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Cui Z, Lin J, Fu X, Zhang S, Li P, Wu X, Wang X, Chen W, Zhu S, Li Y. Construction of the dynamic model of SCI rehabilitation using bidirectional stimulation and its application in rehabilitating with BCI. Cogn Neurodyn 2023; 17:169-181. [PMID: 36704625 PMCID: PMC9871133 DOI: 10.1007/s11571-022-09804-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2021] [Revised: 03/04/2022] [Accepted: 03/26/2022] [Indexed: 01/29/2023] Open
Abstract
Patients with complete spinal cord injury have a complete loss of motor and sensory functions below the injury plane, leading to a complete loss of function of the nerve pathway in the injured area. Improving the microenvironment in the injured area of patients with spinal cord injury, promoting axon regeneration of the nerve cells is challenging research fields. The brain-computer interface rehabilitation system is different from the other rehabilitation techniques. It can exert bidirectional stimulation on the spinal cord injury area, and can make positively rehabilitation effects of the patient with complete spinal cord injury. A dynamic model was constructed for the patient with spinal cord injury under-stimulation therapy, and the mechanism of the brain-computer interface in rehabilitation training was explored. The effects of the three current rehabilitation treatment methods on the microenvironment in a microscopic nonlinear model were innovatively unified and a complex system mapping relationship from the microscopic axon growth to macroscopic motor functions was constructed. The basic structure of the model was determined by simulating and fitting the data of the open rat experiments. A clinical rehabilitation experiment of spinal cord injury based on brain-computer interface was built, recruiting a patient with complete spinal cord injury, and the rehabilitation training and follow-up were conducted. The changes in the motor function of the patient was simulated and predicted through the constructed model, and the trend in the motor function improvement was successfully predicted over time. This proposed model explores the mechanism of brain-computer interface in rehabilitating patients with complete spinal cord injury, and it is also an application of complex system theory in rehabilitation medicine. Supplementary Information The online version contains supplementary material available at 10.1007/s11571-022-09804-3.
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Affiliation(s)
- Zhengzhe Cui
- School of Mechanical Engineering, Zhejiang University, Hangzhou, China
| | - Juan Lin
- Rehabilitation Medicine Center, The First Affiliated Hospital of Nanjing Medical University, Nanjing, China
| | - Xiangxiang Fu
- School of Mechanical Engineering, Zhejiang University, Hangzhou, China
| | | | - Peng Li
- School of Mechanical Engineering, Zhejiang University, Hangzhou, China
| | - Xixi Wu
- Rehabilitation Medicine Center, The First Affiliated Hospital of Nanjing Medical University, Nanjing, China
| | - Xue Wang
- Rehabilitation Medicine Center, The First Affiliated Hospital of Nanjing Medical University, Nanjing, China
| | - Weidong Chen
- Qiushi Academy for Advanced Studies, Zhejiang University, Hangzhou, China
| | - Shiqiang Zhu
- School of Mechanical Engineering, Zhejiang University, Hangzhou, China
| | - Yongqiang Li
- Rehabilitation Medicine Center, The First Affiliated Hospital of Nanjing Medical University, Nanjing, China
- Wuxi Tongren Rehabilitation Hospital, Wuxi, China
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Lu Q, Wang X, Tian J. A new biological central pattern generator model and its relationship with the motor units. Cogn Neurodyn 2022; 16:135-147. [PMID: 35126774 PMCID: PMC8807781 DOI: 10.1007/s11571-021-09710-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2021] [Revised: 06/27/2021] [Accepted: 07/31/2021] [Indexed: 02/03/2023] Open
Abstract
The central pattern generator (CPG) is a key neural-circuit component of the locomotion control system. Recently, numerous molecular and genetic approaches have been proposed for investigating the CPG mechanisms. The rhythm in the CPG locomotor circuits comes from the activity in the ipsilateral excitatory neurons whose output is controlled by inter-neuron inhibitory connections. Conventional models for simulating the CPG mechanism are complex Hodgkin-Huxley-type models. Inspired by biological investigations and the continuous-time Matsuoka model, we propose new integral-order and fractional-order CPG models, which consider time delays and synaptic interfaces. The phase diagrams exhibit limit cycles and periodic solutions, in agreement with the CPG biological characteristics. As well, the fractional-order model shows state transitions with order variations. In addition, we investigate the relationship between the CPG and the motor units through the construction of integral-order and fractional-order coupling models. Simulations of these coupling models show that the states generated by the three motor units are in accordance with the experimentally-obtained states in previous studies. The proposed models reveal that the CPG can regulate limb locomotion patterns through connection weights and synaptic interfaces. Moreover, in comparison to the integral-order models, the fractional-order ones appear to be more effective, and hence more suitable for describing the dynamics of the CPG biological system.
