Knee Joint Modeling Based on Muscle Interactions Using a Central Pattern Generator to Predict Disease Progression and Rehabilitation Techniques in Incomplete Spinal Cord Injury
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Abstract
Purpose: Musculoskeletal systems have a complex and different nature, and it is very difficult to control issues in these systems due to various characteristics such as speed and accuracy. Therefore, investigating these musculoskeletal systems requires simple and analyzable methods. Also, due to sudden changes during the movement process, the speed and accuracy of the calculations should be proportional to the operating speed of the system. Predicting the available system norms and meeting is the next challenge of relevant studies.
Methods: Accordingly, it was attempted in the present study to investigate the knee joint function, the joint condition in an incomplete spinal cord injury (SCI), as well as its rehabilitation conditions by designing a simple mathematical model. This model is designed based on the interactions between hamstring muscles and vasti muscle group. Considering changes in the central pattern generator (CGP) as a variable input, we analyze the model output in fixed point, periodic and chaotic modes.
Results: The results of the present study show that the knee joint model output is chaotic and fixed point in the health and incomplete SCI modes, respectively. In order to rehabilitate the model, stimulation of Ia, II and Ib afferents is used in the CPG, which continues the rehabilitation process due to the change of output from the fixed-point mode to the periodic mode.
Conclusion: According to the results obtained from the knee joint mathematical model, it can be stated that this model, while having simple calculations, has acceptable accuracy and has the ability to predict different norms. It can also be hoped that, better and more accurate results will be achieved in the study of musculoskeletal systems with the development of this model.
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26- Natalia A Shevtsova, Khaldoun Hamade, Samit Chakrabarty, Sergey N Markin, Boris I Prilutsky, and Ilya A Rybak, "Modeling the organization of spinal cord neural circuits controlling two-joint muscles." in Neuromechanical modeling of posture and locomotion: Springer, (2016), pp. 121-62.
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29- Dante R Chialvo, Donald C Michaels, and José Jalife, "Supernormal excitability as a mechanism of chaotic dynamics of activation in cardiac Purkinje fibers." Circulation research, Vol. 66 (No. 2), pp. 525-45, (1990).
30- Viet-Thanh Pham, Sajad Jafari, and Christos Volos, "A novel chaotic system with heart-shaped equilibrium and its circuital implementation." Optik, Vol. 131pp. 343-49, (2017).
31- J Michael T Thompson, "Chaos, fractals and their applications." International Journal of Bifurcation and Chaos, Vol. 26 (No. 13), p. 1630035, (2016).
2- Sajad Jafari, Seyyed Mohammad Reza Hashemi Golpayegani, Amir Homayoun Jafari, and Shahriar Gharibzadeh, "A novel viewpoint on parameter estimation in a chaotic neuron model." The Journal of neuropsychiatry and clinical neurosciences, Vol. 25 (No. 1), pp. E19-E19, (2013).
3- Juan Zhang, Jun Tang, Jun Ma, Jin Ming Luo, and Xian Qing Yang, "The dynamics of spiral tip adjacent to inhomogeneity in cardiac tissue." Physica A: Statistical Mechanics and its Applications, Vol. 491pp. 340-46, (2018).
4- Susan Iversen, Irving Kupfermann, and Eric R Kandel, "Emotional states and feelings." Principles of neural science, Vol. 4pp. 982-97, (2000).
5- Elizabeth M Cherry and Flavio H Fenton, "Visualization of spiral and scroll waves in simulated and experimental cardiac tissue." New Journal of Physics, Vol. 10 (No. 12), p. 125016, (2008).
6- Huaguang Gu, Baobao Pan, and Jian Xu, "Experimental observation of spike, burst and chaos synchronization of calcium concentration oscillations." EPL (Europhysics Letters), Vol. 106 (No. 5), p. 50003, (2014).
7- Chuan Zhang, Xingyuan Wang, Chao Luo, Junqiu Li, and Chunpeng Wang, "Robust outer synchronization between two nonlinear complex networks with parametric disturbances and mixed time-varying delays." Physica A: Statistical Mechanics and its Applications, Vol. 494pp. 251-64, (2018).
8- Zahra Rostami, Mohsen Mousavi, Karthikeyan Rajagopal, Olfa Boubaker, and Sajad Jafari, "Chaotic Solutions in a Forced Two-Dimensional Hindmarsh-Rose Neuron." in Recent Advances in Chaotic Systems and Synchronization: Elsevier, (2019), pp. 187-209.
9- David A McCrea and Ilya A Rybak, "Modeling the mammalian locomotor CPG: insights from mistakes and perturbations." Progress in brain research, Vol. 165pp. 235-53, (2007).
10- Sten Grillner, "Biological pattern generation: the cellular and computational logic of networks in motion." Neuron, Vol. 52 (No. 5), pp. 751-66, (2006).
11- Serge Rossignol, "Neural control of stereotypic limb movements." Exercise: Regulation and integration of multiple systems, (1996).
12- Volker Dietz, "Spinal cord pattern generators for locomotion." Clinical Neurophysiology, Vol. 114 (No. 8), pp. 1379-89, (2003).
13- Serge Rossignol, Réjean Dubuc, and Jean-Pierre Gossard, "Dynamic sensorimotor interactions in locomotion." Physiological reviews, Vol. 86 (No. 1), pp. 89-154, (2006).
