Analysis and Modeling of Subthreshold Neural Multi-Electrode Array Data by Statistical Field Theory

Modulatory effects of real-time electromagnetic stimulation on epileptiform activity in juvenile rat hippocampus based on multi-electrode array recordings

Electromagnetic stimulation (EMS) has proven to be useful for the focal suppression of epileptiform activity (EFA) in the hippocampus. There is a critical period during EFA for achieving the transition from brief interictal discharges (IIDs) to prolonged ictal discharges (IDs), and it is unknown whether EMS can modulate this transition. Therefore, this study aimed to evaluate the intensity- and time-dependent effect of EMS on the transition of EFA. A juvenile rat EFA model was constructed by perfusing magnesium-free artificial cerebrospinal fluid (aCSF) on brain slices, and the induced EFA was recorded using a micro-electrode array (MEA) platform. After a stable EFA event was recorded for some time, real-time pulsed magnetic stimulation with low and high peak-to-peak input magnetic field intensities was carried out. A 5-min intervention with real-time magnetic fields with low intensity was found to reduce the amplitude of IDs (ID events still existed), whereas a 5-min intervention with real-time magnetic fields with high input voltages completely suppressed IDs. Short-time magnetic fields (9s and 1min) with high or low input intensity had no effect on EFA. Real-time magnetic fields can block the normal EFA process from IIDs to IDs (i.e., a complete EFA cycle) and this suppression effect is dependent on input intensities and intervention duration. The experimental findings further indicate that magnetic stimulation may be chosen as an alternative antiepileptic therapy.

Self-consistent formulations for stochastic nonlinear neuronal dynamics

Neural dynamics is often investigated with tools from bifurcation theory. However, many neuron models are stochastic, mimicking fluctuations in the input from unknown parts of the brain or the spiking nature of signals. Noise changes the dynamics with respect to the deterministic model; in particular classical bifurcation theory cannot be applied. We formulate the stochastic neuron dynamics in the Martin-Siggia-Rose de Dominicis-Janssen (MSRDJ) formalism and present the fluctuation expansion of the effective action and the functional renormalization group (fRG) as two systematic ways to incorporate corrections to the mean dynamics and time-dependent statistics due to fluctuations in the presence of nonlinear neuronal gain. To formulate self-consistency equations, we derive a fundamental link between the effective action in the Onsager-Machlup (OM) formalism, which allows the study of phase transitions, and the MSRDJ effective action, which is computationally advantageous. These results in particular allow the derivation of an OM effective action for systems with non-Gaussian noise. This approach naturally leads to effective deterministic equations for the first moment of the stochastic system; they explain how nonlinearities and noise cooperate to produce memory effects. Moreover, the MSRDJ formulation yields an effective linear system that has identical power spectra and linear response. Starting from the better known loopwise approximation, we then discuss the use of the fRG as a method to obtain self-consistency beyond the mean. We present a new efficient truncation scheme for the hierarchy of flow equations for the vertex functions by adapting the Blaizot, Méndez, and Wschebor approximation from the derivative expansion to the vertex expansion. The methods are presented by means of the simplest possible example of a stochastic differential equation that has generic features of neuronal dynamics.

Exploring the form- And time-dependent effect of low-frequency electromagnetic fields on maintenance of hippocampal long-term potentiation

Low-frequency electromagnetic field (LF-EMF) stimulation is an emerging neuromodulation tool that is attracting more attention because of its non-invasive and well-controlled characteristics. However, the effect of different LF-EMF features including the forms and the time of addition on neuronal activity has not been completely understood. In this study, we used multi-electrode array (MEA) systems to develop a flexible in vitro magnetic stimulation device with plug-and-play features that allows for real-time delivery of LF-EMFs to biological tissues. Crucially, the method enables different forms of LF-EMF to be added at any time to a long-term potentiation (LTP) experiment without interrupting the process of LTP induction. We demonstrated that the slope of field excitatory postsynaptic potentials (fEPSPs) decreased significantly under post or priming uninterrupted sine LF-EMFs. The fEPSPs slope would continue to decline significantly when LF-EMFs were added two times with a 20-min interval. Paired-pulse ratio (PPR) was analyzed and the results reflected that LF-EMFs induced LTP was expressed postsynaptically. The results of pharmacological experiments indicated that AMPA receptor activity was involved in the process of LTP loss caused by post-LF-EMFs. Moreover, the effect of priming sine or Quadripulse stimulation (QPS)-patterned LF-EMFs depended on the time interval between the end of LF-EMF and the beginning of baseline recording. Interestingly, the effect of sine LF-EMFs on LTP would not disappear within 120 min, while the impact of QPS-patterned LF-EMFs on LTP might disappear after 90 min. These results indicated that LF-EMF might have a form- and time-dependent effect on LTP.

