Reproducibility of results in biomedical research is an area of concern that should be paramount for all researchers. Importantly, this issue has been examined for experiments concerning cardiac electrophysiology. Specifically, multiple labs have found differences in results when comparing cardiac conduction velocity (CV) between healthy mice and mice that were heterozygous null for the gap junction (GJ) forming protein, Connexin 43. While the results of the comparison study showed differing extracellular ionic concentrations of the perfusates, specifically sodium, potassium, and calcium ([Na+]o, [K+]o, and [Ca2+]o), there was a lack of understanding why certain combinations of the aforementioned ions led to specific CV changes. However, more research from our lab indicates that these changes can predict modifications to a secondary form of cardiac coupling known as ephaptic coupling (EpC). Therefore the work in this dissertation was twofold, 1) to examine the effects of modulating EpC through perfusate ionic concentrations while also modulating GJC and 2) to investigate the effects of modulating all three of the main ions contributed with cardiac conduction (Na+, K+, Ca2+) and the interplay between them. Firstly I designed and tested changes from the use of 3D printed bath for optical mapping procedures. After verification that the bath did not modify electrophysiological or contrile parameters, I studied the effects of physiologic changes to EpC determinants ([Na+]o and [K+]o) on CV during various states of GJ inhibition using the non-specific GJ uncoupler carbenoxolone (CBX). Multiple pacing rates were used to further modify EpC, as an increased pacing rate leads to a decrease in sodium channel availability through modification of the resting membrane potential. with no to low (0 and 15 µM CBX) GJ inhibition, physiologic changes in [Na+]o and [K+]o did not affect CV, however increasing pacing rate decreased CV as expected. When CBX was increased to 30 µM, a combination of decreasing [Na+]o and increasing [K+]o significantly decreased cardiac CV, specifically when pacing rate was increased. Next, the combinatory effects of cations associated with EpC (Na+, K+, and Ca2+) were tested in to examine how cardiac CV reacts to changes in perfusate solution and how this may explain differences in experimental outcomes between laboratories. Briefly, experiments were run where [K+]o was varied throughout an experiment and the values for [Na+]o and [Ca2+]o were at one of two specific values during an experiment. 30 µM CBX was added to half of the experiments to see the changes in the CV-[K+]o relationship with GJ inhibition. With unaltered GJ coupling, elevated [Na+]o maintains CV during hyperkalemia. Interestingly, both [Na+]o and [Ca2+]o must be increased to maintain normal CV during hyperkalemia with reduced GJ coupling. These data suggest that optimized fluids can sustain normal conduction under pathophysiologic conditions like hyperkalemia and GJ uncoupling. Taken as a whole, this dissertation attempts to shed light on the importance of ionic concentration balance in perfusate solutions on cardiac conduction. / Ph. D.

