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1
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Critical delay as a measure for the difficulty of frontal plane balancing on rolling balance board. J Biomech 2022; 138:111117. [DOI: 10.1016/j.jbiomech.2022.111117] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2021] [Revised: 03/29/2022] [Accepted: 04/28/2022] [Indexed: 11/19/2022]
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2
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Gabel CP, Guy B, Mokhtarinia HR, Melloh M. Slacklining: A narrative review on the origins, neuromechanical models and therapeutic use. World J Orthop 2021; 12:360-375. [PMID: 34189074 PMCID: PMC8223719 DOI: 10.5312/wjo.v12.i6.360] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 12/04/2020] [Revised: 01/27/2021] [Accepted: 05/19/2021] [Indexed: 02/06/2023] Open
Abstract
Slacklining, the neuromechanical action of balance retention on a tightened band, is achieved through self-learned strategies combining dynamic stability with optimal energy expenditure. Published slacklining literature is recent and limited, including for neuromechanical control strategy models. This paper explores slacklining's definitions and origins to provide background that facilitates understanding its evolution and progressive incorporation into both prehabilitation and rehabilitation. Existing explanatory slacklining models are considered, their application to balance and stability, and knowledge-gaps highlighted. Current slacklining models predominantly derive from human quiet-standing and frontal plane movement on stable surfaces. These provide a multi-tiered context of the unique and complex neuro-motoric requirements for slacklining's multiple applications, but are not sufficiently comprehensive. This consequently leaves an incomplete understanding of how slacklining is achieved, in relation to multi-directional instability and complex multi-dimensional human movement and behavior. This paper highlights the knowledge-gaps and sets a foundation for the required explanatory control mechanisms that evolve and expand a more detailed model of multi-dimensional slacklining and human functional movement. Such a model facilitates a more complete understanding of existing performance and rehabilitation applications that opens the potential for future applications into broader areas of movement in diverse fields including prostheses, automation and machine-learning related to movement phenotypes.
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Affiliation(s)
| | - Bernard Guy
- Ecole des Mines de Saint-Etienne, Saint Etienne 4200, Loire, France
| | - Hamid Reza Mokhtarinia
- Department of Ergonomics and Physiotherapy, University of Social Welfare and Rehabilitation Sciences, Tehran 12345, Iran
| | - Markus Melloh
- School of Health Professions, Institute of Health Sciences, Zurich University of Applied Sciences, Winterthur 8410, Switzerland
- School of Medicine, The University of Western Australia, Perth WA 6009, Australia
- Curtin Medical School, Curtin University, Bentley WA 6102, Australia
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3
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Molnar CA, Zelei A, Insperger T. Rolling balance board of adjustable geometry as a tool to assess balancing skill and to estimate reaction time delay. J R Soc Interface 2021; 18:20200956. [PMID: 33784884 DOI: 10.1098/rsif.2020.0956] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
The relation between balancing performance and reaction time is investigated for human subjects balancing on rolling balance board of adjustable physical parameters: adjustable rolling radius R and adjustable board elevation h. A well-defined measure of balancing performance is whether a subject can or cannot balance on balance board with a given geometry (R, h). The balancing ability is linked to the stabilizability of the underlying two-degree-of-freedom mechanical model subject to a delayed proportional-derivative feedback control. Although different sensory perceptions involve different reaction times at different hierarchical feedback loops, their effect is modelled as a single lumped reaction time delay. Stabilizability is investigated in terms of the time delay in the mechanical model: if the delay is larger than a critical value (critical delay), then no stabilizing feedback control exists. Series of balancing trials by 15 human subjects show that it is more difficult to balance on balance board configuration associated with smaller critical delay, than on balance boards associated with larger critical delay. Experiments verify the feature of the mechanical model that a change in the rolling radius R results in larger change in the difficulty of the task than the same change in the board elevation h does. The rolling balance board characterized by the two well-defined parameters R and h can therefore be a useful device to assess human balancing skill and to estimate the corresponding lumped reaction time delay.
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Affiliation(s)
- Csenge A Molnar
- Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, Hungary.,MTA-BME Lendület Human Balancing Research Group, Budapest, Hungary
| | - Ambrus Zelei
- MTA-BME Research Group on Dynamics of Machines and Vehicles, Budapest, Hungary
| | - Tamas Insperger
- Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, Hungary.,MTA-BME Lendület Human Balancing Research Group, Budapest, Hungary
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4
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Gyebrószki G, Csernák G, Milton JG, Insperger T. The effects of sensory quantization and control torque saturation on human balance control. CHAOS (WOODBURY, N.Y.) 2021; 31:033145. [PMID: 33810721 DOI: 10.1063/5.0028197] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2020] [Accepted: 02/25/2021] [Indexed: 06/12/2023]
Abstract
The effect of reaction delay, temporal sampling, sensory quantization, and control torque saturation is investigated numerically for a single-degree-of-freedom model of postural sway with respect to stability, stabilizability, and control effort. It is known that reaction delay has a destabilizing effect on the balancing process: the later one reacts to a perturbation, the larger the possibility of falling. If the delay is larger than a critical value, then stabilization is not even possible. In contrast, numerical analysis showed that quantization and control torque saturation have a stabilizing effect: the region of stabilizing control gains is greater than that of the linear model. Control torque saturation allows the application of larger control gains without overcontrol while sensory quantization plays a role of a kind of filter when sensory noise is present. These beneficial effects are reflected in the energy demand of the control process. On the other hand, neither control torque saturation nor sensory quantization improves stabilizability properties. In particular, the critical delay cannot be increased by adding saturation and/or sensory quantization.
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Affiliation(s)
- Gergely Gyebrószki
- Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest 1111, Hungary
| | - Gábor Csernák
- Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest 1111, Hungary
| | - John G Milton
- The Claremont Colleges, W. M. Keck Science Center, Claremont, California 91711, USA
| | - Tamás Insperger
- Department of Applied Mechanics, Budapest University of Technology and Economics and MTA-BME Lendület Human Balancing Research Group, Budapest 1111, Hungary
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5
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Suzuki Y, Nakamura A, Milosevic M, Nomura K, Tanahashi T, Endo T, Sakoda S, Morasso P, Nomura T. Postural instability via a loss of intermittent control in elderly and patients with Parkinson's disease: A model-based and data-driven approach. CHAOS (WOODBURY, N.Y.) 2020; 30:113140. [PMID: 33261318 DOI: 10.1063/5.0022319] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2020] [Accepted: 10/28/2020] [Indexed: 06/12/2023]
Abstract
Postural instability is one of the major symptoms of Parkinson's disease. Here, we assimilated a model of intermittent delay feedback control during quiet standing into postural sway data from healthy young and elderly individuals as well as patients with Parkinson's disease to elucidate the possible mechanisms of instability. Specifically, we estimated the joint probability distribution of a set of parameters in the model using the Bayesian parameter inference such that the model with the inferred parameters can best-fit sway data for each individual. It was expected that the parameter values for three populations would distribute differently in the parameter space depending on their balance capability. Because the intermittent control model is parameterized by a parameter associated with the degree of intermittency in the control, it can represent not only the intermittent model but also the traditional continuous control model with no intermittency. We showed that the inferred parameter values for the three groups of individuals are classified into two major groups in the parameter space: one represents the intermittent control mostly for healthy people and patients with mild postural symptoms and the other the continuous control mostly for some elderly and patients with severe postural symptoms. The results of this study may be interpreted by postulating that increased postural instability in most Parkinson's patients and some elderly persons might be characterized as a dynamical disease.
