Data-informed reconstruction of a bipennate muscle’s aponeurosis and its fibre distribution for performing continuum-mechanical simulations

Abstract

Alternatives to Diffusion-Tensor-Imaging tractography methods for determining fibre orientation fields in skeletal muscle include Laplacian flow simulations. Such methods require flux boundary conditions (BCs) at the tendons and/or along the inner aponeuroses, which can significantly influence the gradients of the resulting Laplacian flow. Herein, we propose a novel method based on solving the 3D steady-state thermal heat equations to determine the fibre architecture in a bi-pennate muscle, specifically the m. rectus femoris. Additionally, we propose a semi-automated algorithm that provides the geometrical representation of the anterior aponeurosis, which, along with the thermal-based fibre field, is particularly well suited for Finite Element (FE) simulations. The semi-automated reconstruction of the aponeurosis shows a good correlation with manual segmentation, yielding a dice coefficient (DSC) of 0.83. The metamodel-based approach resulted in fluxes with a mean angular deviation of \(14.25^\circ \,\pm \,10.36^\circ\) and a fibre inclination from the muscle’s longitudinal axis of \(0.44^\circ \,\pm \,4.48^\circ\). Comparing the mechanical output of the same m. rectus femoris muscle geometry informed by the two respective fibre architectures showed that the most significant contributing factor was the relative fibre inclination. Compared to the standard deviation in the undeformed configuration (\(0.44^\circ \,\pm \,4.48^\circ\)), the standard deviation of relative fibre inclination during passive stretching at low applied loads, for instance, at \(30\%\) of the maximum applied load, showed a significant decrease (\(0.49^\circ \,\pm \,2.24^\circ\)). Similarly, at maximum isometric contraction, the relative fibre inclinations at \(10\%\) initial fibre pre-stretch are \(0.19^\circ \,\pm \,1.23^\circ\), indicating a drop in standard deviation from the undeformed configuration (\(0.44^\circ \,\pm \,4.48^\circ\)). The current study demonstrates that despite the initial deviations in fibre orientations and relative fibre inclinations, thermal flux-based fibre orientations not only exhibit comparable results to DTI-based fibre tractography for the macroscopic analysis of the m. rectus femoris but also result in homogeneous stretch fields and improved numerical convergence. The proposed methods may be applied to determine inner aponeuroses of other bi- or multi-pennate muscles, enabling efficient in-silico computations of the musculoskeletal system.