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Brain rhythms emerge from the mean-field activity of networks of neurons. There have been many efforts to build mathematical and computational embodiments in the form of discrete cell-group activities—termed neural masses—to understand in particular the origins of evoked potentials, intrinsic patterns of activities such as theta, regulation of sleep, Parkinson’s disease related dynamics, and mimic seizure dynamics. As originally utilized, standard neural masses convert input through a sigmoidal function to a firing rate, and firing rate through a synaptic alpha function to other masses. Here we define a process to build mechanistic neural masses (mNMs) as mean-field models of microscopic membrane-type (Hodgkin Huxley type) models of different neuron types that duplicate the stability, firing rate, and associated bifurcations as function of relevant slow variables - such as extracellular potassium - and synaptic current; and whose output is both firing rate and impact on the slow variables - such as transmembrane potassium flux. Small networks composed of just excitatory and inhibitory mNMs demonstrate expected dynamical states including firing, runaway excitation and depolarization block, and these transitions change in biologically observed ways with changes in extracellular potassium and excitatory-inhibitory balance.

Epileptic seizures, sleep, and circadian timing share bilateral interactions, but concerted work to characterize these interactions and to leverage them to the advantage of patients with epilepsy remains in beginning stages. To further the field, a multidisciplinary group of sleep physicians, epileptologists, circadian timing experts, and others met to outline the state of the art, gaps of knowledge, and suggest ways forward in clinical, translational, and basic research. A multidisciplinary panel of experts discussed these interactions, centered on whether improvements in sleep or circadian rhythms improve decrease seizure frequency. In addition, education about sleep was lacking in among patients, their families, and physicians, and that focus on education was an extremely important “low hanging fruit” to harvest. Improvements in monitoring technology, experimental designs sensitive to the rigor required to dissect sleep versus circadian influences, and clinical trials in seizure reduction with sleep improvements were appropriate.

Sudden unexpected death in epilepsy (SUDEP) is the leading cause of death in patients with refractory epilepsy. Likely pathophysiological mechanisms include seizure-induced cardiac and respiratory dysregulation. A frequently identified feature in SUDEP cases is that they occur at night. This raises the question of a role for sleep state in regulating of SUDEP. An association with sleep has been identified in a number of studies with patients and in animal models. The focus of this section of the Sleep and Epilepsy Workshop was on identifying and understanding the role for sleep and time of day in the pathophysiology of SUDEP.

Optical resolution photoacoustic microscopy (OR-PAM) can map the cerebral vasculature at capillary level resolution. However, the OR-PAM setup’s bulky imaging head makes awake mouse brain imaging challenging and inhibits its integration with other optical neuroimaging modalities. Moreover, the glass cranial windows used for optical microscopy are unsuitable for OR-PAM due to the acoustic impedance mismatch between the glass plate and the tissue. To overcome these challenges, we propose a lithium niobate based transparent ultrasound trans-ducer (TUT) as a cranial window on a thinned mouse skull. The TUT cranial window simplifies the imaging head considerably due to its dual functionality as an optical window and ultrasound transducer. The window remains stable for six weeks, with no noticeable inflammation and minimal bone regrowth. The TUT window’s potential is demonstrated by imaging the awake mouse cerebral vasculature using OR-PAM, intrinsic optical signal imaging and two-photon microscopy. The TUT cranial window can potentially also be used for ultrasound stimulation and simultaneous multimodal imaging of the awake mouse brain.

Extensive clinical and experimental evidence links sleep-wake regulation and state of vigilance (SOV) to neurological disorders including schizophrenia and epilepsy. To understand the bidirectional coupling between disease severity and sleep disturbances, we need to investigate the underlying neurophysiological interactions of the sleep-wake regulatory system (SWRS) in normal and pathological brains. We utilized unscented Kalman filter based data assimilation (DA) and physiologically based mathematical models of a sleep-wake regulatory network synchronized with experimental measurements to reconstruct and predict the state of SWRS in chronically implanted animals. Critical to applying this technique to real biological systems is the need to estimate the underlying model parameters. We have developed an estimation method capable of simultaneously fitting and tracking multiple model parameters to optimize the reconstructed system state. We add to this fixed-lag smoothing to improve reconstruction of random input to the system and those that have a delayed effect on the observed dynamics. To demonstrate application of our DA framework, we have experimentally recorded brain activity from freely behaving rodents and classified discrete SOV continuously for many-day long recordings. These discretized observations were then used as the "noisy observables" in the implemented framework to estimate time-dependent model parameters and then to forecast future state and state transitions from out-of-sample recordings.

