There is a growing consensus that life-threatening cardiac arrhythmias like ven- tricular tachycardia (VT) or ventricular fibrillation (VF) arise because of the formation of spiral waves of electrical activation in cardiac tissue; unbroken spiral waves are associated with VT and broken ones with VF. Several experimental studies have shown that in homogeneities in cardiac tissue can have dramatic effects on such spiral waves. In this thesis we focus on spiral-wave dynamics in mathematical models of human ventricular tissue which contain (a) conduction in homogeneities, (b) ionic in- homogeneities, (c) fibroblasts, (d) Purkinje fibers. We also study the effect of a periodic deformation of the simulation domain on spiral wave-dynamics. Chapter 2 contains our study of “Spiral-Wave Dynamics and Its Control in the Presence of In homogeneities in Two Mathematical Models for Human Cardiac Tissue”; this chapter follows closely parts of a paper we have published [1]. Chapter 3 contains our study of “Spiral-wave dynamics in a Mathematical Model of Human Ventricular Tissue with Myocytes and Fibroblasts”; this chapter follows closely a paper that we have submitted for publication. Chapter 4 contains our study of “Spiral-wave Dynamics in Ionically Realistic Mathematical Models for Human Ventricular Tis- sue: The Effects of Periodic Deformation”; this chapter follows closely a paper that we have submitted for publication. Chapter 5 contains our study of “Spiral-wave dynamics in a Mathematical Model of Human Ventricular Tissue with Myocytes and Purkinje fibers”; this chapter follows closely a paper that we will submit for publication soon. In chapter 2, we study systematically the AP morphology in a state-of-the-art mathematical model of human ventricular tissue due to ten-Tusscher, Noble, Noble, and Panfilov (the TNNP04 model); we also look at the contribution of individual ionic currents to the AP by partially or completely blocking ion channels associated with the ionic currents. We then carry out systematic studies of plane- wave and circular-wave dynamics in the TNNP04 model for cardiac tissue model. We present a detailed and systematic study of spiral-wave turbulence and spa- tiotemporal chaos in two mathematical models for human cardiac tissue due to (a) ten-Tusscher and Panfilov (the TP06 model) and (b) ten-Tusscher, Noble, Noble, and Panfilov (the TNNP04 model). In particular, we use extensive numerical simulations to elucidate the interaction of spiral waves in these models with conduction and ionic in homogeneities. Our central qualitative result is that, in all these models, the dynamics of such spiral waves depends very sensitively on such in homogeneities. A major goal here is to develop low amplitude defibrillation schemes for the elimination of VT and VF, especially in the presence of in homogeneities that occur commonly in cardiac tissue. Therefore, we study a control scheme that has been suggested for the control of spiral turbulence, via low-amplitude current pulses, in such mathematical models for cardiac tissue; our investigations here are designed to examine the efficacy of such control scheme in the presence of in homogeneities in biophysical realistic models. We find that a scheme that uses control pulses on a spatially extended mesh is more successful in the elimination of spiral turbulence than other control schemes. We discuss the theoretical and experimental implications of our study that have a direct bearing on defibrillation, the control of life-threatening cardiac arrhythmias such as ventricular fibrillation. In chapter 3, we study the role of cardiac fibroblasts in ventricular tissue; we use the TNNP04 model for the myocyte cell, and the fibroblasts are modelled as passive cells. Cardiac fibroblasts, when coupled functionally with myocytes, can modulate their electrophysiological properties at both cellular and tissue levels. Therefore, it is important to study the effects of such fibroblasts when they are coupled with myocytes. Chapter 3 contains our detailed and systematic study of spiral-wave dynamics in the presence of fibroblasts in both homogeneous and inhomogeneous domains of the TNNP04 model for cardiac tissue. We carry out extensive numerical studies of such modulation of electrophysiological properties in mathematical models for (a) single myocyte fibroblast (MF) units and (b) two-dimensional (2D) arrays of such units; our models build on earlier ones and allow for no, one-way, or two-way MF couplings. Our studies of MF units elucidate the dependence of the action-potential (AP) morphology on parameters such as Ef , the fibroblast resting membrane potential, the fibroblast conductance Gf , and the MF gap-junctional coupling Ggap. Furthermore, we find that our MF composite can show autorhythmic and oscillatory behaviors in addition to an excitable response. Our 2D studies use (a) both homogeneous and inhomogeneous distributions of fibroblasts, (b) various ranges for parameters such as Ggap, Gf , and Ef , and (c) intercellular couplings that can be no, one-way, and two-way connections of fibroblasts with myocytes. We show, in particular, that the plane-wave conduction velocity CV decreases as a function of Ggap, for no and one-way couplings; however, for two-sided coupling, CV decreases initially and then increases as a function of Ggap, and, eventually, we observe that conduction failure occurs for low values of Ggap. In our homogeneous studies, we find that the rotation speed and stability of a spiral wave can be controlled either by controlling Ggap or Ef . Our studies with fibroblast inhomogeneities show that a spiral wave can get anchored to a local fibroblast inhomogeneity. We also study the efficacy of a low-amplitude control scheme, which has been suggested for the control of spiral-wave turbulence in mathematical models for cardiac tissue, in our MF model both with and without heterogeneities. In chapter 4, we carry out a detailed, systematic study of spiral-wave dynamics in the presence of periodic deformation (PD) in two state-of-the-art mathematical models of human ventricular