Maximal dismounts from high bar

In men's artistic gymnastics the triple straight somersault dismount from the high bar has yet to be performed in competition. The present study used a simulation model of a gymnast and the high bar apparatus (J. Appl. Biomech. 19(2003a) 119) to determine whether a gymnast could produce the required angular momentum and flight to complete a triple straight somersault dismount. Optimisations were carried out to maximise the margin for error in timing the bar release for a given number of straight somersaults in flight. The amount of rotation potential (number of straight somersaults) the model could produce whilst maintaining a realistic margin for error was determined. A simulation model of aerial movement (J. Biomech.23 (1990) 85) was used to find what would be possible with this amount of rotation potential. The model was able to produce sufficient angular momentum and time in the air to complete a triple straight somersault dismount. The margin for error when releasing the bar using the optimum technique was 28 ms, which is small when compared with the mean margin for error determined for high bar finalists at the 2000 Sydney Olympic Games (55 ms). Although the triple straight somersault dismount is theoretically possible, it would require close to maximum effort and precise timing of the release from the bar. However, when the model was required to have a realistic margin for error, it was able to produce sufficient angular momentum for a double twisting triple somersault dismount.     

The margin for error when releasing the asymmetric bars for dismounts

It has previously been shown that male gymnasts using the "scooped" giant circling technique were able to flatten the path followed by their mass center, resulting in a larger margin for error when releasing the high bar (Hiley and Yeadon, 2003a). The circling technique prior to performing double layout somersault dismounts from the asymmetric bars in women's artistic gymnastics appears to be similar to the "traditional" technique used by some male gymnasts on the high bar. It was speculated that as a result the female gymnasts would have margins for error similar to those of male gymnasts who use the traditional technique. However, it is unclear how the technique of the female gymnasts is affected by the need to avoid the lower bar. A 4-segment planar simulation model of the gymnast and upper bar was used to determine the margins for error when releasing the bar for 9 double layout somersault dismounts at the Sydney 2000 Olympics. The elastic properties of the gymnast and bar were modeled using damped linear springs. Model parameters, primarily the inertia and spring parameters, were optimized to obtain a close match between simulated and actual performances in terms of rotation angle (1.2 degrees), bar displacement (0.011 m), and release velocities (<1%). Each matching simulation was used to determine the time window around the actual point of release for which the model had appropriate release parameters to complete the dismount successfully. The margins for error of the 9 female gymnasts (release window 43-102 ms) were comparable to those of the 3 male gymnasts using the traditional technique (release window 79-84 ms).     

Influence of optimization constraints in uneven parallel bar dismount swing simulations

Forward dynamics simulations of a dismount preparation swing on the uneven parallel bars were optimized to investigate the sensitivity of dismount revolution potential to the maximum bar force before slipping, and to low-bar avoidance. All optimization constraints were classified as 1-anatomical/physiological; limiting maximum hand force on the high bar before slipping, joint ranges of motion and maximum torques, muscle activation/deactivation timing and 2-geometric; avoiding low-bar contact, and requiring minimum landing distance. The gymnast model included torso/head, arm and two leg segments connected by a planar rotating, compliant shoulder and frictionless ball-and-socket hip joints. Maximum shoulder and hip torques were measured as functions of joint angle and angular velocity. Motions were driven by scaling maximum torques by a joint torque activation function of time which approximated the average activation of all muscles crossing the joint causing extension/flexion, or adduction/abduction. Ten joint torque activation values, and bar release times were optimized to maximize dismount revolutions using the downhill simplex method. Low-bar avoidance and maximum bar-force constraints are necessary because they reduce dismount revolution potential. Compared with the no low-bar performance, optimally avoiding the low bar by piking and straddling (abducting) the hips reduces dismount revolutions by 1.8%. Using previously reported experimentally measured peak uneven bar-force values of 3.6 and 4.0 body weight (BW) as optimization constraints, 1.40 and 1.55 revolutions with the body extended and arms overhead were possible, respectively. The bar-force constraint is not active if larger than 6.9 BW, and instead performances are limited only by maximum shoulder and hip torques. Bar forces accelerate the mass center (CM) when performing muscular work to flex/extend the joints, and increase gymnast mechanical energy. Therefore, the bar-force constraint inherently limits performance by limiting the ability to do work and reducing system energy at bar release.     