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Affiliation(s)
- Yasuyuki Suzuki
- Graduate School of Engineering Science, Osaka University, Osaka 5608531, Japan
| | - Akihiro Nakamura
- Graduate School of Engineering Science, Osaka University, Osaka 5608531, Japan
| | - Matija Milosevic
- Graduate School of Engineering Science, Osaka University, Osaka 5608531, Japan
| | - Kunihiko Nomura
- Department of Information Technology and Social Sciences, Osaka University of Economics, Osaka 5338533, Japan
| | - Takao Tanahashi
- Department of Neurology, Osaka Rosai Hospital, Osaka 5918025, Japan
| | - Takuyuki Endo
- Department of Neurology, Osaka Toneyama Medical Center, Osaka 5608552, Japan
| | - Saburo Sakoda
- Department of Neurology, Osaka Toneyama Medical Center, Osaka 5608552, Japan
| | - Pietro Morasso
- Center for Human Technologies, Istituto Italiano di Tecnologia, Genoa 16163, Italy
| | - Taishin Nomura
- Graduate School of Engineering Science, Osaka University, Osaka 5608531, Japan
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6
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State-space intermittent feedback stabilization of a dual balancing task. Sci Rep 2020; 10:8470. [PMID: 32439947 PMCID: PMC7242428 DOI: 10.1038/s41598-020-64911-7] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2019] [Accepted: 03/13/2020] [Indexed: 12/25/2022] Open
Abstract
Balancing the body in upright standing and balancing a stick on the fingertip are two examples of unstable tasks that, in spite of strong motor and sensory differences, appear to share a similar motor control paradigm, namely a state-space intermittent feedback stabilization mechanism. In this study subjects were required to perform the two tasks simultaneously, with the purpose of highlighting both the coordination between the two skills and the underlying interaction between the corresponding controllers. The experimental results reveal, in particular, that upright standing (the less critical task) is modified in an adaptive way, in order to facilitate the more critical task (stick balancing), but keeping the overall spatio-temporal signature well known in regular upright standing. We were then faced with the following question: to which extent the physical/biomechanical interaction between the two independent intermittent controllers is capable to explain the dual task coordination patterns, without the need to introduce an additional, supervisory layer/module? By comparing the experimental data with the output of a simulation study we support the former hypothesis, suggesting that it is made possible by the intrinsic robustness of both state-space intermittent feedback stabilization mechanisms.
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7
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Zhang L, Stepan G, Insperger T. Saturation limits the contribution of acceleration feedback to balancing against reaction delay. J R Soc Interface 2019; 15:rsif.2017.0771. [PMID: 29386400 DOI: 10.1098/rsif.2017.0771] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2017] [Accepted: 01/09/2018] [Indexed: 11/12/2022] Open
Abstract
A nonlinear model for human balancing subjected to a saturated delayed proportional-derivative-acceleration (PDA) feedback is analysed. Compared to the proportional-derivative (PD) controller, it is confirmed that the PDA controller improves local stability even for large feedback delays. However, it is shown that the saturated PDA controller typically introduces subcritical Hopf bifurcation into the system, which can also lead to falling for large enough perturbations. The subcriticality becomes stronger as the acceleration feedback gain increases or the saturation torque limit decreases. These explain some features of human balancing failure related to the increased reaction delay of inactive elderly people.
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Affiliation(s)
- Li Zhang
- State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, People's Republic of China
| | - Gabor Stepan
- Department of Applied Mechanics, Budapest University of Technology and Economics, 1521 Budapest, Hungary
| | - Tamas Insperger
- Department of Applied Mechanics, Budapest University of Technology and Economics, 1521 Budapest, Hungary.,Economics and MTA-BME Lendület Human Balancing Research Group, 1521 Budapest, Hungary
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8
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Hunt D, Molnár F, Szymanski BK, Korniss G. Extreme fluctuations in stochastic network coordination with time delays. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:062816. [PMID: 26764753 DOI: 10.1103/physreve.92.062816] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2015] [Indexed: 06/05/2023]
Abstract
We study the effects of uniform time delays on the extreme fluctuations in stochastic synchronization and coordination problems with linear couplings in complex networks. We obtain the average size of the fluctuations at the nodes from the behavior of the underlying modes of the network. We then obtain the scaling behavior of the extreme fluctuations with system size, as well as the distribution of the extremes on complex networks, and compare them to those on regular one-dimensional lattices. For large complex networks, when the delay is not too close to the critical one, fluctuations at the nodes effectively decouple, and the limit distributions converge to the Fisher-Tippett-Gumbel density. In contrast, fluctuations in low-dimensional spatial graphs are strongly correlated, and the limit distribution of the extremes is the Airy density. Finally, we also explore the effects of nonlinear couplings on the stability and on the extremes of the synchronization landscapes.
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Affiliation(s)
- D Hunt
- Department of Physics, Applied Physics, and Astronomy
- Network Science and Technology Center
| | - F Molnár
- Department of Physics, Applied Physics, and Astronomy
- Network Science and Technology Center
| | - B K Szymanski
- Network Science and Technology Center
- Department of Computer Science Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA
| | - G Korniss
- Department of Physics, Applied Physics, and Astronomy
- Network Science and Technology Center
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9
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Fu C, Suzuki Y, Kiyono K, Morasso P, Nomura T. An intermittent control model of flexible human gait using a stable manifold of saddle-type unstable limit cycle dynamics. J R Soc Interface 2015; 11:20140958. [PMID: 25339687 PMCID: PMC4223921 DOI: 10.1098/rsif.2014.0958] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022] Open
Abstract
Stability of human gait is the ability to maintain upright posture during walking against external perturbations. It is a complex process determined by a number of cross-related factors, including gait trajectory, joint impedance and neural control strategies. Here, we consider a control strategy that can achieve stable steady-state periodic gait while maintaining joint flexibility with the lowest possible joint impedance. To this end, we carried out a simulation study of a heel-toe footed biped model with hip, knee and ankle joints and a heavy head-arms-trunk element, working in the sagittal plane. For simplicity, the model assumes a periodic desired joint angle trajectory and joint torques generated by a set of feed-forward and proportional-derivative feedback controllers, whereby the joint impedance is parametrized by the feedback gains. We could show that a desired steady-state gait accompanied by the desired joint angle trajectory can be established as a stable limit cycle (LC) for the feedback controller with an appropriate set of large feedback gains. Moreover, as the feedback gains are decreased for lowering the joint stiffness, stability of the LC is lost only in a few dimensions, while leaving the remaining large number of dimensions quite stable: this means that the LC becomes saddle-type, with a low-dimensional unstable manifold and a high-dimensional stable manifold. Remarkably, the unstable manifold remains of low dimensionality even when the feedback gains are decreased far below the instability point. We then developed an intermittent neural feedback controller that is activated only for short periods of time at an optimal phase of each gait stride. We characterized the robustness of this design by showing that it can better stabilize the unstable LC with small feedback gains, leading to a flexible gait, and in particular we demonstrated that such an intermittent controller performs better if it drives the state point to the stable manifold, rather than directly to the LC. The proposed intermittent control strategy might have a high affinity for the inverted pendulum analogy of biped gait, providing a dynamic view of how the step-to-step transition from one pendular stance to the next can be achieved stably in a robust manner by a well-timed neural intervention that exploits the stable modes embedded in the unstable dynamics.
