The elevated metabolic cost of walking at preferred speeds of healthy elderly on treadmills compared to overground is not related to increased self-reported anxiety.

PURPOSE: To investigate whether the elevation in metabolic cost of walking on treadmills compared to overground for healthy elderly is related to self-reported anxiety and if changes in self-reported anxiety are related to changes in heart rate. METHODS: We measured overground preferred walking speed, oxygen consumption rate and heart rates during rest and walking, and self-reported anxiety in 10 elderly (mean age 69.5 ± 3.1 years, 8 males and 2 females). At their preferred speed, the participants first walked overground, then on a high treadmill, and then on a low treadmill. Gross and Net metabolic costs of walking were calculated from the rates of oxygen consumption. RESULTS: Gross and net metabolic cost of walking were higher (p < 0.05) on high treadmill (net cost: 2.64 J kg-1 m-1) and low treadmill (net cost: 2.68 J kg-1 m-1) compared to overground (net cost: 2.44 J kg-1 m-1), and the same was true for heart rate. There were no significant differences (p > 0.05) in metabolic costs and heart rates between the two treadmill conditions. Self-reported anxiety was higher on the high treadmill compared to overground (p = 0.004) and compared to low treadmill (p = 0.02). We found no significant difference (p > 0.05) for self-reported anxiety between overground and the low treadmill. CONCLUSION: These results show that treadmill walking cannot be adequately generalized to overground walking. The differences found in metabolic cost on treadmills compared to overground were not related to differences in self-reported anxiety. Furthermore, the changes in heart rate are not related to changes in self-reported anxiety.

Metabolic cost in healthy fit older adults and young adults during overground and treadmill walking.

PURPOSE: The purpose of this study was to determine whether net metabolic cost of walking is affected by age per se. METHODS: We selected 10 healthy, active older adults (mean age 75 years) and 10 young adults (mean age 26 years), and determined their preferred overground walking speed. On the same day, in a morning and afternoon session, we had them walk at that speed overground and on a treadmill while we measured oxygen consumption rate. From the latter we subtracted the rate in sitting and calculated net metabolic cost. RESULTS: Anthropometrics were not different between the groups nor was preferred walking speed (1.27 m s-1 both groups). There was no difference in net metabolic cost of overground walking between older and young adults (e.g., in the morning 2.64 and 2.56 J kg-1 m-1, respectively, p > 0.05). In the morning session, net metabolic cost of walking was higher on the treadmill than overground in our older adults by 0.6 J kg-1 m-1 (p < 0.05), but not in young adults. CONCLUSION: First, there is no effect of age per se on metabolic cost of overground walking. Second, older adults tend to have higher metabolic cost of walking on a treadmill than walking overground at preferred speed, and adaptation may take a long time. The commonly reported age-related elevation of metabolic cost of walking may be due to confounding factors causing preferred walking speed to be lower in older adults, and/or due to older adults reacting differently to treadmill walking than young adults.

The cost of moving optimally: kinematic path selection.

It is currently unclear whether the brain plans movement kinematics explicitly or whether movement paths arise implicitly through optimization of a cost function that takes into account control and/or dynamic variables. Several cost functions are proposed in the literature that are very different in nature (e.g., control effort, torque change, and jerk), yet each can predict common movement characteristics. We set out to disentangle predictions of the different variables using a combination of modeling and empirical studies. Subjects performed goal-directed arm movements in a force field (FF) in combination with visual perturbations of seen hand position. This FF was designed to have distinct optimal movements for muscle-input and dynamic costs while leaving kinematic cost unchanged. Visual perturbations in turn changed the kinematic cost but left the dynamic and muscle-input costs unchanged. An optimally controlled, physiologically realistic arm model was used to predict movements under the various cost variables. Experimental results were not consistent with a cost function containing any of the control and dynamic costs investigated. Movement patterns of all experimental conditions were adequately predicted by a kinematic cost function comprising both visually and somatosensory perceived jerk. The present study provides clear behavioral evidence that the brain solves kinematic and mechanical redundancy in separate steps: in a first step, movement kinematics are planned; and in a second, separate step, muscle activation patterns are generated.