Optimisation of high bar circling technique for consistent performance of a triple piked somersault dismount

The dismount from the high bar is one of the most spectacular skills performed in Men's Artistic Gymnastics. Hiley and Yeadon [2005. Maximal dismounts from high bar. Journal of Biomechanics 38, 2221-2227] optimised the technique in the backward giant circle prior to release using a computer simulation model to show that a gymnast could generate sufficient linear and angular momentum to perform a triple piked backward somersault dismount with a sufficiently large release window (the period of time during which the gymnast could release the bar and successfully complete the dismount). In the present study, it was found that when the timing of the actions at the hip and shoulder joints from the optimum simulation were perturbed by 30ms the resulting simulation could no longer meet the criteria for sufficient aerial rotation and release window. Since it is to be expected that a gymnast's technique can cope with small errors in timing for consistent performance, a requirement of robustness to timing perturbations should be included within the optimisation process. When the technique in the backward giant circle was optimised to be robust to 30ms perturbations, it was found that sufficient linear and angular momentum for a triple piked dismount could be achieved with a realistic release window.     

Evaluation of a subject-specific female gymnast model and simulation of an uneven parallel bar swing

A gymnast model and forward dynamics simulation of a dismount preparation swing on the uneven parallel bars were evaluated by comparing experimental and predicted joint positions throughout the maneuver. The bar model was a linearly elastic spring with a frictional bar/hand interface, and the gymnast model consisted of torso/head, arm and two leg segments. The hips were frictionless balls and sockets, and shoulder movement was planar with passive compliant structures approximated by a parallel spring and damper. Subject-specific body segment moments of inertia, and shoulder compliance were estimated. Muscles crossing the shoulder and hip were represented as torque generators, and experiments quantified maximum instantaneous torques as functions of joint angle and angular velocity. Maximum torques were scaled by joint torque activations as functions of time to produce realistic motions. The downhill simplex method optimized activations and simulation initial conditions to minimize the difference between experimental and predicted bar-center, shoulder, hip, and ankle positions. Comparing experimental and simulated performances allowed evaluation of bar, shoulder compliance, joint torque, and gymnast models. Errors in all except the gymnast model are random, zero mean, and uncorrelated, verifying that all essential system features are represented. Although the swing simulation using the gymnast model matched experimental joint positions with a 2.15cm root-mean-squared error, errors are correlated. Correlated errors indicate that the gymnast model is not complex enough to exactly reproduce the experimental motion. Possible model improvements including a nonlinear shoulder model with active translational control and a two-segment torso would not have been identified if the objective function did not evaluate the entire system configuration throughout the motion. The model and parameters presented in this study can be effectively used to understand and improve an uneven parallel bar swing, although in the future there may be circumstances where a more complex model is needed.     

Optimization of backward giant circle technique on the asymmetric bars

The release window for a given dismount from the asymmetric bars is the period of time within which release results in a successful dismount. Larger release windows are likely to be associated with more consistent performance because they allow a greater margin for error in timing the release. A computer simulation model was used to investigate optimum technique for maximizing release windows in asymmetric bars dismounts. The model comprised four rigid segments with the elastic properties of the gymnast and bar modeled using damped linear springs. Model parameters were optimized to obtain a close match between simulated and actual performances of three gymnasts in terms of rotation angle (1.5 degrees ), bar displacement (0.014 m), and release velocities (<1%). Three optimizations to maximize the release window were carried out for each gymnast involving no perturbations, 10-ms perturbations, and 20-ms perturbations in the timing of the shoulder and hip joint movements preceding release. It was found that the optimizations robust to 20-ms perturbations produced release windows similar to those of the actual performances whereas the windows for the unperturbed optimizations were up to twice as large. It is concluded that robustness considerations must be included in optimization studies in order to obtain realistic results and that elite performances are likely to be robust to timing perturbations of the order of 20 ms.     

