Dissertations / Theses on the topic 'Electrophysiology - Mathematical models'

Proper heart function results from the periodic execution of a series of coordinated interdependent mechanical, chemical, and electrical processes within the cardiac tissue. Central to these processes is the action potential - the electrochemical event that initiates contraction of the individual cardiac myocytes. Many models of the cardiac action potential exist with varying levels of complexity, but none account for the electrophysiological role played by caveolae - small invaginations of the cardiac cell plasma membrane. Recent electrophysiological studies regarding these microdomains reveal that cardiac caveolae function as reservoirs of 'recruitable' sodium ion channels. As such, caveolar channels constitute a substantial and previously unrecognized source of sodium current that can significantly influence action potential morphology. In this thesis, I formulate and analyze new models of cardiac action potential which account for these caveolar sodium currents and provide a computational venue in which to develop and test new hypotheses. My results provide insight into the role played by caveolar ionic currents in regulating the electrodynamics of cardiac myocytes and suggest that in certain pathological cases, caveolae may play an arrhythmogenic role.

The mechanical action of the heart is made possible in response to electrical events that involve the cardiac cells, a property that classifies the heart tissue between the excitable tissues. At the cellular level, the electrical event is the signal that triggers the mechanical contraction, inducing a transient increase in intracellular calcium which, in turn, carries the message of contraction to the contractile proteins of the cell. The primary goal of my project was to implement in CUDA (Compute Unified Device Architecture, an hardware architecture for parallel processing created by NVIDIA) a tissue model of the rabbit sinoatrial node to evaluate the heterogeneity of its structure and how that variability influences the behavior of the cells. In particular, each cell has an intrinsic discharge frequency, thus different from that of every other cell of the tissue and it is interesting to study the process of synchronization of the cells and look at the value of the last discharge frequency if they synchronized.

Thesis (M.S.)--Georgia State University, 2009.<br>Title from title page (Digital Archive@GSU, viewed July 20, 2010) Andrey Shilnikov, Robert Clewley, Gennady Cymbalyuk, committee co-chairs; Igor Belykh, Vladimir Bondarenko, Mukesh Dhamala, Michael Stewart, committee members. Includes bibliographical references (p. 65-67).

La modélisation du vivant, en particulier la modélisation de l'activité cardiaque, est devenue un défi scientifique majeur. Le but de cette thématique est de mieux comprendre les phénomènes physiologiques et donc d'apporter des solutions à des problèmes cliniques. Nous nous intéressons dans cette thèse à la modélisation et à l'étude numérique de l'activité électrique du cœur, en particulier l'étude des électrocardiogrammes (ECGs). L'onde électrique dans le cœur est gouvernée par un système d'équations de réaction-diffusion appelé modèle bidomaine ce système est couplé à une EDO représentant l'activité cellulaire. Afin simuler des ECGs, nous tenons en compte la propagation de l'onde électrique dans le thorax qui est décrite par une équation de diffusion. Nous commençons par une démonstrer l'existence d'une solution faible du système couplé cœur-thorax pour une classe de modèles ioniques phénoménologiques. Nous prouvons ensuite l'unicité de cette solution sous certaines conditions. Le plus grand apport de cette thèse est l'étude et la simulation numérique du couplage électrique cœur-thorax. Les résultats de simulations sont représentés à l'aide des ECGs. Dans une première partie, nous produisons des simulations pour un cas normal et pour des cas pathologiques (blocs de branche gauche et droit et des arhythmies). Nous étudions également l'impact de certaines hypothèses de modélisation sur les ECGs (couplage faible, utilisation du modèle monodomaine, isotropie, homogénéité cellulaire, comportement résistance-condensateur du péricarde,. . . ). Nous étudions à la fin de cette partie la sensibilité des ECGs par apport aux paramètres du modèle. En deuxième partie, nous effectuons l'analyse numérique de schémas du premier ordre en temps découplant les calculs du potentiel d'action et du potentiel extérieur. Puis, nous combinons ces schémas en temps avec un traîtement explicite du type Robin-Robin des conditions de couplage entre le cœur et le thorax. Nous proposons une analyse de stabilité de ces schémas et nous illustrons les résultats avec des simulations numériques d'ECGs. La dernière partie est consacrée à trois applications. Nous commençons par l'estimation de certains paramètres du modèle (conductivité du thorax et paramètres ioniques). Dans la deuxième application, qui est d'originie industrielle, nous utilisons des méthodes d'apprentissage statistique pour reconstruire des ECGs à partir de mesures ('électrogrammes). Enfin, nous présentons des simulations électro-mécaniques du coeur sur une géométrie réelle dans diverses situations physiologiques et pathologiques. Les indicateurs cliniques, électriques et mécaniques, calculés à partir de ces simulations sont très similaires à ceux observés en réalité.