Bimanual proprioception: are two hands better than one?

Information about the position of an object that is held in both hands, such as a golf club or a tennis racquet, is transmitted to the human central nervous system from peripheral sensors in both left and right arms. How does the brain combine these two sources of information? Using a robot to move participant's passive limbs, we performed psychophysical estimates of proprioceptive function for each limb independently and again when subjects grasped the robot handle with both arms. We compared empirical estimates of bimanual proprioception to several models from the sensory integration literature: some that propose a combination of signals from the left and right arms (such as a Bayesian maximum-likelihood estimate), and some that propose using unimanual signals alone. Our results are consistent with the hypothesis that the nervous system both has knowledge of and uses the limb with the best proprioceptive acuity for bimanual proprioception. Surprisingly, a Bayesian model that postulates optimal combination of sensory signals could not predict empirically observed bimanual acuity. These findings suggest that while the central nervous system seems to have information about the relative sensory acuity of each limb, it uses this information in a rather rudimentary fashion, essentially ignoring information from the less reliable limb.

Increased velocity feedback gains in the presence of sensory noise can explain paradoxical changes in trunk motor control related to back pain.

Literature reports paradoxical findings regarding effects of low-back pain (LBP) on trunk motor control. Compared to healthy individuals, patients with LBP, especially those with high pain-related anxiety, showed stronger trunk extensor reflexes and more resistance against perturbations. On the other hand, LBP patients and especially those with high pain-related anxiety showed decreased precision in unperturbed trunk movement and posture. These paradoxical effects might be explained by arousal potentially increasing average and variance of muscle spindle firing rates. Increased average firing rates could increase resistance against perturbations, but increased variance could decrease precision. We performed a simulation study to test this hypothesis. We modeled the trunk as a 2D inverted pendulum, stabilized by two antagonistic Hill-type muscles, based on their open-loop muscle activation dependent intrinsic stiffness and damping and through 25 ms-delayed, noisy contractile element length and velocity feedback. Reference feedback gains and sensory noise levels were tuned based on previously reported experimental data. We assessed the effect of increasing feedback gains on precision of trunk orientation at different perturbation magnitudes and assessed sensitivity of the effects to open-loop muscle stimulation and noise levels. At low perturbation magnitudes, increasing reflex gains consistently caused an increase in the variance of trunk orientation. At larger perturbation magnitudes, increasing reflex gains consistently caused a decrease in the variance of trunk orientation. Our results support the notion that LBP and related anxiety may increase reflex gains, resulting in an increase in the average and variance of spindle afference, which in turn increase resistance against perturbations and decrease movement precision.

Control of position and movement is simplified by combined muscle spindle and Golgi tendon organ feedback.

Whereas muscle spindles play a prominent role in current theories of human motor control, Golgi tendon organs (GTO) and their associated tendons are often neglected. This is surprising since there is ample evidence that both tendons and GTOs contribute importantly to neuromusculoskeletal dynamics. Using detailed musculoskeletal models, we provide evidence that simple feedback using muscle spindles alone results in very poor control of joint position and movement since muscle spindles cannot sense changes in tendon length that occur with changes in muscle force. We propose that a combination of spindle and GTO afferents can provide an estimate of muscle-tendon complex length, which can be effectively used for low-level feedback during both postural and movement tasks. The feasibility of the proposed scheme was tested using detailed musculoskeletal models of the human arm. Responses to transient and static perturbations were simulated using a 1-degree-of-freedom (DOF) model of the arm and showed that the combined feedback enabled the system to respond faster, reach steady state faster, and achieve smaller static position errors. Finally, we incorporated the proposed scheme in an optimally controlled 2-DOF model of the arm for fast point-to-point shoulder and elbow movements. Simulations showed that the proposed feedback could be easily incorporated in the optimal control framework without complicating the computation of the optimal control solution, yet greatly enhancing the system's response to perturbations. The theoretical analyses in this study might furthermore provide insight about the strong physiological couplings found between muscle spindle and GTO afferents in the human nervous system.

