Towards model-based control of Parkinson's disease

Failure of delayed feedback deep brain stimulation for intermittent pathological synchronization in Parkinson's disease

Suppression of excessively synchronous beta-band oscillatory activity in the brain is believed to suppress hypokinetic motor symptoms of Parkinson's disease. Recently, a lot of interest has been devoted to desynchronizing delayed feedback deep brain stimulation (DBS). This type of synchrony control was shown to destabilize the synchronized state in networks of simple model oscillators as well as in networks of coupled model neurons. However, the dynamics of the neural activity in Parkinson's disease exhibits complex intermittent synchronous patterns, far from the idealized synchronous dynamics used to study the delayed feedback stimulation. This study explores the action of delayed feedback stimulation on partially synchronized oscillatory dynamics, similar to what one observes experimentally in parkinsonian patients. We employ a computational model of the basal ganglia networks which reproduces experimentally observed fine temporal structure of the synchronous dynamics. When the parameters of our model are such that the synchrony is unphysiologically strong, the feedback exerts a desynchronizing action. However, when the network is tuned to reproduce the highly variable temporal patterns observed experimentally, the same kind of delayed feedback may actually increase the synchrony. As network parameters are changed from the range which produces complete synchrony to those favoring less synchronous dynamics, desynchronizing delayed feedback may gradually turn into synchronizing stimulation. This suggests that delayed feedback DBS in Parkinson's disease may boost rather than suppress synchronization and is unlikely to be clinically successful. The study also indicates that delayed feedback stimulation may not necessarily exhibit a desynchronization effect when acting on a physiologically realistic partially synchronous dynamics, and provides an example of how to estimate the stimulation effect.

Reconstructing mammalian sleep dynamics with data assimilation

Data assimilation is a valuable tool in the study of any complex system, where measurements are incomplete, uncertain, or both. It enables the user to take advantage of all available information including experimental measurements and short-term model forecasts of a system. Although data assimilation has been used to study other biological systems, the study of the sleep-wake regulatory network has yet to benefit from this toolset. We present a data assimilation framework based on the unscented Kalman filter (UKF) for combining sparse measurements together with a relatively high-dimensional nonlinear computational model to estimate the state of a model of the sleep-wake regulatory system. We demonstrate with simulation studies that a few noisy variables can be used to accurately reconstruct the remaining hidden variables. We introduce a metric for ranking relative partial observability of computational models, within the UKF framework, that allows us to choose the optimal variables for measurement and also provides a methodology for optimizing framework parameters such as UKF covariance inflation. In addition, we demonstrate a parameter estimation method that allows us to track non-stationary model parameters and accommodate slow dynamics not included in the UKF filter model. Finally, we show that we can even use observed discretized sleep-state, which is not one of the model variables, to reconstruct model state and estimate unknown parameters. Sleep is implicated in many neurological disorders from epilepsy to schizophrenia, but simultaneous observation of the many brain components that regulate this behavior is difficult. We anticipate that this data assimilation framework will enable better understanding of the detailed interactions governing sleep and wake behavior and provide for better, more targeted, therapies.

Mathematical models are developed to better understand interactions between components of a system that together govern the overall behavior. Mathematical models of sleep have helped to elucidate the neuronal cell groups that are involved in promoting sleep and wake behavior and the transitions between them. However, to be able to take full advantage of these models one must be able to estimate the value of all included variables accurately. Data assimilation refers to methods that allow the user to combine noisy measurements of just a few system variables with the mathematical model of that system to estimate all variables, including those originally inaccessible for measurement. Using these techniques we show that we can reconstruct the unmeasured variables and parameters of a mathematical model of the sleep-wake network. These reconstructed estimates can then be used to better understand the underlying neuronal behavior that results in sleep and wake activity. Because sleep is implicated in a wide array of neurological disorders from epilepsy to schizophrenia, we anticipate that this framework will enable better understanding of the link between sleep and the rest of the brain and provide for better, more targeted, therapies.