Introduction: Excitability in cardiomyocytes is dependent on the subthreshold current required to raise transmembrane potential to the activation threshold and subsequent recruitment of voltage gated sodium channels to trigger an action potential. Conduction in cardiomyocytes is dependent on the robustness and speed of action potential propagating through tissue. Both are equally important for normal heart function and claim to be linear correlated (i.e if conduction decreases, excitability decreases) Cardiac sodium channels are densely expressed in the intercalated disc within the perinexus, which is two orders of magnitude narrower than bulk extracellular interstitium. The biphasic relationship between conduction and perinexus is well-researched and consistent between computations models. We hypothesized a biphasic relationship between Excitability and perinexal width (Wp). In addition, we hypothesize that the relationship between excitability and conduction is not linear but dependent on the original width of the perinexus. Methods/and Results: Ex vivo guinea pig hearts were epicardially paced and optically mapped to assess ventricular conduction and excitability. Strength-duration curves were constructed for pacing stimuli to measure rheobase (inversely correlated to excitability). Computation models incorporating ephaptic coupling and sodium channel localization to cleft widths between cardiomyocytes demonstrate these findings. Conclusion: Models and experiments reveal that the excitability and perinexus relationship is biphasic where narrowing and widening perinexus decreases conduction and excitability thus showing a linear relationship between excitability and conduction. However, the excitability and conduction become overly complex in the transition phase from release of self-attenuation to reduced self-activation. Therefore, targeting ephaptic coupling and monitoring plasma ions may be a novel strategy for increasing the efficacy and efficiency of cardiac pacemakers. / Doctor of Philosophy / The heart is a muscular organ that uses electrical impulses to function. The heart is made of cells called cardiomyocytes that allow for electricity to flow through the cells. They are connected via different junctions such as gap junctions, adherens, etc. Any loss of electrical coordination leads to irregular heartbeats which can lead to heart death. There are two ways to study electrical coordination, excitability, how easy is for the current to start in the tissue, and conduction, how easy can that current travel through the tissue. Since the 1900s researchers have stated that if excitability decreases conduction decreases. In other words, if you need more current to start the heart (excitability decreases) then that current will travel slower through the tissue (conduction decreases) thus increasing one chances of irregular heartbeats. However, the understanding of how conduction works has changed but not of excitability. For example, originally current was thought to travel through channels called gap junctions. If you have limited availability of gap junctions, current increases (aka excitability decreases) and conduction decreases. However, other species such as frogs, fishes have limited number of gap junctions and can survive. Therefore, a new mechanism was proposed called ephaptic coupling. There is space next to the gap junctions called perinexus which is rich in a channel called Na channels, which is the main driving force for excitability and conduction. The lab has shown that if you change that space between cells, you can change the conduction response. In other words, if you decrease the space between the cells, conduction will not change therefore reducing the chances of irregular heartbeats. Therefore, my project is to understand if by changing this space between cells, is excitability and conductions are still correlates of each other. Using mathematical and animal models, this dissertation shows excitability and conduction have a very complicated relationship.

Sudden cardiac death occurs due to aberrations in the multifactorial process that is cardiac conduction. Conduction velocity (CV) and its modulation by several determinants, like cellular excitability, tissue structure and electrical coupling by gap junctions (GJ), have been extensively studied. However, there are several discrepancies in cardiac electrophysiology research that have extended over decades, suggesting elements that are still not completely understood about this complex phenomenon. This dissertation will focus on one such mechanism, ephaptic coupling (EpC). The purpose of this work is twofold, 1) to identify ionic determinants of EpC, and its interactions with gap junctional coupling (GJC) and, 2) to investigate the possible role of serum ion modulation in cardiac arrhythmia therapy. First, the effects of altering extracellular ion concentration – sodium, potassium and calcium at varying GJ protein expression were studied. Briefly, reducing sodium was related to CV slowing under conditions of reduced EpC (wide intercalated disc nanodomains – perinexi) and GJC (reduced GJ protein – Connexin43). On the other hand, increasing potassium slowed CV in hearts with wide perinexi independent of GJC. Elevating calcium, reduced perinexal width and was associated with fast CV during physiologic sodium concentration. However, under conditions associated with disease, like hyponatremia, elevating calcium still reduced perinexal width but slowed CV. These findings are the first to suggest that ionic modulators of EpC could modulate CV during health and disease. Next, the potential of perfusate ion modulation in cardiac arrhythmia therapy was investigated. Briefly, in a model of myocardial inflammation, TNFα, a pro-inflammatory cytokine, slowed CV relative to control conditions and this was associated with widening of the perinexus (reduced EpC). Increasing extracellular calcium restored CV to control values by improving not only EpC but also GJC. Finally, in a model of metabolic ischemia in the heart, CV response due to solutions with varying sodium and calcium concentrations were tested. The solutions that were associated with wider perinexi and elevated sodium performed best during ischemia by attenuating CV slowing, reducing arrhythmias and increasing time to asystole. Taken together, these findings provide evidence for the possibility of ionic determinants of EpC in cardiac arrhythmia therapy. / Ph. D.

