Bulging brains

Abstract

Brain swelling is a serious condition associated with an accumulation of fluid inside the brain that can be 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 known as decompressive craniectomy. Decompressive craniectomy has been preformed for more than a century; yet, its effects 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 to 56 ml induce maximum principal strains in excess of 30%. For radially outward-pointing axons, we observe maximal normal stretches of 1.3 deep inside the bulge and maximal tangential stretches of 1.3 around the craniectomy edge. While the stretch magnitude varies with opening site and swelling region, our study suggests that the locations of maximum stretch are universally shared amongst all bulging brains. Our model has the potential to inform neurosurgeons and rationalize the shape and position of the skull opening, with the ultimate goal to reduce brain damage and improve the structural and functional outcomes of decompressive craniectomy in trauma patients.

Keywords: Soft matter; brain; craniectomy; finite element analysis; hyperelasticity; neuromechanics; swelling.

Figures

Fig. 1

Bulging of a hemidisk. We allow an elastic body to swell locally, either in a sector of angle α (A) or in a disk (B). The swelling body bulges out through an opening of angle β.

Fig. 2

Bulging of a hemidisk with a swelling sector. Displacement, vertical displacement, and radial and tangential stretches for frictional contact without sliding (left) and frictionless contact with sliding (right). In frictional contact without sliding, the solid is pushed outward with large displacements along the symmetry axis in the center of the bulge. In frictionless contact with sliding, the solid slides along the boundary and rotates outward around the opening edge.

Fig. 3

Bulging of a hemidisk with a swelling sector. Radial and tangential stretches for varying opening angles of β (rows) and for varying swelling sector angles α (columns) for frictional contact without sliding (left) and frictionless contact with sliding (right). Radial stretches take maximum values of 1.7 in regions deep inside the bulge; tangential stretches take maximum values of 1.7 in regions localized around the craniectomy edge.

Fig. 4

Bulging of a hemidisk with a swelling disk. Radial and tangential stretches (rows) for five different swelling locations (columns). Radial and tangential stretches take maximal and mimimal values around the swelling disk, while large regions of the hemidisk are unaffected by the local swelling.

Fig. 5

Personalized decompressive craniectomy model. Magnetic resonance images (left) and computational model (right). Anatomically detailed and geometrically accurate three-dimensional reconstructions of the individual substructures including the gray matter (red), the white matter (pink), the cerebellum (green), the skin (brown), the skull (gray), and the remaining cerebrospinal fluid, the veins, the meninges, part of the brain stem, the sinuses, the falx, and the ventricles (beige) shown for selected sagittal, coronal, and transverse slices.

Fig. 6

Personalized decompressive craniectomy model. Boundary conditions and loading conditions. Top row: Full model discretized with 1,275,808 linear tetrahedral elements and 241,845 nodes; representative coronal section; anatomic details with cortical folds; frontal flap with 4,279 skull elements removed; lateral flap with 2,494 elements removed. Bottom row: Boundary conditions with lower red region fixed relative to the skull and upper purple region allowed to slide along the skull; swelling of left, right, and both white matter hemispheres.

Fig. 7

Decompressive craniectomy. Displacement and superposed deformation in transverse section facing downward and sagittal section facing left for unilateral and frontal flaps with left and right, left, and right hemispherical swelling. Swelling causes a shift of intracranial tissues, a key indicator of the trauma's severity in clinical practice. The midline shift of the cortical and subcortical layers highlights the immediate release of tissue strain upon removal of the unilateral and frontal flaps.

Fig. 8

Decompressive craniectomy. Radial and tangential stretches in transverse section facing downward and sagittal section facing left for unilateral and frontal flaps with left and right, left, and right hemispherical swelling. Swelling causes maximum radial stretches of up to 1.3 deep inside the bulge, minimum radial stretches of 0.7 around the opening, and maximum tangential stretches of up to 1.3 around the opening.

Fig. 9

Decompressive craniectomy. Displacement, maximum principal strain, radial stretch, and tangential stretch for unilateral and frontal flaps with left and right, left, and right hemispherical swelling. Swelling causes maximum principal strains of up to 30% localized around the opening, maximum radial stretches of up to 1.3 deep inside the bulge, minimum radial stretches of 0.7 around the opening, and maximum tangential stretches of up to 1.3 around the opening.