We introduce data assimilation as a computational method that uses machine learning to combine data with human knowledge in the form of mechanistic models in order to forecast future states, to impute missing data from the past by smoothing, and to infer measurable and unmeasurable quantities that represent clinically and scientifically important phenotypes. We demonstrate the advantages it affords in the context of type 2 diabetes by showing how data assimilation can be used to forecast future glucose values, to impute previously missing glucose values, and to infer type 2 diabetes phenotypes. At the heart of data assimilation is the mechanistic model, here an endocrine model. Such models can vary in complexity, contain testable hypotheses about important mechanics that govern the system (eg, nutrition’s effect on glucose), and, as such, constrain the model space, allowing for accurate estimation using very little data.

Sleep-wake regulation is thought to be governed by interactions among several nuclei in midbrain, pons, and hypothalamic regions. Determination of the causal role of these nuclei in state transitions requires simultaneous measurements from the nuclei with sufficient spatial and temporal resolution. We obtained long-term experimental single- and multi-unit measurements simultaneously from multiple nuclei of the putative hypothalamic and brainstem sleep-wake regulatory network in freely behaving rats. Cortical and hippocampal activity, along with head acceleration were also acquired to assess behavioral state. Here, we confirm that the general activity profile of the recorded sleep-wake regulatory nuclei is similar to the patterns presented previously in brief recordings of individual nuclei in head-fixed animals. However, we found that these activity profiles when studied with respect to cortical and behavioral signs of state transitions differ significantly from previous reports. Our findings pose fundamental questions about the neural mechanisms that maintain specific states and the neural interactions that lead to the emergence of sleep-wake states.

Optical resolution photoacoustic microscopy (OR-PAM) can map the cerebral vasculature at capillary-level resolution. However, the OR-PAM setup’s bulky imaging head makes awake mouse brain imaging challenging and inhibits its integration with other optical neuroimaging modalities. Moreover, the glass cranial windows used for optical microscopy are unsuitable for OR-PAM due to the acoustic impedance mismatch between the glass plate and the tissue. To overcome these challenges, we propose a lithium niobate based transparent ultrasound transducer (TUT) as a cranial window on a thinned mouse skull. The TUT cranial window simplifies the imaging head considerably due to its dual functionality as an optical window and ultrasound transducer. The window remains stable for six weeks, with no noticeable inflammation and minimal bone regrowth. The TUT window’s potential is demonstrated by imaging the awake mouse cerebral vasculature using OR-PAM, intrinsic optical signal imaging, and two-photon microscopy. The TUT cranial window can potentially also be used for ultrasound stimulation and simultaneous multimodal imaging of the awake mouse brain.

Maintaining the ionic and chemical composition of the extracellular spaces in the brain is extremely important for its health and function. However, the brain lacks a conventional lymphatic system to remove metabolic waste. It has been proposed that the fluid movement through the paravascular space (PVS) surrounding penetrating arteries can help remove metabolites from the brain. The dynamics of fluid movement in the PVS and its interaction with arterial dilation and brain mechanics are not well understood. Here, we performed simulations to understand how arterial pulsations and dilations interact with brain deformability to drive fluid flow in the PVS. In simulations with compliant brain tissue, arterial pulsations did not drive appreciable flows in the PVS. In contrast, when the artery dilated with dynamics like those seen during functional hyperemia, there was a marked movement of fluid through the PVS. Our simulations suggest that in addition to its other purposes, functional hyperemia may serve to increase fluid exchange between the PVS and the subarachnoid space, improving the clearance of metabolic waste. We measured displacement of the blood vessels and the brain tissue simultaneously in awake, head-fixed mice using two-photon microscopy. Our measurements show that brain tissue can deform in response to fluid movement in the PVS, as predicted by simulations. The results from our simulations and experiments show that the deformability of the soft brain tissue needs to be accounted for when studying fluid flow and metabolite transport in the brain.

