Prokaryotic voltage-gated sodium channels are more effective than endogenous Nav1.5 channels in rescuing cardiac action potential conduction: an in silico study.

Methods to augment Na+ current in cardiomyocytes hold potential for the treatment of various cardiac arrhythmias involving conduction slowing. Because the gene coding cardiac Na+ channel (Nav1.5) is too large to fit in a single adeno-associated virus (AAV) vector, new gene therapies are being developed to enhance endogenous Nav1.5 current (by overexpression of chaperon molecules or use of multiple AAV vectors) or to exogenously introduce prokaryotic voltage-gated Na+ channels (BacNav) whose gene size is significantly smaller than that of the Nav1.5. In this study, based on experimental measurements in heterologous expression systems, we developed an improved computational model of the BacNav channel, NavSheP D60A. We then compared in silico how NavSheP D60A expression vs. Nav1.5 augmentation affects the electrophysiology of cardiac tissue. We found that the incorporation of BacNav channels in both adult guinea pig and human cardiomyocyte models increased their excitability and reduced action potential duration. When compared with equivalent augmentation of Nav1.5 current in simulated settings of reduced tissue excitability, the addition of the BacNav current was superior in improving the safety of conduction under conditions of current source-load mismatch, reducing the vulnerability to unidirectional conduction block during premature pacing, preventing the instability and breakup of spiral waves, and normalizing the conduction and ECG in Brugada syndrome tissues with mutated Nav1.5. Overall, our studies show that compared with a potential enhancement of the endogenous Nav1.5 current, expression of the BacNav channels with their slower inactivation kinetics can provide greater anti-arrhythmic benefits in hearts with compromised action potential conduction.NEW & NOTEWORTHY Slow action potential conduction is a common cause of various cardiac arrhythmias; yet, current pharmacotherapies cannot augment cardiac conduction. This in silico study compared the efficacy of recently proposed antiarrhythmic gene therapy approaches that increase peak sodium current in cardiomyocytes. When compared with the augmentation of endogenous sodium current, expression of slower-inactivating bacterial sodium channels was superior in preventing conduction block and arrhythmia induction. These results further the promise of antiarrhythmic gene therapies targeting sodium channels.

Excitation properties of computational models of unmyelinated peripheral axons.

Biophysically based computational models of nerve fibers are important tools for designing electrical stimulation therapies, investigating drugs that affect ion channels, and studying diseases that affect neurons. Although peripheral nerves are primarily composed of unmyelinated axons (i.e., C-fibers), most modeling efforts focused on myelinated axons. We implemented the single-compartment model of vagal afferents from Schild et al. (1994) (Schild JH, Clark JW, Hay M, Mendelowitz D, Andresen MC, Kunze DL. J Neurophysiol 71: 2338-2358, 1994) and extended the model into a multicompartment axon, presenting the first cable model of a C-fiber vagal afferent. We also implemented the updated parameters from the Schild and Kunze (1997) model (Schild JH, Kunze DL. J Neurophysiol 78: 3198-3209, 1997). We compared the responses of these novel models with those of three published models of unmyelinated axons (Rattay F, Aberham M. IEEE Trans Biomed Eng 40: 1201-1209, 1993; Sundt D, Gamper N, Jaffe DB. J Neurophysiol 114: 3140-3153, 2015; Tigerholm J, Petersson ME, Obreja O, Lampert A, Carr R, Schmelz M, Fransén E. J Neurophysiol 111: 1721-1735, 2014) and with experimental data from single-fiber recordings. Comparing the two models by Schild et al. (1994, 1997) revealed that differences in rest potential and action potential shape were driven by changes in maximum conductances rather than changes in sodium channel dynamics. Comparing the five model axons, the conduction speeds and strength-duration responses were largely within expected ranges, but none of the models captured the experimental threshold recovery cycle-including a complete absence of late subnormality in the models-and their action potential shapes varied dramatically. The Tigerholm et al. (2014) model best reproduced the experimental data, but these modeling efforts make clear that additional data are needed to parameterize and validate future models of autonomic C-fibers.NEW & NOTEWORTHY 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.

Modeling the effects of sinusoidal stimulation and synaptic plasticity on linked neural oscillators.

