Analysis of the mechanism of action of deep brain stimulation using the concepts of dither injection and the equivalent nonlinearity

Investigation of the mechanism of action of deep brain stimulation for the treatment of Parkinson's disease

Parkinson's disease (PD) is a severe, progressive, neurological disorder. PD is not a single disease, but rather resembles a syndrome. PD includes two types of pathogenesis (i.e., classical PD and new PD). Clinically, PD patients present with a range of motor symptoms including decreased spontaneous movement, bradykinesia, muscle rigidity, changes in speech, and resting tremors. PD patients also often exhibit non-motor symptoms such as fatigue, sleep disorders, and emotional and mental health disturbances. Deep brain stimulation (DBS) performed in clinical neurosurgery has demonstrated considerable efficacy in the treatment of dyskinesia that occurs in PD patients. However, the specific neural mechanism of DBS remains unknown and is limited by several shortcomings that have hampered the popularization and development of the procedure. To address this issue, this study established a theoretical model of DBS for PD to investigate and understand the mechanism of DBS using several artificial intelligence (AI) algorithms. This model was used to investigate both classical PD and unheard-of new PD. The research described in this paper was as follows: a single neuron was used to establish a theoretical model of the basal ganglia circuit and to simulate the characteristic indicators of the potential release of the basal ganglia circuit in both normal and PD states. The state of the deep brain electrical stimulation in PD was then analyzed to identify the critical electrical stimulation index and the optimal target. We showed that the use of AI algorithms such as particle swarm optimization and other AI algorithms was beneficial for more detailed exploration and understanding of the mechanisms of DBS compared to those used in previous studies. This discovery may lead to advances in DBS technology and provide better treatment options for neurological diseases such as PD.

Adaptive Parameter Modulation of Deep Brain Stimulation Based on Improved Supervisory Algorithm

Clinically deployed deep brain stimulation (DBS) for the treatment of Parkinson's disease operates in an open loop with fixed stimulation parameters, and this may result in high energy consumption and suboptimal therapy. The objective of this manuscript is to establish, through simulation in a computational model, a closed-loop control system that can automatically adjust the stimulation parameters to recover normal activity in model neurons. Exaggerated beta band activity is recognized as a hallmark of Parkinson's disease and beta band activity in model neurons of the globus pallidus internus (GPi) was used as the feedback signal to control DBS of the GPi. Traditional proportional controller and proportional-integral controller were not effective in eliminating the error between the target level of beta power and the beta power under Parkinsonian conditions. To overcome the difficulties in tuning the controller parameters and improve tracking performance in the case of changes in the plant, a supervisory control algorithm was implemented by introducing a Radial Basis Function (RBF) network to build the inverse model of the plant. Simulation results show the successful tracking of target beta power in the presence of changes in Parkinsonian state as well as during dynamic changes in the target level of beta power. Our computational study suggests the feasibility of the RBF network-driven supervisory control algorithm for real-time modulation of DBS parameters for the treatment of Parkinson's disease.

Methods for Lowering the Power Consumption of OS-Based Adaptive Deep Brain Stimulation Controllers

The identification of a new generation of adaptive strategies for deep brain stimulation (DBS) will require the development of mixed hardware-software systems for testing and implementing such controllers clinically. Towards this aim, introducing an operating system (OS) that provides high-level features (multitasking, hardware abstraction, and dynamic operation) as the core element of adaptive deep brain stimulation (aDBS) controllers could expand the capabilities and development speed of new control strategies. However, such software frameworks also introduce substantial power consumption overhead that could render this solution unfeasible for implantable devices. To address this, in this work four techniques to reduce this overhead are proposed and evaluated: a tick-less idle operation mode, reduced and dynamic sampling, buffered read mode, and duty cycling. A dual threshold adaptive deep brain stimulation algorithm for suppressing pathological oscillatory neural activity was implemented along with the proposed energy saving techniques on an energy-efficient OS, YetiOS, running on a STM32L476RE microcontroller. The system was then tested using an emulation environment coupled to a mean field model of the parkinsonian basal ganglia to simulate local field potential (LFPs) which acted as a biomarker for the controller. The OS-based controller alone introduced a power consumption overhead of 10.03 mW for a sampling rate of 1 kHz. This was reduced to 12 μW by applying the proposed tick-less idle mode, dynamic sampling, buffered read and duty cycling techniques. The OS-based controller using the proposed methods can facilitate rapid and flexible testing and implementation of new control methods. Furthermore, the approach has the potential to become a central element in future implantable devices to enable energy-efficient implementation of a wide range of control algorithms across different neurological conditions and hardware platforms.

