Search

Previous studies have linked dysfunctional Ito arising from mutations to KCND3-encoded Kv4.3 and KCND2-encoded Kv4.2 to atrial fibrillation (AF). Using computational models, this study aimed to investigate the mechanisms underlying pro-arrhythmic effects of the gain-of-function Kv4.3 (T361S, A545P) and Kv4.2 (S447R) mutations. Wild-type and mutant Ito formulations were developed from and validated against experimental data and incorporated into the Colman et al. model of human atrial cells. Single-cell models were incorporated into one- (1D) and two-dimensional (2D) models of atrial tissue, and a three-dimensional (3D) realistic model of the human atria. The three gain-of-function mutations had similar, albeit quantitatively different, effects: shortening of the action potential duration; lowering the plateau membrane potential, abbreviating the effective refractory period (ERP) and the wavelength (WL) of atrial excitation at the tissue level. Restitution curves for the WL, ERP and the conduction velocity were leftward shifted, facilitating the conduction of atrial excitation waves at high excitation rates. The mutations also increased lifespan and stationarity of re-entry in both 2D and 3D simulations, which further highlighted a mutation-induced increase in spatial dispersion of repolarization. Collectively, these changes account for pro-arrhythmic effects of these Kv4.3 and Kv4.2 mutations in facilitating AF.This article is part of the theme issue ‘The heartbeat: its molecular basis and physiological mechanisms’.

Although for many decades, the day-night rhythm in resting heart rate has been attributed to the parasympathetic branch of the autonomic nervous system (high vagal tone during sleep), recently we have shown that there is a circadian clock in the cardiac pacemaker, the sinus node, and the day-night rhythm in heart rate involves an intrinsic rhythmic transcriptional remodelling of pacemaker ion channels, particularly Hcn4. We have now investigated the role of the sympathetic branch of the autonomic nervous system in this and shown it to have a non-canonical role. In mice, sustained long-term block of cardiac β-adrenergic receptors by propranolol administered in the drinking water abolished the day-night rhythm in pacemaking in the isolated sinus node. Concomitant with this, there was a loss of the normal day-night rhythm in many pacemaker ion channel transcripts. However, there was little or no change in the local circadian clock, indicating that the well-known day-night rhythm in sympathetic nerve activity is directly involved in pacemaker ion channel transcription. The day-night rhythm in pacemaking helps explains the occurrence of clinically significant bradyarrhythmias during sleep and this study improves our understanding of this pathology.This article is part of the theme issue ‘The heartbeat: its molecular basis and physiological mechanisms’.

Supervised deep learning has been widely used in the studies of automatic ECG classification, which largely benefits from sufficient annotation of large datasets. However, most of the existing large ECG datasets are roughly annotated, so the classification model trained on them can only detect the existence of abnormalities in a whole recording, but cannot determine their exact occurrence time. In addition, it may take huge time and economic cost to construct a fine-annotated ECG dataset. Therefore, this study proposes weakly supervised deep learning models for detecting abnormal ECG events and their occurrence time. The available supervision information for the models is limited to the event types in an ECG record, excluding the specific occurring time of each event. By leverage of feature locality of deep convolution neural network, the models first make predictions based on the local features, and then aggregate the local predictions to infer the existence of each event during the whole record. Through training, the local predictions are expected to reflect the specific occurring time of each event. To test their potentials, we apply the models for detecting cardiac rhythmic and morphological arrhythmias by using the AFDB and MITDB datasets, respectively. The results show that the models achieve beat-level accuracies of 99.09% in detecting atrial fibrillation, and 99.13% in detecting morphological arrhythmias, which are comparable to that of fully supervised learning models, demonstrating their effectiveness. The local prediction maps revealed by this method are also helpful to analyze and diagnose the decision logic of record-level classification models.

Cardiovascular disease is associated with high rates of morbidity and mortality, and can be reflected by 19 abnormal features of electrocardiogram (ECG). Detecting changes in the QRS complexes in ECG 20 signals is regarded as a straightforward, noninvasive, inexpensive, and preliminary diagnosis approach 21 for evaluating the cardiac health of patients. Therefore, detecting QRS complexes in ECG signals must 22 be accurate over short times. However, the reliability of automatic QRS detection is restricted by all 23 kinds of noise and complex signal morphologies. In this study, we proposed a new algorithm for 24 short-time detection of QRS complexes using dual channels based on U-Net and bidirectional long 25 short-term memory. First, a proposed preprocessor with mean filtering and discrete wavelet transform 26 was initially applied to remove different types of noise. Next the signal was transformed and 27 annotations were relabeled. Finally, a method combining U-Net and bidirectional long short-term 28 memory with dual channels was used for the short-time detection of QRS complexes. The proposed 29 algorithm was trained and tested using 44 ECG records from the MIT-BIH arrhythmia database. It 30 achieved, on average, high values for detection sensitivity (99.56%), positive predictivity (99.72%), 31 and accuracy (99.28%) on the test set, indicating an improvement compared to algorithms reported in 32 the literature., 18 pages, 8 figures and 7 tables