Limiting radial pedal forces greatly reduces maximal power output and efficiency in sprint cycling: an optimal control study.

A cyclist's performance depends critically on the generated average mechanical power output (AMPO). The instantaneous mechanical power output equals the product of crank angular velocity, crank length, and the tangential pedal force. Radial pedal forces do not contribute to mechanical power. It has been suggested that radial pedal forces arise from suboptimal pedaling technique and that limiting these would increase AMPO and efficiency. Here, we presented an optimal control musculoskeletal model of a cyclist (consisting of five segments driven by nine Hill-type muscle-tendon units) to predict maximal AMPO during sprint cycling at different levels of allowed radial pedal forces. Our findings showed that limiting radial pedal forces has a detrimental effect on maximal AMPO; it dropped from 1,115 W without a limit on radial forces to 528 W when no radial forces were allowed (both at 110 rpm). We explained that avoiding radial pedal forces causes ineffective use of muscles: muscles deliver less positive power and have a higher muscle power dissipation ratio (average mechanical power dissipated per unit of average positive power delivered). We concluded that radial pedal forces are an unavoidable by-product when optimizing for maximal AMPO and that limiting these leads to a performance decrease.NEW & NOTEWORTHY In the literature, but also in the "cycling field" [e.g., trainers, coaches, and (professional) cyclists], it is often suggested that trying to limit/avoid radial pedal forces enhances cycling technique and with that maximal average power output and efficiency. In this paper, we introduce an optimal control model of a human cyclists (consisting of five segments and driven by nine Hill-type muscle-tendon complex models). With that we not only show, but also explain why limiting radial forces is a bad idea: it will decrease maximal attainable AMPO and will decrease efficiency.

The energetic effect of hip flexion and retraction in walking at different speeds: a modeling study.

In human walking, power for propulsion is generated primarily via ankle and hip muscles. The addition of a 'passive' hip spring to simple bipedal models appears more efficient than using only push-off impulse, at least, when hip spring associated energetic costs are not considered. Hip flexion and retraction torques, however, are not 'free', as they are produced by muscles demanding metabolic energy. Studies evaluating the inclusion of hip actuation costs, especially during the swing phase, and the hip actuation's energetic benefits are few and far between. It is also unknown whether these possible benefits/effects may depend on speed. We simulated a planar flat-feet model walking stably over a range of speeds. We asked whether the addition of independent hip flexion and retraction remains energetically beneficial when considering work-based metabolic cost of transport (MCOT) with different efficiencies of doing positive and negative work. We found asymmetric hip actuation can reduce the estimated MCOT relative to ankle actuation by up to 6%, but only at medium speeds. The corresponding optimal strategy is zero hip flexion and some hip retraction actuation. The reason for this reduced MCOT is that the decrease in collision loss is larger than the associated increase in hip negative work. This leads to a reduction in total positive mechanical work, which results in an overall lower MCOT. Our study shows how ankle actuation, hip flexion, and retraction actuation can be coordinated to reduce MCOT.

Does ankle push-off correct for errors in anterior-posterior foot placement relative to center-of-mass states?

Understanding the mechanisms humans use to stabilize walking is vital for predicting falls in elderly. Modeling studies identified two potential mechanisms to stabilize gait in the anterior-posterior direction: foot placement control and ankle push-off control: foot placement depends on position and velocity of the center-of-mass (CoM) and push-off covaries with deviations between actual and predicted CoM trajectories. While both control mechanisms have been reported in humans, it is unknown whether especially the latter one is employed in unperturbed steady-state walking. Based on the finding of Wang and Srinivasan that foot placement deviates in the same direction as the CoM states in the preceding swing phase, and assuming that this covariance serves the role of stabilizing gait, the covariance between the CoM states and foot placement can be seen as a measure of foot placement accuracy. We subsequently interpreted the residual variance in foot placement from a linear regression model as "errors" that must be compensated, and investigated whether these foot placement errors were correlated to push-off kinetic time series of the subsequent double stance phase. We found ankle push-off torque to be correlated to the foot placement errors in 30 participants when walking at normal and slow speeds, with peak correlations over the double stance phase up to 0.39. Our study suggests that humans use a push-off strategy for correcting foot placement errors in steady-state walking.