tissue, namely, the TNNP04 model and the TP06 model. To the best of our knowledge, our work is the first, systematic study of the dynamics of spiral waves of electrical activation and their transitions, in the presence of PD, in such biophysically realistic mathematical models of cardiac tissue. In our studies, we use three types of initial conditions whose time evolutions lead to the following states in the absence of PD: (a) a single rotating spiral (RS), (b) a spiral-turbulence (ST) state, with a single meandering spiral, and (c) an ST state with multiple broken spirals for both these models. We then show that the imposition of PD in these three cases leads to a rich variety of spatiotemporal pat- terns in the transmembrane potential including states with (a) an RS state with n-cycle temporal evolution (here n is a positive integer), (b) rotating-spiral states with quasiperiodic (QP) temporal evolution, (c) a state with a single meandering spiral MS, which displays spatiotemporal chaos, (d) an ST state, with multiple bro- ken spirals, and (e) a quiescent state in which all spirals are absorbed (SA). For all three initial conditions, precisely which one of the states is obtained depends on the amplitudes and the frequencies of the PD in the x and y directions. We also suggest specific experiments that can test the results of our simulations. We also study, in the presence of PD, the efficacy of a low-amplitude control scheme that has been suggested, hitherto only without PD, for the control of spiral-wave turbulence, via low-amplitude current pulses applied on a square mesh, in mathematical models for cardiac tissue. We also develop line-mesh and rectangular-mesh variants of this control scheme. We find that square- and line-mesh-based, low-amplitude control schemes suppress spiral-wave turbulence in both the TP06 and TNNP04 models in the absence of PD; however, we show that the line-based scheme works with PD only if the PD is applied along one spatial direction. We then demonstrate that a minor modification of our line-based control scheme can suppress spiral-wave turbulence: in particular, we introduce a rectangular-mesh-based control scheme, in which we add a few control lines perpendicular to the parallel lines of the line- based control scheme; this rectangular-mesh scheme is a significant improvement over the square-mesh scheme because it uses fewer control lines than the one based on a square mesh. In chapter 5, we have carried out detailed numerical studies of (a) a single unit of an endocardial cell and Purkinje cell (EP) composite and (b) a two-dimensional bilayer, which contains such EP composites at each site. We have considered bio- physically realistic ionic models for human endocardial cells (Ecells) and Purkinje cells (Pcells) to model EP composites. Our study has been designed to elucidate the sensitive dependence, on parameters and initial conditions, of (a) the dynamics of EP composites and (b) the spatiotemporal evolution of spiral waves of electrical activation in EP-bilayer domains. We examine this dependence on myocyte parameters by using the three different parameter sets P1, P2, and P3; to elucidate the initial-condition dependence we vary the time at which we apply the S2 pulse in our S1-S2 protocol; we also investigate the dependence of the spatiotemporal dynamics of our system on the EP coupling Dgap, and on the number of Purkinje- ventricular junctions (PVJs), which are measured here by the ratio R, the ratio of the total number of sites to the number of PVJs in our simulation domain. Our studies on EP composites show that the frequency of autorhythmic activity of a P cell depends on the diffusive gap-junctional conductance Dgap. We perform a set of simulations to understand the source-sink relation between the E and P cells in an EP composite; such a source-sink relation is an important determinant of wave dynamics at the tissue level. Furthermore, we have studied the restitution properties of an isolated E cell and a composite EP unit to uncover this effect on wave dynamics in 2D, bilayers of EP composites. Autorhythmicity is an important property of Purkinje cell; it helps to carry electrical signals rapidly from bundle of His to the endocardium. Our investigation of an EP composite shows that the cycle length (CL) of autorhythmic activity decreases, compared to that of an uncoupled Purkinje cell. Furthermore, we find that the APD increases for an EP composite, compared to that of an uncoupled P cell. In our second set of simulations for an EP-composite unit, we have obtained the AP behaviors and the amount of flux that flows from the E to the P cell during the course of the AP. The direction of flow of this flux is an important quantity that identifies which one of these cells act as a source or a sink in this EP composite. We have found that the P cell in an EP composite acts as a stimulation-current source for the E cell in the depolarization phase of the AP, when the stimulus is applied to both cells or to the P cell only. However, the P cell behaves both as a source and a sink when the stimulus is applied to the E cell only. In our third set of simulations for an EP composite unit, we have calculated the restitution of the APD; this plays an important role in deciding the stability of spiral waves in mathematical models for cardiac tissue. Our simulation shows that, for the EP composite with high coupling (Dgap = Dmm~10), the APDR slope decreases, relative to its value for an isolated E cell, for parameter sets P1 and P2, and first increases (for 50 ≤ DI ≤ 100 ms) and then decreases for the parameter set P3 ; however, for low coupling (Dgap = Dmm~100), the variation of the AP D as function of DI, for an EP composite, shows biphasic behavior for all these three parameter sets. We found that the above dynamics in EP cable type domains, with EP composites, depends sensitively on R. We hope our in silico studies of spiral-wave dynamics in a variety of state-of-the- art ionic models for ventricular tissue will stimulate more experimental studies that examine such dynamics.

