Fractional order controllers increase the robustness of closed-loop deep brain stimulation systems

Computational models advance deep brain stimulation for Parkinson's disease

Deep brain stimulation(DBS) has become an effective intervention for advanced Parkinson's disease(PD), but the exact mechanism of DBS is still unclear. In this review, we discuss the history of DBS, the anatomy and internal architecture of the basal ganglia (BG), the abnormal pathological changes of the BG in PD, and how computational models can help understand and advance DBS. We also describe two types of models: mathematical theoretical models and clinical predictive models. Mathematical theoretical models simulate neurons or neural networks of BG to shed light on the mechanistic principle underlying DBS, while clinical predictive models focus more on patients' outcomes, helping to adapt treatment plans for each patient and advance novel electrode designs. Finally, we provide insights and an outlook on future technologies.

Fractional order memcapacitive neuromorphic elements reproduce and predict neuronal function

There is an increasing need to implement neuromorphic systems that are both energetically and computationally efficient. There is also great interest in using electric elements with memory, memelements, that can implement complex neuronal functions intrinsically. A feature not widely incorporated in neuromorphic systems is history-dependent action potential time adaptation which is widely seen in real cells. Previous theoretical work shows that power-law history dependent spike time adaptation, seen in several brain areas and species, can be modeled with fractional order differential equations. Here, we show that fractional order spiking neurons can be implemented using super-capacitors. The super-capacitors have fractional order derivative and memcapacitive properties. We implemented two circuits, a leaky integrate and fire and a Hodgkin-Huxley. Both circuits show power-law spiking time adaptation and optimal coding properties. The spiking dynamics reproduced previously published computer simulations. However, the fractional order Hodgkin-Huxley circuit showed novel dynamics consistent with criticality. We compared the responses of this circuit to recordings from neurons in the weakly-electric fish that have previously been shown to perform fractional order differentiation of their sensory input. The criticality seen in the circuit was confirmed in spontaneous recordings in the live fish. Furthermore, the circuit also predicted long-lasting stimulation that was also corroborated experimentally. Our work shows that fractional order memcapacitors provide intrinsic memory dependence that could allow implementation of computationally efficient neuromorphic devices. Memcapacitors are static elements that consume less energy than the most widely studied memristors, thus allowing the realization of energetically efficient neuromorphic devices.

Diverse electrical responses in a network of fractional-order conductance-based excitable Morris-Lecar systems

The diverse excitabilities of cells often produce various spiking-bursting oscillations that are found in the neural system. We establish the ability of a fractional-order excitable neuron model with Caputo's fractional derivative to analyze the effects of its dynamics on the spike train features observed in our results. The significance of this generalization relies on a theoretical framework of the model in which memory and hereditary properties are considered. Employing the fractional exponent, we first provide information about the variations in electrical activities. We deal with the 2D class I and class II excitable Morris-Lecar (M-L) neuron models that show the alternation of spiking and bursting features including MMOs & MMBOs of an uncoupled fractional-order neuron. We then extend the study with the 3D slow-fast M-L model in the fractional domain. The considered approach establishes a way to describe various characteristics similarities between fractional-order and classical integer-order dynamics. Using the stability and bifurcation analysis, we discuss different parameter spaces where the quiescent state emerges in uncoupled neurons. We show the characteristics consistent with the analytical results. Next, the Erdös-Rényi network of desynchronized mixed neurons (oscillatory and excitable) is constructed that is coupled through membrane voltage. It can generate complex firing activities where quiescent neurons start to fire. Furthermore, we have shown that increasing coupling can create cluster synchronization, and eventually it can enable the network to fire in unison. Based on cluster synchronization, we develop a reduced-order model which can capture the activities of the entire network. Our results reveal that the effect of fractional-order depends on the synaptic connectivity and the memory trace of the system. Additionally, the dynamics captures spike frequency adaptation and spike latency that occur over multiple timescales as the effects of fractional derivative, which has been observed in neural computation.

[Modulation of motor responses and neural activities with transcranial ultrasound stimulation based on closed-loop control]

Closed-loop transcranial ultrasound stimulation technology is based on real-time feedback signals, and has the potential for precise regulation of neural activity. In this paper, firstly the local field potential (LFP) and electromyogram (EMG) signals of mice under different intensities of ultrasound stimulation were recorded, then the mathematical model of ultrasound intensity and mouse LFP peak/EMG mean was established offline based on the data, and the closed-loop control system of LFP peak and EMG mean based on PID neural network control algorithm was simulated and built to realize closed-loop control of LFP peak and EMG mean of mice. In addition, using the generalized minimum variance control algorithm, the closed-loop control of theta oscillation power was realized. There was no significant difference between the LFP peak, EMG mean and theta power under closed-loop ultrasound control and the given value, indicating a significant control effect on the LFP peak, EMG mean and theta power of mice. Transcranial ultrasound stimulation based on closed-loop control algorithms provides a direct tool for precise modulation of electrophysiological signals in mice.

Closed-loop transcranial ultrasound stimulation with a fuzzy controller for modulation of motor response and neural activity of mice

Objective. We propose a closed-loop transcranial ultrasound stimulation (TUS) with a fuzzy controller to realize real-time and precise control of the motor response and neural activity of mice.Approach. The mean absolute value (MAV) of the electromyogram (EMG) and peak value (PV) of the local field potential (LFP) were measured under different ultrasound intensities. A model comprising the characteristics of the MAV of the EMG, PV of the LFP, and ultrasound intensity was built using a neural network, and a fuzzy controller, proportional-integral-derivative (PID) controller, and immune feedback controller were proposed to adjust the ultrasound intensity using the feedback of the EMG MAV and the LFP PV.Main results. In simulation, the quantitative calculation indicated that the maximum relative errors between the simulated EMG MAV and the expected values were 17% (fuzzy controller), 110% (PID control), 66% (immune feedback control); furthermore, the corresponding values of the LFP PV were 12% (fuzzy controller), 53% (PID control), 55% (immune feedback control). The average relative errors of fuzzy controller, PID control, immune feedback control were 4.97%, 13.15%, 11.52%, in the EMG closed-loop experiment and 7.76%, 11.84%, 13.56%, in the LFP closed-loop experiment.Significance. The simulation and experimental results demonstrate that the closed-loop TUS with a fuzzy controller can realize the tracking control of the motor response and neural activity of mice.

Mathematical assessment of the dynamics of novel coronavirus infection with treatment: A fractional study

In this paper, a mathematical model is formulated to study the transmission dynamics of the novel coronavirus infection under the effect of treatment. The compartmental model is firstly formulated using a system of nonlinear ordinary differential equations. Then, with the help of Caputo operator, the model is reformulated in order to obtain deeper insights into disease dynamics. The basic mathematical features of the time fractional model are rigorously presented. The nonlinear least square procedure is implemented in order to parameterize the model using COVID-19 cumulative cases in Saudi Arabia for the selected time period. The important threshold parameter called the basic reproduction number is evaluated based on the estimated parameters and is found R 0 ≈ 1.60 . The fractional Lyapunov approach is used to prove the global stability of the model around the disease free equilibrium point. Moreover, the model in Caputo sense is solved numerically via an efficient numerical scheme known as the fractional Adamas-Bashforth-Molten approach. Finally, the model is simulated to present the graphical impact of memory index and various intervention strategies such as social-distancing, disinfection of the virus from environment and treatment rate on the pandemic peaks. This study emphasizes the important role of various scenarios in these intervention strategies in curtailing the burden of COVID-19.