Can proprioceptive training improve motor learning?

Recent work has investigated the link between motor learning and sensory function in arm movement control. A number of findings are consistent with the idea that motor learning is associated with systematic changes to proprioception (Haith A, Jackson C, Mial R, Vijayakumar S. Adv Neural Inf Process Syst 21: 593-600, 2008; Ostry DJ, Darainy M, Mattar AA, Wong J, Gribble PL. J Neurosci 30: 5384-5393, 2010; Vahdat S, Darainy M, Milner TE, Ostry DJ. J Neurosci 31: 16907-16915, 2011). Here, we tested whether motor learning could be improved by providing subjects with proprioceptive training on a desired hand trajectory. Subjects were instructed to reproduce both the time-varying position and velocity of novel, complex hand trajectories. Subjects underwent 3 days of training with 90 movement trials per day. Active movement trials were interleaved with demonstration trials. For control subjects, these interleaved demonstration trials consisted of visual demonstration alone. A second group of subjects received visual and proprioceptive demonstration simultaneously; this group was presented with the same visual stimulus, but, in addition, their limb was moved through the target trajectory by a robot using servo control. Subjects who experienced the additional proprioceptive demonstration of the desired trajectory showed greater improvements during training movements than control subjects who only received visual information. This benefit of adding proprioceptive training was seen in both movement speed and position error. Interestingly, additional control subjects who received proprioceptive guidance while actively moving their arm during demonstration trials did not show the same improvement in positional accuracy. These findings support the idea that the addition of proprioceptive training can augment motor learning, and that this benefit is greatest when the subject passively experiences the goal movement.

The validation of new phase-dependent gait stability measures: a modelling approach.

Identification of individuals at risk of falling is important when designing fall prevention methods. Current measures that estimate gait stability and robustness appear limited in predicting falls in older adults. Inspired by recent findings on changes in phase-dependent local stability within a gait cycle, we devised several phase-dependent stability measures and tested for their usefulness to predict gait robustness in compass walker models. These measures are closely related to the often-employed maximum finite-time Lyapunov exponent and maximum Floquet multiplier that both assess a system's response to infinitesimal perturbations. As such, they entail linearizing the system, but this is realized in a rotating hypersurface orthogonal to the period-one solution followed by estimating the trajectory-normal divergence rate of the swing phases and the foot strikes. We correlated the measures with gait robustness, i.e. the largest perturbation a walker can handle, in two compass walker models with either point or circular feet to estimate their prediction accuracy. To also test for the dependence of the measures under state space transform, we represented the point feet walker in both Euler-Lagrange and Hamiltonian canonical form. Our simulations revealed that for most of the measures their correlation with gait robustness differs between models and between different state space forms. In particular, the latter may jeopardize many stability measures' predictive capacity for gait robustness. The only exception that consistently displayed strong correlations is the divergence of foot strike. Our results admit challenges of using phase-dependent stability measures as objective means to estimate the risk of falling.

The central nervous system does not minimize energy cost in arm movements.

It has been widely suggested that the many degrees of freedom of the musculoskeletal system may be exploited by the CNS to minimize energy cost. We tested this idea by having subjects making point-to-point movements while grasping a robotic manipulandum. The robot created a force field chosen such that the minimal energy hand path for reaching movements differed substantially from those observed in a null field. The results show that after extended exposure to the force field, subjects continued to move exactly as they did in the null field and thus used substantially more energy than needed. Even after practicing to move along the minimal energy path, subjects did not adapt their freely chosen hand paths to reduce energy expenditure. The results of this study indicate that for point-to-point arm movements minimization of energy cost is not a dominant factor that influences how the CNS arrives at kinematics and associated muscle activation patterns.

