Analysis of neural clusters due to deep brain stimulation pulses

How to entrain a selected neuronal rhythm but not others: open-loop dithered brain stimulation for selective entrainment

Objective.While brain stimulation therapies such as deep brain stimulation for Parkinson's disease (PD) can be effective, they have yet to reach their full potential across neurological disorders. Entraining neuronal rhythms using rhythmic brain stimulation has been suggested as a new therapeutic mechanism to restore neurotypical behaviour in conditions such as chronic pain, depression, and Alzheimer's disease. However, theoretical and experimental evidence indicate that brain stimulation can also entrain neuronal rhythms at sub- and super-harmonics, far from the stimulation frequency. Crucially, these counterintuitive effects could be harmful to patients, for example by triggering debilitating involuntary movements in PD. We therefore seek a principled approach to selectively promote rhythms close to the stimulation frequency, while avoiding potential harmful effects by preventing entrainment at sub- and super-harmonics.Approach.Our open-loop approach to selective entrainment, dithered stimulation, consists in adding white noise to the stimulation period.Main results.We theoretically establish the ability of dithered stimulation to selectively entrain a given brain rhythm, and verify its efficacy in simulations of uncoupled neural oscillators, and networks of coupled neural oscillators. Furthermore, we show that dithered stimulation can be implemented in neurostimulators with limited capabilities by toggling within a finite set of stimulation frequencies.Significance.Likely implementable across a variety of existing brain stimulation devices, dithering-based selective entrainment has potential to enable new brain stimulation therapies, as well as new neuroscientific research exploiting its ability to modulate higher-order entrainment.

Effects of Different Types of Electric Fields on Mechanical Properties and Microstructure of Ex Vivo Porcine Brain Tissues

Electrotherapy plays a crucial role in regulating neuronal activity. Nevertheless, the relevant therapeutic mechanisms are still unclear; thus, the effects of electric fields on brain tissue's mechanical properties and microstructure need to be explored. In this study, focusing on the changes in mechanical properties and microstructure of ex vivo porcine brain tissues under different types of electric fields, directional and alternating electric fields (frequencies of 5, 20, 50, and 80 Hz, respectively) integrate with a custom-designed indentation device. The experimental results showed that for the ex vivo brain tissue, the directional electric field (DEF) can reduce the elastic properties of brain tissue. Simultaneously, the DEF can increase the cell spacing and reduce the proteoglycan content. The transmission electron microscope (TEM) analysis observed that the DEF can reduce the integrity of the plasma membrane, the endoplasmic reticulum's stress response, and the myelin lamella's separation. The alternating electric field (AEF) can accelerate the stress relaxation process of brain tissue and change the time-dependent mechanical properties of brain tissue. Meanwhile, with the increase in frequency, the cell spacing decreased, and the proteoglycan content gradually approached the control group without electric fields. TEM analysis observed that with the increase in frequency, the integrity of the plasma membrane increases, and the separation of the myelin lamella gradually disappears. Understanding the changes in the mechanical properties and microstructure of brain tissue under AEF and DEF enables a preliminary exploration of the therapeutic mechanism of electrotherapy. Simultaneously, the essential data was provided to support the development of embedded electrodes. In addition, the ex vivo experiments build a solid foundation for future in vivo experiments.

Phase response approaches to neural activity models with distributed delay

In weakly coupled neural oscillator networks describing brain dynamics, the coupling delay is often distributed. We present a theoretical framework to calculate the phase response curve of distributed-delay induced limit cycles with infinite-dimensional phase space. Extending previous works, in which non-delayed or discrete-delay systems were investigated, we develop analytical results for phase response curves of oscillatory systems with distributed delay using Gaussian and log-normal delay distributions. We determine the scalar product and normalization condition for the linearized adjoint of the system required for the calculation of the phase response curve. As a paradigmatic example, we apply our technique to the Wilson-Cowan oscillator model of excitatory and inhibitory neuronal populations under the two delay distributions. We calculate and compare the phase response curves for the Gaussian and log-normal delay distributions. The phase response curves obtained from our adjoint calculations match those compiled by the direct perturbation method, thereby proving that the theory of weakly coupled oscillators can be applied successfully for distributed-delay-induced limit cycles. We further use the obtained phase response curves to derive phase interaction functions and determine the possible phase locked states of multiple inter-coupled populations to illuminate different synchronization scenarios. In numerical simulations, we show that the coupling delay distribution can impact the stability of the synchronization between inter-coupled gamma-oscillatory networks.

Deep brain stimulation for movement disorder treatment: exploring frequency-dependent efficacy in a computational network model

A large-scale computational model of the basal ganglia network and thalamus is proposed to describe movement disorders and treatment effects of deep brain stimulation (DBS). The model of this complex network considers three areas of the basal ganglia region: the subthalamic nucleus (STN) as target area of DBS, the globus pallidus, both pars externa and pars interna (GPe-GPi), and the thalamus. Parkinsonian conditions are simulated by assuming reduced dopaminergic input and corresponding pronounced inhibitory or disinhibited projections to GPe and GPi. Macroscopic quantities are derived which correlate closely to thalamic responses and hence motor programme fidelity. It can be demonstrated that depending on different levels of striatal projections to the GPe and GPi, the dynamics of these macroscopic quantities (synchronisation index, mean synaptic activity and response efficacy) switch from normal to Parkinsonian conditions. Simulating DBS of the STN affects the dynamics of the entire network, increasing the thalamic activity to levels close to normal, while differing from both normal and Parkinsonian dynamics. Using the mentioned macroscopic quantities, the model proposes optimal DBS frequency ranges above 130 Hz.