  Brain injuries resulting from mechanical trauma represent an ongoing global
public health issue. Several $\textit{in vitro}$ and $\textit{in vivo}$ models
for traumatic brain injury (TBI) continue to be developed for delineating the
various complex pathophysiological processes involved in its onset and
progression. Developing an $\textit{in vitro}$ TBI model that is based on
cortical spheroids is especially of great interest currently because they can
replicate key aspects of $\textit{in vivo}$ brain tissue, including its
electrophysiology, physicochemical microenvironment, and extracellular matrix
composition. Being able to mechanically deform the spheroids is a key
requirement in any effective $\textit{in vitro}$ TBI model. The spheroids'
shape and size, however, make mechanically loading them, especially in a
high-throughput, sterile, and reproducible manner, quite challenging. To
address this challenge, we present an idea for a spheroid-based, $\textit{in
vitro}$ TBI model in which the spheroids are mechanically loaded by being spun
by a centrifuge. (An experimental demonstration of this new idea will be
published shortly elsewhere.) An issue that can limit its utility and scope is
that imaging techniques used in 2D and 3D $\textit{in vitro}$ TBI models cannot
be readily applied in it to determine spheroid strains. In order to address
this issue, we developed a continuum mechanics-based theory to estimate the
spheroids' strains when they are being spun at a constant angular velocity. The
mechanics theory, while applicable here to a special case of the
centrifuge-based TBI model, is also of general value since it can help with the
further exploration and development of TBI models.
