Robust Control of Burst Suppression Amid Physical and Neurological Uncertainty

Burst suppression is a clinical term describing a phenomenon in which the electroencephalogram (EEG) of a sedated patient produces behavior that switches between higher frequency and amplitude bursting to lower frequency and lower amplitude suppression. This phenomenon can be observed during general anesthesia, hypothermia, or in an otherwise induced coma state. In a clinical setting, this phenomenon is typically induced by sedation from a drug such as propofol (2,6-diisopropylphenol). The level of sedation can be quantified by something called the burst suppression ratio (BSR), which is defined as the amount of time that a patient’s EEG is in a suppressed state over the amount of time measured. One can vary this ratio by either increasing or decreasing the propofol infusion rate that the patient is given to bring them to a deeper or lighter state of sedation. By measuring the EEG data, one can form a closed loop feedback system where the EEG data is monitored for signs of burst suppression and the propofol is increased or decreased accordingly. Therefore, it becomes desirable to create models of this closed loop system to simulate the kind of behavior that would be expected from a clinical setting such as the one described. Many methods and experimental paradigms have been developed to address this problem including development of pharmacokinetic (PK) models that describe the dynamics of drug infusion in the body as well as signal processing methods for computing the burst suppression estimation such as the burst suppression probability. Some of these paradigms have been tested in rodent experiments, though human studies remain elusive. In this regard, simulations and detailed physiological modeling and control design can play a key role. This thesis seeks to add on the rich body of work that has been done thus far by incorporating a Schnider PK model with the Wilson-Cowan neural mass model to form a closed loop model which we can use as a basis for more detailed analysis which includes real-time burst suppression estimation as well as uncertainty modeling in both the patient’s physical characteristics (such as weight, height, age and gender) in addition to neurological phenomena such as the recovery and consumption rates of neurons during burst suppression behavior. By creating a conversion from the physiological parameters that describe the PK models to the dimensionless and more abstract parameters which guide the Wilson-Cowan equations, and implementing an actuator and burst suppression ratio estimation algorithm, we have effectively modeled the clinical setting with which the BSR is sought to be controlled. Thus, in this study we wished to show that with PID control, one could control this model at a nominal condition (i.e., the patient and neurological parameters which the gains were designed for) as well as at various uncertainty conditions that include both physical and neurological uncertainty, as described above. Using the Zeigler-Nichols tuning method, we were able to design gains to sufficiently control this system at set points of 0.8, 0.5 and 0.2 BSR over a simulation time of roughly 18 hours in both nominal, patient varied with noise added and with reduced performance when including patient variation and noise as well as neurological uncertainty. This time duration was chosen because it was convenient for the model’s time constants but also because it is representative of the time a patient may be sedated. The BSR ranges were chosen so as to show the closed loop system’s ability to maintain control at multiple levels of sedation. The reduced performance due to neurological uncertainty was due to the BSR estimation algorithm estimating a lower bound that was too high for the system to be controlled at a BSR of 0.2. The minimum BSR the system with added neurological uncertainty could be controlled to was 0.38, which is where the system held at during the portion of the trajectory that a BSR of 0.2 was commanded. During the achievable parts of the envelope, however, the control scheme worked with similar performance to that of the nominal case. This would suggest that an adaptive estimation algorithm needs to be developed to estimate the neurological deviations from the nominal case. Further, this suggests that if variations in the BSR of a patient due to neurological uncertainty is expected, then accurate estimation of these parameters are vital to reaching a robust solution in a real-time system

Learning-based Approaches for Controlling Neural Spiking

We consider the problem of controlling populations of interconnected neurons using extrinsic stimulation. Such a problem, which is relevant to applications in both basic neuroscience as well as brain medicine, is challenging due to the nonlinearity of neuronal dynamics and the highly unpredictable structure of underlying neuronal networks. Compounding this difficulty is the fact that most neurostimulation technologies offer a single degree of freedom to actuate tens to hundreds of interconnected neurons. To meet these challenges, here we consider an adaptive, learning-based approach to controlling neural spike trains. Rather than explicitly modeling neural dynamics and designing optimal controls, we instead synthesize a so-called control network (CONET) that interacts with the spiking network by maximizing the Shannon mutual information between it and the realized spiking outputs. Thus, the CONET learns a representation of the spiking network that subsequently allows it to learn suitable control signals through a reinforcement-type mechanism. We demonstrate feasibility of the approach by controlling networks of stochastic spiking neurons, wherein desired patterns are induced for neuron-to-actuator ratios in excess of 10 to 1

Sevoflurane alters spatiotemporal functional connectivity motifs that link resting-state networks during wakefulness

Background: The spatiotemporal patterns of correlated neural activity during the transition from wakefulness to general anesthesia have not been fully characterized. Correlation analysis of blood-oxygen-level dependent (BOLD) functional magnetic resonance imaging (fMRI) allows segmentation of the brain into resting-state networks (RSNs), with functional connectivity referring to the covarying activity that suggests shared functional specialization. We quantified the persistence of these correlations following the induction of general anesthesia in healthy volunteers and assessed for a dynamic nature over time. Methods: We analyzed human fMRI data acquired at 0 and 1.2% vol sevoflurane. The covariance in the correlated activity among different brain regions was calculated over time using bounded Kalman filtering. These time series were then clustered into eight orthogonal motifs using a K-means algorithm, where the structure of correlated activity throughout the brain at any time is the weighted sum of all motifs. Results: Across time scales and under anesthesia, the reorganization of interactions between RSNs is related to the strength of dynamic connections between member pairs. The covariance of correlated activity between RSNs persists compared to that linking individual member pairs of different RSNs. Conclusions: Accounting for the spatiotemporal structure of correlated BOLD signals, anesthetic-induced loss of consciousness is mainly associated with the disruption of motifs with intermediate strength within and between members of different RSNs. In contrast, motifs with higher strength of connections, predominantly with regions-pairs from within-RSN interactions, are conserved among states of wakefulness and sevoflurane general anesthesia