微電列陣今已被廣泛用於各種生理和理的研究。通過把微電列陣連接到肌肉細胞，細胞外的電生理信號會被有效地記錄，我們進而對尖峰信號的傳播模式進行分析，以便了解肌肉收縮的模式。本文旨在對觀測到的電生理信號進行統計模型擬合，從而獲得對於肌肉收縮模式的統計推論。我們提出了三種方法用以提取尖峰信號的激活時間，分別為均值方差法、局部加權回歸法(LOWESS方法)和Butterworth濾波法。然後對抽取出來的尖峰信號應用隨機Hough轉換，識別出多個傳播的信號波，從而得到肌肉收縮的率。對於每個信號波，我們建立了兩個模型來描述信號的傳播模式，即圓形波陣面模型和線性波陣模型。通過這兩種模型擬合，表達信傳播特徵的參數可被估算，例如激發信號波的起源位和起始時間，信號的傳播方向以及速度等。利用根據兩種模型合成的模擬數據，我們證明了隨機霍夫轉換算法和模型擬合的有效性及準確性，並把文中提出的算法用於大鼠心肌培養細胞的一個數據集。由此數據集得出的結果可以用於監測細胞的電生理變化，從而闡明藥物或環條件對心肌細胞產生的影響。<br>The microelectrode array (MEA) has been widely used in physiological and pharmacological research. By attaching the MEA system to muscle cells, extracellular electrophysiological signals can be recorded, and the spike-signal propagation pattern can be analyzed for understanding the muscle contraction pattern. This thesis aims at providing a statistical framework for analyzing the muscle contraction pattern from the observed electrophysiological signals. We first provides three methods for extracting the activation time of signal spikes: the mean-variance method, the LOWESS smoothing method, and the Butterworth filtering method. The randomized Hough transform is then applied to the signal spikes to identify the multiple propagating waves, which gives the rate of beating. For each propagating wave, we propose two models to describe the signal propagation pattern, namely the circular wavefront model and the linear wavefront model. By fitting these two models, parameters that characterize the signal propagation can be estimated, such as the origin and time of excitation, the direction of propagation, and the speed of propagation. We demonstrate the performances of the randomized Hough tranform algorithm and model fitting in two simulation studies, and apply these approaches to a real data set of cultured cardiac myocytes of rats. The result may be used to monitor the electrophysiological changes and thereby elucidate the drug effect or environmental condition on cardiomyocytes.<br>Detailed summary in vernacular field only.<br>Lu, Jiayi.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 2013.<br>Includes bibliographical references (leaves 62-65).<br>Abstracts also in Chinese.<br>Chapter 1 --- Introduction --- p.1<br>Chapter 1.1 --- Motivating problem --- p.1<br>Chapter 1.2 --- An overview of MEA --- p.2<br>Chapter 1.3 --- Electrophysiology of cardiac myocytes --- p.5<br>Chapter 1.4 --- Organization --- p.5<br>Chapter 2 --- A generative model for MEA data --- p.7<br>Chapter 2.1 --- Circular wavefront model --- p.9<br>Chapter 2.2 --- Linear wavefront model --- p.11<br>Chapter 3 --- Computing method for MEA signals --- p.13<br>Chapter 3.1 --- Preliminaries --- p.13<br>Chapter 3.1.1 --- Locally weighted scatterplot smoothing(LOWESS) --- p.13<br>Chapter 3.1.2 --- Butterworth filter --- p.16<br>Chapter 3.1.3 --- Hough transform --- p.16<br>Chapter 3.1.4 --- Nonlinear minimization --- p.21<br>Chapter 3.2 --- Overall procedure for MEA data analysis --- p.24<br>Chapter 3.3 --- Extract the spike activation time --- p.25<br>Chapter 3.4 --- Identification of multiple propagating waves --- p.28<br>Chapter 3.5 --- Model fitting --- p.29<br>Chapter 3.5.1 --- Circular wavefront model --- p.29<br>Chapter 3.5.2 --- Linear wavefront model --- p.33<br>Chapter 4 --- Simulation study based on synthesized data --- p.35<br>Chapter 4.1 --- Wave detection using Hough transform --- p.35<br>Chapter 4.1.1 --- Data synthesis from linear wavefront model --- p.35<br>Chapter 4.1.2 --- Performance of the randomized Hough transform --- p.38<br>Chapter 4.2 --- Model fitting for signal propagating pattern --- p.38<br>Chapter 4.2.1 --- Data Synthesis from circular wavefront model --- p.38<br>Chapter 4.2.2 --- Performance of the model fitting algorithm --- p.42<br>Chapter 5 --- Real data application --- p.47<br>Chapter 5.1 --- Data set --- p.47<br>Chapter 5.2 --- Extract the spike activation time --- p.49<br>Chapter 5.3 --- Identify multiple propagating waves --- p.52<br>Chapter 5.4 --- Model fitting --- p.52<br>Chapter 5.4.1 --- Fitting the circular wavefront model --- p.52<br>Chapter 5.4.2 --- Fitting the linear wavefront model --- p.55<br>Chapter 5.4.3 --- Comparison of the two models --- p.56<br>Chapter 6 --- Conclusions and future directions --- p.60<br>Chapter 6.1 --- Conclusions --- p.60<br>Chapter 6.2 --- Future directions --- p.61

碩士<br>逢甲大學<br>應用數學所<br>100<br>The function of basal ganglia is very much related to motor signal processing and cognition in brain. The input structure of basal ganglia – neo-striatum mostly consists of medium spiny neurons (MSN). The dopamine neuron from substantia nigra pars compacta, SNpc, projects to MSN in neo-striatum and modulates the excitability of MSN via release of dopamine in a reward-dependent manner. This study uses the minimal mathematical model built by Gruber et al. (2003) to study the electrophysiology of MSN. Employing bifurcation analysis, we can understand how dopamine D1 receptor modulate the response to cortical post-synaptic stimulus, and investigate how ion channel conductance affect the excitability of MSN. We can observe from the model that trans-membrane potential has bi-stability phenomenon consisting of hyperpolarized down-state and depolarized up-state when the concentration of dopamine rises. If we augment Kir2 current, it will strengthen the down-state and make the neuron less possible to fire; on other hand, if we block Kir2 current, it will weaken the down-state and make the membrane potential easier to reach the up-state and fire. If we block Ksi current, it will strengthen the up-state and make the neuron more excitable; on the other hand, if we augment Ksi current, it will weaken the up-state and make the neuron more possible retreat to down-state and fire less. If we augment L-Ca current, it will strengthen the up-state and make the neuron fire more; on the other hand, if we block L-Ca current, it will weaken the up-state and make the neuron more possible stay at down-state and fire less. Besides, from the model, blocking Ksi or enhancing L-Ca current at low dopamine level will generate bi-stability of membrane potential that only happens at high dopamine level. This means we can use Ksi blocker or L-Ca agonist to replace the role of dopamine in MSN if dopamine is depleted due to disease like Parkinson’s disease. Though we utilized simplified model here, together with Matcont’s bifurcation analysis, we can study how dopamine level and ion channel conductance affect membrane potential. Mathematical model can help experiment to study the physiological and pathological mechanisms of MSN that furthers help developing drug to cure some neuronal disease like Parkinson’s disease and obsessive compulsive disorder.