The margin for error when releasing the high bar for dismounts

In Men's Artistic Gymnastics the current trend in elite high bar dismounts is to perform two somersaults in an extended body shape with a number of twists. Two techniques have been identified in the backward giant circles leading up to release for these dismounts (J. Biomech. 32 (1999) 811). At the Sydney 2000 Olympic Games 95% of gymnasts used the "scooped" backward giant circle technique rather than the "traditional" technique. It was speculated that the advantage gained from the scooped technique was an increased margin for error when releasing the high bar. A four segment planar simulation model of the gymnast and high bar was used to determine the margin for error when releasing the bar in performances at the Sydney 2000 Olympic Games. The eight high bar finalists and the three gymnasts who used the traditional backward giant circle technique were chosen for analysis. Model parameters were optimised to obtain a close match between simulated and actual performances in terms of rotation angle (1.2 degrees ), bar displacements (0.014 m) and release velocities (2%). Each matching simulation was used to determine the time window around the actual point of release for which the model had appropriate release parameters to complete the dismount successfully. The scooped backward giant circle technique resulted in a greater margin for error (release window 88-157 ms) when releasing the bar compared to the traditional technique (release window 73-84 ms).     

Coping with perturbations to a layout somersault in tumbling

Tumbling is a dynamic movement requiring control of the linear and angular momenta generated during the approach and takeoff phases. Both of these phases are subject to some variability even when the gymnast is trying to perform a given movement repeatedly. This paper used a simulation model of tumbling takeoff to establish how well gymnasts can cope with perturbations of the approach and takeoff phases. A five segment planar simulation model with torque generators at each joint was developed to simulate tumbling takeoffs. The model was customised to an elite gymnast by determining subject specific inertia and torque parameters and a simulation was produced which closely matched a performance of a layout somersault by the gymnast. The performance of a layout somersault was found to be sensitive to the approach characteristics and the activation timings but relatively insensitive to the elasticity of the track and maximum muscle strength. Appropriate variation of the activation timings used during the takeoff phase was capable of coping with moderate perturbations of the approach characteristics. A model of aerial movement established that variation of body configuration in the flight phase was capable of adjusting for takeoff perturbations that would lead to rotation errors of up to 8%. Providing the errors in perceiving approach characteristics are less than 5% or 5 degrees and the errors in timing activations are less than 7ms, perturbations in the approach can be accommodated using adjustments during takeoff and flight.     

Multijoint Control Strategies Transfer Between Tasks

In this paper, the hypothesis that multijoint control strategies are transferred between similar tasks was tested. To test this hypothesis, we studied the take-off phase of two types of backward somersault dives: one while translating backwards (Back), the other while translating forward (Reverse). An experimentally based dynamic model of the musculoskeletal system was employed to simulate the measured kinematics and reaction force data and to study the sensitivity of take-off performance to initial kinematic conditions. It was found that the horizontal velocity of the total body center of mass (CM) was most sensitive to modifications in the initial shank conditions. Consequently, the initial shank kinematics of the Back dive was modified in the optimization procedure while maintaining the joint coordination of the Back in order to generate the CM trajectory and reaction forces of a Reverse. Similarly, the initial shank kinematics of the Reverse dive was modified to simulate the CM trajectory and reaction force of the Back. It was found that small modifications in the initial shank kinematics led to change in direction of horizontal CM velocity at take-off; resulting in a switch from Back to Reverse and vice versa. In both cases, the simulated momentum conditions at departure and the bimodal shape of the reaction force-time curve were consistent with those experimentally observed. The results of this study support the hypothesis that transfer of control strategies between similar tasks is a viable option in multijoint control. This transfer of control strategy is explained using a hierarchical model of the motion control system.     

