components Analysis (PCA) produced three clear components: an ACC glutathione-glutamate component; an insula-visual glutathione-glutamate component; and a glutamine component. Patients with stable schizophrenia had significantly lower scores on the ACC glutathione-glutamate component, an effect almost entirely leveraged by the sub-group of patients with residual schizophrenia. All three metabolite concentration values in the ACC were significantly reduced in this group. These findings are consistent with the hypothesis that excito-toxicity during the acute phase of illness leads to reduced glutathione and glutamate in the residual phase of the illness

Spectrum Estimates and Applications to Geometry

In 1867, E. Beltrami (Ann Mat Pura Appl 1(2):329\u2013366, 1867, [12]) introduced a second order elliptic operator on Riemannian manifolds, extending the Laplace operator on Rn, called the Laplace\u2013Beltrami operator. The Laplace\u2013Beltrami operator became one of the most important operators in Mathematics and Physics, playing a fundamental role in differential geometry, geometric analysis, partial differential equations, probability, potential theory, stochastic process, just to mention a few. It is in important in various differential equations that describe physical phenomena such as the diffusion equation for the heat and fluid flow, wave propagation, Laplace equation and minimal surfaces