This thesis is devoted to the study of the dynamics of spiral and scroll waves in a mathematical model for cardiac tissue. We study the effects of the presence of heterogeneities on electrical-wave dynamics. The heterogeneities in the medium occur because of the variation in the electrophysiological properties of the constituent myocytes in the tissue, or because of the presence of cells like fibroblasts and pathological myocytes that can trigger early afterdepolarizations (EADs). We study how these heterogeneities can lead to the formation of spiral and scroll waves and how they can affect the stability of the spiral and scroll waves in cardiac tissue. We also investigate the role of abnormal cells, which can trigger pathological excitations like EADs, on the formation of spiral and scroll waves, and how such cells can trigger premature electrical pulses like premature-ventricular-complexes (PVCs) in cardiac tissue. Earlier studies have examined the role of ionic heterogeneities on spiral-wave initiation and their effects on spiral-wave stability. However, none of these studies has calculated, in a controlled way, the effects of individual ion-channel conductances on spiral- and scroll-wave properties, such as the frequency of these waves, and the effects of the spatial gradients, in each ion-channel conductance, on their stability; we present these results in Chapter 2. Although many studies in the past have studied the effects of fibroblast coupling on wave-dynamics in cardiac tissue, a detailed study of spiral-wave dynamics in a medium with a well-defined, heterogeneous distribution of fibroblasts (e.g., with a gradient in the fibroblast density (GFD)) has not been performed; therefore, in Chapter 3 we present the effects of such GFD on spiral- and scroll-wave dynamics. Then, in Chapter 4, we present a systematic study of how a clump of fibroblasts can lead to spiral waves via high-frequency pacing. Some studies in the past have studied the role of early afterdepolarizations (EADs) in the formation of arrhythmias in cardiac tissue; we build on such studies and present a detailed study of the effects of EADs on the formation of spiral waves and their dynamics, in Chapter 5. Finally, in Chapter 6 we provide the results of our detailed investigation of the factors that assist the triggering of abnormal electrical pulses like premature ventricular complexes by a cluster of EAD-capable cells. A brief summary of the chapters is provided below: Chapter 2: In this chapter we investigate the effects of spatial gradients in the ion-channel conductances of various ionic currents on spiral-and scroll-wave dynamics. Ionic heterogeneities in cardiac tissue arise from spatial variations in the electrophysiological properties of cells in the tissue. Such variations, which are known to be arrhythmogenic, can be induced by diseases like ischemia. It is important, therefore, to understand the effects of such ionic heterogeneities on electrical-wave dynamics in cardiac tissue. To investigate such effects systematically, of changing the ion-channel properties by modifying the conductances of each ionic currents, on the action-potential duration (APD) of a myocyte cell. We then study how these changes in the APD affect the spiral-wave frequency ω in two-dimensional tissue. We also show that changing the ion-channel conductance not only changes ω but also the meandering pattern of the spiral wave. We then study how spatial gradients in the ion-channel conductances affect the spiral-wave stability. We find that the presence of this ionic gradient induces a spatial variation of the local ω, which leads to an anisotropic reduction of the spiral wavelength in the low-ω region and, thereby, leads to a breakup of the spiral wave. We find that the degree of the spiral-wave stability depends on the magnitude of the spatial variation in ω, induced by the gradient in the ion-channel conductances. We observe that ω varies most drastically with the ion-channel conductance of rapid delayed rectifier K+ current GKr, and, hence, a spiral wave is most unstable in the presence of a gradient in GKr (as compared to other ion-channel conductances). By contrast, we find that ω varies least prominently with the conductances of the transient outward K+ current Gto and the fast inward Na+ current (GNa); hence, gradients in these conduc-tances are least likely to lead to spiral-wave breaks. We also investigate scroll-wave instability in an anatomically-realistic human-ventricular heart model with an ionic gradient along the apico-basal direction. Finally, we show that gradients in the ion-channel densities can also lead to spontaneous initiation of spiral waves when we pace the medium at high frequency. Chapter 3: In this chapter we study the effects of gradients in the density of fibroblasts on wave-dynamics in cardiac tissue. The existence of fibroblast-myocyte coupling can modulate electrical-wave dynamics in cardiac tissue. In diseased hearts, the distribution of fibroblasts is heterogeneous, so there can be gradients in the fibroblast density (henceforth we call this GFD) especially from highly injured regions, like infarcted or ischemic zones, to less-wounded regions of the tissue. Fibrotic hearts are known to be prone to arrhythmias, so it is important to understand the effects of GFD in the formation and sustenance of arrhythmic re-entrant waves, like spiral or scroll waves. Therefore, we investigate the effects of GFD on the stability of spiral and scroll waves of electrical activation in a state-of-the-art mathematical model