A cardiomiopatia arritmogênica do ventrículo direito (CAVD) tem origem genética e é caracterizada pela substituição de células miocárdicas por tecido fibroadiposo. A doença tem uma prevalência aproximada de 1:3500, sendo mais frequentemente diagnosticada em indivíduos jovens, atletas e do sexo masculino. Atualmente, várias alterações genéticas associadas a CAVD foram descritas em 12 genes diferentes. No entanto, existem poucos estudos na literatura que descrevem o espectro mutacional da doença usando um painel abrangente de genes potencialmente causais, em populações diferentes das coortes descendentes de europeus. O sequenciamento de nova geração (NGS) como ferramenta para o diagnóstico molecular da doença, permite um avanço na correlação entre alterações genotípicas e fenotípicas e tem aportado potenciais benefícios que crescem juntamente com os desafios na sua interpretação. Além disso, o uso de hiPSCs como modelo in vitro de determinadas doenças cardíacas, permite avaliar especificamente a relação do genótipo com as diferentes consequências fenotípicas celulares da CAVD. Entretanto, os mecanismos moleculares da doença ainda são pouco esclarecidos e não há na literatura estudos que englobem ao mesmo tempo o perfil mutacional (com um painel extenso de genes) e estudo funcional das alterações encontradas com o uso de hiPSC-CMs. Esta tese teve como objetivo descrever a prevalência de variantes causais em genes associados à CAVD na população brasileira, e caracterizar, do ponto de vista funcional, os cardiomiócitos derivados de hiPSC (hiPSC-CMs) de pacientes com mutações identificadas, a fim de associar o perfil mutacional e a expressão fenotípica celular. Quarenta e sete indivíduos, não aparentados, sendo 38 (80,85%) pacientes do sexo masculino, idade média 40,2 ± 15,56 anos, com diagnóstico clínico de CAVD, foram submetidos ao sequenciamento de um painel genético relacionado à cardiomiopatias hereditárias, compreendendo os 12 genes previamente descritos como causadores de CAVD, utilizando sequenciamento de nova geração (NGS). As variantes foram interpretadas e classificadas de acordo com os critérios da ACMG. Variantes patogênicas ou provavelmente patogênicas foram encontradas em dezoito probandos (38,3%), com maior número de ocorrências no gene PKP2 (38,8%). Entre os 18 casos positivos, treze variantes diferentes foram encontradas, quatro delas novas variantes em genes desmossomais, sem descrição prévia na literatura. Variantes de significado incerto (VSI) foram encontradas em 16 pacientes. A presença de uma variante causal ocorreu em todos os probandos assintomáticos e foi significativamente associada a probandos com histórico familiar de morte súbita cardíaca abaixo de 35 anos. Para a modelagem celular da CAVD, foram geradas hiPSCs de dois pacientes a partir de células progenitoras de urina (UPCs) e fibroblastos, por transfecção episomal. O primeiro paciente possuía alteração missense no gene PKP2 e o segundo, uma inserção no gene DSC2. As hiPSCs foram caracterizadas quanto ao seu potencial de pluripotência e posteriormente diferenciadas em cardiomiócitos (hiPSC-CMs). Nossos resultados demonstraram diferenças fenotípicas significativas entre os CAVD-CMs comparados com os controle-CMs, como: reduções significativas de expressão das proteínas desmossomais e desmossomos estruturalmente alterados; presença de marcadores do acúmulo de gotículas lipídicas e regulação aumentada do fator de transcrição proadipogênico PPAR-gama; aumento de duração do potencial de campo (FPD) e do potencial de ação em 90% de repolarização (APD90); velocidade de condução mais lenta e uma força de contração menor. Em conclusão, este é o primeiro trabalho a caracterizar o perfil genético da CAVD, abrangendo todos os genes descritos até o momento relacionados à doença, na população brasileira. Os dados obtidos neste trabalho sugerem que, pacientes com história familiar de MSC ( < 35 anos) têm maior probabilidade de portar uma variante causal. Além disso, nossos achados sugerem que pacientes com alteração causal no gene PKP2 têm uma maior gravidade da apresentação fenotípica de arritmia. Nosso modelo celular, que contemplou células paciente-específicas com diferentes alterações das estudadas até o presente momento,sugere ser possível o estudo do efeito das alterações genéticas na CAVD e pode ser um acréscimo