# Placental Flattening via Volumetric Parameterization

## TL;DR

This paper introduces a volumetric mesh-based algorithm to flatten placental shapes from MRI data into a canonical template, improving visualization of placental anatomy and function for better pregnancy assessment.

## Contribution

The novel method maps in vivo placental shapes to a flattened template using symmetric Dirichlet energy minimization with local injectivity constraints.

## Key findings

- Achieved sub-voxel accuracy in boundary mapping
- Controlled distortion throughout the volume
- Enhanced visualization of placental anatomy

## Abstract

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 .