Craig S. Henriquez

Peripheral nerves are primarily composed of unmyelinated axons, and there is growing interest in electrical stimulation of the autonomic nervous system to treat various diseases. We present the first cable model of an unmyelinated vagal nerve fiber and compare its ion channel isoforms and conduction responses with other published models of unmyelinated axons, establishing important tools for advancing modeling of autonomic nerves.

The brain exhibits intrinsic oscillatory behavior, which plays a vital role in communication and information processing. Abnormalities in brain rhythms have been linked to numerous disorders, including depression and schizophrenia. Rhythmic electrical stimulation (e.g., transcranial magnetic stimulation and transcranial alternating current stimulation) has been used to modulate these oscillations and produce lasting changes in neural activity. In this computational study, we investigate the combined effects of sinusoidal stimulation and synaptic plasticity on model networks comprised of simple, tunable four-neuron oscillators. While not intended to model a specific brain circuit, this idealization was created to provide some intuition on how electrical modulation can induce plastic changes in the oscillatory state. Linked pairs of oscillators were stimulated with sinusoidal current, and their behavior was measured as a function of their intrinsic frequencies, inter-oscillator synaptic strengths, and stimulus strength and frequency. Under certain stimulus conditions, sinusoidal current can disrupt the network's natural firing patterns. Synaptic plasticity can induce weight imbalances that permanently change the characteristic firing behavior of the network. Grids of 100 oscillators with random frequencies were also subjected to a wide array of stimulus conditions. The characteristics of the post-stimulus network activity depend heavily on the stimulus frequency and amplitude as well as the initial strength of inter-oscillator connections. Synchronization arises at the network level from complex patterns of activity propagation, which are enhanced or disrupted by different stimuli. The findings may prove important to the design of novel neuromodulation treatments and techniques seeking to affect oscillatory activity in the brain.

Objective . Rhythmic brain stimulation has emerged as a powerful tool to modulate cognition and to target pathological oscillations related to neurological and psychiatric disorders. However, we lack a systematic understanding of how periodic stimulation interacts with endogenous neural activity as a function of the brain state and target. Approach . To address this critical issue, we applied periodic stimulation to a unified biophysical thalamic network model that generates multiple distinct oscillations, and examined thoroughly the impact of rhythmic stimulation on different oscillatory states. Main results . We found that rhythmic perturbation induces four basic response mechanisms: entrainment, acceleration, resonance and suppression. Importantly, the appearance and expression of these mechanisms depend highly on the intrinsic cellular dynamics in each state. Specifically, the low-threshold bursting of thalamocortical cells (TCs) in delta ( δ ) oscillation renders the network relatively insensitive to entrainment; the high-threshold bursting of TCs in alpha ( α ) oscillation leads to widespread oscillation suppression while the tonic spiking of TC cells in gamma ( γ ) oscillation results in prominent entrainment and resonance. In addition, we observed entrainment discontinuity during α oscillation that is mediated by firing pattern switching of high-threshold bursting TC cells. Furthermore, we demonstrate that direct excitatory stimulation of the lateral geniculate nucleus (LGN) entrains thalamic oscillations via an asymmetric Arnold tongue that favors higher frequency entrainment and resonance, while stimulation of the inhibitory circuit, the reticular nucleus, induces much weaker and more symmetric entrainment and resonance. These results support the notion that rhythmic stimulation engages brain oscillations in a state- and target-dependent manner. Significance . Overall, our study provides, for the first time, insights into how the biophysics of thalamic oscillations guide the emergence of complex, state-dependent mechanisms of target engagement, which can be leveraged for the future rational design of novel therapeutic stimulation modalities.