às ferramentas disponíveis para estudar o mecanismo desta doença complexa / Arrhythmogenic right ventricular cardiomyopathy (ARVC) has a genetic origin and is mainly characterized by the replacement of myocardial cells with fibroadipose tissue. The disease has a prevalence of approximately 1: 3.500, being more frequently diagnosed in young individuals, athletes and males. Currently, several mutations associated with ARVC have been described in 12 different genes. However, there are few studies in the literature that describe the mutational spectrum of the disease using a comprehensive panel of potentially causal genes in populations other than European-descent cohorts. Next Generation Sequencing (NGS) as a tool for molecular diagnosis of the disease allows an advance in the correlation between genotypic and clinical phenotypic aspects and has potential benefits that grow along with the challenges in its interpretation. In addition, the use of hiPSCs as an in vitro model of certain heart diseases, allows to specifically evaluate the relationship of the genotype with the different cellular phenotypic consequences of ARVC. However, the molecular mechanisms of the disease are still poorly understood and there are no studies in the literature that include both the mutational profile (with an extensive panel of genes) and functional study of different causal variants, with the use of hiPSC-CMs. The aim of this thesis was to describe the prevalence of causal variants in ARVC-associated genes in the Brazilian population, and to characterize, from a functional point of view, cardiomyocytes derived from hiPSC (hiPSC-CMs) from patients with identified mutations, in order to associate the mutational profile and cellular phenotypic expression. Forty-seven unrelated probands, 38 (80.85%) male, mean age 40.2 ± 15.56 years, with clinical diagnosis of ARVC, were submitted to a cardiomyopathy-related gene panel sequencing, comprising 12 genes, using next-generation sequencing (NGS). Variants were interpreted and classified according to the ACMG criteria. Pathogenic or Likely Pathogenic variants were found in eighteen probands (38.3%), with the largest number of occurrences in the PKP2 gene (38.8%). Among the 18 positive cases, thirteen different variants were found, four of them novel mutations in desmosomal genes, without previous description in the literature. Variants of uncertain significance (VUS) were found in 16 patients. The presence of a causal variant was present in all asymptomatic probands and was significantly associated with probands who have a family history of sudden cardiac death under 35 years. For the cellular modeling, from urinary progenitor cells (UPCs) and fibroblasts, hiPSCs from two patients were generated by episomal transfection. The first patient had a missense variant in the PKP2 gene, while the second had an insertion in the DSC2 gene. The hiPSCs were characterized for its pluripotency potential and subsequently differentiated into cardiomyocytes (hiPSC-CMs). Our results demonstrated significant phenotypic differences between the ARVC-CMs compared to the control-CMs, such as: significant reductions in the expression of desmosomal proteins and structurally altered desmosomes; presence of lipid droplet accumulation markers and increased regulation of the proadipogenic transcription factor PPAR-gamma; prolonged field potential duration (FPD) and action potential in 90% repolarization (APD90); slower conduction velocity and a lower active contraction force. In conclusion, this is the first work to characterize the genetic profile of ARVC, covering all genes described to date related to the disease, in the Brazilian population. The data obtained in this study suggests that patients with a family history of sudden cardiac death ( < 35 years) are more likely to carry a causal variant. In addition, our findings suggest that patients with causal variant in the PKP2 gene have a greater severity of the phenotypic presentation of arrhythmia. Our cellular model, which contemplated patient-specific cells with different causal variants of the previous studies, suggests that it is possible to study the effect of the genetic changes in ARVC, and may be an addition to the tools available to study the mechanism of this complex disease

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