Data assimilation (DA) refers to a family of methods used to synchronize a dynamical model to sparse or noisy measurements of model states. In this paper, we propose a wearable DA platform for neurological research and report our progress in translating a DA computational framework from desktop computation to embedded computation. The unscented Kalman filter (UKF) and a neural mass model (NMM) for sleep-wake regulation are introduced. Next, selection of suitable UKF parameters through MATLAB simulations is described. Finally, four variations of the DA framework are run on an embedded microprocessor in order to find the variation that minimizes computation time while maintaining state reconstruction accuracy. By reducing computational precision of the equation integrator and using a piecewise-linear approximation in place of the tanh function, we increased computational speed by a factor of 3.6 while maintaining a high level of state reconstruction fidelity.

Spreading depression or depolarization is a large-scale pathological brain phenomenon related to migraine, stroke, hemorrhage and traumatic brain injury. Once initiated, spreading depression propagates across gray matter extruding potassium and other active molecules, collapsing the resting membrane electro-chemical gradient of cells leading to spike inactivation and cellular swelling, and propagates independently of synaptic transmission. We demonstrate the modulation, suppression and prevention of spreading depression utilizing applied transcortical DC electric fields in brain slices, measured with intrinsic optical imaging and potassium dye epifluorescence. We experimentally observe a surface-positive electric field induced forcing of spreading depression propagation to locations in cortex deeper than the unmodulated propagation path, whereby further propagation is confined and arrested even after field termination. The opposite surface-negative electric field polarity produces an increase in propagation velocity and a confinement of the wave to more superficial layers of cortex than the unmodulated propagation path. These field polarities are of opposite sign to the polarity that blocks neuronal spiking and seizures, and are consistent with biophysical models of spreading depression. The results demonstrate the potential feasibility of electrical control and prevention of spreading depression.

Spreading depression is characterized by slow, propagating wave of cellular depolarization (SD) and is wildly associated with migraine, stroke, and traumatic brain injury. Seizures and spreading depression (or spreading depolarization, SD) have long been reported to coincide in acute seizure induction experiments. However, SD has not been observed associated with spotaneous seizures in animal or clinical recordings. Recently, advances in acquisition systems for neurointensive care units have made routine observations of SD possible. In clinical epilepsy, SD has been suggested as a candidate mechanism for migraine/headache like events following seizures as well as for post-ictal generalized suppression. In animal models of epilepsy, seizure-induced brainstem SD has also been demonstrated as a mechanism of sudden unexplained death in epilepsy (SUDEP). The interplay between seizures and SD has also been suggested in computational models, where the two are components of the repetoir of neuronal activity.However, the spatiotemporal dynamics of SD with respect to spontaneous seizures in chronically epileptic brain remains ambigous. We analyzed continuous long-term DC sensitive EEG measurements from two fundamentally different animal models of chronic epilepsy. We found that SD was associated with approximately one-third of all spontaneous seizures in each model. Additionally, SDs participated in the organization of seizure clusters. These findings demonstrate that the underlying dynamic of epileptic events is broader than seizures alone.Significance StatementSpreading depression is characterized by slow, propagating wave of cellular spreading depolarization (SD) and is wildly associated with migraine, stroke, and traumatic brain injury. Although recently the linkage between SD and induced seizures has been recognized, the mechanistic relationship between SD and spontaneous seizures remains poorly understood. Here, we utilized long-term, stable, near-DC measurements of the brain activity in two fundamentally different animal models of epilepsy to investigate the SD-seizure interplay. We found that SD is a frequent phenomenon in the epileptic brain, in these models is associated with more than a third of all seizures, and appears to connect seizures in seizure clusters. Although in one model SD stereotypically propagates out from a single focus in the hippocampus, depression of the field-potentials is observed synchronously across much of the hippocampus. These observations highlight the value of stable DC measurements for accurate understanding of SD and its propagation. We found that spontaneous ictal events that include both seizures and SD are frequent in animal models of epilepsy. These findings suggest that SD could be a valuable target for treatment and control of epilepsy.