The role of inhibition in oscillatory wave dynamics in the cortex

Cortical oscillations arise during behavioral and mental tasks, and all temporal oscillations have particular spatial patterns. Studying the mechanisms that generate and modulate the spatiotemporal characteristics of oscillations is important for understanding neural information processing and the signs and symptoms of dynamical diseases of the brain. Nevertheless, it remains unclear how GABAergic inhibition modulates these oscillation dynamics. Using voltage-sensitive dye imaging, pharmacological methods, and tangentially cut occipital neocortical brain slices (including layers 3-5) of Sprague-Dawley rat, we found that GABAa disinhibition with bicuculline can progressively simplify oscillation dynamics in the presence of carbachol in a concentration-dependent manner. Additionally, GABAb disinhibition can further simplify oscillation dynamics after GABAa receptors are blocked. Both GABAa and GABAb disinhibition increase the synchronization of the neural network. Theta frequency (5-15-Hz) oscillations are reliably generated by using a combination of GABAa and GABAb antagonists alone. These theta oscillations have basic spatiotemporal patterns similar to those generated by carbachol/bicuculline. These results are illustrative of how GABAergic inhibition increases the complexity of patterns of activity and contributes to the regulation of the cortex.

Minimum energy desynchronizing control for coupled neurons

We employ optimal control theory to design an event-based, minimum energy, desynchronizing control stimulus for a network of pathologically synchronized, heterogeneously coupled neurons. This works by optimally driving the neurons to their phaseless sets, switching the control off, and letting the phases of the neurons randomize under intrinsic background noise. An event-based minimum energy input may be clinically desirable for deep brain stimulation treatment of neurological diseases, like Parkinson's disease. The event-based nature of the input results in its administration only when it is necessary, which, in general, amounts to fewer applications, and hence, less charge transfer to and from the tissue. The minimum energy nature of the input may also help prolong battery life for implanted stimulus generators. For the example considered, it is shown that the proposed control causes a considerable amount of randomization in the timing of each neuron's next spike, leading to desynchronization for the network.

What brain signals are suitable for feedback control of deep brain stimulation in Parkinson's disease?

Feedback control of deep brain stimulation (DBS) in Parkinson's disease has great potential to improve efficacy, reduce side effects, and decrease the cost of treatment. In this, the timing and intensity of stimulation are titrated according to biomarkers that capture current clinical state. Stimulation may be at standard high frequency or intelligently patterned to directly modify specific pathological rhythms. The search for and validation of appropriate feedback signals are therefore crucial. Signals recorded from the DBS electrode currently appear to be the most promising source of feedback. In particular, beta-frequency band oscillations in the local field potential recorded at the stimulation target may capture variation in bradykinesia and rigidity across patients, but this remains to be confirmed within patients. Biomarkers that reliably reflect other impairments, such as tremor, also need to be established. Finally, whether brain signals are causally important needs to be established before stimulation can be specifically patterned rather than delivered at empirically defined high frequency.

The effects of DBS patterns on basal ganglia activity and thalamic relay : a computational study

Thalamic neurons receive inputs from cortex and their responses are modulated by the basal ganglia (BG). This modulation is necessary to properly relay cortical inputs back to cortex and downstream to the brain stem when movements are planned. In Parkinson's disease (PD), the BG input to thalamus becomes pathological and relay of motor-related cortical inputs is compromised, thereby impairing movements. However, high frequency (HF) deep brain stimulation (DBS) may be used to restore relay reliability, thereby restoring movements in PD patients. Although therapeutic, HF stimulation consumes significant power forcing surgical battery replacements, and may cause adverse side effects. Here, we used a biophysical-based model of the BG-Thalamus motor loop in both healthy and PD conditions to assess whether low frequency stimulation can suppress pathological activity in PD and enable the thalamus to reliably relay movement-related cortical inputs. We administered periodic pulse train DBS waveforms to the sub-thalamic nucleus (STN) with frequencies ranging from 0-140 Hz, and computed statistics that quantified pathological bursting, oscillations, and synchronization in the BG as well as thalamic relay of cortical inputs. We found that none of the frequencies suppressed all pathological activity in BG, though the HF waveforms recovered thalamic reliability. Our rigorous study, however, led us to a novel DBS strategy involving low frequency multi-input phase-shifted DBS, which successfully suppressed pathological symptoms in all BG nuclei and enabled reliable thalamic relay. The neural restoration remained robust to changes in the model parameters characterizing early to late PD stages.

