* Corresponding author. Tel.: #31-4024-74837; fax: #31-4024- 47355. E-mail address: renedo@wfw.wtb.tue.nl (C.C. van Donkelaar) Journal of Biomechanics 32 (1999) 755}762 Skeletal muscle transverse strain during isometric contraction at di!erent lengths C.C. van Donkelaar*, P.J.B. Willems, A.M.M. Muijtjens, M.R. Drost Department of Movement Sciences, Cardiovascular Research Institute Maastricht (Carim), The Netherlands Faculty of Mechanical Engineering, Section Materials Technology, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands Department of Medical Informatics, Maastricht University, The Netherlands Received 22 March 1999 Abstract An important assumption in 2D numerical models of skeletal muscle contraction involves deformation in the third dimension of the included muscle section. The present paper studies the often used plane strain description. Therefore, 3D muscle surface deformation is measured from marker displacements during isometric contractions at various muscle lengths. Longitudinal strains at super"cial muscle "bers (!14$2.6% at ¸  , n"57) and aponeurosis (0.8$0.9% at ¸  ) decrease with increasing muscle length. The same holds for transverse muscle surface strains in super"cial muscle "bers and aponeurosis, which are comparable at intermediate muscle length, but di!er at long and short muscle length. Because transverse strains during isometric contraction change with initial muscle length, it is concluded that the e!ect of muscle length on muscle deformation cannot be studied in plane strain models. These results do not counteract the use of these models to study deformation in contractions with approximately !9% longitudinal muscle "ber strain, as transverse strain in super"cial muscle "bers and in aponeurosis tissue is minimal in that case. Aponeurosis surface area change decreases with increasing initial muscle length, but muscle "ber surface area change is !11%, independent of muscle length. Assuming incompressible muscle material, this means that strain perpendicular to the muscle surface equals 11%. Taking the relationship between transverse and longitudinal muscle "ber strain into account, it is hypothesized that super"cial muscle "bers #atten during isometric contractions.  1999 Elsevier Science Ltd. All rights reserved. Keywords: Three-dimensional deformation; Aponeurosis; Gastrocnemius medialis muscle; Plane strain; Finite element model 1. Introduction The basic function of skeletal muscle is to generate movement. To ful"l this function, they can produce force at di!erent lengths and velocities. Force-length and force-velocity curves are well-known descriptions of mechanical muscle functioning that incorporate only one spatial dimension. To study the e!ects of contraction on muscle "ber length, aponeurosis length or pennation angle, this approach is insu$cient. Therefore, a 2D rep- resentation of for instance the midsagittal muscle plane is often used to study muscle deformation (Gielen, 1998; Otten, 1988; Van Leeuwen and Spoor, 1996; Vankan et al., 1997,1998; Woittiez et al., 1984). Except for the model of Gielen (Gielen, 1998), who used a nearly plane stress approximation, these models use plane strain descriptions to calculate deformation. The assumption of constant muscle volume during contrac- tion is e!ectuated in these plane strain models by assum- ing constant muscle longitudinal sectional area. Thus, longitudinal shortening is only accounted for by increas- ing muscle size in the second model dimension, whereas deformation in the third dimension is suppressed. In contrast, free deform in the third dimension is allowed in plane stress simulations. Gielen et al (Gielen et al., 1998) compared plane stress and plane strain approximations in "nite element simula- tions of muscle contraction. Their results show distinct di!erences in tissue pressure and strain in all directions, which stresses the importance of these model 0021-9290/99/$ - see front matter  1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 1 - 9 2 9 0 ( 9 9 ) 0 0 0 7 3 - 1