TO THE EDITOR ON THE ROLE OF BIARTICULAR MUSCLES IN HUMAN JUMPING

Muscle function in the human squat jump has been studied in various ways. van Ingen Schenau and colleagues (reviewed by van Ingen Schenau, 1989) have used the inverse dynamics approach in combination with measurements of ground reaction forces and EMGs from some of the major leg muscles. Calculated peak net joint power (Bobbert and van Ingen Schenau, 1988) was highest in the knee (x 2500 W), it was only slightly lower in the ankle and much lower in the hip (x 1500 W). This is in contrast to the volumes of the muscles crossing the joints. A consideration of muscle volume showed that the muscle fibrcs of the ankle plantar flexors would not be able to generate the high peak net power output. The discrepancy was explained by (i) the actions of the biarticular muscles, which evoke a mechanical coupling ofjoints and (ii) a rapid release of stored elastic energy in the Achilles tendon and tendinous sh&s of the m. gastrocnemius (GAS) and m. soleus. The authors concluded that jumping performance is largely influenced by the action of biarticular muscles. Power generated by the voluminous hip and knee extensors would be transported to more distal joints by a timely activation of biarticular muscles like rectus femoris (RF) and GAS. In our opinion, the coupling action of a biarticular muscle is complicated owing to its complex dynamic properties (e.g. Zajac, 1989; Van Lecuwen, 1992). The coupling is influenced by the activation of muscle fibres, muscle fibre properties, instantaneous muscle-tendon complex length and velocity, strain energy storage and other factors. Thus, coupling is by no means as strict as it would be with an inextensible string. A disadvantage of the usage of biarticular muscles as force transmitters is an energy loss owing to viscous properties of the tendons and the muscle belly. Most of the absorbed energy by tendons and tendinous sheets can be recovered in elastic recoil (Ker, 1981). This is different for muscle fibres. To avoid a substantial energy loss, it is of crucial importance that forcible stretching of muscle fibres is avoided as much as possible. A better understanding of the co-ordination of muscle activity during jumping could be obtained by a direct dynamics analysis with appropriate models for all leg muscles and including joint-angular dependence of muscle moment arms. This would show the complete flow of mechanical power in the jumping apparatus. Search techniques could be employed to find optimum muscle activation patterns. A valuable step towards this goal was recently made in this journal by Pandy et al. (1990) and Pandy and Zajac (1991). They formulated a four-segment model, jointed together with frictionless rcvolutes, and driven by 8 musculo-tendon actuators. The authors challenged the idea that jumping pcrformance could be increased by the unique biarticular action of the GAS by comparing simulated jumps (i) with all muscles, (ii) with all biarticular muscles removed and (iii) with all biarticular muscles removed, but with the addition of a monoarticular GAS (Pandy and Zajac, 1991). Jumping performance was found highest in case (iii) and lowest in case (ii). For the following reasons, we doubt whether these findings allow Pandy and Zajac’s conclusion about the GAS: (a) The moment arms of the simulated muscles were not always very accurate, resulting in particular in a vanishing flexor knee moment of GAS towards knee extension (Pandy et al., 1990; Fig. 4b). Hence, close to full knee extension, the simulated biarticular GAS works effectively as a monoarticular muscle. Since GAS is mainly active just before toeoff, we would indeed expect only a small calculated difference between the simulated biarticular and monoarticular GAS. In simulation (i), RF was calculated to have a significant negative work contribution. Therefore, the absence of RF in case (iii) gives the highest simulated jumping performance. In contrast to Pandy and Zajac’s model assumptions, Spoor et al. (1990) have measured increasing moment arms of GAS with knee extension. Muscle moment arms about the knee vary such that knee angulation is decelerated towards full extension, and leg segmental kinetic energy (associated with rotation) is used to further lift the centre of mass through enhanced net ankle power output. Via the force transmitting limb bones, this power is transported to proximal segments. As explained by Pandy and Zajac (1991), the massive trunk segment gains most energy during the jump, so that one can speak of an energy flow from the leg muscles in a proximd direction. (b) The linear stress-strain relationship of the tendons used by Pandy and Zajac (1991) might have led to a more than realistic initial muscle fibre stretching and, therefore, to an increased energy loss in the biarticular muscles. Furthermore, maximum contraction speed and activation dynamics were chosen the same for all muscle-tendon actuators, whereas the well-known fast properties of the GAS may be essential to avoid, initially, forcible muscle fibre stretching. We conclude that: (i) A leg with a combination of mono and biarticular muscles is still likely to have a higher effective energy output than a leg with monoarticular muscles only (and equal total muscle mass) would have, if forcible muscle fibre stretching in the biarticular muscles is avoided by a fine tuning of activation. Nevertheless, it remains to be proven quantitatively that the energetic advantages more than compensate for the energy losses in biarticular muscles. (ii) The direct dynamics approach is very promising, but it requires implementation of more accurate model descriptions of muscles and joints before the issue of the role of biarticular muscles can be settled.