Eigen-transitions in cantilever cylindrical shells subjected to vertical edge loads

A thin cantilever cylindrical shell subjected to a transverse shear force at the free end can experience two distinct modes of buckling, depending on its relative thickness and length. If the former parameter is fixed then a short cylinder buckles in a diffuse manner, while the eigenmodal deformation of a moderately long shell is localised, both axially and circumferentially, near its fixed end. Donnelltype buckling equations for cylindrical shells are here coupled with a non-symmetric membrane basic state to produce a linear boundary-value problem that is shown to capture the transition between the aforementioned instability modes. The main interest lies in exploring the approximate asymptotic separation of the independent variables in the corresponding stability equations, when the eigen-deformation is doubly localised. Comparisons with direct numerical simulations of the full buckling problem provide further insight into the accuracy and limitations of our approximations

Increased mitochondrial content in remyelinated axons: implications for multiple sclerosis

Mitochondrial content within axons increases following demyelination in the central nervous system, presumably as a response to the changes in energy needs of axons imposed by redistribution of sodium channels. Myelin sheaths can be restored in demyelinated axons and remyelination in some multiple sclerosis lesions is extensive, while in others it is incomplete or absent. The effects of remyelination on axonal mitochondrial content in multiple sclerosis, particularly whether remyelination completely reverses the mitochondrial changes that follow demyelination, are currently unknown. In this study, we analysed axonal mitochondria within demyelinated, remyelinated and myelinated axons in post-mortem tissue from patients with multiple sclerosis and controls, as well as in experimental models of demyelination and remyelination, in vivo and in vitro. Immunofluorescent labelling of mitochondria (porin, a voltage-dependent anion channel expressed on all mitochondria) and axons (neurofilament), and ultrastructural imaging showed that in both multiple sclerosis and experimental demyelination, mitochondrial content within remyelinated axons was significantly less than in acutely and chronically demyelinated axons but more numerous than in myelinated axons. The greater mitochondrial content within remyelinated, compared with myelinated, axons was due to an increase in density of porin elements whereas increase in size accounted for the change observed in demyelinated axons. The increase in mitochondrial content in remyelinated axons was associated with an increase in mitochondrial respiratory chain complex IV activity. In vitro studies showed a significant increase in the number of stationary mitochondria in remyelinated compared with myelinated and demyelinated axons. The number of mobile mitochondria in remyelinated axons did not significantly differ from myelinated axons, although significantly greater than in demyelinated axons. Our neuropathological data and findings in experimental demyelination and remyelination in vivo and in vitro are consistent with a partial amelioration of the supposed increase in energy demand of demyelinated axons by remyelination