SegmentGeometry: A Tool for Measuring Second Moment of Area in 3D Slicer

Abstract

Synopsis Second moment of area is a measure of how well the cross-section of a beam will resist bending because of its shape. Many have used second moment of area to investigate the mechanical adaptations of biological structures from stingray jaws to animal limb bones. In this context it is important to acknowledge the assumptions of beam theory, in which second moment of area plays a key role, if reasonable results are desired. For example, to minimize shear the structure should be at least 10 times longer than it is wide and deflection should be minimal. Analyzing the internal geometry of biological structures has never been easier or more accessible given the wide, and growing availability of micro-CT scans. Here, we offer a guide on the care that needs to be taken when interpreting second moment of area, and present open-access, open-source software that can process hundreds if not thousands of structures in a short time frame. SegmentGeometry, an extension for the open-source imaging platform 3D Slicer, iterates slice-by-slice through 3D structures to calculate second moment of area and other cross-sectional properties. We analyzed 2 case studies to demonstrate the power of this tool and to highlight interpretations that can be gleaned from second moment of area. Second moment of area is just one part of the Euler–Bernoulli beam theory and considering the full equation would greatly increase the number and diversity of questions that can be answered.