Heart disease is one of the most common diseases causing morbidity and mortality. Electrocardiogram (ECG) has been widely used for diagnosing heart diseases for its simplicity and non-invasive property. Automatic ECG analyzing technologies are expected to reduce human working load and increase diagnostic efficacy. However, there are still some challenges to be addressed for achieving this goal. In this study, we develop an algorithm to identify multiple abnormalities from 12-lead ECG recordings. In the algorithm pipeline, several preprocessing methods are firstly applied on the ECG data for denoising, augmentation and balancing recording numbers of variant classes. In consideration of efficiency and consistency of data length, the recordings are padded or truncated into a medium length, where the padding/truncating time windows are selected randomly to sup-press overfitting. Then, the ECGs are used to train deep neural network (DNN) models with a novel structure that combines a deep residual network with an attention mechanism. Finally, an ensemble model is built based on these trained models to make predictions on the test data set. Our method is evaluated based on the test set of the First China ECG Intelligent Competition dataset by using the F1 metric that is regarded as the harmonic mean between the precision and recall. The resultant overall F1 score of the algorithm is 0.875, showing a promising performance and potential for practical use., 8 pages, 2 figures, conference

Background inward sodium current (IB,Na) that influences cardiac pacemaking has been comparatively under-investigated. The aim of this study was to determine for the first time the properties and role of IB,Na in cells from the heart's secondary pacemaker, the atrioventricular node (AVN). Myocytes were isolated from the AVN of adult male rabbits and mice using mechanical and enzymatic dispersion. Background current was measured using whole-cell patch clamp and monovalent ion substitution with major voltage- and time-dependent conductances inhibited. In the absence of a selective pharmacological inhibitor of IB,Na, computer modelling was used to assess the physiological contribution of IB,Na. Net background current during voltage ramps was linear, reversing close to 0 mV. Switching between Tris- and Na+-containing extracellular solution in rabbit and mouse AVN cells revealed an inward IB,Na, with an increase in slope conductance in rabbit cells at − 50 mV from 0.54 ± 0.03 to 0.91 ± 0.05 nS (mean ± SEM; n = 61 cells). IB,Na magnitude varied in proportion to [Na+]o. Other monovalent cations could substitute for Na+ (Rb+ > K+ > Cs+ > Na+ > Li+). The single-channel conductance with Na+ as charge carrier estimated from noise-analysis was 3.2 ± 1.2 pS (n = 6). Ni2 + (10 mM), Gd3 + (100 μM), ruthenium red (100 μM), or amiloride (1 mM) produced modest reductions in IB,Na. Flufenamic acid was without significant effect, whilst La3 + (100 μM) or extracellular acidosis (pH 6.3) inhibited the current by > 60%. Under the conditions of our AVN cell simulations, removal of IB,Na arrested spontaneous activity and, in a simulated 1D-strand, reduced conduction velocity by ~ 20%. IB,Na is carried by distinct low conductance monovalent non-selective cation channels and can influence AVN spontaneous activity and conduction., Highlights • A background sodium current, IB,Na, has been identified in cells from the atrioventricular node (AVN). • AVN IB,Na is carried by non-selective cation channels. • The single channel conductance derived from ‘noise analysis’ is 3.2 ± 1.2 pS. • In AVN cell simulations, removal of IB,Na arrested spontaneous activity and reduced conductance in a 1D strand.