The Metabolic Cost of Walking in healthy young and older adults - A Systematic Review and Meta Analysis.

The Metabolic Cost of Walking (MCoW) is an important variable of daily life that has been studied extensively. Several studies suggest that MCoW is higher in Older Adults (OA) than in Young Adults (YA). However, it is difficult to compare values across studies due to differences in the way MCoW was expressed, the units in which it was reported and the walking speed at which it was measured. To provide an overview of MCoW in OA and YA and to investigate the quantitative effect of age on MCoW, we have conducted a literature review and performed two meta-analyses. We extracted data on MCoW in healthy YA (18-41 years old) and healthy OA (≥59 years old) and calculated, if not already reported, the Gross (GCoW) and Net MCoW (NCoW) in J/kg/m. If studies reported MCoW measured at multiple speeds, we selected those values for YA and OA at which MCoW was minimal. All studies directly comparing YA and OA were selected for meta-analyses. From all studies reviewed, the average GCoW in YA was 3.4 ± 0.4 J/kg/m and 3.8 ± 0.4 J/kg/m in OA (~12% more in OA), and the average NCoW in YA was 2.4 ± 0.4 J/kg/m and 2.8 ± 0.5 J/kg/m in OA (~17% more in OA). Our meta-analyses indicated a statistically significant elevation of both GCoW and NCoW (p < 0.001) for OA. In terms of GCoW, OA expended about 0.3 J/kg/m more metabolic energy than YA and about 0.4 J/kg/m more metabolic energy than YA in terms of NCoW. Our study showed a statistically significant elevation in MCoW of OA over YA. However, from the literature it is unclear if this elevation is directly caused by age or due to an interaction between age and methodology. We recommend further research comparing MCoW in healthy OA and YA during "natural" over-ground walking and treadmill walking, after sufficient familiarization time.

Metabolic Cost of Activation and Mechanical Efficiency of Mouse Soleus Muscle Fiber Bundles During Repetitive Concentric and Eccentric Contractions.

Currently available data on the energetics of isolated muscle preparations are based on bouts of less than 10 muscle contractions, whereas metabolic energy consumption is mostly relevant during steady state tasks such as locomotion. In this study we quantified the energetics of small fiber bundles of mouse soleus muscle during prolonged (2 min) series of contractions. Bundles (N = 9) were subjected to sinusoidal length changes, while measuring force and oxygen consumption. Stimulation (five pulses at 100 Hz) occurred either during shortening or during lengthening. Movement frequency (2-3 Hz) and amplitude (0.25-0.50 mm; corresponding to ± 4-8% muscle fiber strain) were close to that reported for mouse soleus muscle during locomotion. The experiments were performed at 32°C. The contributions of cross-bridge cycling and muscle activation to total metabolic energy expenditure were separated using blebbistatin. The mechanical work per contraction cycle decreased sharply during the first 10 cycles, emphasizing the importance of prolonged series of contractions. The mean ± SD fraction of metabolic energy required for activation was 0.37 ± 0.07 and 0.56 ± 0.17 for concentric and eccentric contractions, respectively (both 0.25 mm, 2 Hz). The mechanical efficiency during concentric contractions increased with contraction velocity from 0.12 ± 0.03 (0.25 mm 2 Hz) to 0.15 ± 0.03 (0.25 mm, 3 Hz) and 0.16 ± 0.02 (0.50 mm, 2 Hz) and was -0.22 ± 0.08 during eccentric contractions (0.25 mm, 2 Hz). The percentage of type I fibers correlated positively with mechanical efficiency during concentric contractions, but did not correlate with the fraction of metabolic energy required for activation.

Inverse dynamics of mechanical multibody systems: An improved algorithm that ensures consistency between kinematics and external forces.

