ORIGINAL ARTICLE Y. Kawakami ® K. Kubo ® H. Kanehisa ® T. Fukunaga Effect of series elasticity on isokinetic torque–angle relationship in humans Accepted: 22 April 2002 / Published online: 3 July 2002 Ó Springer-Verlag 2002 Abstract The influence of muscle series elasticity on the relationship between torque and joint angle during dy- namic contractions was studied. The torque–angle rela- tionship during the maximal isokinetic knee extension was determined for six male subjects (25–45 years) at 0.52, 1.05, 1.57, 2.09, 2.62, 3.49 rad/s. The knee joint angle at which peak torque was observed showed a systematic shift to more extended positions, i.e., the quadriceps muscle–tendon unit length became shorter as the velocity increased [from 1.01 (0.12) rad (0.52 rad/s) to 0.75 (0.14) rad (3.49 rad/s), mean (SD)]. The corre- sponding difference in muscle–tendon unit length be- tween 0.52 and 3.49 rad/s, estimated from the angle shift at peak torque and the moment arm length change of the quadriceps muscles, was 9 (4) mm. The relationship between estimated changes in muscle–tendon unit length and muscle force of the vastus lateralis and intermedius (VLI) over the seven velocities (including isometric contraction, 0 rad/s) coincided with the load-elongation properties of the series elastic component of VLI, determined separately in vivo by ultrasonography when the same subjects performed a ramp isometric knee extension. The results suggest that the torque–angle relationship is affected by the interaction between con- tractile and elastic components, and that peak torque angle shift is attributable to the elongation of tendinous tissues as a function of force applied to them. Keywords Knee extension ® Isometric and isokinetic contractions ® Vastus lateralis muscle ® Ultrasound ® Tendinous tissues Introduction The relationship between force and shortening velocity of a muscle is typically described as a hyperbolic curve where muscle force progressively decreases at higher velocity (Fenn and Marsh 1935; Hill 1938; for human muscle fibers, Coirault et al. 1994). For human muscles, this force–velocity relationship has often been studied from the relationship between torque and angular velocity of a joint that the muscle(s) cross(es), and in many cases, peak torque over the range of motion is reported. However, arguments against this approach exist, and one of the concerns is that the muscle length is not controlled over different velocities. Supporting evi- dence for this claim is that the joint angle at which peak torque is observed shifts to the latter phase of movement (i.e., shorter muscle length) as the velocity increases (Bobbert and van Ingen Schenau 1990; Fuglevand 1987; Taylor et al. 1991; Thorstensson et al. 1976). Previous studies revealed muscle deformation upon contraction: muscle fibers shorten even during fixed-end, isometric contractions while series elastic components (SEC) such as tendinous tissues (Huijing 1992; Kawa- kami and Lieber 2000) is elongated to take up muscle fiber shortening (Fukunaga et al. 1997; Griffiths 1991; Kawakami et al. 1998; Lieber et al. 1992; Maganaris and Paul 1999). This means that muscle fiber lengths are not constant, even at identical joint angles, if muscle force levels are different. This fact prompted us to suppose that the above-peak torque angle shift in the torque–velocity relationship is related to the interaction between muscle fibers and SEC. We hypothesized that the changes in muscle force at different velocities results in changes in the amount of SEC elongation, inducing the shift of peak torque angles to a degree correspond- ing to the SEC length changes. To test this hypothesis, we measured SEC lengthening for human muscles in vivo, and compared it with the change in length of the muscle–tendon unit due to the peak torque angle shift. Eur J Appl Physiol (2002) 87: 381–387 DOI 10.1007/s00421-002-0657-6 Y. Kawakami (&) ® K. Kubo ® H. Kanehisa ® T. Fukunaga Department of Life Sciences (Sports Sciences), Graduate School of Arts and Sciences, University of Tokyo, Komaba, Komaba 3-8-1, Meguro, Tokyo 153-8902, Japan E-mail: kawakami@idaten.c.u-tokyo.ac.jp Tel.: +81-3-54546866 Fax: +81-3-54544317