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.

Microheterogeneity-induced conduction slowing and wavefront collisions govern macroscopic conduction behavior: A computational and experimental study.

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.

Unified thalamic model generates multiple distinct oscillations with state-dependent entrainment by stimulation.

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.

Modeling an Excitable Biosynthetic Tissue with Inherent Variability for Paired Computational-Experimental Studies.

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.

Modeling dynamics in diseased cardiac tissue: Impact of model choice.

Cardiac arrhythmias have been traditionally simulated using continuous models that assume tissue homogeneity and use a relatively large spatial discretization. However, it is believed that the tissue fibrosis and collagen deposition, which occur on a micron-level, are critical factors in arrhythmogenesis in diseased tissues. Consequently, it remains unclear how well continuous models, which use averaged electrical properties, are able to accurately capture complex conduction behaviors such as re-entry in fibrotic tissues. The objective of this study was to compare re-entrant behavior in discrete microstructural models of fibrosis and in two types of equivalent continuous models, a homogenous continuous model and a hybrid continuous model with distinct heterogeneities. In the discrete model, increasing levels of tissue fibrosis lead to a substantial increase in the re-entrant cycle length which is inadequately reflected in the homogenous continuous models. These cycle length increases appear to be primarily due to increases in the tip path length and to altered restitution behavior, and suggest that it is critical to consider the discrete effects of fibrosis on conduction when studying arrhythmogenesis in fibrotic myocardium. Hybrid models are able to accurately capture some aspects of re-entry and, if carefully tuned, may provide a framework for simulating conduction in diseased tissues with both accuracy and efficiency.

A microstructural model of reentry arising from focal breakthrough at sites of source-load mismatch in a central region of slow conduction.

Regions of cardiac tissue that have a combination of focal activity and poor, heterogeneous gap junction coupling are often considered to be arrhythmogenic; however, the relationship between the properties of the cardiac microstructure and patterns of abnormal propagation is not well understood. The objective of this study was to investigate the effect of microstructure on the initiation of reentry from focal stimulation inside a poorly coupled region embedded in more well-coupled tissue. Two-dimensional discrete computer models of ventricular monolayers (1 × 1 cm) were randomly generated to represent heterogeneity in the cardiac microstructure. A small, central poorly coupled patch (0.40 × 0.40 cm) was introduced to represent the site of focal activity. Simulated unipolar electrogram recordings were computed at various points in the tissue. As the gap conductance of the patch decreased, conduction slowed and became increasingly complex, marked by fractionated electrograms with reduced amplitude. Near the limit of conduction block, isolated breakthrough sites occurred at single cells along the patch boundary and were marked by long cell-to-cell delays and negative deflections on electrogram recordings. The strongest determinant of the site of wavefront breakthrough was the connectivity of the brick wall architecture, which enabled current flow through small regions of overlapping cells to drive propagation into the well-coupled zone. In conclusion, breakthroughs at the size scale of a single cell can occur at the boundary of source-load mismatch allowing focal activations from slow conducting regions to produce reentry. These breakthrough regions, identifiable by distinct asymmetric, reduced amplitude electrograms, are sensitive to tissue architecture and may be targets for ablation.

Microscopic variations in interstitial and intracellular structure modulate the distribution of conduction delays and block in cardiac tissue with source-load mismatch.

AIMS: Reentrant activity in the heart is often correlated with heterogeneity in both the intracellular structure and the interstitial structure surrounding cells; however, the combined effect of cardiac microstructure and interstitial resistivity in regions of source-load mismatch is largely unknown. The aim of this study was to investigate how microstructural variations in cell arrangement and increased interstitial resistivity influence the spatial distribution of conduction delays and block in poorly coupled regions of tissue. METHODS AND RESULTS: Two-dimensional 0.6 cm × 0.6 cm computer models with idealized and realistic cellular structure were used to represent a monolayer of ventricular myocytes. Gap junction connections were distributed around the periphery of each cell at 10 µm intervals. Regions of source-load mismatch were added to the models by increasing the gap junction and interstitial resistivity in one-half of the tissue. Heterogeneity in cell shape and cell arrangement along the boundary between well-coupled and poorly coupled tissue increased variability in longitudinal conduction delays to as much as 10 ms before the onset of conduction block, resulting in wavefront breakthroughs with pronounced curvature at distinct points along the boundary. Increasing the effective interstitial resistivity reduced source-load mismatch at the transition boundary, which caused a decrease in longitudinal conduction delay and an increase in the number of wavefront breakthroughs. CONCLUSION: Microstructural variations in cardiac tissue facilitate the formation of isolated sites of wavefront breakthrough that may enable abnormal electrical activity in small regions of diseased tissue to develop into more widespread reentrant activity.

