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Mild traumatic brain injury (mTBI, also known as concussion) caused by thehead impact is a crucial global public health problem, but the physics of mTBIis still unclear. During the impact, the rapid movement of the head injures thebrain, so researchers have been endeavoring to investigate the relationshipbetween head kinematic parameters (e.g., linear acceleration, angular velocity,angular acceleration) and brain strain, which is associated with the injury ofthe brain tissue. Although previous studies have shown that linear accelerationhad a limited contribution to brain strain, whether angular velocity or angularacceleration causes brain strain is still unclear because of theirinterdependency (acceleration being the velocity time-derivative). By reframingthe problem through the lens of inertial forces, we propose to use the skullframe of reference instead of the ground frame of reference to describe braindeformation during head impact. Based on the rigid-body rotation of the brain,we present a theoretical framework of mechanical analysis about how theinertial forces cause brain strain. In this way, we theoretically show thatangular acceleration determines brain strain, and we validate this by numericalsimulations using a finite element head model. We also provide an explanationof why previous studies based on peak values found the opposite: that angularvelocity determined brain strain in certain situations. Furthermore, we use thesame framework to show that linear acceleration causes brain strain in adifferent mechanism from angular acceleration. However, because of the brain'sdifferent resistances to compressing and shearing, the brain strain caused bylinear acceleration is small compared with angular acceleration.

Theoretical and numerical analysis for angular acceleration being determinant of brain strain in mTBI