Osbert C. Zalay

RESPONSIVE NEUROMODULATORS BASED ON ARTIFICIAL NEURAL NETWORKS USED TO CONTROL SEIZURE-LIKE EVENTS IN A COMPUTATIONAL MODEL OF EPILEPSY

Deep brain stimulation (DBS) has been noted for its potential to suppress epileptic seizures. To date, DBS has achieved mixed results as a therapeutic approach to seizure control. Using a computational model, we demonstrate that high-complexity, biologically-inspired responsive neuromodulation is superior to periodic forms of neuromodulation (responsive and non-responsive) such as those implemented in DBS, as well as neuromodulation using random and random repetitive-interval stimulation. We configured radial basis function (RBF) networks to generate outputs modeling interictal time series recorded from rodent hippocampal slices that were perfused with low Mg²⁺/high K⁺ solution. We then compared the performance of RBF-based interictal modulation, periodic biphasic-pulse modulation, random modulation and random repetitive modulation on a cognitive rhythm generator (CRG) model of spontaneous seizure-like events (SLEs), testing efficacy of SLE control. A statistically significant improvement in SLE mitigation for the RBF interictal modulation case versus the periodic and random cases was observed, suggesting that the use of biologically-inspired neuromodulators may achieve better results for the purpose of electrical control of seizures in a clinical setting.

Mapped Clock Oscillators as Ring Devices and Their Application to Neuronal Electrical Rhythms

The mapped clock oscillator (MCO) is a second-order, Winfree-type oscillator generating two instantaneous clock variables (amplitude and phase) that are mapped to an observable output variable (voltage) via a static nonlinearity. Two fundamental classes of ring devices are presented. Their respective dynamics give rise to two oscillator forms-the labile clock and the clock-which can be coupled together in various configurations to create higher-order systems with sufficient complexity to capture the dynamics of neuronal assemblies. To demonstrate the applicability of MCOs in modelling neuronal rhythms, a hippocampal network model of four coupled oscillators was constructed and shown to exhibit rhythmic activity of varying complexity, depending on model parameters. The dynamics of the network were quantified through estimation of the maximum lyapunov exponent and the correlation dimension. Synthesis of complex neuronal rhythms may have therapeutic implications. The modular and efficient design of the MCO should facilitate the process of implementing coupled MCO networks in electronic hardware as potential neural prostheses for treating dynamic diseases such as epilepsy.

Simulated Mossy Fiber Associated Feedforward Circuit Functioning as a Highpass Filter

Learning and memory rely on the strict regulation of communication between neurons in the hippocampus. The mossy fiber (MF) pathway connects the dentate gyrus to the auto-associative CA3 network, and the information it carries is controlled by a feedforward circuit combining disynaptic inhibition with monosynaptic excitation. Analysis of the MF associated circuit using a mapped clock oscillator (MCO) model reveals the circuit to be a highpass filter

Mapping the coherence of ictal high frequency oscillations in human extratemporal lobe epilepsy

High frequency oscillations (HFOs) have recently been recorded in epilepsy patients and proposed as possible novel biomarkers of epileptogenicity. Investigation of additional HFO characteristics that correlate with the clinical manifestation of seizures may yield additional insights for delineating epileptogenic regions. To that end, this study examined the spatiotemporal coherence patterns of HFOs (80–400 Hz) so as to characterize the strength of HFO interactions in the epileptic brain. We hypothesized that regions of strong HFO coherence identified epileptogenic networks believed to possess a pathologic locking nature in relation to regular brain activity.