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Affiliation(s)
- Chunjiang Fu
- Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, Japan
| | - Yasuyuki Suzuki
- Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, Japan
| | - Ken Kiyono
- Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, Japan
| | | | - Taishin Nomura
- Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, Japan
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10
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Hernandez ME, Snider J, Stevenson C, Cauwenberghs G, Poizner H. A Correlation-Based Framework for Evaluating Postural Control Stochastic Dynamics. IEEE Trans Neural Syst Rehabil Eng 2015; 24:551-561. [PMID: 26011886 DOI: 10.1109/tnsre.2015.2436344] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
The inability to maintain balance during varying postural control conditions can lead to falls, a significant cause of mortality and serious injury among older adults. However, our understanding of the underlying dynamical and stochastic processes in human postural control have not been fully explored. To further our understanding of the underlying dynamical processes, we examine a novel conceptual framework for studying human postural control using the center of pressure (COP) velocity autocorrelation function (COP-VAF) and compare its results to Stabilogram Diffusion Analysis (SDA). Eleven healthy young participants were studied under quiet unipedal or bipedal standing conditions with eyes either opened or closed. COP trajectories were analyzed using both the traditional posturographic measure SDA and the proposed COP-VAF. It is shown that the COP-VAF leads to repeatable, physiologically meaningful measures that distinguish postural control differences in unipedal versus bipedal stance trials with and without vision in healthy individuals. More specifically, both a unipedal stance and lack of visual feedback increased initial values of the COP-VAF, magnitude of the first minimum, and diffusion coefficient, particularly in contrast to bipedal stance trials with open eyes. Use of a stochastic postural control model, based on an Ornstein-Uhlenbeck process that accounts for natural weight-shifts, suggests an increase in spring constant and decreased damping coefficient when fitted to experimental data. This work suggests that we can further extend our understanding of the underlying mechanisms behind postural control in quiet stance under varying stance conditions using the COP-VAF and provides a tool for quantifying future neurorehabilitative interventions.
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11
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Adaptive intermittent control: A computational model explaining motor intermittency observed in human behavior. Neural Netw 2015; 67:92-109. [PMID: 25897510 DOI: 10.1016/j.neunet.2015.03.012] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2014] [Revised: 02/27/2015] [Accepted: 03/20/2015] [Indexed: 11/21/2022]
Abstract
It is a fundamental question how our brain performs a given motor task in a real-time fashion with the slow sensorimotor system. Computational theory proposed an influential idea of feed-forward control, but it has mainly treated the case that the movement is ballistic (such as reaching) because the motor commands should be calculated in advance of movement execution. As a possible mechanism for operating feed-forward control in continuous motor tasks (such as target tracking), we propose a control model called "adaptive intermittent control" or "segmented control," that brain adaptively divides the continuous time axis into discrete segments and executes feed-forward control in each segment. The idea of intermittent control has been proposed in the fields of control theory, biological modeling and nonlinear dynamical system. Compared with these previous models, the key of the proposed model is that the system speculatively determines the segmentation based on the future prediction and its uncertainty. The result of computer simulation showed that the proposed model realized faithful visuo-manual tracking with realistic sensorimotor delays and with less computational costs (i.e., with fewer number of segments). Furthermore, it replicated "motor intermittency", that is, intermittent discontinuities commonly observed in human movement trajectories. We discuss that the temporally segmented control is an inevitable strategy for brain which has to achieve a given task with small computational (or cognitive) cost, using a slow control system in an uncertain variable environment, and the motor intermittency is the side-effect of this strategy.
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12
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Yamamoto T, Smith CE, Suzuki Y, Kiyono K, Tanahashi T, Sakoda S, Morasso P, Nomura T. Universal and individual characteristics of postural sway during quiet standing in healthy young adults. Physiol Rep 2015; 3:3/3/e12329. [PMID: 25780094 PMCID: PMC4393163 DOI: 10.14814/phy2.12329] [Citation(s) in RCA: 71] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Abstract
The time course of the center of pressure (CoP) during human quiet standing, corresponding to body sway, is a stochastic process, influenced by a variety of features of the underlying neuro-musculo-skeletal system, such as postural stability and flexibility. Due to complexity of the process, sway patterns have been characterized in an empirical way by a number of indices, such as sway size and mean sway velocity. Here, we describe a statistical approach with the aim of estimating "universal" indices, namely parameters that are independent of individual body characteristics and thus are not "hidden" by the presence of individual, daily, and circadian variations of sway; in this manner it is possible to characterize the common aspects of sway dynamics across healthy young adults, in the assumption that they might reflect underlying neural control during quiet standing. Such universal indices are identified by analyzing intra and inter-subject variability of various indices, after sorting out individual-specific indices that contribute to individual discriminations. It is shown that the universal indices characterize mainly slow components of sway, such as scaling exponents of power-law behavior at a low-frequency regime. On the other hand, most of the individual-specific indices contributing to the individual discriminations exhibit significant correlation with body parameters, and they can be associated with fast oscillatory components of sway. These results are consistent with a mechanistic hypothesis claiming that the slow and the fast components of sway are associated, respectively, with neural control and biomechanics, supporting our assumption that the universal characteristics of postural sway might represent neural control strategies during quiet standing.
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Affiliation(s)
- Tomohisa Yamamoto
- Graduate School of Engineering Science, Osaka University, Toyonaka, Japan
| | - Charles E Smith
- Department of Statistics, North Carolina State University, Raleigh, North Carolina, USA
| | - Yasuyuki Suzuki
- Graduate School of Engineering Science, Osaka University, Toyonaka, Japan
| | - Ken Kiyono
- Graduate School of Engineering Science, Osaka University, Toyonaka, Japan
| | - Takao Tanahashi
- Department of Neurology, Osaka University Graduate School of Medicine, Osaka, Japan
| | - Saburo Sakoda
- Department of Neurology, Toneyama National Hospital, Osaka, Japan
| | - Pietro Morasso
- RBCS Department, Fondazione Istituto Italiano di Tecnologia, Genoa, Italy
| | - Taishin Nomura
- Graduate School of Engineering Science, Osaka University, Toyonaka, Japan
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13
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Lee KY, O'Dwyer N, Halaki M, Smith R. Perceptual and motor learning underlies human stick-balancing skill. J Neurophysiol 2015; 113:156-71. [PMID: 25298388 DOI: 10.1152/jn.00538.2013] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
We investigated the acquisition of skill in balancing a stick (52 cm, 34 g) on the fingertip in nine participants using three-dimensional motion analysis. After 3.5 h of practice over 6 wk, the participants could more consistently balance the stick for longer durations with greatly reduced magnitude and speed of stick and finger movements. Irrespective of level of skill, the balanced stick behaved like a normal noninverted pendulum oscillating under greater-than-gravity torque with simple harmonic motion about a virtual pivot located at the radius of gyration above the center of mass. The control input parameter was the magnitude ratio between the torque applied on the stick by the participant and the torque due to gravity. The participants utilized only a narrow range of this parameter, which did not change with practice, to rotate the stick like a linear mass-spring system. With increased skill, the stick therefore maintained the same period of oscillation but showed marked reductions in magnitude of both oscillation and horizontal translation. Better balancing was associated with 1) more accurate visual localization of the stick and proprioceptive localization of the finger and 2) reduced cross-coupling errors between finger and stick movements in orthogonal directions; i.e., finger movements in the anteroposterior plane became less coupled with stick tip movements in the mediolateral plane, and vice versa. Development of this fine motor skill therefore depended on perceptual and motor learning to provide improved estimation of sensorimotor state and precision of motor commands to an unchanging internal model of the rotational dynamics.