Analysis of kinematic invariances of multijoint reaching movement

 There is a no unique relationship between the trajectory of the hand, represented in cartesian or extrinsic space, and its trajectory in joint angle or intrinsic space in the general condition of joint redundancy. The goal of this work is to analyze the relation between planning the trajectory of a multijoint movement in these two coordinate systems. We show that the cartesian trajectory can be planned based on the task parameters (target coordinates, etc.) prior to and independently of angular trajectories. Angular time profiles are calculated from the cartesian trajectory to serve as a basis for muscle control commands. A unified differential equation that allows planning trajectories in cartesian and angular spaces simultaneously is proposed. Due to joint redundancy, each cartesian trajectory corresponds to a family of angular trajectories which can account for the substantial variability of the latter. A set of strategies for multijoint motor control following from this model is considered; one of them coincides with the frog wiping reflex model and resolves the kinematic inverse problem without inversion. The model trajectories exhibit certain properties observed in human multijoint reaching movements such as movement equifinality, straight end-point paths, bell-shaped tangential velocity profiles, speed-sensitive and speed-insensitive movement strategies, peculiarities of the response to double-step targets, and variations of angular trajectory without variations of the limb end-point trajectory in cartesian space. In humans, those properties are almost independent of limb configuration, target location, movement duration, and load. In the model, these properties are invariant to an affine transform of cartesian space. This implies that these properties are not a special goal of the motor control system but emerge from movement kinematics that reflect limb geometry, dynamics, and elementary principles of motor control used in planning. All the results are given analytically and, in order to compare the model with experimental results, by computer simulations. Received: 6 April 1994/Accepted in revised form: 25 April 1995     

A versatile ODE approximation to a network model for the spread of sexually transmitted diseases

 We develop a moment closure approximation (MCA) to a network model of sexually transmitted disease (STD) spread through a steady/casual partnership network. MCA has been used previously to approximate static, regular lattices, whereas application to dynamic, irregular networks is a new endeavour, and application to sociologically-motivated network models has not been attempted. Our goals are 1) to investigate issues relating to the application of moment closure approximations to dynamic and irregular networks, and 2) to understand the impact of concurrent casual partnerships on STD transmission through a population of predominantly steady monogamous partnerships. We are able to derive a moment closure approximation for a dynamic irregular network representing sexual partnership dynamics, however, we are forced to use a triple approximation due to the large error of the standard pair approximation. This example underscores the importance of doing error analysis for moment closure approximations. We also find that a small number of casual partnerships drastically increases the prevalence and rate of spread of the epidemic. Finally, although the approximation is derived for a specific network model, we can recover approximations to a broad range of network models simply by varying model parameters which control the structure of the dynamic network. Thus our moment closure approximation is very flexible in the kinds of network models it can approximate. Received: 26 August 2001 / Revised version: 15 March 2002 / Published online: 23 August 2002 C.T.B. was supported by the NSF. Key words or phrases: Moment closure approximation – Network model – Pair approximation – Sexually transmitted diseases – Steady/casual partnership network     

Spectral properties of human cognition and skill

 Many interactive human skills are based on real-time error detection and correction. Here we investigate the spectral properties of such skills, focusing on a synchronization task. A simple autoregressive error correction model, based on separate ‘motor’ and ‘cognitive’ sources, provides an excellent fit to experimental spectral data. The model can also apply to recurrent processes not based on error correction, allowing commentary on previous claims of 1/ f-type noise in human cognition. A comparison of expert and non-expert subjects suggests that performance skill is not only based on reduced variance and bias, but also on the construction of richer mental models of error correction. Received: 4 October 1995 / Accepted in revised form: 25 February 1997     

A mathematical high bar–human body model for analysing and interpreting mechanical-energetic processes on the high bar

The aims of this study were:

1. To study the transfer of energy between the high bar and the gymnast.

2. To develop criteria from the utilisation of high bar elasticity and the utilisation of muscle capacity to assess the effectiveness of a movement solution.

