Physiological Cross-Sectional Surfaces: A Method for Estimating Muscle Functional Capacity from 3D Digital Models of Fiber Architecture

Abstract

Physiological cross-sectional area (PCSA) is defined as the summed cross-sectional area of all muscle fibers contracting in parallel and at optimal length. PCSA is widely used, yet the conventional equations used to compute PCSA were developed from two-dimensional (2D) interpretations of muscle architecture and may not accurately represent muscle fiber cross-sections in the case of real three-dimensional (3D) geometries of muscles. Related measures of functional cross-sectional area (FCSA) and geometric cross-sectional area (GCSA) were also developed and interpreted with simplified 2D representations. Using realistic 3D muscle architectures derived from medical imaging, we sought to investigate whether conventional definitions of PCSA, FCSA, and GCSA represent the summed cross-sectional areas of all parallel muscle fibers, the fundamental definition of PCSA. We found that none of these measures consistently represented this definition. Thus, we introduce the physiological cross-sectional surface (PCSS), a curved surface within a muscle volume that is everywhere perpendicular to the local fiber direction. We estimated PCSS in 3D muscle surface meshes reconstructed from MRI data, using fiber orientations derived from Laplacian fiber reconstruction. PCSS-derived estimates were compared with PCSA, FCSA, and GCSA across six muscles representing five architectural classes. PCSS differed from all conventional measures, with the magnitude and direction of disagreement depending on muscle architecture. PCSS-to-PCSA ratios ranged from 0.771 to 1.399, while GCSA underestimated PCSS by up to a factor of 2.256 in bi- and multipennate muscles and overestimated it in muscles with more uniform fiber arrangements. PCSS demonstrated high geometric fidelity (perpendicularity>0.987) and robustness to fiber density across a tenfold range (coefficients of variation 0.39-3.95%). These findings indicate that conventional cross-sectional area measures do not consistently account for all fiber cross-sections in parallel within realistic 3D muscle geometries. PCSS provides a geometrically rigorous alternative that may improve estimation of functional muscle capacity from subject-specific imaging data.