Brain swelling is a serious condition associated with an accumulation of fluid inside the brain caused by trauma, stroke, infection, or tumors. It increases the pressure inside the skull and reduces blood and oxygen supply. To relieve the intracranial pressure, neurosurgeons remove part of the skull and allow the swollen brain to bulge outward, a procedure that is widely known as decompressive craniectomy. Decompressive craniectomy has been preformed for more than a century; yet, its e¿ects on the swollen brain remain poorly understood. Here we characterize the deformation, strain, and stretch in bulging brains using the nonlinear field theories of mechanics. Our study shows that even small swelling volumes of 28 and 56ml induce maximum principal strains in excess of 30%. For radially outward-pointing axons, we observed maximal normal stretches of 1.3 deep inside the bulge and maximal shear stretches of 1.3 around the craniectomy edge. While the stretch magnitude varies with opening site and swelling site, our study suggests that the locations of maximum stretch are universally shared amongst all bulging brains. Our model can inform neurosurgeons and rationalize the shape and position of the skull opening, with the overall goal to reduce brain damage and improve the structural and functional outcomes of decompressive craniectomy.
The final publication is available at Springer via http://dx.doi.org/10.1007/s10659-016-9606-1
Alternative growth and decay estimates, reminiscent of the classical Phragmén-Lindelöf principle, are derived for a linearised thermoelastic body whose plane crosssections increase unboundedly with respect to a given direction. The proof uses a modified Poincaré inequality to construct a differential inequality for a weighted linear combination
of the cross-sectional mechanical and thermal energy fluxes. Decay estimates are deduced also for the cross-sectional mean square measures of the displacement and temperature. An explicit upper bound in terms of base data is established for the amplitude occurring in the decay estimates.
The final publication is available at Springer via http://dx.doi.org/10.1007/s10659-015-9523-8