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Affiliation(s)
- Qiang Lu
- College of Medical Information Engineering, Shandong First Medical University & Shandong Academy of Medical Sciences, Taian, 271000 China
| | - Xiaoyan Wang
- College of Medical Information Engineering, Shandong First Medical University & Shandong Academy of Medical Sciences, Taian, 271000 China
| | - Juan Tian
- College of Medical Information Engineering, Shandong First Medical University & Shandong Academy of Medical Sciences, Taian, 271000 China
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Lu Q. Dynamics and coupling of fractional-order models of the motor cortex and central pattern generators. J Neural Eng 2020; 17:036021. [PMID: 32344390 DOI: 10.1088/1741-2552/ab8dd6] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
OBJECTIVE Fractional calculus plays a key role in the analysis of neural dynamics. In particular, fractional calculus has been recently exploited for analyzing complex biological systems and capturing intrinsic phenomena. Also, artificial neural networks have been shown to have complex neuronal dynamics and characteristics that can be modeled by fractional calculus. Moreover, for a neural microcircuit placed on the spinal cord, fractional calculus can be employed to model the central pattern generator (CPG). However, the relation between the CPG and the motor cortex is still unclear. APPROACH In this paper, fractional-order models of the CPG and the motor cortex are built on the Van der Pol oscillator and the neural mass model (NMM), respectively. A self-consistent mean field approximation is used to construct the potential landscape of the Van der Pol oscillator. This landscape provides a useful tool to observe the 3D dynamics of the oscillator. To infer the relation of the motor cortex and CPG, the coupling model between the fractional-order Van der Pol oscillator and the NMM is built. As well, the influence of the coupling parameters on the CPG and the motor cortex is assessed. MAIN RESULTS Fractional-order NMM and coupling model of the motor cortex and the CPG are first established. The potential landscape is used to show 3D probabilistic evolution of the Van der Pol oscillator states. Detailed observations of the evolution of the system states can be made with fractional calculus. In particular, fractional calculus enables the observation of the creation of stable modes and switching between them. SIGNIFICANCE The results confirm that the motor cortex and CPG have associated modes or states that can be switched based on changes in the fractional order and the time delay. Fractional calculus and the potential landscape are helpful methods for better understanding of the working principles of locomotion systems.
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Affiliation(s)
- Qiang Lu
- College of Medical Information Engineering, Shandong First Medical University & Shandong Academy of Medical Sciences, Taian 271000, People's Republic of China
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Nakamura O, Tateno K. Random pulse induced synchronization and resonance in uncoupled non-identical neuron models. Cogn Neurodyn 2019; 13:303-312. [PMID: 31168334 DOI: 10.1007/s11571-018-09518-5] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2018] [Revised: 11/28/2018] [Accepted: 12/25/2018] [Indexed: 01/19/2023] Open
Abstract
Random pulses contribute to stochastic resonance in neuron models, whereas common random pulses cause stochastic-synchronized excitation in uncoupled neuron models. We studied concurrent phenomena contributing to phase synchronization and stochastic resonance following induction by a weak common random pulse in uncoupled non-identical Hodgkin-Huxley type neuron models. The common random pulse was selected from a gamma distribution and the degree of synchronization depended on the corresponding shape parameter. Specifically, a low shape parameter of the weak random pulse induced well-synchronized spiking in uncoupled neuron models, whereas a high shape parameter of the weak random pulse or a weak periodic pulse caused low degrees of synchronization. These were improved by concurrent inputs of periodic and random pulses with high shape parameters. Finally, the output pulse was synchronized with the periodic pulse, and the common random pulse revealed periodic responses in the present neuron models.