Inverse dynamics is a technique in which measured kinematics and, possibly, external forces are used to calculate net joint torques in a rigid body linked segment model. However, kinematics and forces are usually not consistent due to incorrect modelling assumptions and measurement errors. This is commonly resolved by introducing 'residual forces and torques' which compensate for this problem, but do not exist in reality. In this study a constrained optimization algorithm is proposed that finds the kinematics that are mechanically consistent with measured external forces and mimic the measured kinematics as closely as possible. The algorithm was tested on datasets containing planar kinematics and ground reaction forces obtained during human walking at three velocities (0.8 m/s, 1.25 and 1.8 m/s). Before optimization, the residual force and torque were calculated for a typical example. Both showed substantial values, indicating the necessity of developing a mechanically consistent algorithm. The proposed optimization algorithm converged to a solution in which the residual forces and torques were zero, without changing the ground reaction forces and with only minor changes to the measured kinematics. When using a rigid body approach, our algorithm ensures a consistent description of forces and kinematics, thereby improving the validity of calculated net joint torque and power values.

Searching for strategies to reduce the mechanical demands of the sit-to-stand task with a muscle-actuated optimal control model.

BACKGROUND: The sit-to-stand task, which involves rising unassisted from sitting on a chair to standing, is important in daily life. Many people with muscle weakness, reduced range of motion or loading-related pain in a particular joint have difficulty performing the task. How should a person suffering from such impairment best perform the sit-to-stand task and, in the case of pain in a particular joint, with reduced loading of that joint? METHODS: We developed a musculoskeletal model with reference parameter values based on properties of healthy strong subjects. The model's muscle stimulation-time input was optimized using direct collocation to find strategies that yielded successful sit-to-stand task performance with minimum 'control effort' for the reference set and modified sets of parameter values, and with constraints on tibiofemoral compression force. FINDINGS: The sit-to-stand task could be performed successfully and realistically by the reference model, by a model with isometric knee extensor forces reduced to 40% of reference, by a model with isometric forces of all muscles reduced to 45% of reference, and by the reference model with the tibiofemoral compression force constrained during optimization to 65% of the peak value in the reference condition. INTERPRETATION: The strategies found by the model in conditions other than reference could be interpreted well on the basis of cost function and task biomechanics. The question remains whether it is feasible to teach patients with musculoskeletal impairments or joint pain to perform the sit-to-stand task according to strategies that are optimal according to the simulation model.

Optimizing the Distribution of Leg Muscles for Vertical Jumping.

A goal of biomechanics and motor control is to understand the design of the human musculoskeletal system. Here we investigated human functional morphology by making predictions about the muscle volume distribution that is optimal for a specific motor task. We examined a well-studied and relatively simple human movement, vertical jumping. We investigated how high a human could jump if muscle volume were optimized for jumping, and determined how the optimal parameters improve performance. We used a four-link inverted pendulum model of human vertical jumping actuated by Hill-type muscles, that well-approximates skilled human performance. We optimized muscle volume by allowing the cross-sectional area and muscle fiber optimum length to be changed for each muscle, while maintaining constant total muscle volume. We observed, perhaps surprisingly, that the reference model, based on human anthropometric data, is relatively good for vertical jumping; it achieves 90% of the jump height predicted by a model with muscles designed specifically for jumping. Alteration of cross-sectional areas-which determine the maximum force deliverable by the muscles-constitutes the majority of improvement to jump height. The optimal distribution results in large vastus, gastrocnemius and hamstrings muscles that deliver more work, while producing a kinematic pattern essentially identical to the reference model. Work output is increased by removing muscle from rectus femoris, which cannot do work on the skeleton given its moment arm at the hip and the joint excursions during push-off. The gluteus composes a disproportionate amount of muscle volume and jump height is improved by moving it to other muscles. This approach represents a way to test hypotheses about optimal human functional morphology. Future studies may extend this approach to address other morphological questions in ethological tasks such as locomotion, and feature other sets of parameters such as properties of the skeletal segments.

Length-dependent [Ca2+] sensitivity adds stiffness to muscle.