DFORM: Diffeomorphic vector field alignment for assessing dynamics across learned models

Dynamical system models such as Recurrent Neural Networks (RNNs) have become increasingly popular as hypothesis-generating tools in scientific research. Evaluating the dynamics in such networks is key to understanding their learned generative mechanisms. However, comparison of learned dynamics across models is challenging due to their inherent nonlinearity and because a priori there is no enforced equivalence of their coordinate systems. Here, we propose the DFORM (Diffeomorphic vector field alignment for comparing dynamics across learned models) framework. DFORM learns a nonlinear coordinate transformation which provides a continuous, maximally one-to-one mapping between the trajectories of learned models, thus approximating a diffeomorphism between them. The mismatch between DFORM-transformed vector fields defines the orbital similarity between two models, thus providing a generalization of the concepts of smooth orbital and topological equivalence. As an example, we apply DFORM to models trained on a canonical neuroscience task, showing that learned dynamics may be functionally similar, despite overt differences in attractor landscapes.Comment: 12 pages, 8 figure

Astrocytes as a mechanism for contextually-guided network dynamics and function

Astrocytes are a ubiquitous and enigmatic type of non-neuronal cell and are found in the brain of all vertebrates. While traditionally viewed as being supportive of neurons, it is increasingly recognized that astrocytes play a more direct and active role in brain function and neural computation. On account of their sensitivity to a host of physiological covariates and ability to modulate neuronal activity and connectivity on slower time scales, astrocytes may be particularly well poised to modulate the dynamics of neural circuits in functionally salient ways. In the current paper, we seek to capture these features via actionable abstractions within computational models of neuron-astrocyte interaction. Specifically, we engage how nested feedback loops of neuron-astrocyte interaction, acting over separated time-scales, may endow astrocytes with the capability to enable learning in context-dependent settings, where fluctuations in task parameters may occur much more slowly than within-task requirements. We pose a general model of neuron-synapse-astrocyte interaction and use formal analysis to characterize how astrocytic modulation may constitute a form of meta-plasticity, altering the ways in which synapses and neurons adapt as a function of time. We then embed this model in a bandit-based reinforcement learning task environment, and show how the presence of time-scale separated astrocytic modulation enables learning over multiple fluctuating contexts. Indeed, these networks learn far more reliably compared to dynamically homogeneous networks and conventional non-network-based bandit algorithms. Our results fuel the notion that neuron-astrocyte interactions in the brain benefit learning over different time-scales and the conveyance of task-relevant contextual information onto circuit dynamics

Astrocytes as a mechanism for meta-plasticity and contextually-guided network function

Astrocytes are a ubiquitous and enigmatic type of non-neuronal cell and are found in the brain of all vertebrates. While traditionally viewed as being supportive of neurons, it is increasingly recognized that astrocytes may play a more direct and active role in brain function and neural computation. On account of their sensitivity to a host of physiological covariates and ability to modulate neuronal activity and connectivity on slower time scales, astrocytes may be particularly well poised to modulate the dynamics of neural circuits in functionally salient ways. In the current paper, we seek to capture these features via actionable abstractions within computational models of neuron-astrocyte interaction. Specifically, we engage how nested feedback loops of neuron-astrocyte interaction, acting over separated time-scales may endow astrocytes with the capability to enable learning in context-dependent settings, where fluctuations in task parameters may occur much more slowly than within-task requirements. We pose a general model of neuron-synapse-astrocyte interaction and use formal analysis to characterize how astrocytic modulation may constitute a form of meta-plasticity, altering the ways in which synapses and neurons adapt as a function of time. We then embed this model in a bandit-based reinforcement learning task environment, and show how the presence of time-scale separated astrocytic modulation enables learning over multiple fluctuating contexts. Indeed, these networks learn far more reliably versus dynamically homogeneous networks and conventional non-network-based bandit algorithms. Our results indicate how the presence of neuron-astrocyte interaction in the brain may benefit learning over different time-scales and the conveyance of task-relevant contextual information onto circuit dynamics.Comment: 42 pages, 14 figure

Primates chunk simultaneously-presented memoranda

Though much research has characterized both the behavior and electrophysiology of spatial memory for single targets in non-human primates, we know much less about how multiple memoranda are handled. Multiple memoranda may interact in the brain, affecting the underlying representations. Mnemonic resources are famously limited, so items may compete for space in memory or may be encoded cooperatively or in a combined fashion. Understanding the mode of interaction will inform future neural studies. As a first step, we quantified interactions during a multi-item spatial memory task. Two monkeys were shown 1-4 target locations. After a delay, the targets reappeared with a novel target and the animal was rewarded for fixating the novel target. Targets could appear either all at once (simultaneous) or with intervening delays (sequential). We quantified the degree of interaction with memory rate correlations. We found that simultaneously presented targets were stored cooperatively while sequentially presented targets were stored independently. These findings demonstrate how interaction between concurrently memorized items depends on task context. Future studies of multi-item memory would be served by designing experiments to either control or measure the mode of this interaction