for cardiac tissue in which we also include fibroblasts. By introducing GFD in controlled ways, we show that spiral and scroll waves can be unstable in the presence of GFDs because of regions with varying spiral or scroll-wave frequency ω, induced by the GFD. We examine the effects of the resting membrane potential of the fibroblast and the number of fibroblasts attached to the myocytes on the stability of these waves. Finally, we show that the presence of GFDs can lead to the formation of spiral waves at high-frequency pacing. Chapter 4: In this chapter we study the arrhythmogenic effects of lo-calized fibrobblast clumps. Localized heterogeneities, caused by the regional proliferation of fibroblasts, occur in mammalian hearts because of diseases like myocardial infarction. Such fibroblast clumps can become sources of pathological reentrant activities, e.g., spiral or scroll waves of electrical activation in cardiac tissue. The occurrence of reentry in cardiac tissue with heterogeneities, such as fibroblast clumps, can depend on the frequency at which the medium is paced. Therefore, it is important to study the reentry-initiating potential of such fibroblast clumps at different frequencies of pacing. We investigate the arrhythmogenic effects of fibroblast clumps at high- and low-frequency pacing. We find that reentrant waves are induced in the medium more prominently at high-frequency pacing than with low-frequency pacing. We also study the other factors that affect the potential of fibroblast clumps to induce reentry in cardiac tissue. In particular, we show that the ability of a fibroblast clump to induce reentry depends on the size of the clump, the distribution and percentage of fibroblasts in the clump, and the excitability of the medium. We study the process of reentry in two-dimensional and a three-dimensional mathematical models for cardiac tissue. Chapter 5: In this chapter we investigate the role of early afterdepolarizations (EADs) on the formation of spiral and scroll waves. Early after depolarizations, which are abnormal oscillations of the membrane poten-tial at the plateau phase of an action potential, are implicated in the de-velopment of cardiac arrhythmias like Torsade de Pointes. We carry out extensive numerical simulations of the TP06 and ORd mathematical models for human ventricular cells with EADs. We investigate the different regimes in both these models, namely, the parameter regimes where they exhibit (1) a normal action potential (AP) with no EADs, (2) an AP with EADs, and (3) an AP with EADs that does not go back to the resting potential. We also study the dependence of EADs on the rate of at which we pace a cell, with the specific goal of elucidating EADs that are induced by slow or fast rate pacing. In our simulations in two- and three-dimensional domains, in the presence of EADs, we find the following wave types: (A) waves driven by the fast sodium current and the L-type calcium current (Na-Ca-mediated waves); (B) waves driven only by the L-type calcium current (Ca-mediated waves); (C) phase waves, which are pseudo-travelling waves. Furthermore, we compare the wave patterns of the various wave-types (Na-Ca-mediated, Ca-mediated, and phase waves) in both these models. We find that the two models produce qualitatively similar results in terms of exhibiting Na-Ca- mediated wave patterns that are more chaotic than those for the Ca-mediated and phase waves. However, there are quantitative differences in the wave patterns of each wave type. The Na-Ca-mediated waves in the ORd model show short-lived spirals but the TP06 model does not. The TP06 model supports more Ca-mediated spirals than those in the ORd model, and the TP06 model exhibits more phase-wave patterns than does the ORd model. Chapter 6: In this chapter we study the role of EAD-capable cells, and fibroblasts on the trigerring of abnormal electrical pulses called premature ventricular complexes (PVCs). Premature ventricular complexes, which are abnormal impulse propagations in cardiac tissue, can develop because of various reasons including early afterdepolarizations (EADs). We show how a cluster of EAD-generating cells (EAD clump) can lead to PVCs in a model of cardiac tissue, and also investigate the factors that assist such clumps in triggering PVCs. In particular, we study, through computer simulations, the effects of the following factors on the PVC-triggering ability of an EAD clump: (1) the repolarization reserve (RR) of the EAD cells; (2) the size of the EAD clump; (3) the coupling strength between the EAD cells in the clump; and (4) the presence of fibroblasts in the EAD clump. We find that, although a low value of RR is necessary to generate EADs and hence PVCs, a very low value of RR leads to low-amplitude EAD oscillations that decay with time and do not lead to PVCs. We demonstrate that a certain threshold size of the EAD clump, or a reduction in the coupling strength between the EAD cells, in the clump, is required to trigger PVCs. We illustrate how randomly distributed inexcitable obstacles, which we use to model collagen deposits, affect PVC-triggering by an EAD clump. We show that the gap-junctional coupling of fibroblasts with myocytes can either assist or impede the PVC-triggering ability of an EAD clump, depending on the resting membrane potential of the fibroblasts and the coupling strength between the myocyte and fibroblasts. We also find that the triggering of PVCs by an EAD clump depends sensitively on factors like the pacing cycle length and the distribution pattern of the fibroblasts.