Direct estimation of the parameters of a delayed, intermittent activation feedback model of postural sway during quiet standing
Autoři:
Kevin L. McKee aff001; Michael C. Neale aff001
Působiště autorů:
Virginia Commonwealth University, Virginia Institute of Psychiatric and Behavioral Genetics, Richmond, Virginia, United States of America
aff001
Vyšlo v časopise:
PLoS ONE 14(9)
Kategorie:
Research Article
prolekare.web.journal.doi_sk:
https://doi.org/10.1371/journal.pone.0222664
Souhrn
Human postural sway during quiet standing has been characterized as a proportional-integral-derivative controller with intermittent activation. In the model, patterns of sway result from both instantaneous, passive, mechanical resistance and delayed, intermittent resistance signaled by the central nervous system. A Kalman-Filter framework was designed to directly estimate from experimental data the parameters of the model’s stochastic delay differential equations with discrete dynamic switching conditions. Simulations showed that all parameters could be estimated over a variety of possible data-generating configurations with varying degrees of bias and variance depending on their empirical identification. Applications to experimental data reveal distributions of each parameter that correspond well to previous findings, suggesting that many useful, physiological measures may be extracted from sway data. Individuals varied in degree and type of deviation from theoretical expectations, ranging from harmonic oscillation to non-equilibrium Langevin dynamics.
Klíčová slova:
Biology and life sciences – Physical sciences – Engineering and technology – Research and analysis methods – Neuroscience – Cognitive science – Computer and information sciences – Mathematics – Simulation and modeling – Anatomy – Medicine and health sciences – Cognitive neuroscience – Applied mathematics – Algorithms – Musculoskeletal system – Body limbs – Signal processing – Systems science – Motor reactions – Postural control – Legs – Control engineering – Ankles – Kalman filter – Control theory – Noise reduction – Differential equations – Numerical analysis – Interpolation
Zdroje
1. Asai Y, Tasaka Y, Nomura K, Nomura T, Casadio M, Morasso P. A Model of Postural Control in Quiet Standing: Robust Compensation of Delay-Induced Instability Using Intermittent Activation of Feedback Control (Intermittent Postural Control). PLoS ONE. 2009;4(7). doi: 10.1371/annotation/96e08e7f-22f0-445d-8fb3-fe7b071d0a3a
2. Milton JG, Insperger T, Cook W, Harris DM, Stepan G. Microchaos in human postural balance: Sensory dead zones and sampled time-delayed feedback. Physical review E. 2018;98(2-1). doi: 10.1103/PhysRevE.98.022223 30253531
3. Collins JJ, De Luca CJ. Random walking during quiet standing. Physical review letters. 1994;73(5). doi: 10.1103/PhysRevLett.73.764
4. Lafond D, Duarte M, Prince F. Comparison of three methods to estimate the center of mass during balance assessment. Journal of Biomechanics. 2004;37(9):1421–1426. doi: 10.1016/S0021-9290(03)00251-3 15275850
5. Collins JJ, De Luca CJ. Open-loop and closed-loop control of posture: A random-walk analysis of center-of-pressure trajectories. Experimental Brain Research. 1993;95(2):308–318. doi: 10.1007/bf00229788 8224055
6. Yamamoto T, Smith CE, Suzuki Y, Kiyono K, Tanahashi T, Sakoda S, et al. Universal and individual characteristics of postural sway during quiet standing in healthy young adults. Physiological Reports. 2015;3(3):n/a–n/a. doi: 10.14814/phy2.12329
7. Zatsiorsky VM, Duarte M. Rambling and trembling in quiet standing. Motor control. 2000;4(2). doi: 10.1123/mcj.4.2.185 11500575
8. Maurer C, Peterka R. A New Interpretation of Spontaneous Sway Measures Based on a Simple Model of Human Postural Control. Journal of Neurophysiology. 2005;93(1):189–200. doi: 10.1152/jn.00221.2004 15331614
9. Gawthrop P, Loram I, Lakie M, Gollee H. Intermittent control: a computational theory of human control. Biological Cybernetics. 2011;104(1):31–51. doi: 10.1007/s00422-010-0416-4 21327829
10. Milton J, Meyer R, Zhvanetsky M, Ridge S, Insperger T. Control at stability’s edge minimizes energetic costs: expert stick balancing. Journal of the Royal Society, Interface. 2016;13(119). doi: 10.1098/rsif.2016.0212 27278361
11. Michimoto K, Suzuki Y, Kiyono K, Kobayashi Y, Morasso P, Nomura T. Reinforcement learning for stabilizing an inverted pendulum naturally leads to intermittent feedback control as in human quiet standing. Conference proceedings: Annual International Conference of the IEEE Engineering in Medicine and Biology Society IEEE Engineering in Medicine and Biology Society Annual Conference. 2016;2016:37–40.