Postinjury epilepsy is an potentially preventable sequela in as many as 20% of patients with brain insults. For these cases biomarkers of epileptogenesis are critical to facilitate identification of patients at high-risk of developing epilepsy and to introduce effective anti-epileptogenic interventions. Here, we demonstrate that delayed brain–heart coincidences serve as a reliable biomarker. In a murine model of post-infection acquired epilepsy, we used long-term simultaneous measurements of the brain activity via electroencephalography and autonomic cardiac activity via electrocardiography, in male mice, to quantitatively track brain–heart interactions during epileptogenesis. We find that abnormal cortical discharges precede abnormal fluctuations in the cardiac rhythm at the resolution of single beat-to-beat intervals. The delayed brain–heart coincidence is detectable as early as the onset of chronic measurements, 2–14 weeks before the first seizure, only in animals that become epileptic, and increases during epileptogenesis. Therefore, delayed brain–heart coincidence serves as a biomarker of epileptogenesis and could be used for phenotyping, diagnostic, and therapeutic purposes.SIGNIFICANCE STATEMENTNo biomarker that readily predicts and tracks epileptogenesis currently exists for the wide range of human acquired epilepsies. Here, we used long-term measurements of brain and heart activity in a mouse model of post-infection acquired epilepsy to investigate the potential of brain–heart interaction as a biomarker of epileptogenesis. We found that delayed coincidences from brain to heart can clearly separate the mice that became epileptic from those that did not weeks before development of epilepsy. Our findings allow for phenotyping and tracking of epileptogenesis in this and likely other models of acquired epilepsy. Such capability is critical for efficient adjunctive treatment development and for tracking the efficacy of such treatments.

Epilepsy is a common neurological disorder that affects nearly 1% of the world’s population, and is characterized by the occurrence of recurrent spontaneous seizures. The apparent unpredictability of seizures is both a hallmark of the disorder and one of the primary factors contributing to the degradation in quality of life and increased potential for accidental injury (Arthurs et al. 2010). Unpredictability also increases the difficulty of achieving good seizure control. Patients with uncontrolled seizures have been shown to have increased risk of comorbid conditions that include sudden unexplained death in epilepsy (SUDEP), and increases the overall burden of the disorder on family members and caregivers. In November of 2013 we had the opportunity, along with Bjorn Schelter and Susan Arthurs, to organize the Sixth of the International Workshops on Seizure Prediction (IWSP). This is an interdisciplinary gathering of engineers, physicists, mathematicians, epileptologists, neurosurgeons and neuroscientists, self-termed the International Seizure Prediction Group (ISPG). The goals of the ISPG are to bring quantitative and technological approaches to addressing the prediction and control of epilepsy. There are two widely quoted targeted products from seizure prediction. First, successful seizure prediction enables development of devices and strategies for seizure intervention and improvement in quality of life. A simple advance warning of a high likelihood of a seizure can potentially enable a person with epilepsy to avoid situations that might place themselves or others at risk. Second, reliable and accurate seizure prediction would result in useful insights into the mechanistic underpinnings of seizure generation and related brain activity abnormalities. In particular, these may enable us to accomplish the “holy grail” of epilepsy treatment: focal seizure prevention to minimize the cognitive, behavioral and quality of life effects from both the treatments and the seizure events. We expect that articulating these and placing them into the context of human seizures and EEG recordings will increase the chances that the twin goals of seizure prediction and technology-based development of new prevention strategies will be realized. The IWSP series was initiated at the beginning of this century as a platform within which the ISPG can exchange ideas and identify high priority avenues for future investigation, with progress documented in summaries following each meeting. Thus, these meetings and their output serve a similar role as the formal Epilepsy Benchmarks (Kelley et al. 2009), to which many ISPG members have contributed. By way of introduction, we provide here a short history of seizure prediction from the last century leading up to the birth of the IWSP series, followed by a summary of the identified goals as emerging from the previous IWSPs. We then outline the significant achievements made in seizure prediction and the future goals of the ISPG as further detailed in the invited reviews. We close with an attached letter from Susan Arthurs, IWSP6 co-organizer and Chair of the Alliance for Epilepsy Research, which provides a patient’s perspective on the import of this research.

One of the largest single sources of epilepsy in the world is produced as a neurological sequela in survivors of cerebral malaria. Nevertheless, the pathophysiological mechanisms of such epileptogenesis remain unknown and no adjunctive therapy during cerebral malaria has been shown to reduce the rate of subsequent epilepsy. There is no existing animal model of postmalarial epilepsy. In this technical report we demonstrate the first such animal models. These models were created from multiple mouse and parasite strain combinations, so that the epilepsy observed retained universality with respect to genetic background. We also discovered spontaneous sudden unexpected death in epilepsy (SUDEP) in two of our strain combinations. These models offer a platform to enable new preclinical research into mechanisms and prevention of epilepsy and SUDEP.