In this dissertation, we investigate coupling between axons in a tract, when the tract has an arbitrary cross-section, with the coupling being mediated by currents as well as electric fields. Under the current mediated setting, we develop a new master equation which captures the relative axonal geometry, specifically, the axon inclinations θi and the inter-axon distances Wip and perform a number of simulations. We observe synchronization in our simulations of axons with differing diameters and separation-dependent coupling delays in the case of non-trivial tract geometries. For the field-mediated interaction setting, we determine the electric near-field of a firing axon’s node of Ranvier - its strength and direction - by a volume conduction approach as well as a more microscopic, dipole-based approach. We obtain field strengths of about 105V/m at a few hundred micron distance from the source at the node. With the field levels having been found significant enough to cause 100 mV voltage drops across 1 micron-diameter axons, we develop an alternate, field-mediated model for synchronization between axons based on the dipole fields generated during action potential propagation. This model shows that synchronization between action potentials on differing axons depends on the phases of the synchronizing action potentials and not merely their separation. Since synchronization takes place in both settings, but currents are generated by fields, when constrained to a specific direction, we find that the field picture is a generalization of the presently prevalent current mediated picture for interaction between axons.

An agent based model (ABM) is a computational model with ``agents'' that interact with each other in an ``environment.'' This paper analyzes a particular ABM simulating individual ions in cardiac tissue, with the goal of modelling the strength and consistency of the electrical signals needed for a healthy heartbeat. We build several frameworks based on work by M. A. Yereniuk and S. D. Olson to demonstrate robustness of the original model. We conclude a moderate level of robustness using those frameworks, through a combination of proofs and empirical evidence.

Despite decades of research and thousands of studies on cardiac electrophysiology, cardiovascular disease remains among the leading causes of death in the United States today. Despite substantially beneficial advances, we have largely shifted cardiovascular disease from an acute to a chronic issue. It is therefore clear that our current understanding of the heart's functions remain inadequate and we must search for untapped therapeutic approaches to eliminate these deadly and costly ailments once and for all. This thesis will focus on the electrophysiology of the heart, specifically the mechanisms of cell-to-cell conduction. Canonically, the understood mechanism of cardiac conduction is through gap junctions (GJ) following a cable-like conduction model. While both experimentally and mathematically, this understanding of conduction has explained cardiac electrical behavior, it is also incomplete, as evidenced by recent conflicting modeling and experimental data. The overall goal of this thesis is to explore a structure modulating an ephaptic, or electric field, cellular coupling mechanism: the GJ-adjacent perinexus, with three specific aims. First, I identified the perinexus – a recently-established structure in rodent myocardium – in human atrial tissue. I also observed a significant tendency for open-heart surgery patients with pre-operative atrial fibrillation to have wider perinexi, indicating a possibly targetable mechanism of atrial fibrillation, one of the costliest, and most poorly-understood cardiac diseases. Next, I developed a high-throughput, high-resolution method for quantifying the perinexus. Finally, I sought to reconcile a major controversy in the field: whether cardiac edema could either be beneficial or harmful to cardiac conduction. Using a Langendorff perfusion model, I added osmotic agents of various sizes to guinea pig hearts and measured electrical and structural parameters. My findings suggest that while cardiac conduction is multifaceted and influenced by several parameters, the strongest correlation is an inverse relationship between conduction velocity and the width of the perinexus. This study is the first to osmotically expand and narrow the perinexus and show an inverse correlation with conduction. Importantly, my conduction data cannot be explained by factors consistent with a cable-like conduction mechanism, indicating once again that the perinexus could be a therapeutic target for a myriad of cardiac conduction diseases. / Doctor of Philosophy / The ways by which cells in the heart communicate have been studied extensively and are thought to be well-understood. However, despite decades of research, cardiovascular disease is a major problem in the developed world today and we remain unable to develop treatments to truly cure many major cardiac diseases. Because of this lack of clinical success in preventing or treating conditions such as atrial fibrillation, Brugada syndrome and sudden cardiac death, all of which are associated with disruptions in the heart’s electrical communication systems, I have sought to better understand the ways by which cellular communication is achieved. Currently, we think of cardiac tissue to propagate electrical signals as if it was a series of cables, just like the electrical wires over our streets and in our homes. However, we have seen experimental evidence, along with computer simulations, that supports the idea of a second mechanism of cellular electrical conduction. This second mechanism is called ephaptic, or electric field, coupling and relies on changes in charges inside and outside the cell to trigger the action potential – the electrical signal which tells the cell to contract. In order for ephaptic coupling to occur, two main conditions must be met. First, there must be a suitably-sized cleft, or ephapse, between adjacent cells. Models have estimated this space to be between 10-100 nm wide. Second, there must be a large concentration of sodium channels, as sodium ions are primarily used to set off the action potential. The region in which I am most interested is the cardiac perinexus, which is the space immediately adjacent to plaques of connexin proteins which link adjacent cells. The perinexus is both of an appropriate size (we’ve measured it between 10 and 25 nm on average) and rich in sodium channels, making it an ideal candidate to be a cardiac ephapse. In recent years, our lab has shown experimentally that expanding this space can disrupt cardiac conduction and my first study showed that clinically, patients with chronic atrial fibrillation (a-fib) prior to open-heart surgery have wider perinexi than patients without chronic a-fib. No one, however, has been able to demonstrate that narrowing the perinexus would be therapeutic by making it easier for cells to communicate via this ephaptic mechanism. Knowing I would need a better method for measuring the width of huge numbers of perinexi, I then developed a faster, more precise measurement program. Finally, I perfused several osmotic agents – substances which would theoretically draw fluid into or out of various compartments of cardiac tissue – into guinea pig hearts and observed changes to both their electrical behavior and tissue structure. Using my new perinexal measurement program, I found that changing the perinexus was the only factor that could explain the conduction changes I observed with each osmotic agent and that parameters associated with cable theory, such as gap junctional protein expression or interstitial resistance, could not explain conduction changes. Therefore, I have indicated, along with my clinical study, that the cardiac perinexus could be a therapeutic target for preventing, managing, or possibly even curing cardiac conduction diseases.

