  Mild traumatic brain injury (mTBI, also known as concussion) caused by the
head impact is a crucial global public health problem, but the physics of mTBI
is still unclear. During the impact, the rapid movement of the head injures the
brain, so researchers have been endeavoring to investigate the relationship
between head kinematic parameters (e.g., linear acceleration, angular velocity,
angular acceleration) and brain strain, which is associated with the injury of
the brain tissue. Although previous studies have shown that linear acceleration
had a limited contribution to brain strain, whether angular velocity or angular
acceleration causes brain strain is still unclear because of their
interdependency (acceleration being the velocity time-derivative). By reframing
the problem through the lens of inertial forces, we propose to use the skull
frame of reference instead of the ground frame of reference to describe brain
deformation during head impact. Based on the rigid-body rotation of the brain,
we present a theoretical framework of mechanical analysis about how the
inertial forces cause brain strain. In this way, we theoretically show that
angular acceleration determines brain strain, and we validate this by numerical
simulations using a finite element head model. We also provide an explanation
of why previous studies based on peak values found the opposite: that angular
velocity determined brain strain in certain situations. Furthermore, we use the
same framework to show that linear acceleration causes brain strain in a
different mechanism from angular acceleration. However, because of the brain's
different resistances to compressing and shearing, the brain strain caused by
linear acceleration is small compared with angular acceleration.

Biological Physics