Pennation angles of the intrinsic muscles of the foot

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Abstract

As mathematical models of the musculoskeletal system become increasingly detailed and precise, they require more accurate information about the architectural parameters of the individual muscles. These muscles are typically represented as Hill-type models, which require data on fiber length, physiological cross-sectional area (PCSA) and pennation angle. Most of this information for lower limb muscles has been published, except for data on the pennation angle of the intrinsic muscles of the foot. Each (n=20) intrinsic muscle of three human feet was dissected free. The dorsal and plantar surfaces were photographed and a digitized color image was imported into Abobe PhotoshopTM. The muscles were divided into “anatomical units”. For each anatomical unit (n=26), a line was drawn along the tendon axis and a number of other lines were drawn along individual muscle fibers. The angle between the tendon line and each fiber line was defined as the pennation angle of that fiber. By visual inspection, an effort was made to take measurements such that they represented the distribution of fibers in various parts of the muscle. Although some individual muscles had higher or lower pennation angles, when averaged for all specimens, the second dorsal interosseous had the smallest pennation angle (6.7±6.81°) while the abductor digiti minimi had the largest (19.1±11.19°). Since the cosines of the angles range from 0.9932 to 0.9449, the effect of the pennation angle on the force generated by the muscle was not great.

Introduction

Mathematical muscle models, such as the Hill-type, require architectural information. As these models become more complex, there is an increased need for accurate physiological parameters to correctly predict the behavior of muscles. The pertinent muscular characteristics are fiber length, total physiological cross-sectional area (PCSA) and pennation angle (the angle between the muscle fiber and the tendon). These parameters, when considered along with other information such as the elastic properties of tendon, electromyographic signals and activation dynamics, may be employed in Hill-type muscle models to generate computer simulations of muscles (Zajac, 1989). Muscle models of this nature have been used in a variety of musculoskeletal simulations (Delp et al., 1990; Delp and Loan, 1995; Piazza and Delp, 1996; Schutte, 1993; Yamaguchi, 1989).

In order to develop complete musculoskeletal models of the lower extremity, these parameters must be quantified for all pertinent muscles. Several studies have addressed this issue, but none has determined the pennation angle of the intrinsic musculature of the foot.

The relationship of each parameter (fiber length, PCSA and pennation angle) to the force generating characteristics of muscle is important. Fiber length corresponds to the number of sarcomeres in series; a longer fiber has a potentially faster shortening velocity. PCSA represents the number of fibers in parallel, which is related to the total amount of force a muscle can generate. Finally, the larger the pennation angle the less effect a muscle, both in shortening velocity and force generation, will have on the tendon.

Several authors have reported the architectural parameters of the major muscles of the lower extremity, excluding the intrinsics of the foot (Brand et al., 1986; Friederich and Brand, 1990; Spoor et al., 1991; Wickiewicz et al., 1983). There have also been two studies of the intrinsic musculature of the foot but neither included the pennation angles (Kura et al., 1997; Silver et al., 1985).

Therefore, the pennation angles of the intrinsic musculature of the foot represent some of the last pieces of information required for complete lower extremity musculoskeletal modeling. The purpose of this work was to quantify the pennation angles of the intrinsic musculature.

Section snippets

Materials and methods

Three embalmed feet from two elderly Caucasian cadavers, obtained through the Humanity Gifts Registry of the Commonwealth of Pennsylvania, were dissected. No other specific information was provided on the specimens. The Temple University Institutional Review Board approved the use of the specimens for this protocol. All dorsal and plantar intrinsic muscles (n=20) were dissected from the feet. The intrinsic muscles are organized into a dorsal layer with two muscles (extensor hallucis brevis

Results

The pennation angles for the twenty muscles are listed in Table 1, where they are grouped as dorsal or plantar, and the plantar muscles are further subdivided by layer. The average, standard deviation, number of measurements and coefficient of variation are provided.

The pennation angles in all cases were fairly acute. In several of the smaller muscles all fibers were essentially parallel to the line of pull. The largest pennation angle was in one specimen of abductor digiti minimi, where the

Discussion

Pennation angles were determined for 22 anatomical units representing 20 intrinsic muscles from each of the three human cadaveric feet. A number of fibers, distributed throughout each muscle, were used to calculate an average angle for each of the muscles.

Improper fiber selection can lead to inaccurate results if the pennation angles of different fibers vary greatly. Unfortunately, there is no way to ensure that the fibers selected are a truly representative sample of the muscle as a whole.

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This work was completed while the first author was finishing his studies in the Department of Bioengineering at the University of Pennsylvania.

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