Crank inertial load has little effect on steady-state pedaling coordination

Inertial load can affect the control of a dynamic system whenever parts of the system are accelerated ordeclerated. During steady-state pedating, because within-cycle variations in crank angular acceleration still exist, the amount of crank inertia present (which varies widely with road-riding gear ratio) may affect the within-cycle coordination of muscles. However, the effect of inertial load on steady-state pedaling coordination is almos always assumed to be negligible, since the net mechanical energy per cycle developed by muscles only depends on the constant cadence and workload. This study tests the hypothesis that under steady-state conditions, the net joint torques produced by muscles at the hip, knee, and ankle are unaffected by crank inertial load. To perform the investigation, we constructed a pedaling apparatus which could emulate the low inertial load of a standard ergometer or the high inertial load of a road bicycle in high gear. Crank angle and bilateral pedal force and angle data were collected from ten subjects instructed to pedal steadily (i.e. constant speed across cycles) and smoothly (i.e. constant speed within a cycle) against both inertias at a constant workload. Virtually no statistically significant changes were found in the net hip and knee muscle joint torques calculated from an inverse dynamics analysis. Though the net ankle muscle joint torque, as well as the one- and two-legged crank torque, showed statistically significant increases at the higher inertia, the changes were small. In contrast, large statistically significant reductions were found in crank kinematic variability both within a cycle and between cycles (i.e. cadence), primarily because a larger inertial load means a slower crank dynamic response. Nonetheless, the reduction in cadence variability was somewhat attenuated by a large statistically significant increase in one-legged crank torque variability. We suggest, therefore, that muscle coordination during steady-state pedaling is largely unaffected, though less well regulated, when crank inertial load is increased.     

Classification of dynamics of a model of motor coordination and comparison with Parkinson's disease data

In our recent reports motor coordination of human lower limbs has been investigated during pedaling a special kind of ergometer which allows its left and right pedals to rotate independently. In particular, relative phase between left and right rotational-velocity waveforms of the pedals and their amplitude modulation have been analyzed for patients with Parkinson's disease (PD). Several patients showed peculiar interlimb coordination different from the regular anti-phase pattern of normal subjects. We have reported that these disordered patterns could be classified into four groups. Moreover, it has been demonstrated that a mathematical model could reproduce most of the disordered patterns. Such a model includes a schematization of the central pattern generator with two identical half-centers mutually coupled and two tonic control signals from higher motor centers, each of which inputs to one of the half-centers. Depending on the intensities of the tonic signals and on the differences between them, the model could generate a range of dynamics comparable to the clinically observed disordered patterns. In this paper, we explore the dynamics of the model by varying the intensities of the tonic signals in the model. Using the same method used for classifying the clinical data, the dynamics of the model are classified into several groups. The classified groups for the simulated data are compared with those for the clinical data to look at qualitative correspondence. Our systematic exploration of the model's dynamics in a wide range of the parameter space has revealed global organization of the bifurcations including Hopf bifurcations and cascades of period-doubling bifurcations among others, suggesting that the bifurcations, induced by instability of stable dynamics of the human motor control system, are responsible for the emergence of the disordered coordination in PD patients.     

A coupled oscillator model of disordered interlimb coordination in patients with Parkinson's disease

Coordination between the left and right limbs during cyclic movements, which can be characterized by the amplitude of each limb's oscillatory movement and relative phase, is impaired in patients with Parkinson's disease (PD). A pedaling exercise on an ergometer in a recent clinical study revealed several types of coordination disorder in PD patients. These include an irregular and burst-like amplitude modulation with intermittent changes in its relative phase, a typical sign of chaotic behavior in nonlinear dynamical systems. This clinical observation leads us to hypothesize that emergence of the rhythmic motor behaviors might be concerned with nonlinearity of an underlying dynamical system. In order to gain insight into this hypothesis, we consider a simple hard-wired central pattern generator model consisting of two identical oscillators connected by reciprocal inhibition. In the model, each oscillator acts as a neural half-center controlling movement of a single limb, either left or right, and receives a control input modeling a flow of descending signals from higher motor centers. When these two control inputs are tonic-constant and identical, the model has left-right symmetry and basically exhibits ordered coordination with an alternating periodic oscillation. We show that, depending on the intensities of these two control inputs and on the difference between them that introduces asymmetry into the model, the model can reproduce several behaviors observed in the clinical study. Bifurcation analysis of the model clarifies two possible mechanisms for the generation of disordered coordination in the model: one is the spontaneous symmetry-breaking bifurcation in the model with the left-right symmetry. The other is related to the degree of asymmetry reflecting the difference between the two control inputs. Finally, clinical implications by the model's dynamics are briefly discussed.     