3. To study the influence of varying segment movement upon release parameters.

For these purposes a model of the human body attached to the high bar (high bar–human body model) was developed. The human body was modelled using a 15-segment body system. The joint-beam element method (superelement) was employed for modelling the high bar. A superelement consists of four rigid segments connected by joints (two Cardan joints and one rotational–translational joint) and springs (seven rotation springs and one tension–compression spring). The high bar was modelled using three superelements. The input data required for the high bar–human body model were collected with video-kinematographic (50 Hz) and dynamometric (500 Hz) techniques. Masses and moments of inertia of the 15 segments were calculated using the data from the Zatsiorsky et al. (1984) model. There are two major phases characteristic of the giant swing prior to dismounts from the high bar. In the first phase the gymnast attempts to supply energy to the high bar–human body system through muscle activity and to store this energy in the high bar. The difference between the energy transferred to the high bar and the reduction in the total energy of the body could be adopted as a criterion for the utilisation of high bar elasticity. The energy previously transferred into the high bar is returned to the body during the second phase. An advantageous increase in total body energy at the end of the exercise could only be obtained through muscle energy supply. An index characterising the utilisation of muscle capacity was developed out of the difference between the increase in total body energy and the energy returned from the high bar. A delayed and initially slow but even reduction of hip and shoulder angles provided more advantageous release conditions. The total body energy could be improved by up to 15%, the vertical CM release velocity by up to 10% and the angular momentum by up to 35%.     

Internal models for visual perception

 Although the extrapolation of past perceptual history into the immediate and distant future is a fundamental phenomenon in everyday life, the underlying processing mechanisms are not well understood. A network model consisting of interacting excitatory and inhibitory cell populations coding for stimulus position is used to study the neuronal population response to a continuously moving stimulus. An adaptation mechanism is proposed that offers the possibility to control and modulate motion-induced extrapolation without changing the spatial interaction structure within the network. Using an occluder paradigm, functional advantages of an internally generated model of a moving stimulus are discussed. It is shown that the integration of such a model in processing leads to a faster and more reliable recognition of the input stream and allows for object permanence following occlusion. The modeling results are discussed in relation to recent experimental findings that show motion-induced extrapolation. Received: 19 December 2001 / Accepted: 26 November 2002 / Published online: 3 April 2003 Correspondence to: W. Erlhagen (e-mail: wolfram.erlhagen@mct.uminho.pt) Acknowledgements. The author would like to thank D. Jancke for useful discussions and two anonymous reviewers for helpful comments and suggestions on a previous version of this paper. This research was supported by a European grant (IST-2000-29689) and by the Portuguese Science Foundation (POSI/SRI/38051/2001).     

Uptake of lactose and continuous lactic acid fermentation by entrapped non-growing Lactobacillus helveticus in whey permeate

 Continuous production of lactic acid from lactose has been carried out in a stirred-tank reactor with non-growing Lactobacillus helveticus entrapped in calcium alginate beads. A considerably longer operation half-life was obtained in a continuously operated reactor than in a batch-operated reactor. It is possible to simulate the action of entrapped non-growing cells on the basis of information from diffusion and kinetic experiments with suspended free cells. The simulation fit the experimental data over a broad range of substrate concentrations if the specific lactic acid production rate, q _P, was used as a variable parameter in the model. The dynamic mathematical model used is divided into three parts: the reactor model, which describes the mass balance in a continuously operated stirred-tank reactor with immobilized biomass, the mass-transfer model including both external diffusion and internal mass transfer, and the kinetic model for uptake of substrate on the basis of a Michaelis-Menten-type mechanism. From kinetic data obtained for free biomass experiments it was found, with the use of non-linear parameter estimation techniques, that the conversion rate of lactose by L. helveticus followed a Michaelis-Menten-type mechanism with K _S at half-saturation=0.22±0.01 g/l. The maximum specific lactose uptake rate for growing cells, q _S,max, varied between 4.32±0.02 g lactose g cells^-1 h^-1 and 4.89 ±0.02 g lactose g cells^-1 h^-1. The initial specific lactose uptake rate for non-growing cells, q _S,0, was found to be approximately 40% of the maximum specific lactose uptake rate for growing cells. Received: 4 October 1995/Received last revision: 23 April 1996/Accepted: 29 April 1996     

Effect of hip flexibility on optimal stalder performances on high bar

In the optimisation of sports movements using computer simulation models, the joint actuators must be constrained in order to obtain realistic results. In models of a gymnast, the main constraint used in previous studies was maximum voluntary active joint torque. In the stalder, gymnasts reach their maximal hip flexion under the bar. The purpose of this study was to introduce a model of passive torque to assess the effect of the gymnast's flexibility on the technique of the straddled stalder. A three-dimensional kinematics driven simulation model was developed. The kinematics of the shoulder flexion, hip flexion and hip abduction were optimised to minimise torques for four hip flexion flexibilities: 100°, 110°, 120° and 130°. With decreased flexibility, the piked posture period is shorter and occurs later. Moreover the peaks of shoulder and hip torques increase. Gymnasts with low hip flexibility need to be stronger to achieve a stalder; hip flexibility should be considered by coaches before teaching this skill.     