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Affiliation(s)
- Osamu Nakamura
- 1Department of Life Science and Systems Engineering, Kyushu Institute of Technology, Kitakyushu, Japan
| | - Katsumi Tateno
- 2Department of Human Intelligence Systems, Kyushu Institute of Technology, 2-4 Hibikino, Wakamatsu-ku, Kitakyushu, 808-0196 Japan
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Zhang Y, Zheng R, Shimono K, Kaizuka T, Nakano K. Effectiveness Testing of a Piezoelectric Energy Harvester for an Automobile Wheel Using Stochastic Resonance. SENSORS 2016; 16:s16101727. [PMID: 27763522 PMCID: PMC5087514 DOI: 10.3390/s16101727] [Citation(s) in RCA: 52] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/26/2016] [Revised: 10/06/2016] [Accepted: 10/13/2016] [Indexed: 11/16/2022]
Abstract
The collection of clean power from ambient vibrations is considered a promising method for energy harvesting. For the case of wheel rotation, the present study investigates the effectiveness of a piezoelectric energy harvester, with the application of stochastic resonance to optimize the efficiency of energy harvesting. It is hypothesized that when the wheel rotates at variable speeds, the energy harvester is subjected to on-road noise as ambient excitations and a tangentially acting gravity force as a periodic modulation force, which can stimulate stochastic resonance. The energy harvester was miniaturized with a bistable cantilever structure, and the on-road noise was measured for the implementation of a vibrator in an experimental setting. A validation experiment revealed that the harvesting system was optimized to capture power that was approximately 12 times that captured under only on-road noise excitation and 50 times that captured under only the periodic gravity force. Moreover, the investigation of up-sweep excitations with increasing rotational frequency confirmed that stochastic resonance is effective in optimizing the performance of the energy harvester, with a certain bandwidth of vehicle speeds. An actual-vehicle experiment validates that the prototype harvester using stochastic resonance is capable of improving power generation performance for practical tire application.
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Affiliation(s)
- Yunshun Zhang
- Institute of Industrial Science, The University of Tokyo, 4-6-1, Komaba, Meguro, Tokyo 153-8505, Japan.
| | - Rencheng Zheng
- Institute of Industrial Science, The University of Tokyo, 4-6-1, Komaba, Meguro, Tokyo 153-8505, Japan.
| | - Keisuke Shimono
- Department of Mechanical Systems Engineering, Graduate School of Engineering, Tokyo University of Agriculture and Technology, 2-24-16, Naka-cho, Koganei-shi, Tokyo 184-8588, Japan.
| | - Tsutomu Kaizuka
- Institute of Industrial Science, The University of Tokyo, 4-6-1, Komaba, Meguro, Tokyo 153-8505, Japan.
| | - Kimihiko Nakano
- Interfaculty Initiative in Information Studies, The University of Tokyo, 4-6-1, Komaba, Meguro, Tokyo 153-8505, Japan.
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Lu Q. Coupling relationship between the central pattern generator and the cerebral cortex with time delay. Cogn Neurodyn 2015; 9:423-36. [PMID: 26157515 DOI: 10.1007/s11571-015-9338-0] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2014] [Revised: 12/24/2014] [Accepted: 03/03/2015] [Indexed: 01/17/2023] Open
Abstract
Brain activity is a cooperative process among neurons and involves the coupling relationship, which is crucial to perform operational tasks in various specialized areas of the nervous system. A finite signal transmission speed along the axons results in a space-dependent time delay. The central pattern generator (CPG) can in principle produce basic locomotor rhythm in the absence of inputs from higher brain centers and peripheral sensory feedback. To study the dynamic performance of CPG with time delay and its coupling relationship with the cerebral cortex, a new CPG model with time delay and a model of the neural mass model (NMM) and the CPG are developed. The coupling model is based on biological experimental results. Bifurcation theories and maximal Lyapunov exponent are used to analyze the dynamic performance. From the results, some CPGs are suggested to be embedded in limbs and composed of the parameters space which corresponds to the one of the cerebral cortex. This embodiment of humans can reduce the burden of the brain and simplify the control of the locomotion. The results also show that the phase diagram of the CPG cannot keep the limit cycle, and that the state of the NMM becomes increasingly chaotic as time delay increases. This finding implies that a person with slow reaction can easily lose the stability of his or her locomotion.