Generating dynamic simulations of movement using computed muscle control

Computation of muscle excitation patterns that produce coordinated movements of muscle-actuated dynamic models is an important and challenging problem. Using dynamic optimization to compute excitation patterns comes at a large computational cost, which has limited the use of muscle-actuated simulations. This paper introduces a new algorithm, which we call computed muscle control, that uses static optimization along with feedforward and feedback controls to drive the kinematic trajectory of a musculoskeletal model toward a set of desired kinematics. We illustrate the algorithm by computing a set of muscle excitations that drive a 30-muscle, 3-degree-of-freedom model of pedaling to track measured pedaling kinematics and forces. Only 10 min of computer time were required to compute muscle excitations that reproduced the measured pedaling dynamics, which is over two orders of magnitude faster than conventional dynamic optimization techniques. Simulated kinematics were within 1 degrees of experimental values, simulated pedal forces were within one standard deviation of measured pedal forces for nearly all of the crank cycle, and computed muscle excitations were similar in timing to measured electromyographic patterns. The speed and accuracy of this new algorithm improves the feasibility of using detailed musculoskeletal models to simulate and analyze movement.     

Laboratory versus outdoor cycling conditions: differences in pedaling biomechanics

The aim of our study was to compare crank torque profile and perceived exertion between the Monark ergometer (818 E) and two outdoor cycling conditions: level ground and uphill road cycling. Seven male cyclists performed seven tests in seated position at different pedaling cadences: (a) in the laboratory at 60, 80, and 100 rpm; (b) on level terrain at 80 and 100 rpm; and (c) on uphill terrain (9.25% grade) at 60 and 80 rpm. The cyclists exercised for 1 min at their maximal aerobic power. The Monark ergometer and the bicycle were equipped with the SRM Training System (Schoberer, Germany) for the measurement of power output (W), torque (Nxm), pedaling cadence (rpm), and cycling velocity (kmxh-1). The most important findings of this study indicate that at maximal aerobic power the crank torque profiles in the Monark ergometer (818 E) were significantly different (especially on dead points of the crank cycle) and generate a higher perceived exertion compared with road cycling conditions.     

The influence of seat configuration on maximal average crank power during pedaling: a simulation study

Manipulating seat configuration (i.e., seat tube angle, seat height and pelvic orientation) alters the bicycle-rider geometry, which influences lower extremity muscle kinematics and ultimately muscle force and power generation during pedaling. Previous studies have sought to identify the optimal configuration, but isolating the effects of specific variables on rider performance from the confounding effect of rider adaptation makes such studies challenging. Of particular interest is the influence of seat tube angle on rider performance, as seat tube angle varies across riding disciplines (e.g., road racers vs. triathletes). The goals of the current study were to use muscle-actuated forward dynamics simulations of pedaling to 1) identify the overall optimal seat configuration that produces maximum crank power and 2) systematically vary seat tube angle to assess how it influences maximum crank power. The simulations showed that a seat height of 0.76 m (or 102% greater than trochanter height), seat tube angle of 85.1 deg, and pelvic orientation of 20.5 deg placed the major power-producing muscles on more favorable regions of the intrinsic force-length-velocity relationships to generate a maximum average crank power of 981 W. However, seat tube angle had little influence on crank power, with maximal values varying at most by 1% across a wide range of seat tube angles (65 to 110 deg). The similar power values across the wide range of seat tube angles were the result of nearly identical joint kinematics, which occurred using a similar optimal seat height and pelvic orientation while systematically shifting the pedal angle with increasing seat tube angles.     