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Affiliation(s)
- Kwee-Yum Lee
- School of Exercise Science, Australian Catholic University, Strathfield, New South Wales, Australia; Discipline of Exercise and Sport Science, The University of Sydney, New South Wales, Australia
| | - Nicholas O'Dwyer
- School of Human Movement Studies, Charles Sturt University, Bathurst, New South Wales, Australia; and Discipline of Exercise and Sport Science, The University of Sydney, New South Wales, Australia
| | - Mark Halaki
- Discipline of Exercise and Sport Science, The University of Sydney, New South Wales, Australia
| | - Richard Smith
- Discipline of Exercise and Sport Science, The University of Sydney, New South Wales, Australia
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14
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Zgonnikov A, Lubashevsky I, Kanemoto S, Miyazawa T, Suzuki T. To react or not to react? Intrinsic stochasticity of human control in virtual stick balancing. J R Soc Interface 2014; 11:20140636. [PMID: 25056217 PMCID: PMC4233747 DOI: 10.1098/rsif.2014.0636] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2014] [Accepted: 07/02/2014] [Indexed: 11/12/2022] Open
Abstract
Understanding how humans control unstable systems is central to many research problems, with applications ranging from quiet standing to aircraft landing. Increasingly, much evidence appears in favour of event-driven control hypothesis: human operators only start actively controlling the system when the discrepancy between the current and desired system states becomes large enough. The event-driven models based on the concept of threshold can explain many features of the experimentally observed dynamics. However, much still remains unclear about the dynamics of human-controlled systems, which likely indicates that humans use more intricate control mechanisms. This paper argues that control activation in humans may be not threshold-driven, but instead intrinsically stochastic, noise-driven. Specifically, we suggest that control activation stems from stochastic interplay between the operator's need to keep the controlled system near the goal state, on the one hand, and the tendency to postpone interrupting the system dynamics, on the other hand. We propose a model capturing this interplay and show that it matches the experimental data on human balancing of virtual overdamped stick. Our results illuminate that the noise-driven activation mechanism plays a crucial role at least in the considered task, and, hypothetically, in a broad range of human-controlled processes.
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Affiliation(s)
- Arkady Zgonnikov
- University of Aizu, Tsuruga, Ikki-machi, Aizuwakamatsu, Fukushima 965-8580, Japan
| | - Ihor Lubashevsky
- University of Aizu, Tsuruga, Ikki-machi, Aizuwakamatsu, Fukushima 965-8580, Japan
| | - Shigeru Kanemoto
- University of Aizu, Tsuruga, Ikki-machi, Aizuwakamatsu, Fukushima 965-8580, Japan
| | - Toru Miyazawa
- University of Aizu, Tsuruga, Ikki-machi, Aizuwakamatsu, Fukushima 965-8580, Japan
| | - Takashi Suzuki
- University of Aizu, Tsuruga, Ikki-machi, Aizuwakamatsu, Fukushima 965-8580, Japan
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15
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Zhang H, Nussbaum MA, Agnew MJ. A time–frequency approach to estimate critical time intervals in postural control. Comput Methods Biomech Biomed Engin 2014; 18:1693-703. [DOI: 10.1080/10255842.2014.946915] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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16
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Zenzeri J, De Santis D, Morasso P. Strategy switching in the stabilization of unstable dynamics. PLoS One 2014; 9:e99087. [PMID: 24921254 PMCID: PMC4055681 DOI: 10.1371/journal.pone.0099087] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2013] [Accepted: 05/11/2014] [Indexed: 11/26/2022] Open
Abstract
In order to understand mechanisms of strategy switching in the stabilization of unstable dynamics, this work investigates how human subjects learn to become skilled users of an underactuated bimanual tool in an unstable environment. The tool, which consists of a mass and two hand-held non-linear springs, is affected by a saddle-like force-field. The non-linearity of the springs allows the users to determine size and orientation of the tool stiffness ellipse, by using different patterns of bimanual coordination: minimal stiffness occurs when the two spring terminals are aligned and stiffness size grows by stretching them apart. Tool parameters were set such that minimal stiffness is insufficient to provide stable equilibrium whereas asymptotic stability can be achieved with sufficient stretching, although at the expense of greater effort. As a consequence, tool users have two possible strategies for stabilizing the mass in different regions of the workspace: 1) high stiffness feedforward strategy, aiming at asymptotic stability and 2) low stiffness positional feedback strategy aiming at bounded stability. The tool was simulated by a bimanual haptic robot with direct torque control of the motors. In a previous study we analyzed the behavior of naïve users and we found that they spontaneously clustered into two groups of approximately equal size. In this study we trained subjects to become expert users of both strategies in a discrete reaching task. Then we tested generalization capabilities and mechanism of strategy-switching by means of stabilization tasks which consist of tracking moving targets in the workspace. The uniqueness of the experimental setup is that it addresses the general problem of strategy-switching in an unstable environment, suggesting that complex behaviors cannot be explained in terms of a global optimization criterion but rather require the ability to switch between different sub-optimal mechanisms.
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Affiliation(s)
- Jacopo Zenzeri
- Robotics, Brain and Cognitive Sciences Department, Istituto Italiano di Tecnologia, Genoa, Italy
- * E-mail:
| | - Dalia De Santis
- Robotics, Brain and Cognitive Sciences Department, Istituto Italiano di Tecnologia, Genoa, Italy
| | - Pietro Morasso
- Robotics, Brain and Cognitive Sciences Department, Istituto Italiano di Tecnologia, Genoa, Italy
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17
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Kowalczyk P, Nema S, Glendinning P, Loram I, Brown M. Auto-regressive moving average analysis of linear and discontinuous models of human balance during quiet standing. CHAOS (WOODBURY, N.Y.) 2014; 24:022101. [PMID: 24985413 DOI: 10.1063/1.4871880] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Linear Time Invariant (LTI) processes can be modelled by means of Auto-Regressive Moving Average (ARMA) model systems. In this paper, we examine whether an ARMA model can be fitted to a process characterised by switched nonlinearities. In particular, we conduct the following test: we generate data from known LTI and nonlinear (threshold/dead-zone) models of human balance and analyse the output using ARMA. We show that both these known systems can be fitted, according to standard criteria, with low order ARMA models. To check if there are some obvious effects of the dead-zone, we compare the power spectra of both systems with the power spectra of their ARMA models. We then examine spectral properties of three posturographic data sets and their ARMA models and compare them with the power spectra of our model systems. Finally, we examine the dynamics of our model systems in the absence of noise to determine what is the effect of the switching threshold (dead-zone) on the asymptotic dynamics.