System characterization of neuronal excitability in the hippocampus and its relevance to observed dynamics of spontaneous seizure-like transitions

Most forms of epilepsy are marked by seizure episodes that arise spontaneously. The low-magnesium/high-potassium (low-Mg(2+)/high-K(+)) experimental model of epilepsy is an acute model that produces spontaneous, recurring seizure-like events (SLEs). To elucidate the nature of spontaneous seizure transitions and their relationship to neuronal excitability, whole-cell recordings from the intact hippocampus were undertaken in vitro, and the response of hippocampal CA3 neurons to Gaussian white noise injection was obtained before and after treatment with various concentrations of low-Mg(2+)/high-K(+) solution. A second-order Volterra kernel model was estimated for each of the input-output response pairs. The spectral energy of the responses was also computed, providing a quantitative measure of neuronal excitability. Changes in duration and amplitude of the first-order kernel correlated positively with the spectral energy increase following treatment with low-Mg(2+)/high-K(+) solution, suggesting that variations in neuronal excitability are coded by the system kernels, in part by differences to the profile of the first-order kernel. In particular, kernel duration was more sensitive than amplitude to changes in spectral energy, and correlated more strongly with kernel area. An oscillator network model of the hippocampal CA3 was constructed to investigate the relationship of kernel duration to network excitability, and the model was able to generate spontaneous, recurrent SLEs by increasing the duration of a mode function analogous to the first-order kernel. Results from the model indicated that disruption to the dynamic balance of feedback was responsible for seizure-like transitions and the observed intermittency of SLEs. A physiological candidate for feedback imbalance consistent with the network model is the destabilizing interaction of extracellular potassium and paroxysmal neuronal activation. Altogether, these results (1) validate a mathematical model for epileptiform activity in the hippocampus by quantifying and subsequently correlating its behavior with an experimental, in vitro model of epilepsy; (2) elucidate a possible mechanism for epileptogenesis; and (3) pave the way for control studies in epilepsy utilizing the herein proposed experimental and mathematical setup.

Complexity in Neuronal Noise Depends on Network Interconnectivity

Abstract“Noise,” or noise-like activity (NLA), defines background electrical membrane potential fluctuations at the cellular level of the nervous system, comprising an important aspect of brain dynamics. Using whole-cell voltage recordings from fast-spiking stratum oriens interneurons and stratum pyramidale neurons located in the CA3 region of the intact mouse hippocampus, we applied complexity measures from dynamical systems theory (i.e., 1/fγ noise and correlation dimension) and found evidence for complexity in neuronal NLA, ranging from high- to low-complexity dynamics. Importantly, these high- and low-complexity signal features were largely dependent on gap junction and chemical synaptic transmission. Progressive neuronal isolation from the surrounding local network via gap junction blockade (abolishing gap junction-dependent spikelets) and then chemical synaptic blockade (abolishing excitatory and inhibitory post-synaptic potentials), or the reverse order of these treatments, resulted in emergence of high-complexity NLA dynamics. Restoring local network interconnectivity via blockade washout resulted in resolution to low-complexity behavior. These results suggest that the observed increase in background NLA complexity is the result of reduced network interconnectivity, thereby highlighting the potential importance of the NLA signal to the study of network state transitions arising in normal and abnormal brain dynamics (such as in epilepsy, for example).

Theta phase precession and phase selectivity: a cognitive device description of neural coding

Information in neural systems is carried by way of phase and rate codes. Neuronal signals are processed through transformative biophysical mechanisms at the cellular and network levels. Neural coding transformations can be represented mathematically in a device called the cognitive rhythm generator (CRG). Incoming signals to the CRG are parsed through a bank of neuronal modes that orchestrate proportional, integrative and derivative transformations associated with neural coding. Mode outputs are then mixed through static nonlinearities to encode (spatio) temporal phase relationships. The static nonlinear outputs feed and modulate a ring device (limit cycle) encoding output dynamics. Small coupled CRG networks were created to investigate coding functionality associated with neuronal phase preference and theta precession in the hippocampus. Phase selectivity was found to be dependent on mode shape and polarity, while phase precession was a product of modal mixing (i.e. changes in the relative contribution or amplitude of mode outputs resulted in shifting phase preference). Nonlinear system identification was implemented to help validate the model and explain response characteristics associated with modal mixing; in particular, principal dynamic modes experimentally derived from a hippocampal neuron were inserted into a CRG and the neurons dynamic response was successfully cloned. From our results, small CRG networks possessing disynaptic feedforward inhibition in combination with feedforward excitation exhibited frequency-dependent inhibitory-to-excitatory and excitatory-to-inhibitory transitions that were similar to transitions seen in a single CRG with quadratic modal mixing. This suggests nonlinear modal mixing to be a coding manifestation of the effect of network connectivity in shaping system dynamic behavior. We hypothesize that circuits containing disynaptic feedforward inhibition in the nervous system may be candidates for interpreting upstream rate codes to guide downstream processes such as phase precession, because of their demonstrated frequency-selective properties.

