Characterisation of the biomechanical, passive, and active properties of femur-tibia joint leg muscles in the stick insect Carausius morosus

The understanding of locomotive behaviour of an animal necessitates the knowledge not only about its neural activity but also about the transformation of this activity patterns into muscle activity. The stick insect is a well studied system with respect to its motor output which is shaped by the interplay between sensory signals, the central neural networks for each leg joint and the coordination between the legs. The muscles of the FT (femur-tibia) joint are described in their morphologies and their motoneuronal innervation patterns, however little is known about how motoneuronal stimulation affects their force development and shortening behaviour. One of the two muscles moving the joint is the extensor tibiae, which is particularly suitable for such an investigation as it features only three motoneurons that can be activated simultaneously, which comes close to a physiologically occuring activation pattern. Its antagonist, the flexor tibiae, has a more complex innervation and a biomechanical investigation is only reasonable at full motoneuronal recruitment. Muscle force and length changes were measured using a dual-mode lever system that was connected to the cut muscle tendon. Both tibial muscles of all legs were studied in terms of their geometry: extensor tibiae muscle length changes with the cosine of the FT joint angle, while flexor tibiae length changes with the negative cosine, except for extreme angles (close to 30° and 180°). For all three legs, effective flexor tibiae moment arm length (0.564 mm) is twice that of the extensor tibiae (0.282 mm). Flexor tibiae fibres are 1.5 times longer (2.11 mm) than extensor tibiae fibres (1.41 mm). Active isometric force measurements demonstrated that extensor tibiae single twitch force is notably smaller than its maximal tetanical force at 200 Hz (2-6 mN compared to 100-190 mN) and takes a long time to decrease completely (> 140 ms). Increasing either frequency or duration of the stimulation extends maximal force production and prolongs the relaxation time of the extensor tibiae. The muscle reveals `latch´ properties in response to a short-term increase in activation. Its working range is on the ascending limb of the force-length relationship (see Gordon et al. (1966b)) with a shift in maximum force development towards longer fibre lengths at lower activation. The passive static force increases exponentially with increasing stretch. Maximum forces of 5 mN for the extensor, and 15 mN for the flexor tibiae occur within the muscles´ working ranges. The combined passive torques of both muscles determine the rest position of the joint without any muscle activity. Dynamically generated forces of both muscles can become as large as 50-70 mN when stretch ramps mimick a fast middle leg swing phase. FT joint torques alone (with ablated muscles) do not depend on FT joint angle, but on deflection amplitude and velocity. Isotonic force experiments using physiological activation patterns demonstrate that the extensor tibiae acts like a low-pass filter by contracting smoothly to fast instantaneous stimulation frequency changes. Hill hyperbolas at 200 Hz vary a great deal with respect to maximal force (P0) but much less in terms of contraction velocity (V0) for both tibial muscles. Maximally stimulated flexor tibiae muscles are on average 2.7 times stronger than extensor tibiae muscles (415 mN and 151 mN), but contract only 1.4 times faster (6.05 mm/s and 4.39 mm/s). The dependence of extensor tibiae V0 and P0 on stimulation frequency can be described with an exponential saturation curve. V0 increases linearly with length within the muscle´s working range. Loaded release experiments characterise extensor and flexor tibiae series elastic components as quadratic springs. The mean spring constant of the flexor tibiae is 1.6 times larger than of the extensor tibiae at maximal stimulation. Extensor tibiae stretch and relaxation ramps show that muscle relaxation time constant slowly changes with muscle length, and thus muscle dynamics have a long-lasting dependence on muscle length history. High-speed video recordings show that changes in tibial movement dynamics match extensor tibiae relaxation changes at increasing stimulation duration.