Chaotic desynchronization as the therapeutic mechanism of deep brain stimulation

High frequency deep-brain stimulation of the subthalamic nucleus (deep brain stimulation, DBS) relieves many of the symptoms of Parkinson's disease in humans and animal models. Although the treatment has seen widespread use, its therapeutic mechanism remains paradoxical. The subthalamic nucleus is excitatory, so its stimulation at rates higher than its normal firing rate should worsen the disease by increasing subthalamic excitation of the globus pallidus. The therapeutic effectiveness of DBS is also frequency and intensity sensitive, and the stimulation must be periodic; aperiodic stimulation at the same mean rate is ineffective. These requirements are not adequately explained by existing models, whether based on firing rate changes or on reduced bursting. Here we report modeling studies suggesting that high frequency periodic excitation of the subthalamic nucleus may act by desynchronizing the firing of neurons in the globus pallidus, rather than by changing the firing rate or pattern of individual cells. Globus pallidus neurons are normally desynchronized, but their activity becomes correlated in Parkinson's disease. Periodic stimulation may induce chaotic desynchronization by interacting with the intrinsic oscillatory mechanism of globus pallidus neurons. Our modeling results suggest a mechanism of action of DBS and a pathophysiology of Parkinsonism in which synchrony, rather than firing rate, is the critical pathological feature.

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

Several stochastic models, with various degrees of complexity, have been proposed to model the neuronal activity from different parts of the human brain. In this article, we use a simple Ornstein-Uhlenbeck process (OUP) to model the spike activity recorded from the subthalamic nucleus of patients suffering from Parkinson's disease at the time of implantation of the electrodes for deep brain stimulation. From the recorded data, which contains information about the spike times of a single neuron, we identify and extract the model parameters of the OUP. We then use these parameters to numerically simulate the inter-spike intervals and the voltage across the neuron membrane. We finally assess how well the proposed mathematical model fits to the measured data and compare it with other commonly adopted stochastic models. We show an excellent agreement between the computer-generated data according to the OUP model and the measured one, as well as the superiority of the OUP model when compared to the Poisson process model and the random walk model; thus, establishing the validity of the OUP as a simple yet biologically plausible model of the neuronal activity recorded from the subthalamic nucleus of Parkinson's disease patients.

Assimilating seizure dynamics

Observability of a dynamical system requires an understanding of its state-the collective values of its variables. However, existing techniques are too limited to measure all but a small fraction of the physical variables and parameters of neuronal networks. We constructed models of the biophysical properties of neuronal membrane, synaptic, and microenvironment dynamics, and incorporated them into a model-based predictor-controller framework from modern control theory. We demonstrate that it is now possible to meaningfully estimate the dynamics of small neuronal networks using as few as a single measured variable. Specifically, we assimilate noisy membrane potential measurements from individual hippocampal neurons to reconstruct the dynamics of networks of these cells, their extracellular microenvironment, and the activities of different neuronal types during seizures. We use reconstruction to account for unmeasured parts of the neuronal system, relating micro-domain metabolic processes to cellular excitability, and validate the reconstruction of cellular dynamical interactions against actual measurements. Data assimilation, the fusing of measurement with computational models, has significant potential to improve the way we observe and understand brain dynamics.