Examination of the λ equilibrium point hypothesis when applied to single degree of freedom movements performed with different inertial loads

 One of the theories of human motor control is the λ Equilibrium Point Hypothesis. It is an attractive theory since it offers an easy control scheme where the planned trajectory shifts monotionically from an initial to a final equilibrium state. The feasibility of this model was tested by reconstructing the virtual trajectory and the stiffness profiles for movements performed with different inertial loads and examining them. Three types of movements were tested: passive movements, targeted movements, and repetitive movements. Each of the movements was performed with five different inertial loads. Plausible virtual trajectories and stiffness profiles were reconstructed based on the λ Equilibrium Point Hypothesis for the three different types of movements performed with different inertial loads. However, the simple control strategy supported by the model, where the planned trajectory shifts monotonically from an initial to a final equilibrium state, could not be supported for targeted movements performed with added inertial load. To test the feasibility of the model further we must examine the probability that the human motor control system would choose a trajectory more complicated than the actual trajectory to control. Received: 20 June 1995 / Accepted in revised form: 6 August 1996     

Dynamics of wrist rotations

Understanding the dynamics of wrist rotations is important for many fields, including biomechanics, rehabilitation and motor neuroscience. This paper provides an experimentally based mathematical model of wrist rotation dynamics in Flexion-Extension (FE) and Radial-Ulnar Deviation (RUD), and characterizes the torques required to overcome the passive mechanical impedance of wrist rotations. We modeled the wrist as a universal joint with non-intersecting axes. The equations of motion of the hand rotating about the wrist joint include inertial, damping, and stiffness terms, with parameter values based on direct measurements (stiffness) or measurements combined with data available in the literature (inertia, damping). We measured the wrist kinematics of six young, healthy subjects making comfortable and fast-paced wrist rotations (±15° in FE, RUD, and combinations) and inserted these kinematic data into the model of wrist rotation dynamics. With this we quantified the torques required to overcome the impedance of wrist rotations and evaluated the relative importance of individual impedance terms as well as interactions between the degrees of freedom. We found that the wrist's passive stiffness is the major impedance the neuromuscular system must overcome to rotate the wrist. Inertia and passive damping only become important for very fast movements. Unlike elbow and shoulder reaching movements, inertial interaction torques are negligible for wrist rotations. Interaction torques due to stiffness and damping, however, are significant. Finally, we found that some model terms (inertial interaction torques, axis offset, and, for moderately sized rotations, non-linearities) can be neglected with little loss of accuracy, resulting in a simple, linear model useful for studies in biomechanics, motor neuroscience, and rehabilitation.     

Muscle contributions to specific biomechanical functions do not change in forward versus backward pedaling

Previous work had identified six biomechanical functions that need to be executed by each limb in order to produce a variety of pedaling tasks. The functions can be organized into three antagonistic pairs: an Ext/Flex pair that accelerates the foot into extension or flexion with respect to the pelvis, an Ant/Post pair that accelerates the foot anteriorly or posteriorly with respect to the pelvis, and a Plant/Dorsi pair that accelerates the foot into plantarflexion or dorsiflexion. Previous analyses of experimental data have inferred that muscles perform the same function during different pedaling tasks (e.g. forward versus backward pedaling) because the EMG timing was similar, but they did not present rigorous biomechanical analyses to assess whether a muscle performed the same biomechanical function, and if so, to what degree. Therefore, the objective of this study was to determine how individual muscles contribute to these biomechanical functions during two different motor tasks, forward and backward pedaling, through a theoretical analysis of experimental data. To achieve this objective, forward and backward pedaling simulations were generated and a mechanical energy analysis was used to examine how muscles generate, absorb or transfer energy to perform the pedaling tasks. The results showed that the muscles contributed to the same primary Biomechanical functions in both pedaling directions and that synergistic performance of certain functions effectively accelerated the crank. The gluteus maximus worked synergistically with the soleus, the hip flexors worked synergistically with the tibialis anterior, and the vasti and hamstrings functioned independently to accelerate the crank. The rectus femoris used complex biomechanical mechanisms including negative muscle work to accelerate the crank. The negative muscle work was used to transfer energy generated elsewhere (primarily from other muscles) to the pedal reaction force in order to accelerate the crank. Consistent with experimental data, a phase shift was required from those muscles contributing to the Ant/Post functions as a result of the different limb kinematics between forward and backward pedaling, although they performed the same biomechanical function. The pedaling simulations proved necessary to interpret the experimental data and identify motor control mechanisms used to accomplish specific motor tasks, as the mechanisms were often complex and not always intuitively obvious.     