Rule-based definition of muscle bundles in patient-specific models of the left atrium.

Atrial fibrillation (AF) is the most common arrhythmia encountered clinically, and as the population ages, its prevalence is increasing. Although the CHA2DS2- VASc score is the most used risk-stratification system for stroke risk in AF, it lacks personalization. Patient-specific computer models of the atria can facilitate personalized risk assessment and treatment planning. However, a challenge faced in creating such models is the complexity of the atrial muscle arrangement and its influence on the atrial fiber architecture. This work proposes a semi-automated rule-based algorithm to generate the local fiber orientation in the left atrium (LA). We use the solutions of several harmonic equations to decompose the LA anatomy into subregions. Solution gradients define a two-layer fiber field in each subregion. The robustness of our approach is demonstrated by recreating the fiber orientation on nine models of the LA obtained from AF patients who underwent WATCHMAN device implantation. This cohort of patients encompasses a variety of morphology variants of the left atrium, both in terms of the left atrial appendages (LAAs) and the number of pulmonary veins (PVs). We test the fiber construction algorithm by performing electrophysiology (EP) simulations. Furthermore, this study is the first to compare its results with other rule-based algorithms for the LA fiber architecture definition available in the literature. This analysis suggests that a multi-layer fiber architecture is important to capture complex electrical activation patterns. A notable advantage of our approach is the ability to reconstruct the main LA fiber bundles in a variety of morphologies while solving for a small number of harmonic fields, leading to a comparatively straightforward and reproducible approach.

A computer model of engineered cardiac monolayers.

Engineered monolayers created using microabrasion and micropatterning methods have provided a simplified in vitro system to study the effects of anisotropy and fiber direction on electrical propagation. Interpreting the behavior in these culture systems has often been performed using classical computer models with continuous properties. However, such models do not account for the effects of random cell shapes, cell orientations, and cleft spaces inherent in these monolayers on the resulting wavefront conduction. This work presents a novel methodology for modeling a monolayer of cardiac tissue in which the factors governing cell shape, cell-to-cell coupling, and degree of cleft space are not constant but rather are treated as spatially random with assigned distributions. This modeling approach makes it possible to simulate wavefront propagation in a manner analogous to performing experiments on engineered monolayer tissues. Simulated results are compared to previously published measured data from monolayers used to investigate the role of cellular architecture on conduction velocities and anisotropy ratios. We also present an estimate for obtaining the electrical properties from these networks and demonstrate how variations in the discrete cellular architecture affect the macroscopic conductivities. The simulations support the common assumption that under normal ranges of coupling strength, tissues with relatively uniform distributions of cell shapes and connectivity can be represented using continuous models with conductivities derived from random discrete cellular architecture using either global or local estimates. The results also reveal that in the presence of abrupt changes in cell orientation, local estimates of tissue properties predict smoother changes in conductivity that may not adequately predict the discrete nature of propagation at the transition sites.

Collision-based spiral acceleration in cardiac media: roles of wavefront curvature and excitable gap.