3D left ventricle (LV) segmentation on echocardiography is very important for diagnosis and treatment of cardiac disease. It is not only because of that echocardiography is a real-time imaging technology and widespread in clinical application, but also because of that LV segmentation on 3D echocardiography can provide more full volume information of heart than LV segmentation on 2D echocardiography. However, 3D LV segmentation on echocardiography is still an open and challenging task owing to the lower contrast, higher noise and data dimensionality, limited annotation of 3D echocardiography. In this paper, we proposed a novel real-time framework, i.e., VoxelAtlasGAN, for 3D LV segmentation on 3D echocardiography. This framework has three contributions: 1) It is based on voxel-to-voxel conditional generative adversarial nets (cGAN). For the first time, cGAN is used for 3D LV segmentation on echocardiography. And cGAN advantageously fuses substantial 3D spatial context information from 3D echocardiography by self-learning structured loss; 2) For the first time, it embeds the atlas into an end-to-end optimization framework, which uses 3D LV atlas as a powerful prior knowledge to improve the inference speed, address the lower contrast and the limited annotation problems of 3D echocardiography; 3) It combines traditional discrimination loss and the new proposed consistent constraint, which further improves the generalization of the proposed framework. VoxelAtlasGAN was validated on 60 subjects on 3D echocardiography and it achieved satisfactory segmentation results and high inference speed. The mean surface distance is 1.85 mm, the mean hausdorff surface distance is 7.26 mm, mean dice is 0.953, the correlation of EF is 0.918, and the mean inference speed is 0.1s. These results have demonstrated that our proposed method has great potential for clinical application, Comment: Accepted by MICCAI 2018

Elucidating the function of specific cell types in a highly complex multicellular system such as the heart often requires detailed anatomic reconstruction. We recently described a distinctive class of phenylethanolamine n-methyltransferase (Pnmt+) cell-derived cardiomyocytes (PdCMs), a new cardiomyocyte population with a potential endocrine role. In this dataset, a 3D reconstruction was carried out to visualise the distribution of PdCMs throughout the murine heart. Rigid registration (stiff rotation and translation) was applied to properly align the fused heart slice images based on landmarks using TrakEM2, an open source plug-in in Fiji. The registered slices were then analysed and reconstructed using MATLAB (MATLAB ®. Version 8.3.0.532). The final reconstructed 3D volume was 561×866×48 pixels (corresponding to spatial resolutions of 5.8, 8.9 and 2.5 mm in the x-, y- and z-direction respectively), and visualised in Paraview. The reconstruction allows for detailed analyses of morphology, projections and cellular features of different cell types, enabling further geometrical and topological analyses. Image data can be accessed and viewed through Figshare.

Cardiac arrhythmias and conduction disturbances are accompanied by structural remodelling of the specialised cardiomyocytes known collectively as the cardiac conduction system. Here, using contrast enhanced micro-computed tomography, we present, in attitudinally appropriate fashion, the first 3-dimensional representations of the cardiac conduction system within the intact human heart. We show that cardiomyocyte orientation can be extracted from these datasets at spatial resolutions approaching the single cell. These data show that commonly accepted anatomical representations are oversimplified. We have incorporated the high-resolution anatomical data into mathematical simulations of cardiac electrical depolarisation. The data presented should have multidisciplinary impact. Since the rate of depolarisation is dictated by cardiac microstructure, and the precise orientation of the cardiomyocytes, our data should improve the fidelity of mathematical models. By showing the precise 3-dimensional relationships between the cardiac conduction system and surrounding structures, we provide new insights relevant to valvar replacement surgery and ablation therapies. We also offer a practical method for investigation of remodelling in disease, and thus, virtual pathology and archiving. Such data presented as 3D images or 3D printed models, will inform discussions between medical teams and their patients, and aid the education of medical and surgical trainees.

Gain-of-function mutations in KCNJ2-encoded Kir2.1 channels underlie variant 3 (SQT3) of the short QT syndrome, which is associated with atrial fibrillation (AF). Using biophysically-detailed human atria computer models, this study investigated the mechanistic link between SQT3 mutations and atrial arrhythmogenesis, and potential ion channel targets for treatment of SQT3. A contemporary model of the human atrial action potential (AP) was modified to recapitulate functional changes in IK1 due to heterozygous and homozygous forms of the D172N and E299V Kir2.1 mutations. Wild-type (WT) and mutant formulations were incorporated into multi-scale homogeneous and heterogeneous tissue models. Effects of mutations on AP duration (APD), conduction velocity (CV), effective refractory period (ERP), tissue excitation threshold and their rate-dependence, as well as the wavelength of re-entry (WL) were quantified. The D172N and E299V Kir2.1 mutations produced distinct effects on IK1 and APD shortening. Both mutations decreased WL for re-entry through a reduction in ERP and CV. Stability of re-entrant excitation waves in 2D and 3D tissue models was mediated by changes to tissue excitability and dispersion of APD in mutation conditions. Combined block of IK1 and IKr was effective in terminating re-entry associated with heterozygous D172N conditions, whereas IKr block alone may be a safer alternative for the E299V mutation. Combined inhibition of IKr and IKur produced a synergistic anti-arrhythmic effect in both forms of SQT3. In conclusion, this study provides mechanistic insights into atrial proarrhythmia with SQT3 Kir2.1 mutations and highlights possible pharmacological strategies for management of SQT3-linked AF., Author summary Atrial fibrillation (AF) is the most common cardiac arrhythmia, and is characterised by complex and irregular electrical activation of the upper chambers of the heart. One rare, genetic condition associated with increased risk of AF is the short QT syndrome (SQTS), which is caused by mutations in genes involved in normal electrical function of the heart. Underlying mechanisms by which SQTS-related gene mutations facilitate development of arrhythmias in the human atria are not well understood. In this study, sophisticated computer models representing ‘virtual’ human atria, incorporating detailed electrophysiological data at the ‘ion channel’ protein level into both idealised and realistic multi-scale tissue geometries, were used to dissect mechanisms by which two mutations in the KCNJ2 gene responsible for SQTS variant 3 (SQT3) promote initiation and sustenance of arrhythmias. It was found that the D172N and E299V mutations to KCNJ2 accelerated the repolarisation process at the cellular level through distinct mechanisms. This, along with the way the mutations affected heterogeneity in electrical behaviour at the organ level, mediated stability of arrhythmias and response to simulated ion channel block. This study improves understanding of mechanisms underlying increased AF risk associated with D172N and E299V KCNJ2 mutations, and outlines potential therapeutic strategies.