Evaluation of performance criteria for simulation of submaximal steady-state cycling using a forward dynamic model.

The objectives of this study were twofold. The first was to develop a forward dynamic model of cycling and an optimization framework to simulate pedaling during submaximal steady-state cycling conditions. The second was to use the model and framework to identify the kinetic, kinematic, and muscle timing quantities that should be included in a performance criterion to reproduce natural pedaling mechanics best during these pedaling conditions. To make this identification, kinetic and kinematic data were collected from 6 subjects who pedaled at 90 rpm and 225 W. Intersegmental joint moments were computed using an inverse dynamics technique and the muscle excitation onset and offset were taken from electromyographic (EMG) data collected previously (Neptune et al., 1997). Average cycles and their standard deviations for the various quantities were used to describe normal pedaling mechanics. The model of the bicycle-rider system was driven by 15 muscle actuators per leg. The optimization framework determined both the timing and magnitude of the muscle excitations to simulate pedaling at 90 rpm and 225 W. Using the model and optimization framework, seven performance criteria were evaluated. The criterion that included all of the kinematic and kinetic quantities combined with the EMG timing was the most successful in replicating the experimental data. The close agreement between the simulation results and the experimentally collected kinetic, kinematic, and EMG data gives confidence in the model to investigate individual muscle coordination during submaximal steady-state pedaling conditions from a theoretical perspective, which to date has only been performed experimentally.     

Effect of fatigue on maximal power output at different contraction velocities in humans.

The effect of fatigue as a result of a standard submaximal dynamic exercise on maximal short-term power output generated at different contraction velocities was studied in humans. Six subjects performed 25-s maximal efforts on an isokinetic cycle ergometer at five different pedaling rates (60, 75, 90, 105, and 120 rpm). Measurements of maximal power output were made under control conditions [after 6 min of cycling at 30% maximal O2 uptake (VO2max)] and after fatiguing exercise that consisted of 6 min of cycling at 90% VO2max with a pedaling rate of 90 rpm. Compared with control values, maximal peak power measured after fatiguing exercise was significantly reduced by 23 +/- 19, 28 +/- 11, and 25 +/- 11% at pedaling rates of 90, 105, and 120 rpm, respectively. Reductions in maximum peak power of 11 +/- 8 and 14 +/- 8% at 60 and 75 rpm, respectively, were not significant. The rate of decline in peak power during the 25-s control measurement was least at 60 rpm (5.1 +/- 2.3 W/s) and greatest at 120 rpm (26.3 +/- 13.9 W/s). After fatiguing exercise, the rate of decline in peak power at pedaling rates of 105 and 120 rpm decreased significantly from 21.5 +/- 9.0 and 26.3 +/- 13.9 W/s to 10.0 +/- 7.3 and 13.3 +/- 6.9 W/s, respectively. These experiments indicate that fatigue induced by submaximal dynamic exercise results in a velocity-dependent effect on muscle power. It is suggested that the reduced maximal power at the higher velocities was due to a selective effect of fatigue on the faster fatigue-sensitive fibers of the active muscle mass.     

Stable walking with asymmetric legs

Asymmetric leg function is often an undesired side-effect in artificial legged systems and may reflect functional deficits or variations in the mechanical construction. It can also be found in legged locomotion in humans and animals such as after an accident or in specific gait patterns. So far, it is not clear to what extent differences in the leg function of contralateral limbs can be tolerated during walking or running. Here, we address this issue using a bipedal spring-mass model for simulating walking with compliant legs. With the help of the model, we show that considerable differences between contralateral legs can be tolerated and may even provide advantages to the robustness of the system dynamics. A better understanding of the mechanisms and potential benefits of asymmetric leg operation may help to guide the development of artificial limbs or the design novel therapeutic concepts and rehabilitation strategies.     