Electrical stimulation offers the potential to develop novel strategies for the treatment of refractory medial temporal lobe epilepsy. In particular, direct electrical stimulation of the hippocampus presents the opportunity to modulate pathological dynamics at the ictal focus, although the neuroanatomical substrate of this region renders it susceptible to altering cognition and affective processing as a side effect. We investigated the effects of three electrical stimulation paradigms on separate groups of freely moving rats (sham, 8-Hz and 40-Hz sine-wave stimulation of the ventral/intermediate hippocampus, where 8- and 40-Hz stimulation were chosen to mimic naturally occurring hippocampal oscillations). Animals exhibited attenuated locomotor and exploratory activity upon stimulation at 40 Hz, but not at sham or 8-Hz stimulation. Such behavioral modifications were characterized by a significant reduction in rearing frequency, together with increased freezing behavior. Logistic regression analysis linked the observed changes in animal locomotion to 40-Hz electrical stimulation independently of time-related variables occurring during testing. Spectral analysis, conducted to monitor the electrophysiological profile in the CA1 area of the dorsal hippocampus, showed a significant reduction in peak theta frequency, together with reduced theta power in the 40-Hz vs. the sham stimulation animal group, independent of locomotion speed (theta range: 4–12 Hz). These findings contribute to the development of novel and safe medical protocols by indicating a strategy to constrain or optimize parameters in direct hippocampal electrical stimulation.

Improved understanding of the interaction between state of vigilance (SOV) and seizure onset has therapeutic potential. Six rats received injections of tetanus toxin (TeTX) in the ventral hippocampus that resulted in chronic spontaneous seizures. The distribution of SOV before 486 seizures was analyzed for a total of 19 d of recording. Rapid eye movement sleep (REM) and exploratory wake, both of which express prominent hippocampal theta rhythm, preceded 47 and 34%, for a total of 81%, of all seizures. Nonrapid eye movement sleep (NREM) and nonexploratory wake, neither of which expresses prominent theta, preceded 6.8 and 13% of seizures. We demonstrate that identification of SOV yields significant differentiation of seizure susceptibilities, with the instantaneous seizure rate during REM nearly 10 times higher than baseline and the rate for NREM less than half of baseline. Survival analysis indicated a shorter duration of preseizure REM bouts, with a maximum transition to seizure at ∼90 s after the onset of REM. This study provides the first analysis of a correlation between SOV and seizure onset in the TeTX model of temporal lobe epilepsy, as well as the first demonstration that hippocampal theta rhythms associated with natural behavioral states can serve a seizure-promoting role. Our findings are in contrast with previous studies suggesting that the correlations between SOV and seizures are primarily governed by circadian oscillations and the notion that hippocampal theta rhythms inhibit seizures. The documentation of significant SOV-dependent seizure susceptibilities indicates the potential utility of SOV and its time course in seizure prediction and control.

Visual Abstract, A multielectrode system that can address widely separated targets at multiple sites across multiple brain regions with independent implant angling is needed to investigate neural function and signaling in systems and circuits of small animals. Here, we present the systemDrive, a novel multisite, multiregion microdrive that is capable of moving microwire electrode bundles into targets along independent and nonparallel drive trajectories. Our design decouples the stereotaxic surgical placement of individual guide cannulas for each trajectory from the placement of a flexible drive structure. This separation enables placement of many microwire multitrodes along widely spaced and independent drive axes with user-set electrode trajectories and depths from a single microdrive body, and achieves stereotaxic precision with each. The system leverages tight tube–cannula tolerances and geometric constraints on flexible drive axes to ensure concentric alignment of electrode bundles within guide cannulas. Additionally, the headmount and microdrive both have an open-center design to allow for the placement of additional sensing modalities. This design is the first, in the context of small rodent chronic research, to provide the capability to finely position microwires through multiple widely distributed cell groups, each with stereotaxic precision, along arbitrary and nonparallel trajectories that are not restricted to emanate from a single source. We demonstrate the use of the systemDrive in male Long–Evans rats to observe simultaneous single-unit and multiunit activity from multiple widely separated sleep–wake regulatory brainstem cell groups, along with cortical and hippocampal activity, during free behavior over multiple many-day continuous recording periods.