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Affiliation(s)
- Qiang Lu
- College of Information and Engineering, Taishan Medical University, Taian, 271016 China
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Effects on hypothalamus when CPG is fed back to basal ganglia based on KIV model. Cogn Neurodyn 2015; 9:85-92. [PMID: 26052364 DOI: 10.1007/s11571-014-9302-4] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2014] [Revised: 06/03/2014] [Accepted: 07/08/2014] [Indexed: 10/25/2022] Open
Abstract
The KIV model approximates the operation of the basic vertebrate forebrain together with the basal ganglia and motor systems. In KIV model, the hypothalamus and the basal ganglia which are two important parts in the midline forebrain are closely associated with the locomotion. The CPG model with time delay is established in this paper and the stability of this CPG model is discussed. The CPG output is treated as the proprioception and fed back to the basal ganglia. We focus on the effects on the hypothalamus and the basal ganglia when the time delay parameter a d , the CPG amplitude parameter e and the CPG frequency parameter T r are changed. Through analysis, we find that there exists optimum value of the parameters a d or T r which can make the synchronization of the hypothalamus optimum when the CPG is added into the basal ganglia. The results could have important implications for biological processes which are about interaction between the neural network and the CPG.
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Kim SY, Lim W. Noise-induced burst and spike synchronizations in an inhibitory small-world network of subthreshold bursting neurons. Cogn Neurodyn 2015; 9:179-200. [PMID: 25834648 DOI: 10.1007/s11571-014-9314-0] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2014] [Revised: 09/14/2014] [Accepted: 10/07/2014] [Indexed: 12/13/2022] Open
Abstract
We are interested in noise-induced firings of subthreshold neurons which may be used for encoding environmental stimuli. Noise-induced population synchronization was previously studied only for the case of global coupling, unlike the case of subthreshold spiking neurons. Hence, we investigate the effect of complex network architecture on noise-induced synchronization in an inhibitory population of subthreshold bursting Hindmarsh-Rose neurons. For modeling complex synaptic connectivity, we consider the Watts-Strogatz small-world network which interpolates between regular lattice and random network via rewiring, and investigate the effect of small-world connectivity on emergence of noise-induced population synchronization. Thus, noise-induced burst synchronization (synchrony on the slow bursting time scale) and spike synchronization (synchrony on the fast spike time scale) are found to appear in a synchronized region of the [Formula: see text]-[Formula: see text] plane ([Formula: see text]: synaptic inhibition strength and [Formula: see text]: noise intensity). As the rewiring probability [Formula: see text] is decreased from 1 (random network) to 0 (regular lattice), the region of spike synchronization shrinks rapidly in the [Formula: see text]-[Formula: see text] plane, while the region of the burst synchronization decreases slowly. We separate the slow bursting and the fast spiking time scales via frequency filtering, and characterize the noise-induced burst and spike synchronizations by employing realistic order parameters and statistical-mechanical measures introduced in our recent work. Thus, the bursting and spiking thresholds for the burst and spike synchronization transitions are determined in terms of the bursting and spiking order parameters, respectively. Furthermore, we also measure the degrees of burst and spike synchronizations in terms of the statistical-mechanical bursting and spiking measures, respectively.
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Affiliation(s)
- Sang-Yoon Kim
- Computational Neuroscience Lab., Department of Science Education, Daegu National University of Education, Daegu, 705-115 Korea
| | - Woochang Lim
- Computational Neuroscience Lab., Department of Science Education, Daegu National University of Education, Daegu, 705-115 Korea
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Abstract
The octopus arm has attracted many researchers’ interests and became a research hot spot because of its amazing features. Several dynamic models inspired by an octopus arm are presented to realize the structure with a large number of degrees of freedom. The octopus arm is made of a soft material introducing high-dimensionality, nonlinearity, and elasticity, which makes the octopus arm difficult to control. In this paper, three coupled central pattern generators (CPGs) are built and a 2-dimensional dynamic model of the octopus arm is presented to explore possible strategies of the octopus movement control. And the CPGs’ signals treated as activation are added on the ventral, dorsal, and transversal sides, respectively. The effects of the octopus arm are discussed when the parameters of the CPGs are changed. Simulations show that the octopus arm movements are mainly determined by the shapes of three CPGs’ phase diagrams. Therefore, some locomotion modes are supposed to be embedded in the neuromuscular system of the octopus arm. And the octopus arm movements can be achieved by modulating the parameters of the CPGs. The results are beneficial for researchers to understand the octopus movement further.
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