No description available.

<p>Non-invasive electromagnetic brain stimulation uses electrodes and/or coils to modulate brain activity via the induced E-fields. E-field dosimetry solvers have improved non-invasive electromagnetic brain stimulation protocol and our understanding of neuroscience. However, E-field dosimetry techniques are incomplete in that the contributions of non-linear neuron activity are left unaccounted for. To better understand the neurological effects of non-invasive electromagnetic stimulation, we introduce an integral equation formulation for modeling the non-linear behavior of neurons due to an incident E-field generated by electrode and coil sources. We formulate the new integral equation using a boundary element approach. We compare the boundary element solver accuracy with an established finite element solver and multi-scale cable equation approaches. Unlike previous approaches, this new boundary integral formulation avoids multi-scaling challenges from meshing while retaining the accuracy and the robust spatial support of integral equation-based methods. The memory savings from switching to surface meshes makes simulations with more complex morphologies computationally tractable. Additionally, we examine the ability of neurons to couple to one another via the local extracellular fields. Examples of simulations with both transcranial electric and magnetic stimulation results for simple geometries are used to illustrate the capabilities of a boundary integral approach. This boundary integral method will aid the development of better neurological understanding, delineate the mechanisms by which electromagnetic stimulation engenders neuronal activity, and aid in modeling local E-field coupling.</p>

