  We present a volumetric mesh-based algorithm for flattening the placenta to a
canonical template to enable effective visualization of local anatomy and
function. Monitoring placental function in vivo promises to support pregnancy
assessment and to improve care outcomes. We aim to alleviate visualization and
interpretation challenges presented by the shape of the placenta when it is
attached to the curved uterine wall. To do so, we flatten the volumetric mesh
that captures placental shape to resemble the well-studied ex vivo shape. We
formulate our method as a map from the in vivo shape to a flattened template
that minimizes the symmetric Dirichlet energy to control distortion throughout
the volume. Local injectivity is enforced via constrained line search during
gradient descent. We evaluate the proposed method on 28 placenta shapes
extracted from MRI images in a clinical study of placental function. We achieve
sub-voxel accuracy in mapping the boundary of the placenta to the template
while successfully controlling distortion throughout the volume. We illustrate
how the resulting mapping of the placenta enhances visualization of placental
anatomy and function. Our code is freely available at
https://github.com/mabulnaga/placenta-flattening .
