Mathematical Modeling for Description of Oscillation Suppression Induced by Deep Brain Stimulation

Suppression of beta oscillations by delayed feedback in a cortex-basal ganglia-thalamus-pedunculopontine nucleus neural loop model

Excessive neural synchronization of neural populations in the beta (β) frequency range (12-35 Hz) is intimately related to the symptoms of hypokinesia in Parkinson's disease (PD). Studies have shown that delayed feedback stimulation strategies can interrupt excessive neural synchronization and effectively alleviate symptoms associated with PD dyskinesia. Work on optimizing delayed feedback algorithms continues to progress, yet it remains challenging to further improve the inhibitory effect with reduced energy expenditure. Therefore, we first established a neural mass model of the cortex-basal ganglia-thalamus-pedunculopontine nucleus (CBGTh-PPN) closed-loop system, which can reflect the internal properties of cortical and basal ganglia neurons and their intrinsic connections with thalamic and pedunculopontine nucleus neurons. Second, the inhibitory effects of three delayed feedback schemes based on the external globus pallidum (GPe) on β oscillations were investigated separately and compared with those based on the subthalamic nucleus (STN) only. Our results show that all four delayed feedback schemes achieve effective suppression of pathological β oscillations when using the linear delayed feedback algorithm. The comparison revealed that the three GPe-based delayed feedback stimulation strategies were able to have a greater range of oscillation suppression with reduced energy consumption, thus improving control performance effectively, suggesting that they may be more effective for the relief of Parkinson's motor symptoms in practical applications.

Models of communication and control for brain networks: distinctions, convergence, and future outlook

Recent advances in computational models of signal propagation and routing in the human brain have underscored the critical role of white-matter structure. A complementary approach has utilized the framework of network control theory to better understand how white matter constrains the manner in which a region or set of regions can direct or control the activity of other regions. Despite the potential for both of these approaches to enhance our understanding of the role of network structure in brain function, little work has sought to understand the relations between them. Here, we seek to explicitly bridge computational models of communication and principles of network control in a conceptual review of the current literature. By drawing comparisons between communication and control models in terms of the level of abstraction, the dynamical complexity, the dependence on network attributes, and the interplay of multiple spatiotemporal scales, we highlight the convergence of and distinctions between the two frameworks. Based on the understanding of the intertwined nature of communication and control in human brain networks, this work provides an integrative perspective for the field and outlines exciting directions for future work.

Frequency-dependent response in cortical network with periodic electrical stimulation

Electrical stimulation can shape oscillations in brain activity. However, the mechanism of how periodic electrical stimulation modulates brain oscillations by time-delayed neural networks is poorly understood at present. To address this question, we investigate the effects of periodic stimulations on the oscillations generated via a time-delayed neural network. We specifically study the effect of unipolar and asymmetric bidirectional pulse stimulations by altering amplitude and frequency in a systematic manner. Our findings suggest that electrical stimulations play a central role in altering oscillations in the time-delayed neural network and that these alterations are strongly dependent on the stimulus frequency. We observe that the time-delayed neural network responds differently as the stimulation frequency is altered, as manifested by changes in resonance, entrainment, non-linear oscillation, or oscillation suppression. The results also indicate that the network presents similar response activities with increasing stimulus frequency under different excitation-inhibition ratios. Collectively, our findings pave the way for exploring the potential mechanism underlying the frequency-dependent modulation of network activity via electrical stimulations and provide new insights into possible electrical stimulation therapies to the neurological and psychological disorders in clinical practice.

Sinusoidal stimulation on afferent fibers can selectively activate different types of neurons in rat hippocampus

Deep brain stimulation (DBS) is a promising therapy for treating various brain disorders. Although narrow electrical pulses have been commonly used by DBS, sinusoidal waveforms have also been investigated to improve the effects of DBS therapy and to save electrical energy. However, the effect of sinusoidal stimulation on neurons is unclear yet. To investigate the modulation of sinusoidal stimulation on different types of neurons in networks, sinusoidal stimulations (50 Hz) with lower-intensity and higher-intensity were applied to the afferent axons (Schaffer collaterals) in rat hippocampal CA1 region. The firing of inhibitory interneurons and excitatory pyramidal cells (the principal neurons of CA1) during the stimulations were detected and were compared with their baseline firing before stimulations. Results showed that sinusoidal stimulation with a lower-intensity (~30 μA) can selectively activate the interneurons thereby suppressing the firing of pyramidal cells in the downstream post-synaptic region. However, sinusoidal stimulation with a higher-intensity (~60 μA) can increase the firing of both types of neurons significantly. Presumably, the two different effects of inhibition and excitation on the principal neurons by different stimulation intensities could be caused by the fact that the firing threshold of interneurons is lower than that of pyramidal cells. The results provide important clues for selective modulation of neuronal activity by brain stimulations thereby developing different stimulation paradigms to treat various brain disorders.