Local and global effects of inertial force components producing brain strain during head impacts

Traumatic brain injury (TBI) is a brain dysfunction caused by an external mechanical force and is a leading cause of disability worldwide. In traumatic brain injury, the brain strain is driven by inertial force associated with the head acceleration. We identified three distinct mechanisms by which inertial forces induce brain strain: the global rotation effect, the global translation effect, and the local force effect. The global rotation and translation effects arise from whole-brain movement relative to the skull, produce brain strain through shearing, pushing and pulling, respectively. In contrast, the local force effect refers to the strain produced inside the brain by the local force without the whole brain movement. The effects are produced by different inertial force components: Euler force (angular acceleration) produces brain strain by the global rotation effect, the linear force (linear acceleration) produces brain strain by the global translation effect, and the centrifugal force (angular velocity) produces brain strain by the local force effect. Although inertial force components are well recognized, their individual contributions to brain strain during head impacts remain unclear. In this study, we applied impact loading by each inertial force component independently in the simulation, rather than by head accelerations where all components act together, with the aim of quantifying their distinct contributions and clarifying the conditions under which Holbourn's hypothesis applies. We found that 97 % of the total MPS was produced by the Euler force in American football head impacts. However, when the range of head kinematics was deliberately extended beyond typical sports impacts to simulate extreme scenarios, such as those potentially occurring in aviation or high-impact accidents, both linear and centrifugal forces were also found capable of producing significant brain strain, highlighting clear biomechanical conditions under which Holbourn's hypothesis is insufficient. Furthermore, we estimated the independent kinematic thresholds for producing brain strain at injury-relevant levels and found that most injurious head impacts are consistently associated with angular accelerations exceeding these thresholds, while corresponding linear accelerations and angular velocities remain below them.