BACKGROUND:Ventricular arrhythmia is a leading cause of cardiac mortality. Most antiarrhythmics present paradoxical proarrhythmic side effects, culminating in a greater risk of sudden death.METHODS:We describe a new regulatory mechanism linking mitogen-activated kinase kinase-7 deficiency with increased arrhythmia vulnerability in hypertrophied and failing hearts using mouse models harboring mitogen-activated kinase kinase-7 knockout or overexpression. The human relevance of this arrhythmogenic mechanism is evaluated in human-induced pluripotent stem cell-derived cardiomyocytes. Therapeutic potentials by targeting this mechanism are explored in the mouse models and human-induced pluripotent stem cell-derived cardiomyocytes.RESULTS:Mechanistically, hypertrophic stress dampens expression and phosphorylation of mitogen-activated kinase kinase-7. Such mitogen-activated kinase kinase-7 deficiency leaves histone deacetylase-2 unphosphorylated and filamin-A accumulated in the nucleus to form a complex with Krüppel-like factor-4. This complex leads to Krüppel-like factor-4 disassociation from the promoter regions of multiple key potassium channel genes (Kv4.2, KChIP2, Kv1.5, ERG1, and Kir6.2) and reduction of their transcript levels. Consequent repolarization delays result in ventricular arrhythmias. Therapeutically, targeting the repressive function of the Krüppel-like factor-4/histone deacetylase-2/filamin-A complex with the histone deacetylase-2 inhibitor valproic acid restores K+ channel expression and alleviates ventricular arrhythmias in pathologically remodeled hearts.CONCLUSIONS:Our findings unveil this new gene regulatory avenue as a new antiarrhythmic target where repurposing of the antiepileptic drug valproic acid as an antiarrhythmic is supported.

Rapid atrial arrhythmias such as atrial fibrillation (AF) predispose to ventricular arrhythmias, sudden cardiac death and stroke. Identifying the origin of atrial ectopic activity from the electrocardiogram (ECG) can help to diagnose the early onset of AF in a cost-effective manner. The complex and rapid atrial electrical activity during AF makes it difficult to obtain detailed information on atrial activation using the standard 12-lead ECG alone. Compared to conventional 12-lead ECG, more detailed ECG lead configurations may provide further information about spatio-temporal dynamics of the body surface potential (BSP) during atrial excitation. We apply a recently developed 3D human atrial model to simulate electrical activity during normal sinus rhythm and ectopic pacing. The atrial model is placed into a newly developed torso model which considers the presence of the lungs, liver and spinal cord. A boundary element method is used to compute the BSP resulting from atrial excitation. Elements of the torso mesh corresponding to the locations of the placement of the electrodes in the standard 12-lead and a more detailed 64-lead ECG configuration were selected. The ectopic focal activity was simulated at various origins across all the different regions of the atria. Simulated BSP maps during normal atrial excitation (i.e. sinoatrial node excitation) were compared to those observed experimentally (obtained from the 64-lead ECG system), showing a strong agreement between the evolution in time of the simulated and experimental data in the P-wave morphology of the ECG and dipole evolution. An algorithm to obtain the location of the stimulus from a 64-lead ECG system was developed. The algorithm presented had a success rate of 93%, meaning that it correctly identified the origin of atrial focus in 75/80 simulations, and involved a general approach relevant to any multi-lead ECG system. This represents a significant improvement over previously developed algorithms., Author Summary Ectopic activity is associated with multiple cardiac disorders and has been implicated in the initiation of self-sustaining re-entrant excitation. Identifying the presence and origin of ectopic activity may be vital in improving diagnosis and treatment of disorders such as atrial fibrillation, and has been the subject of multiple studies. The electrical activity of the heart can be non-invasively monitored through the electrocardiogram. However, the standard 12-lead electrocardiogram may not provide sufficient information to resolve the focus of ectopic activity satisfactorily and accurately; more detailed multi-lead electrocardiograms may provide more information to be able to produce an algorithm to locate the origin of ectopic activity. Using a 3D computational atria-torso model developed in our laboratory, we simulated the electrical activity of the atria under normal and different ectopic conditions. The model was first validated by comparison to experimental data, and then used to develop an algorithm to identify the location of atrial ectopic focus using a 64-lead electrocardiogram. The algorithm developed was able to identify the origin of atrial ectopic activity in 75/80 simulations, which is a significant improvement compared to previously developed algorithms. Furthermore, the study suggests that multi-lead electrocardiograms provide significant benefits over the standard 12-lead configuration.

