Stochastic modeling of the neuronal activity in the subthalamic nucleus and model parameter identification from Parkinson patient data

Long-Term Alleviation of Parkinsonian Resting Tremor Using Wireless Optogenetic Nanonetworks

Resting tremor is one of the major symptoms of Parkinson's disease, which causes havoc in motor functions of the body, has its genesis in communication impairments in the subthalamic nucleus of the basal ganglia. The modern sophisticated surgical treatments, including electrical deep brain stimulation do not yield satisfactory results due to their inability to provide long-term cure and minimize side effects, such as discomfort and increased infection rates. In this work, we propose a novel system based on the emerging communication technology of wireless optogenetic networks of neural dusts to provide a long-term solution for the alleviation of resting tremor. Interfaced with neural dusts, each of the subthalamic nucleus neurons can be controlled and stimulated by the ultrasonic waves which are transmitted from a single/multiple subdural transducer(s) that are placed in the dura mater of the brain. Moreover, in order to address the challenging tasks of charging and addressing each of the neural dusts, we propose a protocol, named as Single Time Instant addressing Protocol, which outperforms the state-of-the-art parallel charging protocol. The basic idea of our protocol is that it selects most frequently occurring spike patterns in a single time instant and assigns the pattern with an ultrasonic frequency. With the improved efficiency of Single Time Instant addressing Protocol validated with empirical datasets, the proposed system is expected to revolutionize the way of treatment of parkinsonian resting tremor.

On modeling the neuronal activity in movement disorder patients by using the Ornstein Uhlenbeck process

Mathematical models of the neuronal activity in the affected brain regions of Essential Tremor (ET) and Parkinson's Disease (PD) patients could shed light into the underlying pathophysiology of these diseases, which in turn could help develop personalized treatments including adaptive Deep Brain Stimulation (DBS). In this paper, we use an Ornstein Uhlenbeck Process (OUP) to model the neuronal spiking activity recorded from the brain of ET and PD patients during DBS stereotactic surgery. The parameters of the OUP are estimated based on Inter Spike Interval (ISI) measurements, i.e., the time interval between two consecutive neuronal firings, by means of the Fortet Integral Equation (FIE). The OUP model parameters identified with the FIE method (OUP-FIE) are then used to simulate the ISI distribution resulting from the OUP. Other widely used neuronal activity models, such as the Poisson Process (PP), the Brownian Motion (BM), and the OUP whose parameters are extracted by matching the first two moments of the ISI (OUP-MOM), are also considered. To quantify how close the simulated ISI distribution is to the measured ISI distribution, the Integral Square Error (ISE) criterion is adopted. Amongst all considered stochastic processes, the ISI distribution generated by the OUP-FIE method is shown to produce the least ISE. Finally, a directional Wilcoxon signed rank test is used to show statistically significant reduction in the ISE value obtained from the OUP-FIE compared to the other stochastic processes.

Closing the loop of deep brain stimulation

High-frequency deep brain stimulation is used to treat a wide range of brain disorders, like Parkinson's disease. The stimulated networks usually share common electrophysiological signatures, including hyperactivity and/or dysrhythmia. From a clinical perspective, HFS is expected to alleviate clinical signs without generating adverse effects. Here, we consider whether the classical open-loop HFS fulfills these criteria and outline current experimental or theoretical research on the different types of closed-loop DBS that could provide better clinical outcomes. In the first part of the review, the two routes followed by HFS-evoked axonal spikes are explored. In one direction, orthodromic spikes functionally de-afferent the stimulated nucleus from its downstream target networks. In the opposite direction, antidromic spikes prevent this nucleus from being influenced by its afferent networks. As a result, the pathological synchronized activity no longer propagates from the cortical networks to the stimulated nucleus. The overall result can be described as a reversible functional de-afferentation of the stimulated nucleus from its upstream and downstream nuclei. In the second part of the review, the latest advances in closed-loop DBS are considered. Some of the proposed approaches are based on mathematical models, which emphasize different aspects of the parkinsonian basal ganglia: excessive synchronization, abnormal firing-rate rhythms, and a deficient thalamo-cortical relay. The stimulation strategies are classified depending on the control-theory techniques on which they are based: adaptive and on-demand stimulation schemes, delayed and multi-site approaches, stimulations based on proportional and/or derivative control actions, optimal control strategies. Some of these strategies have been validated experimentally, but there is still a large reservoir of theoretical work that may point to ways of improving practical treatment.