Measuring 3D Hand and Finger Kinematics—A Comparison between Inertial Sensing and an Opto-Electronic Marker System

Objective analysis of hand and finger kinematics is important to increase understanding of hand function and to quantify motor symptoms for clinical diagnosis. The aim of this paper is to compare a new 3D measurement system containing multiple miniature inertial sensors (PowerGlove) with an opto-electronic marker system during specific finger tasks in three healthy subjects. Various finger movements tasks were performed: flexion, fast flexion, tapping, hand open/closing, ab/adduction and circular pointing. 3D joint angles of the index finger joints and position of the thumb and index were compared between systems. Median root mean square differences of the main joint angles of interest ranged between 3.3 and 8.4deg. Largest differences were found in fast and circular pointing tasks, mainly in range of motion. Smallest differences for all 3D joint angles were observed in the flexion tasks. For fast finger tapping, the thumb/index amplitude showed a median difference of 15.8mm. Differences could be explained by skin movement artifacts caused by relative marker movements of the marker system, particularly during fast tasks; large movement accelerations and angular velocities which exceeded the range of the inertial sensors; and by differences in segment calibrations between systems. The PowerGlove is a system that can be of value to measure 3D hand and finger kinematics and positions in an ambulatory setting. The reported differences need to be taken into account when applying the system in studies understanding the hand function and quantifying hand motor symptoms in clinical practice.     

Calcium dynamics and vasomotion in arteries subject to isometric, isobaric, and isotonic conditions

In vitro, different techniques are used to study the smooth muscle cells’ calcium dynamics and contraction/relaxation mechanisms on arteries. Most experimental studies use either an isometric or an isobaric setup. However, in vivo, a blood vessel is neither isobaric nor isometric nor isotonic, as it is continuously submitted to intraluminal pressure variations arising from heart beat. We use a theoretical model of the smooth muscle calcium and arterial radius dynamics to determine whether results may be considerably different depending on the experimental conditions (isometric, isobaric, isotonic, or cyclic pressure variations). We show that isobaric conditions appear to be more realistic than isometric or isotonic situations, as the calcium dynamics is similar under cyclic intraluminal pressure variations (in vivo-like situation) and under a constant pressure (isobaric situation). The arterial contraction is less pronounced in isotonic than in isobaric conditions, and the vasoconstrictor sensitivity higher in isometric than isobaric or isotonic conditions, in agreement with experimental observations. Interestingly, the model predicts that isometric conditions may generate artifacts like the coexistence of multiple stable states. We have verified this model prediction experimentally using rat mesenteric arteries mounted on a wire myograph and stimulated with phenylephrine.     

Lactate acidosis and the increase in VE/VO2 during incremental exercise

The purpose of this investigation was to determine whether the onset of lactate acidosis is responsible for the increase in ventilatory equivalent (VE/VO2) during exercise of increasing intensity. Eight male subjects performed maximal incremental exercise tests on a cycle ergometer on two separate occasions. For the control (C) treatment, the initial work rates consisted of 4 min of unloaded pedaling (60 rpm) and 1 min of pedaling at a work rate of 30 W. Thereafter, the work rate was increased each minute by 22 W until volitional fatigue. Venous blood samples were taken before the onset of exercise and at the end of each work rate for determination of pH and lactate. Ventilatory parameters at each work rate were also monitored. Before the experimental treatment (E), the subjects performed two 3-min work bouts at high intensity (210-330 W) on the cycle ergometer in order to prematurely raise blood lactate levels and lower blood pH. The same incremental exercise test as C was then performed. The results indicated that the increase in VE/VO2 occurred at similar work rates and %VO2max although the venous H+ and lactate concentrations were significantly elevated during the E treatment. These results suggest that a decrease in the blood pH resulting from blood lactate accumulation is not responsible for the increase in VE/VO2 during incremental exercise.     

An equilibrium-point model of electromyographic patterns during single-joint movements based on experimentally reconstructed control signals

The purpose of this work has been to develop a model of electromyographic (EMG) patterns during single-joint movements based on a version of the equilibrium-point hypothesis, a method for experimental reconstruction of the joint compliant characteristics, the dual-strategy hypothesis, and a kinematic model of movement trajectory. EMG patterns are considered emergent properties of hypothetical control patterns that are equally affected by the control signals and peripheral feedback reflecting actual movement trajectory. A computer model generated the EMG patterns based on simulated movement kinematics and hypothetical control signals derived from the reconstructed joint compliant characteristics. The model predictions have been compared to published recordings of movement kinematics and EMG patterns in a variety of movement conditions, including movements over different distances, at different speeds, against different-known inertial loads, and in conditions of possible unexpected decrease in the inertial load. Changes in task parameters within the model led to simulated EMG patterns qualitatively similar to the experimentally recorded EMG patterns. The model's predictive power compares it favourably to the existing models of the EMG patterns.     

