A theory of cognitive mapping is developed that depends only on accepted properties of hippocampal function, namely, long-term potentiation, the place cell phenomenon, and the associative or recurrent connections made among CA3 pyramidal ceils. It is proposed that the distance between the firing fields of connected pairs of CA3 place cells is encoded as synaptic resistance (reciprocal synaptic strength). The encoding occurs because pairs of ceils with coincident or overlapping fields will tend to fire together in time, thereby causing a decrease in synaptic resistance via long-term potentiation; in contrast, ceils with widely separated fields will tend never to fire together, causing no change or perhaps (via long-term depression) an increase in synaptic resistance. A network whose connection pattern mimics that of CA3 and whose connection weights are proportional to synaptic resistance can be formally treated as a weighted, directed graph. In such a graph, a "node" is assigned to each CA3 cell and two nodes are connected by a "directed edge" if and only if the two corresponding cells are connected by a synapse. Weighted, directed graphs can be searched for an optimal path between any pair of nodes with standard algorithms. Here, we are interested in finding the path along which the sum of the synaptic resistances from one cell to another is minimal. Since each cell is a place cell, such a path also corresponds to a path in two-dimensional space. Our basic finding is that minimizing the sum of the synaptic resistances along a path in neural space yields the shortest (optimal) path in unobstructed two-dimensional space, so long as the connectivity of the network is great enough. In addition to being able to find geodesics in unobstructed space, the same network enables solutions to the "detour" and "shortcut" problems, in which it is necessary to find an optimal path around a newly introduced barrier and to take a shorter path through a hole opened up in a preexisting barrier, respectively. We argue that the ability to solve such problems qualifies the proposed hippocampal object as a cognitive map. Graph theory thus provides a sort of existence proof demonstrating that the hippocampus contains the necessary information to function as a map, in the sense postulated by others (O'Keefe,J., and L. Nadel. 1978. The Hippocampus as a Cognitive Map. Clarendon Press, Oxford, UK). It is also possible that the cognitive mapping functions of the hippocampus are carried out by parallel graph searching algorithms implemented as neural processes. This possibility has the great attraction that the hippocampus could then operate in much the same way to find paths in general problem space; it would only be necessary for pyramidal cells to exhibit a strong nonpositional firing correlate.

Focal seizures appear to start abruptly and unpredictably when recorded from volumes of brain probed by clinical intracranial electroencephalograms. To investigate the spatiotemporal scale of focal epilepsy, wide-bandwidth electrophysiological recordings were obtained using clinical macro- and research microelectrodes in patients with epilepsy and control subjects with intractable facial pain. Seizure-like events not detectable on clinical macroelectrodes were observed on isolated microelectrodes. These 'microseizures' were sparsely distributed, more frequent in brain regions that generated seizures, and sporadically evolved into large-scale clinical seizures. Rare microseizures observed in control patients suggest that this phenomenon is ubiquitous, but their density distinguishes normal from epileptic brain. Epileptogenesis may involve the creation of these topographically fractured microdomains and ictogenesis (seizure generation), the dynamics of their interaction and spread.

Warren CP, Hu S, Stead M, Brinkmann BH, Bower MR, Worrell GA. Synchrony in normal and focal epileptic brain: the seizure onset zone is functionally disconnected.

Brain stimulation has emerged as an effective treatment for a wide range of neurological and psychiatric diseases. Parkinson’s disease, epilepsy, and essential tremor have FDA indications for electrical brain stimulation using intracranially implanted electrodes. Interfacing implantable brain devices with local and cloud computing resources have the potential to improve electrical stimulation efficacy, disease tracking, and management. Epilepsy, in particular, is a neurological disease that might benefit from the integration of brain implants with off-the-body computing for tracking disease and therapy. Recent clinical trials have demonstrated seizure forecasting, seizure detection, and therapeutic electrical stimulation in patients with drug-resistant focal epilepsy. In this paper, we describe a next-generation epilepsy management system that integrates local handheld and cloud-computing resources wirelessly coupled to an implanted device with embedded payloads (sensors, intracranial EEG telemetry, electrical stimulation, classifiers, and control policy implementation). The handheld device and cloud computing resources can provide a seamless interface between patients and physicians, and realtime intracranial EEG can be used to classify brain state (wake/sleep, preseizure, and seizure), implement control policies for electrical stimulation, and track patient health. This system creates a flexible platform in which low demand analytics requiring fast response times are embedded in the implanted device and more complex algorithms are implemented in offthebody local and distributed cloud computing environments. The system enables tracking and management of epileptic neural networks operating over time scales ranging from milliseconds to months.

Transient high-frequency (100-500 Hz) oscillations of the local field potential have been studied extensively in human mesial temporal lobe. Previous studies report that both ripple (100-250 Hz) and fast ripple (250-500 Hz) oscillations are increased in the seizure-onset zone of patients with mesial temporal lobe epilepsy. Comparatively little is known, however, about their spatial distribution with respect to seizure-onset zone in neocortical epilepsy, or their prevalence in normal brain. We present a quantitative analysis of high-frequency oscillations and their rates of occurrence in a group of nine patients with neocortical epilepsy and two control patients with no history of seizures. Oscillations were automatically detected and classified using an unsupervised approach in a data set of unprecedented volume in epilepsy research, over 12 terabytes of continuous long-term micro- and macro-electrode intracranial recordings, without human preprocessing, enabling selection-bias-free estimates of oscillation rates. There are three main results: (i) a cluster of ripple frequency oscillations with median spectral centroid = 137 Hz is increased in the seizure-onset zone more frequently than a cluster of fast ripple frequency oscillations (median spectral centroid = 305 Hz); (ii) we found no difference in the rates of high frequency oscillations in control neocortex and the non-seizure-onset zone neocortex of patients with epilepsy, despite the possibility of different underlying mechanisms of generation; and (iii) while previous studies have demonstrated that oscillations recorded by parenchyma-penetrating micro-electrodes have higher peak 100-500 Hz frequencies than penetrating macro-electrodes, this was not found for the epipial electrodes used here to record from the neocortical surface. We conclude that the relative rate of ripple frequency oscillations is a potential biomarker for epileptic neocortex, but that larger prospective studies correlating high-frequency oscillations rates with seizure-onset zone, resected tissue and surgical outcome are required to determine the true predictive value.