Recommended Citation
Babbs, Charles F., "A continuum mechanical model of the brain during closed head injury" (2025). Weldon School of Biomedical Engineering Faculty Working Papers. Paper 38.
https://docs.lib.purdue.edu/bmewp/38
Date of this Version
1-4-2025
Keywords
acceleration, biomechanics, blunt trauma, brain, concussion, deformation, diffusion tensor imaging, impact, microbleeds; strain, shear, trauma, traumatic brain injury
Abstract
Exactly how traumatic axonal injury happens as a result of brief, intense acceleration of the head remains a mystery. The same can be said about traumatic microbleeds observed in MRI scans of people suffering concussions. This paper explores the mechanism of injury in terms of continuum biomechanics. A full-sized viscoelastic model of the human brain is developed that is subjected to impact with the rigid skull after crossing the subarachnoid space in response to brief, intense whole head acceleration, as might occur in falls or in contact sports. The brain is considered a compressible viscoelastic body of approximately uniform density, elasticity, and viscosity. Classical physics describes the propagation of compressive strain waves through the brain after initial brain-skull contact. At the point of maximal compression against the skull, the whole brain is for an instant, motionless. The local magnitude of compression varies inversely with the cross-sectional area in a plane perpendicular to strain wave propagation. For a blow to the forehead maximal deformation occurs near the site of contact with the frontal bone, becoming less in middle regions, and rising again near the occipital pole to a less than maximal level, owing to viscous energy loss. For a clearly damaging acceleration, as would happen in an adult human falling forward from higher than a standing position and striking a hard surface, the maximal compressive strain approaches 50% in the frontal lobes, 20% in the middle regions, and 30% in the occipital lobes, even in the absence of rebound and contrecoup. These compressive strains are accompanied by corresponding elongation strains from Poisson’s ratio expansion, perpendicular to the axis of acceleration, of roughly 25%, 10%, and 15%, which may be adequate in themselves to stretch axons and capillaries to their breaking points.