Assessment of Spontaneous Neuronal Activity In Vitro Using Multi-Well Multi-Electrode Arrays: Implications for Assay Development

Multi-electrode arrays (MEAs) are being more widely used by researchers as an instrument platform for monitoring prolonged, non-destructive recordings of spontaneously firing neurons in vitro for applications in modeling Alzheimer's, Parkinson's, schizophrenia, and many other diseases of the human CNS. With the more widespread use of these instruments, there is a need to examine the prior art of studies utilizing MEAs and delineate best practices for data acquisition and analysis to avoid errors in interpretation of the resultant data. Using a dataset of recordings from primary rat (Rattus norvegicus) cortical cultures, methods and statistical power for discerning changes in neuronal activity on the array level are examined. Further, a method for unsupervised spike sorting is implemented, allowing for the resolution of action potential incidents down to the single neuron level. Following implementation of spike sorting, the dynamics of firing frequency across populations of individual neurons and networks are examined longitudinally. Finally, the ability to detect a frequency independent phenotype, the change in action potential amplitude, is demonstrated through the use of pore-forming neurotoxin treatments. Taken together, this study provides guidance and tools for users wishing to incorporate multi-well MEA usage into their studies.

Anti-correlated cortical networks arise from spontaneous neuronal dynamics at slow timescales

In the highly interconnected architectures of the cerebral cortex, recurrent intracortical loops disproportionately outnumber thalamo-cortical inputs. These networks are also capable of generating neuronal activity without feedforward sensory drive. It is unknown, however, what spatiotemporal patterns may be solely attributed to intrinsic connections of the local cortical network. Using high-density microelectrode arrays, here we show that in the isolated, primary somatosensory cortex of mice, neuronal firing fluctuates on timescales from milliseconds to tens of seconds. Slower firing fluctuations reveal two spatially distinct neuronal ensembles, which correspond to superficial and deeper layers. These ensembles are anti-correlated: when one fires more, the other fires less and vice versa. This interplay is clearest at timescales of several seconds and is therefore consistent with shifts between active sensing and anticipatory behavioral states in mice.

Graph-based analysis of brain connectivity in schizophrenia

The present study evaluated brain connectivity using electroencephalography (EEG) data from 14 patients with schizophrenia and 14 healthy controls. Phase-Locking Value (PLV), Phase-Lag Index (PLI) and Directed Transfer Function (DTF) were calculated for the original EEG data and following current source density (CSD) transformation, re-referencing using the average reference electrode (AVERAGE) and reference electrode standardization techniques (REST). The statistical analysis of adjacency matrices was carried out using indices based on graph theory. Both CSD and REST reduced the influence of volume conducted currents. The largest group differences in connectivity were observed for the alpha band. Schizophrenic patients showed reduced connectivity strength, as well as a lower clustering coefficient and shorter characteristic path length for both measures of phase synchronization following CSD transformation or REST re-referencing. Reduced synchronization was accompanied by increased directional flow from the occipital region for the alpha band. Following the REST re-referencing, the sources of alpha activity were located at parietal rather than occipital derivations. The results of PLV and DTF demonstrated group differences in fronto-posterior asymmetry following CSD transformation, while for PLI the differences were significant only using REST. The only analysis that identified group differences in inter-hemispheric asymmetry was DTF calculated for REST. Our results suggest that a comparison of different connectivity measures using graph-based indices for each frequency band, separately, may be a useful tool in the study of disconnectivity disorders such as schizophrenia.