L. J. Richard Casius

Humans adjust control to initial squat depth in vertical squat jumping

The purpose of this study was to gain insight into the control strategy that humans use in jumping. Eight male gymnasts performed vertical squat jumps from five initial postures that differed in squat depth (P1-P5) while kinematic data, ground reaction forces, and electromyograms (EMGs) of leg muscles were collected; the latter were rectified and smoothed to obtain SREMGs. P3 was the preferred initial posture; in P1, P2, P4, and P5 height of the mass center was +13, +7, -7 and -14 cm, respectively, relative to that in P3. Furthermore, maximum-height jumps from the initial postures observed in the subjects were simulated with a model comprising four body segments and six Hill-type muscles. The only input was the onset of stimulation of each of the muscles (Stim). The subjects were able to perform well-coordinated squat jumps from all postures. Peak SREMG levels did not vary among P1-P5, but SREMG onset of plantarflexors occurred before that of gluteus maximus in P1 and > 90 ms after that in P5 (P < 0.05). In the simulation study, similar systematic shifts occurred in Stim onsets across the optimal control solutions for jumps from P1-P5. Because the adjustments in SREMG onsets to initial posture observed in the subjects were very similar to the adjustments in optimal Stim onsets of the model, it was concluded that the SREMG adjustments were functional, in the sense that they contributed to achieving the greatest jump height possible from each initial posture. For the model, we were able to develop a mapping from initial posture to Stim onsets that generated successful jumps from P1-P5. It appears that to explain how subjects adjust their control to initial posture there is no need to assume that the brain contains an internal dynamics model of the musculoskeletal system.

The merits of a parallel genetic algorithm in solving hard optimization problems

A parallel genetic algorithm for optimization is outlined, and its performance on both mathematical and biomechanical optimization problems is compared to a sequential quadratic programming algorithm, a downhill simplex algorithm and a simulated annealing algorithm. When high-dimensional non-smooth or discontinuous problems with numerous local optima are considered, only the simulated annealing and the genetic algorithm, which are both characterized by a weak search heuristic, are successful in finding the optimal region in parameter space. The key advantage of the genetic algorithm is that it can easily be parallelized at negligible overhead.

Robust passive dynamics of the musculoskeletal system compensate for unexpected surface changes during human hopping

When human hoppers are surprised by a change in surface stiffness, they adapt almost instantly by changing leg stiffness, implying that neural feedback is not necessary. The goal of this simulation study was first to investigate whether leg stiffness can change without neural control adjustment when landing on an unexpected hard or unexpected compliant (soft) surface, and second to determine what underlying mechanisms are responsible for this change in leg stiffness. The muscle stimulation pattern of a forward dynamic musculoskeletal model was optimized to make the model match experimental hopping kinematics on hard and soft surfaces. Next, only surface stiffness was changed to determine how the mechanical interaction of the musculoskeletal model with the unexpected surface affected leg stiffness. It was found that leg stiffness adapted passively to both unexpected surfaces. On the unexpected hard surface, leg stiffness was lower than on the soft surface, resulting in close-to-normal center of mass displacement. This reduction in leg stiffness was a result of reduced joint stiffness caused by lower effective muscle stiffness. Faster flexion of the joints due to the interaction with the hard surface led to larger changes in muscle length, while the prescribed increase in active state and resulting muscle force remained nearly constant in time. Opposite effects were found on the unexpected soft surface, demonstrating the bidirectional stabilizing properties of passive dynamics. These passive adaptations to unexpected surfaces may be critical when negotiating disturbances during locomotion across variable terrain.

Spring-like leg behaviour, musculoskeletal mechanics and control in maximum and submaximum height human hopping

The purpose of this study was to understand how humans regulate their ‘leg stiffness’ in hopping, and to determine whether this regulation is intended to minimize energy expenditure. ‘Leg stiffness’ is the slope of the relationship between ground reaction force and displacement of the centre of mass (CM). Variations in leg stiffness were achieved in six subjects by having them hop at maximum and submaximum heights at a frequency of 1.7 Hz. Kinematics, ground reaction forces and electromyograms were measured. Leg stiffness decreased with hopping height, from 350 N m−1 kg−1 at 26 cm to 150 N m−1 kg−1 at 14 cm. Subjects reduced hopping height primarily by reducing the amplitude of muscle activation. Experimental results were reproduced with a model of the musculoskeletal system comprising four body segments and nine Hill-type muscles, with muscle stimulation STIM(t) as only input. Correspondence between simulated hops and experimental hops was poor when STIM(t) was optimized to minimize mechanical energy expenditure, but good when an objective function was used that penalized jerk of CM motion, suggesting that hopping subjects are not minimizing energy expenditure. Instead, we speculated, subjects are using a simple control strategy that results in smooth movements and a decrease in leg stiffness with hopping height.

Consequences of Ankle Joint Fixation on Fes Cycling Power Output: A Simulation Study

INTRODUCTION During fixed-ankle FES cycling in paraplegics, in which the leg position is completely determined by the crank angle, mechanical power output is low. This low power output limits the cardiovascular load that could be realized during FES ergometer cycling, and limits possibilities for FES cycling as a means of locomotion. Stimulation of ankle musculature in a released-ankle setup might increase power output. However, releasing the ankle joint introduces a degree of freedom in the leg that has to be controlled, which imposes constraints on the stimulation pattern. METHODS In this study, a forward dynamics modeling/simulation approach was used to assess the potential effect of releasing the ankle on the maximal mechanical power output. RESULTS For the released-ankle setup, the optimal stimulation pattern was found to be less tightly related to muscle shortening/lengthening than for the fixed-ankle setup, which indicates the importance of the constraints introduced by releasing the ankle. As a result, the maximal power output for 45-RPM cycling in the released-ankle setup was found to be about 10% lower than with a fixed ankle, despite the additional muscle mass available for stimulation. Power output for the released-ankle setup can be improved by tuning the point of contact between the foot and pedal to the relative strength of the ankle plantar flexors. For the model used, power output was 14% higher than for the fixed-ankle setup when this point of contact was moved posteriorly by 0.075 m. CONCLUSION Releasing the ankle joint and stimulating the triceps surae and tibialis anterior is expected to result in a modest increase in power output at best.

The relationship between pedal force and crank angular velocity in sprint cycling

PURPOSE Relationships between tangential pedal force and crank angular velocity in sprint cycling tend to be linear. We set out to understand why they are not hyperbolic, like the intrinsic force-velocity relationship of muscles. METHODS We simulated isokinetic sprint cycling at crank angular velocities ranging from 30 to 150 rpm with a forward dynamic model of the human musculoskeletal system actuated by eight lower extremity muscle groups. The input of the model was muscle stimulation over time, which we optimized to maximize average power output over a cycle. RESULTS Peak tangential pedal force was found to drop more with crank angular velocity than expected based on intrinsic muscle properties. This linearizing effect was not due to segmental dynamics but rather due to active state dynamics. Maximizing average power in cycling requires muscles to bring their active state from as high as possible during shortening to as low as possible during lengthening. Reducing the active state is a relatively slow process, and hence must be initiated a certain amount of time before lengthening starts. As crank angular velocity goes up, this amount of time corresponds to a greater angular displacement, so the instant of switching off extensor muscle stimulation must occur earlier relative to the angle at which pedal force was extracted for the force-velocity relationship. CONCLUSION Relationships between pedal force and crank angular velocity in sprint cycling do not reflect solely the intrinsic force-velocity relationship of muscles but also the consequences of activation dynamics.