Optimal muscle fascicle length and tendon stiffness for maximising gastrocnemius efficiency during human walking and running
Introduction
There is a trade-off in muscle architecture between a muscle being energetically economical at resisting force or at performing work during a contraction. The cost of generating force is a direct function of fibre length (and hence the number of activated sarcomeres in series). Force-generating muscles therefore have short fibres. This also acts to increase the cross-sectional area per unit volume and hence force producing capacity of the muscle. Muscles have to generate forces at a range of lengths in a movement. This defines a minimum fibre length, though in many human locomotor muscles much of the length change will occur in series elastic components rather than the muscle fibres. Muscles also need to generate force whilst shortening to perform mechanical work. Here, due to the force velocity relationship, a longer fibre can achieve the same absolute fibre velocity with a lower sarcomere velocity and a higher fibre force. In addition, maximum power output is achieved at approximately one third of maximum shortening velocity (Vmax) and efficiency is greatest at velocities of about one-quarter of Vmax (Alexander, 1997, Alexander, 2002; Hill, 1950; Hof et al., 2002; Woledge et al., 1985). It is therefore energetically sensible for a muscle fibre to shorten between one-quarter and one-third of Vmax during movements where a muscle is required to do mechanical work. This favours longer fibres with a length concomitant with the maximum velocity (and force) required of the fibre.
In a muscle which must both generate isometric force and undertake work (e.g. a limb extensor), there is a trade-off where short fibres reduce activation cost but long fibres reduce the sarcomere shortening velocity for any given shortening speed. A third factor is that if a muscle is contracting slowly and around optimal length it can have a higher force and hence the muscle can have a smaller activated physiological cross-sectional area (PCSA) and can therefore be smaller and hence lighter, which reduces limb inertia and basal metabolic costs (Rall, 1985). There should therefore be an energetic optimum where the required volume is a minimum.
Series elastic tissue, specifically the tendon and the aponeurosis sheets in the muscle, also aid muscle versatility. Legs appear as springs during running and most of the muscle tendon unit (MTU) length change occurs in series elastic tissues (Biewener et al., 1998; Roberts et al., 1997; Wilson et al., 2003). We have shown in human running that the medial gastrocnemius (MG) fascicles shorten at a velocity concomitant with maximum power (one third of Vmax) whilst the MTU is shortening three times faster; i.e. at fascicle Vmax (Lichtwark and Wilson, 2006). In addition, we have used relatively simple models to demonstrate that the Achilles tendon (AT) is of appropriate stiffness to maximise gastrocnemius efficiency during locomotion in average, young adults (Lichtwark and Wilson, 2007). This research also showed that increasing or decreasing the stiffness of tendons beyond that of the average stiffness would reduce the efficiency of the muscle. However, AT stiffness varies substantially between individuals (Hof, 1997; Lichtwark and Wilson, 2006; Maganaris and Paul, 2002). Does this imply that some individuals may have substantially less efficient muscle than others? This is unlikely, because individuals may also have different muscle properties that are not accounted for in the previous model. For instance, individuals also have varied muscle fascicle lengths and volumes, which both influence the force producing capacity and efficiency of a muscle.
Fascicle length, muscle volume and tendon stiffness differ between individuals with different sporting histories (Arampatzis et al., 2006; Muraoka et al., 2005; Roy and Edgerton, 1992). It would be logical if these differences reflect an optimum for an athlete's chosen sport but it is not clear whether muscle architecture defines the sport an athlete will be best at or whether the architecture reflects the outcome of long-term training. Here we determine the influence of human MG fascicle length and AT stiffness on muscle efficiency for walking and running. We assume that kinematics and kinetics (and hence MTU force and length over time) do not change and vary fascicle length and tendon stiffness of a Hill type muscle model representing the MG. This allows us to determine the active muscle volume required to generate the muscle force for a given fascicle velocity and calculate the metabolic cost incurred by the muscle to undertake the movement. Our hypothesis is that there is an optimum combination of fascicle length and tendon stiffness which maximises efficiency and minimises activated muscle volume for each gait type. Due to the differences in power, force and velocity required from the muscle at each gait and speed, we expect the optimal fascicle length and tendon stiffness combination to be different for each gait.
Section snippets
Kinematic and kinetic data
Average sagittal plane ankle and knee joint angles and ankle joint moments for walking (1.2 m/s), running (3.2 m/s) and fast running (3.9 m/s) were digitised from Novacheck (1998) and filtered using a zero-phase shift, fourth order, 15 Hz low pass Butterworth filter. Ankle and knee angles were used to estimate the MG MTU strain using the polynomial equations of Grieve and colleagues (1978). The moment arm of the AT at the ankle joint for each angle of dorsi/plantar flexion was estimated using the
Results
Fig. 4A shows how efficiency is influenced by fascicle length and linear AT stiffness. With increase in speed, it is apparent that a longer muscle fascicle with a stiffer tendon will maximise fascicle efficiency. The model predicts that with optimum architecture efficiency is slightly higher in both running and fast running (40.2% and 40.1%, respectively) than in walking (37.5%). However, a relatively broad range of muscle fascicle lengths and tendon stiffness values can achieve high efficiency
Discussion
The efficiency of a muscle working in series with a tendon is task specific. We demonstrate that different muscle fascicle lengths and tendon compliance combinations are required to maximise efficiency under different gait conditions and speeds. To maximise efficiency during walking requires shorter muscle fascicles and more compliant tendons than for running. A broad range of muscle fascicle lengths (ranging from 45 to 70 mm) and tendon stiffness values (150–500 N/mm) can, however, achieve close
Acknowledgements
G.L. is supported by a NHMRC Peter Doherty Postdoctoral Fellowship (Australia). A.W. is a holder of a BBSRC Research Development Fellowship and a Royal Society Wolfson Research Merit Award (UK).
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