Rehabilitation of the Parkinson's tremor by using robust adaptive sliding mode controller: a simulation study

One of the efficient methods in controlling the Parkinson's tremor is Deep Brain Stimulation (DBS) therapy. The stimulation of Basal Ganglia (BG) by DBS brings no feedback though the existence of feedback reduces the additional stimulatory signal delivered to the brain. So this study offers a new adaptive architecture of a closed-loop control system in which two areas of BG are stimulated simultaneously to decrease the following three indicators: hand tremor, the level of a delivered stimulation signal in the disease condition, and the level of a delivered stimulation signal in health condition to the disease condition. One area (STN: subthalamic nucleus) is stimulated with an adaptive sliding mode controller and the other area (GPi: Globus Pallidus internal) with partial state feedback controller. The simulation results of stimulating two areas of BG showed satisfactory performance.

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

A mathematical modeling for description of oscillation suppression by deep brain stimulation (DBS) is explored in this paper. High-frequency DBS introduced to the basal ganglia network can suppress pathological neural oscillations that occur in the Parkinsonian state. However, selecting appropriate stimulation parameters remains a challenging issue due to the limited understanding of the underlying mechanisms of the Parkinsonian state and its control. In this paper, we use a describing function analysis to provide an intuitive way to select the optimal stimulation parameters based on a biologically plausible computational model of the Parkinsonian neural network. By the stability analysis using the describing function method, effective DBS parameter regions for inhibiting the pathological oscillations can be predicted. Additionally, it is also found that a novel sinusoidal-shaped DBS may become an alternative stimulation pattern and expends less energy, but with a different mechanism. This paper provides new insight into the possible mechanisms underlying DBS and a prediction of optimal DBS parameter settings, and even suggests how to select novel DBS wave patterns for the treatment of movement disorders, such as Parkinson's disease.

Analytically determining frequency and amplitude of spontaneous alpha oscillation in Jansen's neural mass model using the describing function method

Spontaneous alpha oscillations are a ubiquitous phenomenon in the brain and play a key role in neural information processing and various cognitive functions. Jansen's neural mass model (NMM) was initially proposed to study the origin of alpha oscillations. Most of previous studies of the spontaneous alpha oscillations in the NMM were conducted using numerical methods. In this study, we aim to propose an analytical approach using the describing function method to elucidate the spontaneous alpha oscillation mechanism in the NMM. First, the sigmoid nonlinear function in the NMM is approximated by its describing function, allowing us to reformulate the NMM and derive its standard form composed of one nonlinear part and one linear part. Second, by conducting a theoretical analysis, we can assess whether or not the spontaneous alpha oscillation would occur in the NMM and, furthermore, accurately determine its amplitude and frequency. The results reveal analytically that the interaction between linearity and nonlinearity of the NMM plays a key role in generating the spontaneous alpha oscillations. Furthermore, strong nonlinearity and large linear strength are required to generate the spontaneous alpha oscillations.

A Possible Explanation of How High-Frequency Deep Brain Stimulation Suppresses Low-Frequency Tremors in Parkinson's Disease

Parkinson's disease (PD) is a neurodegenerative disorder of the central nervous system and one of its key symptoms is rest tremor. Deep brain stimulation (DBS) effectively suppresses rest tremor in Parkinson's disease. Despite being a successful treatment option, its underlying principle and the mechanism by which it attenuates tremors is not yet fully understood. Since existing methods for tuning DBS parameters are largely trial and error, understanding how DBS works can help to reduce time and costs, and could also ultimately lead to better treatment strategies for PD. In this paper, we set out to analyze how a high-frequency stimulation applied through DBS can help reduce the low-frequency rest tremors observed in PD patients. We identify key elements in the sensorimotor loop (the feedback loop consisting of sensory feedbacks and motor responses) that play a role in the interaction of high-frequency DBS signal and the low-frequency tremor. Based on the analysis of these elements, we draw insights about the working of DBS and the role of frequency and the nature of stimulation. We verify these observations with numerical examples and a bench top experimental example.

