The mechanics of decompressive craniectomy: Bulging in idealized geometries

In extreme cases of traumatic brain injury or a stroke, the resulting uncontrollable swelling of the brain may lead to a harmful increase of the intracranial pressure. As a common measure for immediate release of pressure on the brain, part of the skull is surgically removed allowing for the brain to bulge outwards, a procedure known as a decompressive craniectomy. During this excessive brain swelling, the affected tissue typically undergoes large deformations resulting in a complex three-dimensional mechanical loading state with several important implications on optimal treatment strategies and outcome. Here, as a first step towards a better understanding of the mechanics of a decompressive craniectomy, we consider simple models for the bulging of elastic solids under geometric constraints representative of the surgical intervention. In small deformations and simple geometries, the exact solution of this problem is derived from the theory of contact mechanics. The analysis of these solutions reveals a number of interesting generic features relevant for the mechanics of craniectomy.