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Muscle force-length dynamics are governed by intrinsic contractile properties, motor stimulation and mechanical load. Although intrinsic properties are well-characterised, physiologists lack in vitro instrumentation accounting for combined effects of limb inertia, musculoskeletal architecture and contractile dynamics. We introduce in vitro virtual-reality (in vitro-VR) which enables in vitro muscle tissue to drive a musculoskeletal jumping simulation. In hardware, muscle force from a frog plantaris was transmitted to a software model where joint torques, inertia and ground reaction forces were computed to advance the simulation at 1 kHz. To close the loop, simulated muscle strain was returned to update in vitro length. We manipulated 1) stimulation timing and, 2) the virtual muscle's anatomical origin. This influenced interactions among muscular, inertial, gravitational and contact forces dictating limb kinematics and jump performance. We propose that in vitro-VR can be used to illustrate how neuromuscular control and musculoskeletal anatomy influence muscle dynamics and biomechanical performance.

A striking feature among jumping frogs is a sharp pelvic bend about the ilio-sacral (IS) joint, unique to anurans. Although this sagittal plane hinge has been interpreted as crucial for the evolution of jumping, its mechanical contribution has not been quantified. Using a model based on Kassina maculata and animated with kinematics from prior experiments, we solved the ground contact dynamics in MuJoCo enabling inverse dynamics without force plate measurements. We altered the magnitude, speed and direction of IS extension (leaving remaining kinematics unaltered) to determine its role in jumping. Ground reaction forces (GRFs) matched recorded data. Prior work postulated that IS rotation facilitates jumping by aligning the torso with the GRF. However, our simulations revealed that static torso orientation has little effect on GRF due to the close proximity of the IS joint with the COM, failing to support the ‘torso alignment’ hypothesis. Rather than a postural role, IS rotation has a dynamic function whereby angular acceleration (i) influences GRF direction to modulate jump direction and (ii) increases joint loading, particularly at the ankle and knee, perhaps increasing tendon elastic energy storage early in jumps. Findings suggest that the pelvic hinge mechanism is not obligatory for jumping, but rather crucial for the fine tuning of jump trajectory, particularly in complex habitats.

We developed a novel reverse haptic interface to augment forward dynamic simulations with real-world contact forces. In contrast with traditional haptics, in which a realworld user drives an interaction with a simulated environment, reverse haptics allows a simulated mechanism to probe the realworld environment through a force-sensing robotic manipulator. This method can implicitly extend computer models of biomechanics and robotic control with complex ground interactions. A 3- DoF manipulator and a biologically inspired musculoskeletal model were developed to test jumping performance on a diverse range of real-world substrates. Jumps were of similar height despite differences in material properties and no active muscle control. Muscle power was lower at the hip, yet total muscle work was higher, against compliant surfaces compared to stiff surfaces. Through reverse haptics, the forces of actuation, inertia and contacts could be measured simultaneously to reveal how intrinsic muscle properties may compensate for substrate dynamics.

Although the red-legged running frog Kassina maculata is secondarily a walker/runner, it retains the capacity for multiple locomotor modes, including jumping at a wide range of angles (nearly 70°). Using simultaneous hind limb kinematics and single-foot ground reaction forces, we performed inverse dynamics analyses to calculate moment arms and torques about the hind limb joints during jumping at different angles in K. maculata. We show that forward thrust is generated primarily at the hip and ankle, while body elevation is primarily driven by the ankle. Steeper jumps are achieved by increased thrust at the hip and ankle and greater downward rotation of the distal limb segments. Due to its proximity to the GRF vector, knee posture appears to be important in controlling torque directions about this joint and, potentially, torque magnitudes at more distal joints. Other factors correlated with higher jump angles include increased body angle in the preparatory phase, faster joint openings and increased joint excursion, higher ventrally-directed force, and greater acceleration and velocity. Finally, we demonstrate that jumping performance in K. maculata does not appear to be compromised by presumed adaptation to walking/running. Our results provide new insights into how frogs engage in a wide range of locomotor behaviours and the multi-functionality of anuran limbs.