Design of robust adaptive controller and feedback error learning for rehabilitation in Parkinson's disease: a simulation study

Deep brain stimulation (DBS) is an efficient therapy to control movement disorders of Parkinson's tremor. Stimulation of one area of basal ganglia (BG) by DBS with no feedback is the prevalent opinion. Reduction of additional stimulatory signal delivered to the brain is the advantage of using feedback. This results in reduction of side effects caused by the excessive stimulation intensity. In fact, the stimulatory intensity of controllers is decreased proportional to reduction of hand tremor. The objective of this study is to design a new controller structure to decrease three indicators: (i) the hand tremor; (ii) the level of delivered stimulation in disease condition; and (iii) the ratio of the level of delivered stimulation in health condition to disease condition. For this purpose, the authors offer a new closed-loop control structure to stimulate two areas of BG simultaneously. One area (STN: subthalamic nucleus) is stimulated by an adaptive controller with feedback error learning. The other area (GPi: globus pallidus internal) is stimulated by a partial state feedback (PSF) controller. Considering the three indicators, the results show that, stimulating two areas simultaneously leads to better performance compared with stimulating one area only. It is shown that both PSF and adaptive controllers are robust regarding system parameter uncertainties. In addition, a method is proposed to update the parameters of the BG model in real time. As a result, the parameters of the controllers can be updated based on the new parameters of the BG model.

Neural mass models describing possible origin of the excessive beta oscillations correlated with Parkinsonian state

In Parkinson's disease, the enhanced beta rhythm is closely associated with akinesia/bradykinesia and rigidity. An increase in beta oscillations (12-35 Hz) within the basal ganglia (BG) nuclei does not proliferate throughout the cortico-basal ganglia loop in uniform fashion; rather it can be subdivided into two distinct frequency bands, i.e. the lower beta (12-20 Hz) and upper beta (21-35 Hz). A computational model of the excitatory and inhibitory neural network that focuses on the population properties is proposed to explore the mechanism underlying the pathological beta oscillations. Simulation results show several findings. The upper beta frequency in the BG originates from a high frequency cortical beta, while the emergence of exaggerated lower beta frequency in the BG depends greatly on the enhanced excitation of a reciprocal network consisting of the globus pallidus externus (GPe) and the subthalamic nucleus (STN). There is also a transition mechanism between the upper and lower beta oscillatory activities, and we explore the impact of self-inhibition within the GPe on the relationship between the upper beta and lower beta oscillations. It is shown that increased self-inhibition within the GPe contributes to increased upper beta oscillations driven by the cortical rhythm, while decrease in the self-inhibition within the GPe facilitates an enhancement of the lower beta oscillations induced by the increased excitability of the BG. This work provides an analysis for understanding the mechanism underlying pathological synchronization in neurological diseases.

Designing a robust backstepping controller for rehabilitation in Parkinson's disease: a simulation study

In this study, a model of basal ganglia (BG) is applied to develop a deep brain stimulation controller to reduce Parkinson's tremor. Conventionally, one area in BG is stimulated, with no feedback, to control Parkinson's tremor. In this study, a new architecture is proposed to develop feedback controller as well as to stimulate two areas of BG simultaneously. To this end, two controllers are designed and implemented in globus pallidus internal (GPi) and subthalamic nucleus (STN) in the brain. A proportional controller and a backstepping controller are designed and implemented in GPi and STN, respectively. The proposed controllers deliver suitable stimulatory control signals to GPi and STN based on hand tremor amplitude (as the feedback). When tremor reduces, these controllers decrease the stimulatory energy intensity proportionally. Therefore, additional stimulatory signal is not delivered to the brain. Subsequently, the side effects from the excessive stimulation intensity become much less. Comparing with one area stimulation, the results show that stimulating two areas of BG results in reduction of the level of the stimulation intensity. It is observed that these two controllers are both robust in terms of changing the system parameters.

A charge-metering method for voltage-mode neural stimulation

Electrical neural stimulation is the technique used to modulate neural activity by inducing an instantaneous charge imbalance. This is typically achieved by injecting a constant current and controlling the stimulation time. However, constant voltage stimulation is found to be more energy-efficient although it is challenging to control the amount of charge delivered. This paper presents a novel, fully integrated circuit for facilitating charge-metering in constant voltage stimulation. It utilises two complementary stimulation paths. Each path includes a small capacitor, a comparator and a counter. They form a mixed-signal integrator that integrates the stimulation current onto the capacitor while monitoring its voltage against a threshold using the comparator. The pulses from the comparator are used to increment the counter and reset the capacitor. Therefore, by knowing the value of the capacitor, threshold voltage and output of the counter, the quantity of charge delivered can be calculated. The system has been fabricated in 0.18 μm CMOS technology, occupying a total active area of 339 μm × 110 μm. Experimental results were taken using: (1) a resistor-capacitor EEI model and (2) platinum electrodes with ringer solution. The viability of this method in recruiting action potentials has been demonstrated using a cuff electrode with Xenopus sciatic nerve. For a 10 nC target charge delivery, the results of (2) show a charge delivery error of 3.4% and a typical residual charge of 77.19pC without passive charge recycling. The total power consumption is 45 μW. The performance is comparable with other publications. Therefore, the proposed stimulation method can be used as a new approach for neural stimulation.