14- Hugues Barbeau, David A McCrea, Michael J O'Donovan, Serge Rossignol, Warren M Grill, and Michel A Lemay, "Tapping into spinal circuits to restore motor function." Brain Research Reviews, Vol. 30 (No. 1), pp. 27-51, (1999).
15- S Rossignol, L Bouyer, D Barthelemy, C Langlet, and H Leblond, "Recovery of locomotion in the cat following spinal cord lesions." Brain Research Reviews, Vol. 40 (No. 1-3), pp. 257-66, (2002).
16- V Reggie Edgerton, Niranjala JK Tillakaratne, Allison J Bigbee, Ray D de Leon, and Roland R Roy, "Plasticity of the spinal neural circuitry after injury." Annual review of neuroscience, Vol. 27 (No. 1), pp. 145-67, (2004).
17- P Guertin, MJ Angel, MC Perreault, and DA McCrea, "Ankle extensor group I afferents excite extensors throughout the hindlimb during fictive locomotion in the cat." The Journal of Physiology, Vol. 487 (No. 1), pp. 197-209, (1995).
18- Mohaddeseh Hedayatzadeh and Hamid Reza Kobravi, "Movement Stabilizing Using Afferent Control of Spinal Locomotor CPG Using Chaotic Takagi-Sugeno Fuzzy Logic Systems: A Simulation Study." International Clinical Neuroscience Journal, Vol. 5 (No. 1), pp. 28-34, (2018).
19- Chandana Paul, Mario Bellotti, Sašo Jezernik, and Armin Curt, "Development of a human neuro-musculo-skeletal model for investigation of spinal cord injury." Biological cybernetics, Vol. 93 (No. 3), pp. 153-70, (2005).
20- Sergey N Markin, Alexander N Klishko, Natalia A Shevtsova, Michel A Lemay, Boris I Prilutsky, and Ilya A Rybak, "Afferent control of locomotor CPG: insights from a simple neuromechanical model." Annals of the New York Academy of Sciences, Vol. 1198 (No. 1), pp. 21-34, (2010).
21- Mohsen Abedi, Majid M Moghaddam, and Mohammad Firoozabadi, "A neuromechanical modeling of spinal cord injury locomotor system for simulating the rehabilitation effects." Biocybernetics and Biomedical Engineering, Vol. 36 (No. 1), pp. 193-204, (2016).
22- Michèle Hubli and Volker Dietz, "The physiological basis of neurorehabilitation-locomotor training after spinal cord injury." Journal of neuroengineering and rehabilitation, Vol. 10 (No. 1), pp. 1-8, (2013).
23- Ilya A Rybak, Katinka Stecina, Natalia A Shevtsova, and David A McCrea, "Modelling spinal circuitry involved in locomotor pattern generation: insights from the effects of afferent stimulation." The Journal of Physiology, Vol. 577 (No. 2), pp. 641-58, (2006).
24- Jacques Duysens and Arturo Forner-Cordero, "A controller perspective on biological gait control: Reflexes and central pattern generators." Annual Reviews in Control, Vol. 48pp. 392-400, (2019).
25- Andrii Dmytrovych Shachykov, Patrick Hénaff, and Alexander Shulyak, "Modeling of human gait control using CPGs." in JNRH 2018-Journées Nationales de la Robotique Humanoïde, (2018).
26- Natalia A Shevtsova, Khaldoun Hamade, Samit Chakrabarty, Sergey N Markin, Boris I Prilutsky, and Ilya A Rybak, "Modeling the organization of spinal cord neural circuits controlling two-joint muscles." in Neuromechanical modeling of posture and locomotion: Springer, (2016), pp. 121-62.
27- Sajad Jafari, Julien C Sprott, and SMRH Golpayegani, "Layla and Majnun: a complex love story." Nonlinear Dynamics, Vol. 83 (No. 1), pp. 615-22, (2016).
28- Digesh Chitrakar and Per Sebastian Skardal, "Chaos in nonlinear random walks with nonmonotonic transition probabilities." Physical Review Research, Vol. 3 (No. 4), p. 043189, (2021).
29- Dante R Chialvo, Donald C Michaels, and José Jalife, "Supernormal excitability as a mechanism of chaotic dynamics of activation in cardiac Purkinje fibers." Circulation research, Vol. 66 (No. 2), pp. 525-45, (1990).
30- Viet-Thanh Pham, Sajad Jafari, and Christos Volos, "A novel chaotic system with heart-shaped equilibrium and its circuital implementation." Optik, Vol. 131pp. 343-49, (2017).
31- J Michael T Thompson, "Chaos, fractals and their applications." International Journal of Bifurcation and Chaos, Vol. 26 (No. 13), p. 1630035, (2016).
| Files | ||
| Issue | Vol 10 No 2 (2023) | |
| Section | Original Article(s) | |
| DOI | https://doi.org/10.18502/fbt.v10i2.12225 | |
| Keywords | ||
| Knee Joint Central Pattern Generator Spinal Cord Injury Rehabilitation Hamstring Muscles Vasti Muscle Group | ||
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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. |
How to Cite
1.
Maleki M, Nowshiravan Rahatabad F, Pouladian M. Knee Joint Modeling Based on Muscle Interactions Using a Central Pattern Generator to Predict Disease Progression and Rehabilitation Techniques in Incomplete Spinal Cord Injury. Frontiers Biomed Technol. 2023;10(2):204-212.