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Affiliation(s)
- Piotr Kowalczyk
- School of Computing, Mathematics and Digital Technology, Manchester Metropolitan University, Chester Street, Manchester M1 5GD, United Kingdom
| | - Salam Nema
- School of Computing, Mathematics and Digital Technology, Manchester Metropolitan University, Chester Street, Manchester M1 5GD, United Kingdom
| | - Paul Glendinning
- School of Mathematics and Centre for Interdisciplinary Computational and Dynamical Analysis (CICADA), University of Manchester, Manchester M13 9PL, United Kingdom
| | - Ian Loram
- Institute for Biomedical Research into Human Movement and Health (IRM), Manchester Metropolitan University, Chester Street, Manchester M1 5GD, United Kingdom
| | - Martin Brown
- School of Electrical and Electronic Engineering, The University of Manchester, Manchester M13 9PL, United Kingdom
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18
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Asai Y, Tateyama S, Nomura T. Learning an intermittent control strategy for postural balancing using an EMG-based human-computer interface. PLoS One 2013; 8:e62956. [PMID: 23717398 PMCID: PMC3661733 DOI: 10.1371/journal.pone.0062956] [Citation(s) in RCA: 40] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2012] [Accepted: 03/26/2013] [Indexed: 11/22/2022] Open
Abstract
It has been considered that the brain stabilizes unstable body dynamics by regulating co-activation levels of antagonist muscles. Here we critically reexamined this established theory of impedance control in a postural balancing task using a novel EMG-based human-computer interface, in which subjects were asked to balance a virtual inverted pendulum using visual feedback information on the pendulum's position. The pendulum was actuated by a pair of antagonist joint torques determined in real-time by activations of the corresponding pair of antagonist ankle muscles of subjects standing upright. This motor-task raises a frustrated environment; a large feedback time delay in the sensorimotor loop, as a source of instability, might favor adopting the non-reactive, preprogrammed impedance control, but the ankle muscles are relatively hard to co-activate, which hinders subjects from adopting the impedance control. This study aimed at discovering how experimental subjects resolved this frustrated environment through motor learning. One third of subjects adapted to the balancing task in a way of the impedance-like control. It was remarkable, however, that the majority of subjects did not adopt the impedance control. Instead, they acquired a smart and energetically efficient strategy, in which two muscles were inactivated simultaneously at a sequence of optimal timings, leading to intermittent appearance of periods of time during which the pendulum was not actively actuated. Characterizations of muscle inactivations and the pendulum¡Çs sway showed that the strategy adopted by those subjects was a type of intermittent control that utilizes a stable manifold of saddle-type unstable upright equilibrium that appeared in the state space of the pendulum when the active actuation was turned off.
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Affiliation(s)
- Yoshiyuki Asai
- Okinawa Institute of Science and Technology Graduate University, Okinawa, Japan
| | - Shota Tateyama
- Graduate School of Engineering Science, Osaka University, Osaka, Japan
| | - Taishin Nomura
- Graduate School of Engineering Science, Osaka University, Osaka, Japan
- * E-mail:
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19
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Insperger T, Milton J, Stépán G. Acceleration feedback improves balancing against reflex delay. J R Soc Interface 2013; 10:20120763. [PMID: 23173196 DOI: 10.1098/rsif.2012.0763] [Citation(s) in RCA: 86] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
A model for human postural balance is considered in which the time-delayed feedback depends on position, velocity and acceleration (proportional-derivative-acceleration (PDA) feedback). It is shown that a PDA controller is equivalent to a predictive controller, in which the prediction is based on the most recent information of the state, but the control input is not involved into the prediction. A PDA controller is superior to the corresponding proportional-derivative controller in the sense that the PDA controller can stabilize systems with approximately 40 per cent larger feedback delays. The addition of a sensory dead zone to account for the finite thresholds for detection by sensory receptors results in highly intermittent, complex oscillations that are a typical feature of human postural sway.
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Affiliation(s)
- Tamás Insperger
- Department of Applied Mechanics, Budapest University of Technology and Economics, 1521 Budapest, Hungary
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20
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Modeling human postural sway using an intermittent control and hemodynamic perturbations. Math Biosci 2013; 245:86-95. [PMID: 23435118 DOI: 10.1016/j.mbs.2013.02.002] [Citation(s) in RCA: 61] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2012] [Revised: 01/26/2013] [Accepted: 02/06/2013] [Indexed: 11/22/2022]
Abstract
Ground reaction force during human quiet stance is modulated synchronously with the cardiac cycle through hemodynamics [1]. This almost periodic hemodynamic force induces a small disturbance torque to the ankle joint, which is considered as a source of endogenous perturbation that induces postural sway. Here we consider postural sway dynamics of an inverted pendulum model with an intermittent control strategy, in comparison with the traditional continuous-time feedback controller. We examine whether each control model can exhibit human-like postural sway, characterized by its power law behavior at the low frequency band 0.1-0.7Hz, when it is weakly perturbed by periodic and/or random forcing mimicking the hemodynamic perturbation. We show that the continuous control model with typical feedback gain parameters hardly exhibits the human-like sway pattern, in contrast with the intermittent control model. Further analyses suggest that deterministic, including chaotic, slow oscillations that characterize the intermittent control strategy, together with the small hemodynamic perturbation, could be a possible mechanism for generating the postural sway.
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21
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Intermittent Motor Control: The “drift-and-act” Hypothesis. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2013; 782:169-93. [DOI: 10.1007/978-1-4614-5465-6_9] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/10/2023]
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22
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Hunt D, Szymanski BK, Korniss G. Network coordination and synchronization in a noisy environment with time delays. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:056114. [PMID: 23214850 DOI: 10.1103/physreve.86.056114] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2012] [Indexed: 06/01/2023]
Abstract
We study the effects of nonzero time delays in stochastic synchronization problems with linear couplings in complex networks. We consider two types of time delays: transmission delays between interacting nodes and local delays at each node (due to processing, cognitive, or execution delays). By investigating the underlying fluctuations for several delay schemes, we obtain the synchronizability threshold (phase boundary) and the scaling behavior of the width of the synchronization landscape, in some cases for arbitrary networks and in others for specific weighted networks. Numerical computations allow the behavior of these networks to be explored when direct analytical results are not available. We comment on the implications of these findings for simple locally or globally weighted network couplings and possible trade-offs present in such systems.