12. Gawthrop PJ, Wang L. Intermittent model predictive control. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering. 2007;221(7):1007–1018.
13. Gawthrop P, Loram I, Gollee H, Lakie M. Intermittent control models of human standing: similarities and differences. Biological cybernetics. 2014;108(2). doi: 10.1007/s00422-014-0587-5 24500616
14. Eurich, Milton. Noise-induced transitions in human postural sway. Physical review E, Statistical physics, plasmas, fluids, and related interdisciplinary topics. 1996;54(6). doi: 10.1103/physreve.54.6681 9965894
15. Bottaro A, Yasutake Y, Nomura T, Casadio M, Morasso P. Bounded stability of the quiet standing posture: An intermittent control model. Human Movement Science. 2008;27(3):473–495. doi: 10.1016/j.humov.2007.11.005 18342382
16. Nomura T, Oshikawa S, Suzuki Y, Kiyono K, Morasso P. Modeling human postural sway using an intermittent control and hemodynamic perturbations. Mathematical Biosciences. 2013;245(1):86–95. doi: 10.1016/j.mbs.2013.02.002 23435118
17. Wang H, Li J. Adaptive Gaussian Process Approximation for Bayesian Inference with Expensive Likelihood Functions. Neural Computation. 2018;30(11):3072–3094. doi: 10.1162/neco_a_01127
18. Tietäväinen A, Gutmann MU, Keski-Vakkuri E, Corander J, Hæggström E. Bayesian inference of physiologically meaningful parameters from body sway measurements. Scientific reports. 2017;7(1). doi: 10.1038/s41598-017-02372-1 28630413
19. Aandahl RZ, Stadler T, Sisson SA, Tanaka MM. Exact vs. approximate computation: reconciling different estimates of Mycobacterium tuberculosis epidemiological parameters. Genetics. 2014;196(4). doi: 10.1534/genetics.113.158808 24496011
20. Santos DAD, Fukuchi CA, Fukuchi RK, Duarte M. A data set with kinematic and ground reaction forces of human balance. PeerJ. 2017;5(7).
21. Peterka RJ. Sensorimotor integration in human postural control. Journal of neurophysiology. 2002;88(3):1097–1118. doi: 10.1152/jn.2002.88.3.1097 12205132
22. Loram ID, Lakie M. Direct measurement of human ankle stiffness during quiet standing: the intrinsic mechanical stiffness is insufficient for stability. Journal of Physiology. 2002;545(3):1041–1053. doi: 10.1113/jphysiol.2002.025049 12482906
23. Casadio M, Morasso PG, Sanguineti V. Direct measurement of ankle stiffness during quiet standing: implications for control modelling and clinical application. Gait & Posture. 2005;21(4):410–424. doi: 10.1016/j.gaitpost.2004.05.005
24. Li Y, Levine WS, Loeb GE. A Two-Joint Human Posture Control Model With Realistic Neural Delays. IEEE Transactions on Neural Systems and Rehabilitation Engineering. 2012;20(5):738–748. doi: 10.1109/TNSRE.2012.2199333 22692939
25. Woollacott M, Hosten C, Rösblad B. Relation between muscle response onset and body segmental movements during postural perturbations in humans. Experimental Brain Research. 1988;72(3):593–604. doi: 10.1007/bf00250604 3234505
26. Kalman RE, Bucy RS. New Results in Linear Filtering and Prediction Theory. Journal of Basic Engineering. 1961;83(1).
27. Wei WWS. Time series analysis: univariate and multivariate methods. 2nd ed. Boston: Pearson Addison Wesley; 2006.
28. Price KV, Storn RM, Lampinen JA. Differential Evolution—A Practical Approach to Global Optimization. Natural Computing. Springer-Verlag; 2006.