Non-driving intersegmental knee moments in cycling computed using a model that includes three-dimensional kinematics of the shank/foot and the effect of simplifying assumptions

Assessing the importance of non-driving intersegmental knee moments (i.e. varus/valgus and internal/external axial moments) on over-use knee injuries in cycling requires the use of a three-dimensional (3-D) model to compute these loads. The objectives of this study were: (1) to develop a complete, 3-D model of the lower limb to calculate the 3-D knee loads during pedaling for a sample of the competitive cycling population, and (2) to examine the effects of simplifying assumptions on the calculations of the non-driving knee moments. The non-driving knee moments were computed using a complete 3-D model that allowed three rotational degrees of freedom at the knee joint, included the 3-D inertial loads of the shank/foot, and computed knee loads in a shank-fixed coordinate system. All input data, which included the 3-D segment kinematics and the six pedal load components, were collected from the right limb of 15 competitive cyclists while pedaling at 225 W and 90 rpm. On average, the peak varus and internal axial moments of 7.8 and 1.5 N m respectively occurred during the power stroke whereas the peak valgus and external axial moments of 8.1 and 2.5 N m respectively occurred during the recovery stroke. However, the non-driving knee moments were highly variable between subjects; the coefficients of variability in the peak values ranged from 38.7% to 72.6%. When it was assumed that the inertial loads of the shank/foot for motion out of the sagittal plane were zero, the root-mean-squared difference (RMSD) in the non-driving knee moments relative to those for the complete model was 12% of the peak varus/valgus moment and 25% of the peak axial moment. When it was also assumed that the knee joint was revolute with the flexion/extension axis perpendicular to the sagittal plane, the RMSD increased to 24% of the peak varus/valgus moment and 204% of the peak axial moment. Thus, the 3-D orientation of the shank segment has a major affect on the computation of the non-driving knee moments, while the inertial contributions to these loads for motions out of the sagittal plane are less important.     

A two dimensional model for saccade generation

A model for the generation of oblique saccades is constructed by extending and modifying the one dimensional local feedback model. It is proposed that the visual system stores target location in inertial coordinates, but that the feedback loop which guides saccades works in retinotopic coordinates. To achieve straight trajectories for centripetal and centrifugal saccades in all meridians, a comparator computes motor error as a vector and uses the vectorial error signal to drive two orthogonally-acting burst generators. The generation of straight saccade trajectories when the extraocular muscles are of unequal strengths requires the introduction of a burst-tonic cell input to motor neurons. The model accounts for the results of two-site stimulation of the superior colliculus and frontal eye fields by allowing simultaneous activation of more than one comparator. The postulated existence of multiple comparators suggests that motor error may be computed topographically.     

Motor control and learning in altered dynamic environments

Dynamic perturbations of reaching movements are an important technique for studying motor learning and adaptation. Adaptation to non-contacting, velocity-dependent inertial Coriolis forces generated by arm movements during passive body rotation is very rapid, and when complete the Coriolis forces are no longer sensed. Adaptation to velocity-dependent forces delivered by a robotic manipulandum takes longer and the perturbations continue to be perceived even when adaptation is complete. These differences reflect adaptive self-calibration of motor control versus learning the behavior of an external object or 'tool'. Velocity-dependent inertial Coriolis forces also arise in everyday behavior during voluntary turn and reach movements but because of anticipatory feedforward motor compensations do not affect movement accuracy despite being larger than the velocity-dependent forces typically used in experimental studies. Progress has been made in understanding: the common features that determine adaptive responses to velocity-dependent perturbations of jaw and limb movements; the transfer of adaptation to mechanical perturbations across different contact sites on a limb; and the parcellation and separate representation of the static and dynamic components of multiforce perturbations.