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

Observability and Controllability of Nonlinear Networks: The Role of Symmetry

Observability and controllability are essential concepts to the design of predictive observer models and feedback controllers of networked systems. For example, noncontrollable mathematical models of real systems have subspaces that influence model behavior, but cannot be controlled by an input. Such subspaces can be difficult to determine in complex nonlinear networks. Since almost all of the present theory was developed for linear networks without symmetries, here we present a numerical and group representational framework, to quantify the observability and controllability of nonlinear networks with explicit symmetries that shows the connection between symmetries and nonlinear measures of observability and controllability. We numerically observe and theoretically predict that not all symmetries have the same effect on network observation and control. Our analysis shows that the presence of symmetry in a network may decrease observability and controllability, although networks containing only rotational symmetries remain controllable and observable. These results alter our view of the nature of observability and controllability in complex networks, change our understanding of structural controllability, and affect the design of mathematical models to observe and control such networks.Comment: 19 pages, 9 figure

Regional cerebral metabolic patterns demonstrate the role of anterior forebrain mesocircuit dysfunction in the severely injured brain

peer reviewedAlthough disorders of consciousness (DOCs) demonstrate widely varying clinical presentations and patterns of structural injury, global down-regulation and bilateral reductions in metabolism of the thalamus and frontoparietal network are consistent findings. We test the hypothesis that global reductions of background synaptic activity in DOCs will associate with changes in the pattern of metabolic activity in the central thalamus and globus pallidus. We compared 32 [18F]fluorodeoxyglucose PETs obtained from severely brain-injured patients (BIs) and 10 normal volunteers (NVs). We defined components of the anterior forebrain mesocircuit on high-resolution T1-MRI (ventral, associative, and sensorimotor striatum; globus pallidus; central thalamus and noncentral thalamus). Metabolic profiles for BI and NV demonstrated distinct changes in the pattern of uptake: ventral and association striatum (but not sensorimotor) were significantly reduced relative to global mean uptake after BI; a relative increase in globus pallidus metabolism was evident in BI subjects who also showed a relative reduction of metabolism in the central thalamus. The reversal of globus pallidus and central thalamus profiles across BIs and NVs supports the mesocircuit hypothesis that broad functional (or anatomic) deafferentation may combine to reduce central thalamus activity and release globus pallidus activity in DOCs. In addition, BI subjects showed broad frontoparietal metabolic down-regulation consistent with prior studies supporting the link between central thalamic/pallidal metabolism and down-regulation of the frontoparietal network. Recovery of left hemisphere frontoparietal metabolic activity was further associated with command following