Frequency interactions in human epileptic brain

We have used two algorithms, wavelet phase coherence (WPC) and modulation index (MI) analysis to study frequency interactions in the human epileptic brain. Quantitative analyses were performed on intracranial electroencephalographic (iEEG) segments from three patients with neocortical epilepsy. Interelectrode coherence was measured using WPC and intraelectrode frequency interactions were analyzed using MI. WPC was performed on electrode pairings and the temporal evolution of phase couplings in the following frequency ranges: 1–4Hz, 4–8Hz, 8–13Hz, 13–30Hz and 30–100Hz was studied. WPC was strongest in the 1–4Hz frequency range during both seizure and non-seizure activities; however, WPC values varied minimally between electrode pairings. The 13–30Hz band showed the lowest WPC values during seizure activity. MI analysis yielded two prominent patterns of frequency-specific activity, during seizure and non-seizure activities, which were present across all patients.

Transformation of neuronal modes associated with low-Mg2+/high-K+ conditions in an in vitro model of epilepsy.

Nonparametric system modeling constitutes a robust method for the analysis of physiological systems as it can be used to identify nonlinear dynamic input–output relationships and facilitate their description. First- and second-order kernels of hippocampal CA3 pyramidal neurons in an in vitro slice preparation were computed using the Volterra–Wiener approach to investigate system changes associated with epileptogenic low-magnesium/high-potassium (low-Mg2 + /high-K + ) conditions. The principal dynamic modes (PDMs) of neurons were calculated from the first- and second-order kernel estimates in order to characterize changes in neural coding functionality. From our analysis, an increase in nonlinear properties was observed in kernels under low-Mg2 + /high-K + . Furthermore, the PDMs revealed that the sampled hippocampal CA3 neurons were primarily of integrating character and that the contribution of a differentiating mode component was enhanced under low-Mg2 + /high-K + .

Synthesis of high-complexity rhythmic signals for closed-loop electrical neuromodulation

We propose an approach to synthesizing high-complexity rhythmic signals for closed-loop electrical neuromodulation using cognitive rhythm generator (CRG) networks, wherein the CRG is a hybrid oscillator comprised of (1) a bank of neuronal modes, (2) a ring device (clock), and (3) a static output nonlinearity (mapper). Networks of coupled CRGs have been previously implemented to simulate the electrical activity of biological neural networks, including in silico models of epilepsy, producing outputs of similar waveform and complexity to the biological system. This has enabled CRG network models to be used as platforms for testing seizure control strategies. Presently, we take the application one step further, envisioning therapeutic CRG networks as rhythmic signal generators creating neuromimetic signals for stimulation purposes, motivated by recent research indicating that stimulus complexity and waveform characteristics influence neuromodulation efficacy. To demonstrate this concept, an epileptiform CRG network generating spontaneous seizure-like events (SLEs) was coupled to a therapeutic CRG network, forming a closed-loop neuromodulation system. SLEs are associated with low-complexity dynamics and high phase coherence in the network. The tuned therapeutic network generated a high-complexity, multi-banded rhythmic stimulation signal with prominent theta and gamma-frequency power that suppressed SLEs and increased dynamic complexity in the epileptiform network, as measured by a relative increase in the maximum Lyapunov exponent and decrease in phase coherence. CRG-based neuromodulation outperformed both low and high-frequency periodic pulse stimulation, suggesting that neuromodulation using complex, biomimetic signals may provide an improvement over conventional electrical stimulation techniques for treating neurological disorders such as epilepsy.