It is well documented that muscle fibers become more sensitive for [Ca2+] with increasing sarcomere length. In mechanical terms this length-dependent [Ca2+] sensitivity (LDCS) adds to the stiffness of muscle fibers, because muscle force, normalized for the force-length relationship at maximal stimulation, increases with contractile element (CE) length. Although LDCS is well-documented in the physiological literature, it is ignored in most motor control studies. The aim of the present study was to investigate the importance of LDCS as a contributor to the stiffness of a muscle. Comparison of experimental data with predictions derived from the model of activation dynamics proposed by Hatze (Myocybernetic Control Models of Skeletal Muscle, University of South Africa, Pretoria, 1981, pp. 31-42) indicated that this model captures the main characteristics of LDCS well. It was shown that LDCS accounts for the experimentally observed shifts in optimum length at sub-maximal stimulation levels. Furthermore, it was shown that in conditions with low-to-medium muscle stimulation, the contribution of LDCS to the total amount of stiffness provided by the muscle is substantial. It was concluded that LDCS is an important muscle property and should be taken into account in studies concerning motor control.

Humans make near-optimal adjustments of control to initial body configuration in vertical squat jumping.

We investigated adjustments of control to initial posture in squat jumping. Eleven male subjects jumped from three initial postures: preferred initial posture (PP), a posture in which the trunk was rotated 18° more backward (BP) and a posture in which it was rotated 15° more forward (FP) than in PP. Kinematics, ground reaction forces and electromyograms (EMG) were collected. EMG was rectified and smoothed to obtain smoothed rectified EMG (srEMG). Subjects showed adjustments in srEMG histories, most conspicuously a shift in srEMG-onset of rectus femoris (REC): from early in BP to late in FP. Jumps from the subjects' initial postures were simulated with a musculoskeletal model comprising four segments and six Hill-type muscles, which had muscle stimulation (STIM) over time as input. STIM of each muscle changed from initial to maximal at STIM-onset, and STIM-onsets were optimized using jump height as criterion. Optimal simulated jumps from BP, PP and FP were similar to jumps of the subjects. Optimal solutions primarily differed in STIM-onset of REC: from early in BP to late in FP. Because the subjects' adjustments in srEMG-onsets were similar to adjustments of the model's optimal STIM-onsets, it was concluded that the former were near-optimal. With the model we also showed that near-maximum jumps from BP, PP and FP could be achieved when STIM-onset of REC depended on initial hip joint angle and STIM-onsets of the other muscles were posture-independent. A control theory that relies on a mapping from initial posture to STIM-onsets seems a parsimonious alternative to theories relying on internal optimal control models.

In vivo dynamics of the musculoskeletal system cannot be adequately described using a stiffness-damping-inertia model.

BACKGROUND: Visco-elastic properties of the (neuro-)musculoskeletal system play a fundamental role in the control of posture and movement. Often, these properties are described and identified using stiffness-damping-inertia (KBI) models. In such an approach, perturbations are applied to the (neuro-)musculoskeletal system and subsequently KBI-model parameters are optimized to obtain a best fit between simulated and experimentally observed responses. Problems with this approach may arise because a KBI-model neglects critical aspects of the real musculoskeletal system. METHODOLOGY/PRINCIPAL FINDINGS: The purpose of this study was to analyze the relation between the musculoskeletal properties and the stiffness and damping estimated using a KBI-model, to analyze how this relation is affected by the nature of the perturbation and to assess the sensitivity of the estimated stiffness and damping to measurement errors. Our analyses show that the estimated stiffness and damping using KBI-models do not resemble any of the dynamical parameters of the underlying system, not even when the responses are very accurately fitted by the KBI-model. Furthermore, the stiffness and damping depend non-linearly on all the dynamical parameters of the underlying system, influenced by the nature of the perturbation and the time interval over which the KBI-model is optimized. Moreover, our analyses predict a very high sensitivity of estimated parameters to measurement errors. CONCLUSIONS/SIGNIFICANCE: The results of this study suggest that the usage of stiffness-damping-inertia models to investigate the dynamical properties of the musculoskeletal system under control by the CNS should be reconsidered.