Theta (4---12 Hz) and gamma (30---80 Hz) rhythms are considered important for cortical and hippocampal function. Although several neuron types are implicated in rhythmogenesis, the exact cellular mechanisms remain unknown. Subthreshold electric fields provide a flexible, area-specific tool to modulate neural activity and directly test functional hypotheses. Here we present experimental and computational evidence of the interplay among hippocampal synaptic circuitry, neuronal morphology, external electric fields, and network activity. Electrophysiological data are used to constrain and validate an anatomically and biophysically realistic model of area CA1 containing pyramidal cells and two interneuron types: dendritic- and perisomatic-targeting. We report two lines of results: addressing the network structure capable of generating theta-modulated gamma rhythms, and demonstrating electric field effects on those rhythms. First, theta-modulated gamma rhythms require specific inhibitory connectivity. In one configuration, GABAergic axo-dendritic feedback on pyramidal cells is only effective in proximal but not distal layers. An alternative configuration requires two distinct perisomatic interneuron classes, one exclusively receiving excitatory contacts, the other additionally targeted by inhibition. These observations suggest novel roles for particular classes of oriens and basket cells. The second major finding is that subthreshold electric fields robustly alter the balance between different rhythms. Independent of network configuration, positive electric fields decrease, while negative fields increase the theta/gamma ratio. Moreover, electric fields differentially affect average theta frequency depending on specific synaptic connectivity. These results support the testable prediction that subthreshold electric fields can alter hippocampal rhythms, suggesting new approaches to explore their cognitive functions and underlying circuitry.

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.

Although it is difficult to point to a definite origin of the field of nonlinear dynamics, it evolved in part from attempts to understand two fundamentally different types of deterministic systems—very simple systems with as few as three variables on the one side that generate erratic non-periodic

Electrical stimulation is emerging as a viable alternative for patients with epilepsy whose seizures are not alleviated by drugs or surgery. Its attractions are temporal and spatial specificity of action, flexibility of waveform parameters and timing, and the perception that its effects are reversible unlike resective surgery. However, despite significant advances in our understanding of mechanisms of neural electrical stimulation, clinical electrotherapy for seizures relies heavily on empirical tuning of parameters and protocols. We highlight concurrent treatment goals with potentially conflicting design constraints that must be resolved when formulating rational strategies for epilepsy electrotherapy, namely, seizure reduction versus cognitive impairment, stimulation efficacy versus tissue safety, and mechanistic insight versus clinical pragmatism. First, treatment markers, objectives, and metrics relevant to electrical stimulation for epilepsy are discussed from a clinical perspective. Then the experimental perspective is presented, with the biophysical mechanisms and modalities of open-loop electrical stimulation, and the potential benefits of closed-loop control for epilepsy.

We examine the effects of applied electric fields on neuronal synchronization. Two-compartment model neurons were synaptically coupled and embedded within a resistive array, thus allowing the neurons to interact both chemically and electrically. In addition, an external electric field was imposed on the array. The effects of this field were found to be nontrivial, giving rise to domains of synchrony and asynchrony as a function of the heterogeneity among the neurons. A simple phase oscillator reduction was successful in qualitatively reproducing these domains. The findings form several readily testable experimental predictions, and the model can be extended to a larger scale in which the effects of electric fields on seizure activity may be simulated.

A prototype neural probe designed for chronic measurements and recordings of localized temperature field in brain has been fabricated and tested. An array of through-film vanadium oxide thermistors has been deposited onto glass and flexible 20- $\mu \text{m}$ polyimide substrates. High resistivity vanadium oxide was deposited using bias target ion-beam deposition. Functioning sensors were 10 $\mu \text{m} \times 10~\mu \text{m} \times 85$ -nm thick. Tested samples on glass showed a mean thermistor temperature coefficient of resistance of −4.060 ± 0.004%/°C and nominal resistance $R_{0}$ of 1.3 $\text{M}\Omega $ .

Weak electric fields modulate neuronal activity, and knowledge of the interaction threshold is important in the understanding of neuronal synchronization, in neural prosthetic design, and in the public health assessment of environmental extremely low frequency fields. Previous experimental measurements have placed the threshold between 1 and 5 mV/mm, although theory predicts that elongated neurons should have submillivolt per millimeter sensitivity near 100 microV/mm. We here provide the first experimental confirmation that neuronal networks are detectably sensitive to submillivolt per millimeter electrical fields [Gaussian pulses 26 msec full width at half-maximal, 140 microV/mm root mean square (rms), 295 microV/mm peak amplitude], an order of magnitude below previous findings, and further demonstrate that these networks are more sensitive than the average single neuron threshold (185 microV/mm rms, 394 microV/mm peak amplitude) to field modulation.