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Affiliation(s)
- D Hunt
- Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA
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23
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Suzuki Y, Nomura T, Casadio M, Morasso P. Intermittent control with ankle, hip, and mixed strategies during quiet standing: a theoretical proposal based on a double inverted pendulum model. J Theor Biol 2012; 310:55-79. [PMID: 22732276 DOI: 10.1016/j.jtbi.2012.06.019] [Citation(s) in RCA: 111] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2012] [Revised: 06/13/2012] [Accepted: 06/14/2012] [Indexed: 10/28/2022]
Abstract
Human upright posture, as a mechanical system, is characterized by an instability of saddle type, involving both stable and unstable dynamic modes. The brain stabilizes such system by generating active joint torques, according to a time-delayed neural feedback control. What is still unsolved is a clear understanding of the control strategies and the control mechanisms that are used by the central nervous system in order to stabilize the unstable posture in a robust way while maintaining flexibility. Most studies in this direction have been limited to the single inverted pendulum model, which is useful for formalizing fundamental mechanical aspects but insufficient for addressing more general issues concerning neural control strategies. Here we consider a double inverted pendulum model in the sagittal plane with small passive viscoelasticity at the ankle and hip joints. Despite difficulties in stabilizing the double pendulum model in the presence of the large feedback delay, we show that robust and flexible stabilization of the upright posture can be established by an intermittent control mechanism that achieves the goal of stabilizing the body posture according to a "divide and conquer strategy", which switches among different controllers in different parts of the state space of the double inverted pendulum. Remarkably, it is shown that a global, robust stability is achieved even if the individual controllers are unstable and the information exploited for switching from one controller to another is severely delayed, as it happens in biological reality. Moreover, the intermittent controller can automatically resolve coordination among multiple active torques associated with the muscle synergy, leading to the emergence of distinct temporally coordinated active torque patterns, referred to as the intermittent ankle, hip, and mixed strategies during quiet standing, depending on the passive elasticity at the hip joint.
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Affiliation(s)
- Yasuyuki Suzuki
- Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 5608531, Japan
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24
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Abstract
Balancing on a tightrope or a slackline is an example of a neuromechanical task where the whole body both drives and responds to the dynamics of the external environment, often on multiple timescales. Motivated by a range of neurophysiological observations, here we formulate a minimal model for this system and use optimal control theory to design a strategy for maintaining an upright position. Our analysis of the open and closed-loop dynamics shows the existence of an optimal rope sag where balancing requires minimal effort, consistent with qualitative observations and suggestive of strategies for optimizing balancing performance while standing and walking. Our consideration of the effects of nonlinearities, potential parameter coupling and delays on the overall performance shows that although these factors change the results quantitatively, the existence of an optimal strategy persists.
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Affiliation(s)
- P Paoletti
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
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25
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Abstract
Recent advances in the study of delay differential equations draw attention to the potential benefits of the interplay between random perturbations ('noise') and delay in neural control. The phenomena include transient stabilizations of unstable steady states by noise, control of fast movements using time-delayed feedback and the occurrence of long-lived delay-induced transients. In particular, this research suggests that the interplay between noise and delay necessitates the use of intermittent, discontinuous control strategies in which corrective movements are made only when controlled variables cross certain thresholds. A potential benefit of such strategies is that they may be optimal for minimizing energy expenditures associated with control. In this paper, the concepts are made accessible by introducing them through simple illustrative examples that can be readily reproduced using software packages, such as XPPAUT.
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Affiliation(s)
- John G Milton
- Joint Science Department, W. M. Keck Science Center, Claremont, CA 91711, USA.
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26
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Yamamoto T, Suzuki Y, Nomura K, Nomura T, Tanahashi T, Fukada K, Endo T, Sakoda S. A Classification of Postural Sway Patterns During Upright Stance in Healthy Adults and Patients with Parkinson’s Disease. JOURNAL OF ADVANCED COMPUTATIONAL INTELLIGENCE AND INTELLIGENT INFORMATICS 2011. [DOI: 10.20965/jaciii.2011.p0997] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
The intermittent control during human quiet upright stance is a new hypothesis which claims that the active neural feedback control generating the ankle muscle torque is switched off and on intermittently at appropriate timings. The intermittent strategy is capable of providing compliant posture while ensuring robust stability. Contrastingly, impairment of postural reflexes in patients with Parkinson’s disease (PD) causes postural instability. Here we hypothesize that the instability in PD patients might be due to a loss of appropriate intermittent activations in the feedback muscle torque during stance. In order to provide evidence for this hypothesis, we characterized stochastic postural sway patterns measured as changes in center of pressure (CoP) and activities of ankle muscles during quiet stance in healthy young and elderly subjects as well as PD patients. To this end, sway patterns and associated ankle muscle activities were quantified by several indices including the CoP sway area, scaling factors of double-power-law power spectra of the sway, as well as levels and patterns of the muscle activations. Hierarchical cluster analysis was performed to suggest that the sway patterns could be classified into two major types. The first type consisted mainly of sway and muscle activation patterns from healthy subjects and some PD patients with the mild level of severity, and they showed features indicating the intermittent control. The second type, consisting mainly of PD patients with relatively severe levels of motor symptoms, was accompanied with non-intermittent but tonic muscle activities and sway areas either smaller or larger than those in the first type. Moreover, the major two types were further classified into several subtypes with distinguishable characteristics. Results suggested that a loss of the intermittent activations in the ankle muscles could be a cause of the postural instability for a population of PD patients.
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27
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Kowalczyk P, Glendinning P, Brown M, Medrano-Cerda G, Dallali H, Shapiro J. Modelling human balance using switched systems with linear feedback control. J R Soc Interface 2011; 9:234-45. [PMID: 21697168 DOI: 10.1098/rsif.2011.0212] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
We are interested in understanding the mechanisms behind and the character of the sway motion of healthy human subjects during quiet standing. We assume that a human body can be modelled as a single-link inverted pendulum, and the balance is achieved using linear feedback control. Using these assumptions, we derive a switched model which we then investigate. Stable periodic motions (limit cycles) about an upright position are found. The existence of these limit cycles is studied as a function of system parameters. The exploration of the parameter space leads to the detection of multi-stability and homoclinic bifurcations.
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Affiliation(s)
- Piotr Kowalczyk
- School of Computing, Mathematics and Digital Technology, John Dalton Building, Manchester Metropolitan University, Chester Street, Manchester M1 5GD, UK.
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28
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Nomura T. Toward integration of biological and physiological functions at multiple levels. Front Physiol 2010; 1:164. [PMID: 21423399 PMCID: PMC3059937 DOI: 10.3389/fphys.2010.00164] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2010] [Accepted: 12/09/2010] [Indexed: 11/13/2022] Open
Abstract
An aim of systems physiology today can be stated as to establish logical and quantitative bridges between phenomenological attributes of physiological entities such as cells and organs and physical attributes of biological entities, i.e., biological molecules, allowing us to describe and better understand physiological functions in terms of underlying biological functions. This article illustrates possible schema that can be used for promoting systems physiology by integrating quantitative knowledge of biological and physiological functions at multiple levels of time and space with the use of information technology infrastructure. Emphasis will be made for systematic, modular, hierarchical, and standardized descriptions of mathematical models of the functions and advantages for the use of them.
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Affiliation(s)
- Taishin Nomura
- Division of Bioengineering, Graduate School of Engineering Science, Osaka University Toyonaka, Osaka, Japan.