Sudden cardiac death is largely attributable to sudden onset ventricular arrhythmias. Alterations in cardiac conduction, particularly the slowing of conduction velocity is one major factor in arrhythmogenesis. By understanding the mechanisms and factors that modulate cardiac conduction velocity, we can assess and perhaps mitigate the risk of arrhythmia in patients for whom slowed conduction is a arrhythmogenic substrate. Cardiac conduction has traditionally been described by cable theory, which predicts an inverse relationship between extracellular resistance and conduction velocity (CV). However, in studies that reduce extracellular resistance by inducing interstitial edema, there are conflicting results, with some labs showing increased CV when edema is induced with one agent, and others showing reduced CV when edema is induced with a different agent. In the first part of this dissertation, we present experimental data in support of ephaptic coupling (EpC), a theorized mechanism of conduction that resolves these apparent contradictions. In the later part of this dissertation, we address how changes in sodium concentration can alter conduction, despite conventional wisdom suggesting that it should not. We show that when sodium channels are impaired, such as by genetic mutation or pharmacologic blockade, that conduction is sensitized to changes in sodium concentrations that would not otherwise induce changes in CV. We go on to explore the mechanisms that modulate this sensitivity and present data that show it is a function of both EpC and outward potassium currents. Taken together, these data expand our understanding of the mechanics behind cardiac conduction and demonstrate that EpC has a clinically relevant impact on conduction and represents a new pathway to explore in regard to the treatment and management of arrhythmogenic and conduction disorders. / Doctor of Philosophy / In all large animals, life is sustained by the regular coordinated beating of the heart to pump blood throughout the body. Throughout this continuous activity, and even with minute-to-minute changes in heart rate, this electrically driven activity continues without major disruption. Until it doesn't. Major arrhythmias can occur suddenly, and without warning. Over the last century, we have begun to understand some of the reasons why heart, even an injured one, will work normally for hundreds of thousands of beats, and on the next fall into a life-threatening new pattern, and one of the most important of these reasons is the speed of conduction: the spread of electrical activation throughout the heart tissue. Understanding the mechanisms of conduction provides a way to assess and mitigate the risk of arrhythmias and may open up new avenues for treatment and prevention. This dissertation presents evidence for a previously theoretical mechanism of conduction called ephaptic coupling. We show that this electric field mediated form of conduction can be modulated with clinically used osmotic agents, and that it has a physiologically relevant impact on conduction. We also show that hyponatremia (i.e. low sodium), a condition that is traditionally thought to have minimal impact on cardiac conduction, because a significant modulator of conduction when sodium channel functions are impaired. As a great many drugs block sodium channels, this sensitization to hyponatremia and the factors that mediate it are underappreciated concerns that are relevant to a wide array of patients. The new findings presented in this dissertation advance our collective understanding of the mechanisms of cardiac conduction and provide evidence for new avenues of exploration in the prevention and management of arrhythmias and conduction disorders.

abstract: A general continuum model for simulating the flow of ions in the salt baths that surround and fill excitable neurons is developed and presented. The ion densities and electric potential are computed using the drift-diffusion equations. In addition, a detailed model is given for handling the electrical dynamics on interior membrane boundaries, including a model for ion channels in the membranes that facilitate the transfer of ions in and out of cells. The model is applied to the triad synapse found in the outer plexiform layer of the retina in most species. Experimental evidence suggests the existence of a negative feedback pathway between horizontal cells and cone photoreceptors that modulates the flow of calcium ions into the synaptic terminals of cones. However, the underlying mechanism for this feedback is controversial and there are currently three competing hypotheses: the ephaptic hypothesis, the pH hypothesis and the GABA hypothesis. The goal of this work is to test some features of the ephaptic hypothesis using detailed simulations that employ rigorous numerical methods. The model is first applied in a simple rectangular geometry to demonstrate the effects of feedback for different extracellular gap widths. The model is then applied to a more complex and realistic geometry to demonstrate the existence of strictly electrical feedback, as predicted by the ephaptic hypothesis. Lastly, the effects of electrical feedback in regards to the behavior of the bipolar cell membrane potential is explored. Figures for the ion densities and electric potential are presented to verify key features of the model. The computed steady state IV curves for several cases are presented, which can be compared to experimental data. The results provide convincing evidence in favor of the ephaptic hypothesis since the existence of feedback that is strictly electrical in nature is shown, without any dependence on pH effects or chemical transmitters. / Dissertation/Thesis / Ph.D. Applied Mathematics 2013