A slow axon antidromic blockade hypothesis for tremor reduction via deep brain stimulation

Parkinsonian and essential tremor can often be effectively treated by deep brain stimulation. We propose a novel explanation for the mechanism by which this technique ameliorates tremor: a reduction of the delay in the relevant motor control loops via preferential antidromic blockade of slow axons. The antidromic blockade is preferential because the pulses more rapidly clear fast axons, and the distribution of axonal diameters, and therefore velocities, in the involved tracts, is sufficiently long-tailed to make this effect quite significant. The preferential blockade of slow axons, combined with gain adaptation, results in a reduction of the mean delay in the motor control loop, which serves to stabilize the feedback system, thus ameliorating tremor. This theory, without any tuning, accounts for several previously perplexing phenomena, and makes a variety of novel predictions.

Simulation of cortico-basal ganglia oscillations and their suppression by closed loop deep brain stimulation

A new model of deep brain stimulation (DBS) is presented that integrates volume conduction effects with a neural model of pathological beta-band oscillations in the cortico-basal ganglia network. The model is used to test the clinical hypothesis that closed-loop control of the amplitude of DBS may be possible, based on the average rectified value of beta-band oscillations in the local field potential. Simulation of closed-loop high-frequency DBS was shown to yield energy savings, with the magnitude of the energy saved dependent on the strength of coupling between the subthalamic nucleus and the remainder of the cortico-basal ganglia network. When closed-loop DBS was applied to a strongly coupled cortico-basal ganglia network, the stimulation energy delivered over a 480 s period was reduced by up to 42%. Greater energy reductions were observed for weakly coupled networks, as the stimulation amplitude reduced to zero once the initial desynchronization had occurred. The results provide support for the application of closed-loop high-frequency DBS based on electrophysiological biomarkers.

Application of non-linear control theory to a model of deep brain stimulation

Deep brain stimulation (DBS) effectively alleviates the pathological neural activity associated with Parkinson's disease. Its exact mode of action is not entirely understood. This paper explores theoretically the optimum stimulation parameters necessary to quench oscillations in a neural-mass type model with second order dynamics. This model applies well established nonlinear control system theory to DBS. The analysis here determines the minimum criteria in terms of amplitude and pulse duration of stimulation, necessary to quench the unwanted oscillations in a closed loop system, and outlines the relationship between this model and the actual physiological system.

Commentary: the pedunculopontine nucleus: clinical experience, basic questions and future directions

This issue is dedicated to a potential new target for the treatment of movement disorders, the pedunculopontine tegmental nucleus (PPTg), or, more simply, the pedunculopontine nucleus, that some authors abbreviate as PPN. We provide an overview of the field as an introduction to the general reader, beginning with the clinical experience to date of Mazzone and co-workers in Rome, some basic questions that need to be addressed, and potential future directions required in order to ensure that the potential benefits of this work are realized.

A model of pathological oscillations in the basal ganglia and deep brain stimulation in Parkinson's disease

A model of pathological oscillatory activity within the basal ganglia in Parkinson's disease is presented. Synchronous oscillatory activity of the subthalamic nucleus (STN) and globus pallidus external (GPe) is simulated at both the parkinsonian tremor (3-9) Hz and beta (15-30) Hz frequencies. The model extends previous models to incorporate cortical inputs to the subthalamic nucleus through the 'hyperdirect' pathway, changes in coupling between STN neurons due to dopamine depletion and the plateau potential generating capacity of STN neurons. The effect of deep brain stimulation (DBS) across a range of frequencies on the oscillatory activity is examined. High frequency DBS attenuates synchronous oscillatory activity within the STN-GPe network at both the tremor and beta frequencies. The efficacy of the DBS input in quenching the pathological oscillations is shown to vary systematically with the frequency, pulse width and amplitude of the applied stimulus.