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29
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Cluff T, Gharib T, Balasubramaniam R. Attentional influences on the performance of secondary physical tasks during posture control. Exp Brain Res 2010; 203:647-58. [PMID: 20454784 DOI: 10.1007/s00221-010-2274-7] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2010] [Accepted: 04/17/2010] [Indexed: 11/29/2022]
Abstract
We examined the influence of attentional focus and cognitive load on motor performance in a dynamic stick balancing task during the maintenance of upright posture. Dynamical analyses of postural fluctuations revealed the existence of a drift and correct mechanism, with correlational structure reflecting the demands of the stick balancing task. In contrast, experimentally manipulated attentional foci (internal, external) did not influence the variability of postural or fingertip trajectories. However, dual-task cognitive stick balancing performance resulted in decreased variability of postural and fingertip time series. These results are discussed in the context of dual timescale models for posture control and stick balancing.
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Affiliation(s)
- Tyler Cluff
- Sensorimotor Neuroscience Laboratory, McMaster University, 1280 Main Street West, Hamilton, ON, L8S 2K1, Canada
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30
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Boulet J, Balasubramaniam R, Daffertshofer A, Longtin A. Stochastic two-delay differential model of delayed visual feedback effects on postural dynamics. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2010; 368:423-438. [PMID: 20008409 DOI: 10.1098/rsta.2009.0214] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
We report on experiments and modelling involving the 'visuo-postural control loop' in the upright stance. We experimentally manipulated an artificial delay to the visual feedback during standing, presented at delays ranging from 0 to 1 s in increments of 250 ms. Using stochastic delay differential equations, we explicitly modelled the centre-of-pressure (COP) and centre-of-mass (COM) dynamics with two independent delay terms for vision and proprioception. A novel 'drifting fixed point' hypothesis was used to describe the fluctuations of the COM with the COP being modelled as a faster, corrective process of the COM. The model was in good agreement with the data in terms of probability density functions, power spectral densities, short- and long-term correlations (Hurst exponents) as well the critical time between the two ranges.
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Affiliation(s)
- Jason Boulet
- Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada.
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31
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Milton JG, Ohira T, Cabrera JL, Fraiser RM, Gyorffy JB, Ruiz FK, Strauss MA, Balch EC, Marin PJ, Alexander JL. Balancing with vibration: a prelude for "drift and act" balance control. PLoS One 2009; 4:e7427. [PMID: 19841741 PMCID: PMC2759542 DOI: 10.1371/journal.pone.0007427] [Citation(s) in RCA: 61] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2009] [Accepted: 09/19/2009] [Indexed: 11/19/2022] Open
Abstract
Stick balancing at the fingertip is a powerful paradigm for the study of the control of human balance. Here we show that the mean stick balancing time is increased by about two-fold when a subject stands on a vibrating platform that produces vertical vibrations at the fingertip (0.001 m, 15-50 Hz). High speed motion capture measurements in three dimensions demonstrate that vibration does not shorten the neural latency for stick balancing or change the distribution of the changes in speed made by the fingertip during stick balancing, but does decrease the amplitude of the fluctuations in the relative positions of the fingertip and the tip of the stick in the horizontal plane, A(x,y). The findings are interpreted in terms of a time-delayed "drift and act" control mechanism in which controlling movements are made only when controlled variables exceed a threshold, i.e. the stick survival time measures the time to cross a threshold. The amplitude of the oscillations produced by this mechanism can be decreased by parametric excitation. It is shown that a plot of the logarithm of the vibration-induced increase in stick balancing skill, a measure of the mean first passage time, versus the standard deviation of the A(x,y) fluctuations, a measure of the distance to the threshold, is linear as expected for the times to cross a threshold in a stochastic dynamical system. These observations suggest that the balanced state represents a complex time-dependent state which is situated in a basin of attraction that is of the same order of size. The fact that vibration amplitude can benefit balance control raises the possibility of minimizing risk of falling through appropriate changes in the design of footwear and roughness of the walking surfaces.
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Affiliation(s)
- John G Milton
- Joint Science Department, The Claremont Colleges, Claremont, California, United States of America.
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32
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Gawthrop P, Loram I, Lakie M. Predictive feedback in human simulated pendulum balancing. BIOLOGICAL CYBERNETICS 2009; 101:131-46. [PMID: 19588160 DOI: 10.1007/s00422-009-0325-6] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2009] [Accepted: 06/10/2009] [Indexed: 05/21/2023]
Abstract
In studies of human balance, it is common to fit stimulus-response data by tuning the time-delay and gain parameters of a simple delayed feedback model. Many interpret this fitted model, a simple delayed feedback model, as evidence that predictive processes are not required to explain existing data on standing balance. However, two questions lead us to doubt this approach. First, does fitting a delayed feedback model lead to reliable estimates of the time-delay? Second, can a non-predictive controller provide an explanation compatible with the independently estimated time delay? For methodological and experimental clarity, we study human balancing of a simulated inverted pendulum via joystick and screen. A two-step approach to data analysis is used: firstly a non-parametric model--the closed-loop impulse response--is estimated from the experimental data; second, a parametric model is fitted to the non-parametric impulse-response by adjusting time-delay and controller parameters. To support the second step, a new explicit formula relating controller parameters to closed-loop impulse response is derived. Two classes of controller are investigated within a common state-space context: non-predictive and predictive. It is found that the time-delay estimate arising from the second step is strongly dependent on which controller class is assumed; in particular, the non-predictive control assumption leads to time-delay estimates that are smaller than those arising from the predictive assumption. Moreover, the time-delays estimated using the non-predictive control assumption are not consistent with a lower-bound on the time-delay of the non-parametric model whereas the corresponding predictive result is consistent. Thus while the goodness of fit only marginally favoured predictive over non-predictive control, if we add the additional constraint that the model must reproduce the non-parametric time delay, then the non-predictive control model fails. We conclude (1) the time-delay should be estimated independently of fitting a low order parametric model, (2) that balance of the simulated inverted pendulum could not be explained by the non-predictive control model and (3) that predictive control provided a better explanation than non-predictive control.
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Affiliation(s)
- Peter Gawthrop
- Department of Mechanical Engineering, Centre for Systems and Control, University of Glasgow, Glasgow G12 8QQ, UK.