The incidence of cardiac arrhythmias is known to be associated with tissue heterogeneities including fibrosis. However, the impact of microscopic structural heterogeneities on conduction in excitable tissues remains poorly understood. In this study, we investigated how acellular microheterogeneities affect macroscopic conduction under conditions of normal and reduced excitability by utilizing a novel platform of paired in vitro and in silico studies to examine the mechanisms of conduction. Regular patterns of nonconductive micro-obstacles were created in confluent monolayers of the previously described engineered-excitable Ex293 cell line. Increasing the relative ratio of obstacle size to intra-obstacle strand width resulted in significant conduction slowing up to 23.6% and a significant increase in wavefront curvature anisotropy, a measure of spatial variation in wavefront shape. Changes in bulk electrical conductivity and in path tortuosity were insufficient to explain these observed macroscopic changes. Rather, microscale behaviors including local conduction slowing due to microscale branching, and conduction acceleration due to wavefront merging were shown to contribute to macroscopic phenomena. Conditions of reduced excitability led to further conduction slowing and a reversal of wavefront curvature anisotropy due to spatially non-uniform effects on microscopic slowing and acceleration. This unique experimental and computation platform provided critical mechanistic insights in the impact of microscopic heterogeneities on macroscopic conduction, pertinent to settings of fibrotic heart disease. It is well known that perturbations in the heart structure are associated with the initiation and maintenance of clinically significant cardiac arrhythmia. While previous studies have examined how single structural perturbations affect local electrical conduction, our understanding of how numerous microscopic heterogeneities act in aggregate to alter macroscopic electrical behavior is limited. In this study, we utilized simplified engineered excitable cells that contain the minimal machinery of excitability and can be directly computationally modeled. By pairing experimental and computational studies, we showed that the microscopic branching and collisions of electrical waves slow and speed conduction, respectively, resulting in macroscopic changes in the speed and pattern of electrical activation. These microscale behaviors are significantly altered under reduced excitability, resulting in exaggerated collision effects. Overall, this study helps improve our understanding of how microscopic structural heterogeneities in excitable tissue lead to abnormal action potential propagation, conducive to arrhythmias.

Objective . Neuromodulation of the central and peripheral nervous systems is becoming increasingly important for treating a diverse set of diseases—ranging from Parkinson’s Disease and epilepsy to chronic pain. However, neuromodulation of the gastrointestinal (GI) tract has achieved relatively limited success in treating functional GI disorders, which affect a significant population, because the effects of stimulation on the enteric nervous system (ENS) and gut motility are not well understood. Here we develop an integrated neuromechanical model of the ENS and assess neurostimulation strategies for enhancing gut motility, validated by in vivo experiments. Approach . The computational model included a network of enteric neurons, smooth muscle fibers, and interstitial cells of Cajal, which regulated propulsion of a virtual pellet in a model of gut motility. Main results . Simulated extracellular stimulation of ENS-mediated motility revealed that sinusoidal current at 0.5 Hz was more effective at increasing intrinsic peristalsis and reducing colon transit time than conventional higher frequency rectangular current pulses, as commonly used for neuromodulation therapy. Further analysis of the model revealed that the 0.5 Hz sinusoidal currents were more effective at modulating the pacemaker frequency of interstitial cells of Cajal. To test the predictions of the model, we conducted in vivo electrical stimulation of the distal colon while measuring bead propulsion in awake rats. Experimental results confirmed that 0.5 Hz sinusoidal currents were more effective than higher frequency pulses at enhancing gut motility. Significance . This work demonstrates an in silico GI neuromuscular model to enable GI neuromodulation parameter optimization and suggests that low frequency sinusoidal currents may improve the efficacy of GI pacing.