A mode hypothesis for finger interaction during multi-finger force-production tasks

 Finger forces are known to change involuntarily during multi-finger force-production tasks, even when a finger's involvement in a task is not consciously changed (the enslaving effect). Furthermore, during maximal force-production (MVC) tests, the force produced by a given finger in a multi-finger task is smaller than the force generated by this finger in its single-finger MVC test (the force-deficit effect). A set of hypothetical control variables – modes – is introduced. Modes can be estimated based on individual finger forces during single-finger MVC tests. We show that a simple formal model based on modes with only one free parameter accounts for finger forces during a variety of multi-finger MVC tests. The free parameter accounts for the force-deficit effect, and its value depends only on the number of explicitly involved fingers. This approach offers a simple framework for the analysis of finger interaction during multi-finger actions. Received: 7 December 2001 / Accepted in revised form: 17 April 2002 Correspondence to: F. Danion (e-mail: danion@laps.univ-mrs.fr, Tel.: +33-491-172265, Fax: +33-491-172252)     

Migraine aura dynamics after reverse retinotopic mapping of weak excitation waves in the primary visual cortex

 A kinematical model for excitable wave propagation is analyzed to describe the dynamics of a typical neurological symptom of migraine. The kinematical model equation is solved analytically for a linear dependency between front curvature and velocity. The resulting wave starts from an initial excitation and moves in the medium that represents the primary visual cortex. Due to very weak excitability the wave propagates only across a confined area and eventually disappears. This cortical excitation pattern is projected onto a visual hemifield by reverse retinotopic mapping. Weak excitability explains the confined appearance of aura symptoms in time and sensory space. The affected area in the visual field matches in growth and form the one reported by migraine sufferers. The results can be extended from visual to tactile and to other sensory symptoms. If the spatiotemporal pattern from our model can be matched in future investigations with those from introspectives, it would allow one to draw conclusions on topographic mapping of sensory input in human cortex. Received: 25 April 2002 / Accepted: 20 February 2003 / Published online: 20 May 2003 RID="*" ID="*" Present address: M. A. Dahlem Leibniz-Institut für Neurobiologie, Brenneckestr. 6, 39118 Magdeburg, Germany Acknowledgements. We would like to thank V. Zykov for useful discussions on wave Propagation, and one of us (MAD) would like to thank Ed Chronicle for useful discussions on functional excitability. This project was supported by a scholarship Landesstipendium Sachsen-Anhalt to MAD. Correspondence to: M. A. Dahlem (e-mail: dahlem@ifn-magdeburg.de)     

PARATI – A dynamic model for radiological assessments in urban areas

After a large-scale contamination of an urban area with γ-ray emitting radionuclides (e.g. caesium isotopes) decision makers will need guidance as to its potential radiological consequences and to optimum means of mitigation. To provide such information, a dynamic radioecological model PARATI has been developed and used to simulate the contamination of realistic urban environments in a computer model and to estimate the various radiation fields in such environments. In this study, the computer-simulated realistic behaviour and movements of individuals and populations in such radiation fields are described, and the resulting radiation exposures and their variabilities are estimated. For the scenarios considered, the doses of individuals in the same contaminated environment may vary by more than one order of magnitude. Studies on population habits and on the behaviour of radionuclides on important urban surfaces even a long time after the contamination might reduce the uncertainty considerably. Received: 12 April 1996 / Accepted in revised form: 4 August 1997     

Models for the molybdenum hydroxylases

 This commentary reviews structural, spectroscopic, and chemical models for the molybdenum hydroxylases. It briefly describes the current state of modeling and identifies areas where model chemistry may play a future role in understanding these enzymes. Received: 28 April 1997 / Accepted: 20 August 1997