29. R Core Team. R: A Language and Environment for Statistical Computing; 2018. Available from: https://www.R-project.org/.
30. Mullen KM, Ardia D, Gil DL, Windover D, Cline J. DEoptim: An R Package for Global Optimization by Differential Evolution. Journal of Statistical Software. 2011;40(6). doi: 10.18637/jss.v040.i06
31. Eddelbuettel D, Balamuta JJ. Extending extitR with extitC++: A Brief Introduction to extitRcpp. PeerJ Preprints. 2017;5:e3188v1.
32. Eddelbuettel D, Sanderson C. RcppArmadillo: Accelerating R with high-performance C++ linear algebra. Computational Statistics and Data Analysis. 2014;71:1054–1063. doi: 10.1016/j.csda.2013.02.005
33. Akaike H. A new look at the statistical model identification. IEEE Transactions on Automatic Control. 1974;19(6):716–723. doi: 10.1109/TAC.1974.1100705
34. Bosek M, Grzegorzewski B, Kowalczyk A. Two-dimensional Langevin approach to the human stabilogram. Human Movement Science. 2004;22(6):649–660. doi: 10.1016/j.humov.2004.02.005 15063046
35. Bosek M, Grzegorzewski B, Kowalczyk A, Lubiński I. Degradation of postural control system as a consequence of Parkinson’s disease and ageing. Neuroscience letters. 2005;376(3). doi: 10.1016/j.neulet.2004.11.056 15721224
36. Gottschall J, Peinke J, Lippens V, Nagel V. Exploring the dynamics of balance data—movement variability in terms of drift and diffusion. Physics Letters A. 2009;373(8):811–816. doi: 10.1016/j.physleta.2008.12.026
37. Lauk M, Chow CC, Pavlik AE, Collins JJ. Human Balance out of Equilibrium: Nonequilibrium Statistical Mechanics in Posture Control. Physical Review Letters. 1998;80(2):413–416. doi: 10.1103/PhysRevLett.80.413
38. Vieira TdMM, Oliveira LFd, Nadal J. An overview of age-related changes in postural control during quiet standing tasks using classical and modern stabilometric descriptors. Journal of Electromyography and Kinesiology. 2009;19(6):e513–e519. doi: 10.1016/j.jelekin.2008.10.007
39. Hageman PA, Leibowitz JM, Blanke D. Age and gender effects on postural control measures. Archives of physical medicine and rehabilitation. 1995;76(10). doi: 10.1016/s0003-9993(95)80075-1 7487439
40. Lin D, Seol H, Nussbaum MA, Madigan ML. Reliability of COP-based postural sway measures and age-related differences. Gait & Posture. 2008;28(2):337–342. doi: 10.1016/j.gaitpost.2008.01.005
41. Collins JJ, De Luca CJ, Burrows A, Lipsitz LA. Age-related changes in open-loop and closed-loop postural control mechanisms. Experimental brain research. 1995;104(3). doi: 10.1007/bf00231982 7589299
42. Cenciarini M, Loughlin PJ, Sparto PJ, Redfern MS. Stiffness and Damping in Postural Control Increase With Age. IEEE Transactions on Biomedical Engineering. 2010;57(2):267–275. doi: 10.1109/TBME.2009.2031874 19770083
Článok vyšiel v časopise
PLOS One
2019 Číslo 9
- Metamizol jako analgetikum první volby: kdy, pro koho, jak a proč?
- Nejasný stín na plicích – kazuistika
- Masturbační chování žen v ČR − dotazníková studie
- Úspěšná resuscitativní thorakotomie v přednemocniční neodkladné péči
- Fixní kombinace paracetamol/kodein nabízí synergické analgetické účinky
Najčítanejšie v tomto čísle
- Graviola (Annona muricata) attenuates behavioural alterations and testicular oxidative stress induced by streptozotocin in diabetic rats
- CH(II), a cerebroprotein hydrolysate, exhibits potential neuro-protective effect on Alzheimer’s disease
- Comparison between Aptima Assays (Hologic) and the Allplex STI Essential Assay (Seegene) for the diagnosis of Sexually transmitted infections
- Assessment of glucose-6-phosphate dehydrogenase activity using CareStart G6PD rapid diagnostic test and associated genetic variants in Plasmodium vivax malaria endemic setting in Mauritania