The thalamus plays a critical role in the genesis of thalamocortical oscillations, yet the underlying mechanisms remain elusive. To understand whether the isolated thalamus can generate multiple distinct oscillations, we developed a biophysical thalamic model to test the hypothesis that generation of and transition between distinct thalamic oscillations can be explained as a function of neuromodulation by acetylcholine (ACh) and norepinephrine (NE) and afferent synaptic excitation. Indeed, the model exhibited four distinct thalamic rhythms (delta, sleep spindle, alpha and gamma oscillations) that span the physiological states corresponding to different arousal levels from deep sleep to focused attention. Our simulation results indicate that generation of these distinct thalamic oscillations is a result of both intrinsic oscillatory cellular properties and specific network connectivity patterns. We then systematically varied the ACh/NE and input levels to generate a complete map of the different oscillatory states and their transitions. Lastly, we applied periodic stimulation to the thalamic network and found that entrainment of thalamic oscillations is highly state-dependent. Our results support the hypothesis that ACh/NE modulation and afferent excitation define thalamic oscillatory states and their response to brain stimulation. Our model proposes a broader and more central role of the thalamus in the genesis of multiple distinct thalamo-cortical rhythms than previously assumed. Computational modeling has served as an important tool to understand the cellular and circuit mechanisms of thalamocortical oscillations. However, most of the existing thalamic models focus on only one particular oscillatory pattern such as alpha or spindle oscillations. Thus, it remains unclear whether the same thalamic circuitry on its own could generate all major oscillatory patterns and if so what mechanisms underlie the transition among these distinct states. Here we present a unified model of the thalamus that is capable of independently generating multiple distinct oscillations corresponding to different physiological conditions. We then mapped out the different thalamic oscillations by varying the ACh/NE modulatory level and input level systematically. Our simulation results offer a mechanistic understanding of thalamic oscillations and support the long standing notion of a thalamic “pacemaker”. It also suggests that pathological oscillations associated with neurological and psychiatric disorders may stem from malfunction of the thalamic circuitry.

To understand how excitable tissues give rise to arrhythmias, it is crucially necessary to understand the electrical dynamics of cells in the context of their environment. Multicellular monolayer cultures have proven useful for investigating arrhythmias and other conduction anomalies, and because of their relatively simple structure, these constructs lend themselves to paired computational studies that often help elucidate mechanisms of the observed behavior. However, tissue cultures of cardiomyocyte monolayers currently require the use of neonatal cells with ionic properties that change rapidly during development and have thus been poorly characterized and modeled to date. Recently, Kirkton and Bursac demonstrated the ability to create biosynthetic excitable tissues from genetically engineered and immortalized HEK293 cells with well-characterized electrical properties and the ability to propagate action potentials. In this study, we developed and validated a computational model of these excitable HEK293 cells (called “Ex293” cells) using existing electrophysiological data and a genetic search algorithm. In order to reproduce not only the mean but also the variability of experimental observations, we examined what sources of variation were required in the computational model. Random cell-to-cell and inter-monolayer variation in both ionic conductances and tissue conductivity was necessary to explain the experimentally observed variability in action potential shape and macroscopic conduction, and the spatial organization of cell-to-cell conductance variation was found to not impact macroscopic behavior; the resulting model accurately reproduces both normal and drug-modified conduction behavior. The development of a computational Ex293 cell and tissue model provides a novel framework to perform paired computational-experimental studies to study normal and abnormal conduction in multidimensional excitable tissue, and the methodology of modeling variation can be applied to models of any excitable cell. One of the major challenges in trying to understand how arrhythmias can form in cardiac tissue is studying how the electrical activity of cardiac cells is affected by their surroundings. Current approaches have focused on studying cardiac cells in vitro and using computational models to elucidate the mechanisms behind experimental findings. However, tissue culture techniques are limited to working with neonatal, rather than adult, cells, and computational modeling of these cells has proven challenging. In this work, we have a developed a new approach for conducting paired experimental and computational studies by using a cell line engineered with the minimum machinery for excitability, and a computational model derived and validated directly from this cell line. In order to create a model that reproduces the diversity, rather than simply the average behavior, of experimental studies, we have incorporated a simple yet novel method of inherent variability, and explored what types of experimental variation must be incorporated into the model to recapitulate experimental findings. Using this new platform for paired experimental-computational studies with inherent variability, we will be able to study and better understand how changes in cardiac structure such as fibrosis and heterogeneity lead to conduction slowing, conduction failure, and arrhythmogenesis.