We have previously shown in experimental cardiac cell monolayers that rapid point pacing can convert basic functional reentry (single spiral) into a stable multiwave spiral that activates the tissue at an accelerated rate. Here, our goal is to further elucidate the biophysical mechanisms of this rate acceleration without the potential confounding effects of microscopic tissue heterogeneities inherent to experimental preparations. We use computer simulations to show that, similar to experimental observations, single spirals can be converted by point stimuli into stable multiwave spirals. In multiwave spirals, individual waves collide, yielding regions with negative wavefront curvature. When a sufficient excitable gap is present and the negative-curvature regions are close to spiral tips, an electrotonic spread of excitatory currents from these regions propels each colliding spiral to rotate faster than the single spiral, causing an overall rate acceleration. As observed experimentally, the degree of rate acceleration increases with the number of colliding spiral waves. Conversely, if collision sites are far from spiral tips, excitatory currents have no effect on spiral rotation and multiple spirals rotate independently, without rate acceleration. Understanding the mechanisms of spiral rate acceleration may yield new strategies for preventing the transition from monomorphic tachycardia to polymorphic tachycardia and fibrillation.

Increased interstitial loading reduces the effect of microstructural variations in cardiac tissue.

Electrical propagation in diseased and aging hearts is strongly influenced by structural changes that occur in both the intracellular and interstitial spaces of cardiac tissue; however, very few studies have investigated how interactions between the two spaces affect propagation at the microscale. In this study, we used one-dimensional microstructural computer models of interconnected ventricular myocytes to systematically investigate how increasing the effective interstitial resistivity (rho(oeff)) influences action potential propagation in fibers with variations in intracellular properties such as cell coupling and cell length. Changes in rho(oeff) were incorporated into a monodomain model using a correction to the intracellular properties that was based on bidomain simulations. The results showed that increasing rho(oeff) in poorly coupled one-dimensional fibers alters the distribution of electrical load at the microscale and causes propagation to become more continuous. In the poorly coupled fiber, this continuous state is characterized by decreased gap junction delay, sustained conduction velocity, increased sodium current, reduced maximum upstroke velocity, and increased safety factor. Long, poorly coupled cells experience greater loading effects than short cells and show the greatest initial response to changes in rho(oeff). In inhomogeneous fibers with adjacent well-coupled and poorly coupled regions, increasing rho(oeff) in the poorly coupled region also reduces source-load mismatch, which delays the onset of conduction block and reduces the dispersion of repolarization at the transition between the two regions. Increasing the rho(oeff) minimizes the effect of cell-to-cell variations and may influence the pattern of activation in critical regimes characterized by low intercellular coupling, microstructural heterogeneity, and reduced or abnormal membrane excitability.

Composite Backward Differentiation Formula for the Bidomain Equations.

The bidomain equations have been widely used to model the electrical activity of cardiac tissue. While it is well-known that implicit methods have much better stability than explicit methods, implicit methods usually require the solution of a very large nonlinear system of equations at each timestep which is computationally prohibitive. In this work, we present two fully implicit time integration methods for the bidomain equations: the backward Euler method and a second-order one-step two-stage composite backward differentiation formula (CBDF2) which is an L-stable time integration method. Using the backward Euler method as fundamental building blocks, the CBDF2 scheme is easily implementable. After solving the nonlinear system resulting from application of the above two fully implicit schemes by a nonlinear elimination method, the obtained nonlinear global system has a much smaller size, whose Jacobian is symmetric and possibly positive definite. Thus, the residual equation of the approximate Newton approach for the global system can be efficiently solved by standard optimal solvers. As an alternative, we point out that the above two implicit methods combined with operator splittings can also efficiently solve the bidomain equations. Numerical results show that the CBDF2 scheme is an efficient time integration method while achieving high stability and accuracy.

A binary method for simple and accurate two-dimensional cursor control from EEG with minimal subject training.

BACKGROUND: Brain-computer interfaces (BCI) use electroencephalography (EEG) to interpret user intention and control an output device accordingly. We describe a novel BCI method to use a signal from five EEG channels (comprising one primary channel with four additional channels used to calculate its Laplacian derivation) to provide two-dimensional (2-D) control of a cursor on a computer screen, with simple threshold-based binary classification of band power readings taken over pre-defined time windows during subject hand movement. METHODS: We tested the paradigm with four healthy subjects, none of whom had prior BCI experience. Each subject played a game wherein he or she attempted to move a cursor to a target within a grid while avoiding a trap. We also present supplementary results including one healthy subject using motor imagery, one primary lateral sclerosis (PLS) patient, and one healthy subject using a single EEG channel without Laplacian derivation. RESULTS: For the four healthy subjects using real hand movement, the system provided accurate cursor control with little or no required user training. The average accuracy of the cursor movement was 86.1% (SD 9.8%), which is significantly better than chance (p = 0.0015). The best subject achieved a control accuracy of 96%, with only one incorrect bit classification out of 47. The supplementary results showed that control can be achieved under the respective experimental conditions, but with reduced accuracy. CONCLUSION: The binary method provides naïve subjects with real-time control of a cursor in 2-D using dichotomous classification of synchronous EEG band power readings from a small number of channels during hand movement. The primary strengths of our method are simplicity of hardware and software, and high accuracy when used by untrained subjects.