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33
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A model of postural control in quiet standing: robust compensation of delay-induced instability using intermittent activation of feedback control. PLoS One 2009; 4:e6169. [PMID: 19584944 PMCID: PMC2704954 DOI: 10.1371/journal.pone.0006169] [Citation(s) in RCA: 144] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2009] [Accepted: 06/03/2009] [Indexed: 11/19/2022] Open
Abstract
The main purpose of this study is to compare two different feedback controllers for the stabilization of quiet standing in humans, taking into account that the intrinsic ankle stiffness is insufficient and that there is a large delay inducing instability in the feedback loop: 1) a standard linear, continuous-time PD controller and 2) an intermittent PD controller characterized by a switching function defined in the phase plane, with or without a dead zone around the nominal equilibrium state. The stability analysis of the first controller is carried out by using the standard tools of linear control systems, whereas the analysis of the intermittent controllers is based on the use of Poincaré maps defined in the phase plane. When the PD-control is off, the dynamics of the system is characterized by a saddle-like equilibrium, with a stable and an unstable manifold. The switching function of the intermittent controller is implemented in such a way that PD-control is 'off' when the state vector is near the stable manifold of the saddle and is 'on' otherwise. A theoretical analysis and a related simulation study show that the intermittent control model is much more robust than the standard model because the size of the region in the parameter space of the feedback control gains (P vs. D) that characterizes stable behavior is much larger in the latter case than in the former one. Moreover, the intermittent controller can use feedback parameters that are much smaller than the standard model. Typical sway patterns generated by the intermittent controller are the result of an alternation between slow motion along the stable manifold of the saddle, when the PD-control is off, and spiral motion away from the upright equilibrium determined by the activation of the PD-control with low feedback gains. Remarkably, overall dynamic stability can be achieved by combining in a smart way two unstable regimes: a saddle and an unstable spiral. The intermittent controller exploits the stabilizing effect of one part of the saddle, letting the system evolve by alone when it slides on or near the stable manifold; when the state vector enters the strongly unstable part of the saddle it switches on a mild feedback which is not supposed to impose a strict stable regime but rather to mitigate the impending fall. The presence of a dead zone in the intermittent controller does not alter the stability properties but improves the similarity with biological sway patterns. The two types of controllers are also compared in the frequency domain by considering the power spectral density (PSD) of the sway sequences generated by the models with additive noise. Different from the standard continuous model, whose PSD function is similar to an over-damped second order system without a resonance, the intermittent control model is capable to exhibit the two power law scaling regimes that are typical of physiological sway movements in humans.
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34
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Milton J, Cabrera JL, Ohira T, Tajima S, Tonosaki Y, Eurich CW, Campbell SA. The time-delayed inverted pendulum: implications for human balance control. CHAOS (WOODBURY, N.Y.) 2009; 19:026110. [PMID: 19566270 DOI: 10.1063/1.3141429] [Citation(s) in RCA: 66] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
The inverted pendulum is frequently used as a starting point for discussions of how human balance is maintained during standing and locomotion. Here we examine three experimental paradigms of time-delayed balance control: (1) mechanical inverted time-delayed pendulum, (2) stick balancing at the fingertip, and (3) human postural sway during quiet standing. Measurements of the transfer function (mechanical stick balancing) and the two-point correlation function (Hurst exponent) for the movements of the fingertip (real stick balancing) and the fluctuations in the center of pressure (postural sway) demonstrate that the upright fixed point is unstable in all three paradigms. These observations imply that the balanced state represents a more complex and bounded time-dependent state than a fixed-point attractor. Although mathematical models indicate that a sufficient condition for instability is for the time delay to make a corrective movement, tau(n), be greater than a critical delay tau(c) that is proportional to the length of the pendulum, this condition is satisfied only in the case of human stick balancing at the fingertip. Thus it is suggested that a common cause of instability in all three paradigms stems from the difficulty of controlling both the angle of the inverted pendulum and the position of the controller simultaneously using time-delayed feedback. Considerations of the problematic nature of control in the presence of delay and random perturbations ("noise") suggest that neural control for the upright position likely resembles an adaptive-type controller in which the displacement angle is allowed to drift for small displacements with active corrections made only when theta exceeds a threshold. This mechanism draws attention to an overlooked type of passive control that arises from the interplay between retarded variables and noise.
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Affiliation(s)
- John Milton
- Joint Science Department, W. M. Keck Science Center, The Claremont Colleges, Claremont, California 91711, USA
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Beuter A, Modolo J. Delayed and lasting effects of deep brain stimulation on locomotion in Parkinson's disease. CHAOS (WOODBURY, N.Y.) 2009; 19:026114. [PMID: 19566274 DOI: 10.1063/1.3127585] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Parkinson's disease (PD) is a neurodegenerative disorder characterized by a variety of motor signs affecting gait, postural stability, and tremor. These symptoms can be improved when electrodes are implanted in deep brain structures and electrical stimulation is delivered chronically at high frequency (>100 Hz). Deep brain stimulation (DBS) onset or cessation affects PD signs with different latencies, and the long-term improvements of symptoms affecting the body axis and those affecting the limbs vary in duration. Interestingly, these effects have not been systematically analyzed and modeled. We compare these timing phenomena in relation to one axial (i.e., locomotion) and one distal (i.e., tremor) signs. We suggest that during DBS, these symptoms are improved by different network mechanisms operating at multiple time scales. Locomotion improvement may involve a delayed plastic reorganization, which takes hours to develop, whereas rest tremor is probably alleviated by an almost instantaneous desynchronization of neural activity in subcortical structures. Even if all PD patients develop both distal and axial symptoms sooner or later, current computational models of locomotion and rest tremor are separate. Furthermore, a few computational models of locomotion focus on PD and none exploring the effect of DBS was found in the literature. We, therefore, discuss a model of a neuronal network during DBS, general enough to explore the subcircuits controlling locomotion and rest tremor simultaneously. This model accounts for synchronization and plasticity, two mechanisms that are believed to underlie the two types of symptoms analyzed. We suggest that a hysteretic effect caused by DBS-induced plasticity and synchronization modulation contributes to the different therapeutic latencies observed. Such a comprehensive, generic computational model of DBS effects, incorporating these timing phenomena, should assist in developing a more efficient, faster, durable treatment of distal and axial signs in PD.
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Affiliation(s)
- Anne Beuter
- IMS Laboratory (Site ENSCPB), Polytechnic Institute of Bordeaux (IPB), 16 avenue Pey-Berland, 33607 Pessac Cedex, France
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Stepan G. Delay effects in brain dynamics. Introduction. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2009; 367:1059-62. [PMID: 19218150 DOI: 10.1098/rsta.2008.0279] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
This brief introductory paper reviews the methods and the results presented in the special issue. The general destabilizing effects of time delays in nonlinear dynamical systems are summarized and some similarities in the philosophical approaches of neural systems research in distinct disciplines are pointed out. All the invited papers focus on the central role of time delays in the dynamics of neural systems. The research contributions are set in order according to the increasing number of neurons involved in the corresponding study from a couple of neurons through neural fields to populations and clusters of neurons.
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Affiliation(s)
- Gabor Stepan
- Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest 1521, Hungary.
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Stepan G. Delay effects in the human sensory system during balancing. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2009; 367:1195-212. [PMID: 19218159 DOI: 10.1098/rsta.2008.0278] [Citation(s) in RCA: 50] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
Abstract
Mechanical models of human self-balancing often use the Newtonian equations of inverted pendula. While these mathematical models are precise enough on the mechanical side, the ways humans balance themselves are still quite unexplored on the control side. Time delays in the sensory and motoric neural pathways give essential limitations to the stabilization of the human body as a multiple inverted pendulum. The sensory systems supporting each other provide the necessary signals for these control tasks; but the more complicated the system is, the larger delay is introduced. Human ageing as well as our actual physical and mental state affects the time delays in the neural system, and the mechanical structure of the human body also changes in a large range during our lives. The human balancing organ, the labyrinth, and the vision system essentially adapted to these relatively large time delays and parameter regions occurring during balancing. The analytical study of the simplified large-scale time-delayed models of balancing provides a Newtonian insight into the functioning of these organs that may also serve as a basis to support theories and hypotheses on balancing and vision.
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Affiliation(s)
- Gabor Stepan
- Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest 1521, Hungary.
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