Forward Modelling for Magnetospinography: Systematic Comparison of Boundary Element and Finite Element Methods

Abstract

Magnetospinography (MSG) enables non-invasive measurement of spinal cord electrophysiology, but accurate interpretation of these signals depends critically on forward modelling assumptions. We compared four vertebral bone representations: continuous, homogeneous-toroidal, inhomogeneous-toroidal, and MRI-derived-realistic, implemented within both boundary element method (BEM) and finite element method (FEM) frameworks. Lead-fields were computed across the full spinal cord for three orthogonal source orientations. When comparing matched model pairs, BEM and FEM produced consistent forward solutions, with median relative errors below 3.1% and median squared correlation coefficients exceeding 0.998 across all bone geometries. Vertebral bone geometry exerted a systematic and orientation-dependent influence on predicted lead fields. The dominant distinction was between continuous and segmented bone representations rather than between simplified and anatomically detailed segmented models. For left-right oriented sources, segmented geometries produced substantially higher field amplitudes (fT/nAm) than the continuous model throughout the cord (35-72%), while toroidal and MRI-derived realistic models produced comparable results across both frameworks, with median r2 exceeding 0.97 between segmented models compared to 0.67-0.85 for continuous versus segmented comparisons. Sensor placement further modulated sensitivity profiles, with posterior arrays exhibiting greater sensitivity lower down the cord, but anterior and posterior sensors showing comparable sensitivity in the cervical region.