Rhythmic modulation of thalamic oscillations depends on intrinsic cellular dynamics.

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.

Effect of nonuniform interstitial space properties on impulse propagation: a discrete multidomain model.

This work presents a discrete multidomain model that describes ionic diffusion pathways between connected cells and within the interstitium. Unlike classical models of impulse propagation, the intracellular and extracellular spaces are represented as spatially distinct volumes with dynamic/static boundary conditions that electrically couple neighboring spaces. The model is used to investigate the impact of nonuniform geometrical and electrical properties of the interstitial space surrounding a fiber on conduction velocity and action potential waveshape. Comparison of the multidomain and bidomain models shows that although the conduction velocity is relatively insensitive to cases that confine 50% of the membrane surface by narrow extracellular depths (> or =2 nm), the action potential morphology varies greatly around the fiber perimeter, resulting in changes in the magnitude of extracellular potential in the tight spaces. Results also show that when the conductivity of the tight spaces is sufficiently reduced, the membrane adjacent to the tight space is eliminated from participating in propagation, and the conduction velocity increases. Owing to its ability to describe the spatial discontinuity of cardiac microstructure, the discrete multidomain can be used to determine appropriate tissue properties for use in classical macroscopic models such as the bidomain during normal and pathophysiological conditions.

Muscle Thickness and Curvature Influence Atrial Conduction Velocities.

Electroanatomical mapping is currently used to provide clinicians with information about the electrophysiological state of the heart and to guide interventions like ablation. These maps can be used to identify ectopic triggers of an arrhythmia such as atrial fibrillation (AF) or changes in the conduction velocity (CV) that have been associated with poor cell to cell coupling or fibrosis. Unfortunately, many factors are known to affect CV, including membrane excitability, pacing rate, wavefront curvature, and bath loading, making interpretation challenging. In this work, we show how endocardial conduction velocities are also affected by the geometrical factors of muscle thickness and wall curvature. Using an idealized three-dimensional strand, we show that transverse conductivities and boundary conditions can slow down or speed up signal propagation, depending on the curvature of the muscle tissue. In fact, a planar wavefront that is parallel to a straight line normal to the mid-surface does not remain normal to the mid-surface in a curved domain. We further demonstrate that the conclusions drawn from the idealized test case can be used to explain spatial changes in conduction velocities in a patient-specific reconstruction of the left atrial posterior wall. The simulations suggest that the widespread assumption of treating atrial muscle as a two-dimensional manifold for electrophysiological simulations will not accurately represent the endocardial conduction velocities in regions of the heart thicker than 0.5 mm with significant wall curvature.

Learning to control a brain-machine interface for reaching and grasping by primates.

Reaching and grasping in primates depend on the coordination of neural activity in large frontoparietal ensembles. Here we demonstrate that primates can learn to reach and grasp virtual objects by controlling a robot arm through a closed-loop brain-machine interface (BMIc) that uses multiple mathematical models to extract several motor parameters (i.e., hand position, velocity, gripping force, and the EMGs of multiple arm muscles) from the electrical activity of frontoparietal neuronal ensembles. As single neurons typically contribute to the encoding of several motor parameters, we observed that high BMIc accuracy required recording from large neuronal ensembles. Continuous BMIc operation by monkeys led to significant improvements in both model predictions and behavioral performance. Using visual feedback, monkeys succeeded in producing robot reach-and-grasp movements even when their arms did not move. Learning to operate the BMIc was paralleled by functional reorganization in multiple cortical areas, suggesting that the dynamic properties of the BMIc were incorporated into motor and sensory cortical representations.