Coupling relationship between the central pattern generator and the cerebral cortex with time delay

Construction of the dynamic model of SCI rehabilitation using bidirectional stimulation and its application in rehabilitating with BCI

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.

A new biological central pattern generator model and its relationship with the motor units

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.

Dynamics and coupling of fractional-order models of the motor cortex and central pattern generators

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.