A 3D model of muscle reveals the causes of nonuniform strains in the biceps brachii

Abstract

Biomechanical models generally assume that muscle fascicles shorten uniformly. However, dynamic magnetic resonance (MR) images of the biceps brachii have recently shown nonuniform shortening along some muscle fascicles during low-load elbow flexion (J. Appl. Physiol. 92 (2002) 2381). The purpose of this study was to uncover the features of the biceps brachii architecture and material properties that could lead to nonuniform shortening. We created a three-dimensional finite-element model of the biceps brachii and compared the tissue strains predicted by the model with experimentally measured tissue strains. The finite-element model predicted strains that were within one standard deviation of the experimentally measured strains. Analysis of the model revealed that the variation in fascicle lengths within the muscle and the curvature of the fascicles were the primary factors contributing to nonuniform strains. Continuum representations of muscle, combined with in vivo image data, are needed to deepen our understanding of how complex geometric arrangements of muscle fibers affect muscle contraction mechanics.

Introduction

Skeletal muscle has a complex hierarchical organization in which thousands of force-producing muscle fibers are arranged within a connective tissue network. The properties of individual fibers have been studied in isolation over the last four decades (e.g., Gordon et al., 1966; Denoth et al., 2002). However, how the behaviors of muscle fibers may change once they are arranged within muscle is not well understood. Therefore, “lumped-parameter” models, which assume that all fibers act independently and shorten uniformly, are used to mathematically represent whole muscle.

Recent experimental studies have reported nonuniform shortening along fascicles (bundles of fibers) within muscle (Ahn et al., 2003; Pappas et al., 2002; Drost et al., 2003). In one study, dynamic magnetic resonance (MR) images taken of the long head of the biceps brachii showed nonuniform shortening along some muscle fascicles during low-load elbow flexion (Pappas et al., 2002). These data challenge the simplifying assumptions made in lumped-parameter models of muscle and motivate us to identify the features of the biceps architecture that could contribute to nonuniform strains.

Even though the biceps brachii is typically considered to have a parallel-fibered architecture, the fascicles have a more complex geometrical arrangement (Fig. 1) that could potentially contribute to nonuniform shortening. For example, muscle shortening could be affected by the difference in the lengths of the centerline fascicles and the anterior fascicles and/or the curvature of the anterior fascicles (Asakawa et al., 2002). Stretch in passive structures, such as the internal aponeuroses or the external fascia, also has the potential to create complex strain distributions. There is evidence that lateral transmission of tension between fibers is present (Street, 1983; Trotter, 1993), which plays a significant role in force production and transmission (Huijing, 1999; Purslow, 2002). The resistance to shearing between fibers and muscle volume preservation also affect the tissue deformations. To explore the effects of fascicle geometry and passive structures on the strain distributions, a model that incorporates the fiber properties, volume preservation, shear properties, and detailed fascicle geometry of the biceps muscle is needed.

The purpose of this work was to uncover the features of the biceps architecture that contribute to the nonuniform strains. We developed a new constitutive model for muscle that represents the active and passive muscle fiber characteristics, intramuscular connective tissue properties, and muscle volume preservation. In this model, we used a new set of parameters to characterize tissue deformations that represents transverse properties of the tissue in a novel and intuitive manner. We created a finite-element model that replicated the major features of the biceps brachii muscle internal geometry, simulated the conditions imposed in a previous dynamic imaging study (Pappas et al., 2002), and compared tissue strains in the model with these in vivo data. We then varied the model's fascicle geometry to explore the effects of the architecture on the strain distributions in the muscle. Specifically, we examined the effects of the nonuniform fiber lengths, fascicle curvature, aponeurosis stretch, and external fascia on the distribution of fascicle strains.