Aims: Atrial anti-arrhythmic effects of β-adrenoceptor antagonists (β-blockers) may involve both a suppression of pro-arrhythmic effects of catecholamines, and an adaptational electrophysiological response to chronic β-blocker use; so-called ‘pharmacological remodelling’. In human atrium, such remodelling decreases the transient outward (Ito) and inward rectifier (IK1) K+ currents, and increases the cellular action potential duration (APD) and effective refractory period (ERP). However, the consequences of these changes on mechanisms of genesis and maintenance of atrial fibrillation (AF) are unknown. Using mathematical modelling, we tested the hypothesis that the long-term adaptational decrease in human atrial Ito and IK1 caused by chronic β-blocker therapy, i.e. independent of acute electrophysiological effects of β-blockers, in an otherwise un-remodelled atrium, could suppress AF.\ud \ud Methods and results: Contemporarily, biophysically detailed human atrial cell and tissue models were used to investigate effects of the β-blocker-based pharmacological remodelling. Chronic β-blockade remodelling prolonged atrial cell APD and ERP. The incidence of small amplitude APD alternans in the CRN model was reduced. At the 1D tissue level, β-blocker remodelling decreased the maximum pacing rate at which APs could be conducted. At the three-dimensional organ level, β-blocker remodelling reduced the life span of re-entry scroll waves.\ud \ud Conclusion: This study improves our understanding of the electrophysiological mechanisms of AF suppression by chronic β-blocker therapy. Atrial fibrillation suppression may involve a reduced propensity for maintenance of re-entrant excitation waves, as a consequence of increased APD and ERP.

X-ray computed tomography (XCT) has been shown to be an effective imaging technique for a variety of materials. Due to the relatively low differential attenuation of X-rays in biological tissue, a high density contrast agent is often required to obtain optimal contrast. The contrast agent, iodine potassium iodide ([Formula: see text]), has been used in several biological studies to augment the use of XCT scanning. Recently I2KI was used in XCT scans of animal hearts to study cardiac structure and to generate 3D anatomical computer models. However, to date there has been no thorough study into the optimal use of I2KI as a contrast agent in cardiac muscle with respect to the staining times required, which has been shown to impact significantly upon the quality of results. In this study we address this issue by systematically scanning samples at various stages of the staining process. To achieve this, mouse hearts were stained for up to 58 hours and scanned at regular intervals of 6-7 hours throughout this process. Optimal staining was found to depend upon the thickness of the tissue; a simple empirical exponential relationship was derived to allow calculation of the required staining time for cardiac samples of an arbitrary size.

The aim of the study was to develop a three-dimensional (3D) anatomically-detailed model of the rabbit right atrium containing the sinoatrial and atrioventricular nodes to study the electrophysiology of the nodes. A model was generated based on 3D images of a rabbit heart (atria and part of ventricles), obtained using high-resolution magnetic resonance imaging. Segmentation was carried out semi-manually. A 3D right atrium array model (∼3.16 million elements), including eighteen objects, was constructed. For description of cellular electrophysiology, the Rogers-modified FitzHugh-Nagumo model was further modified to allow control of the major characteristics of the action potential with relatively low computational resource requirements. Model parameters were chosen to simulate the action potentials in the sinoatrial node, atrial muscle, inferior nodal extension and penetrating bundle. The block zone was simulated as passive tissue. The sinoatrial node, crista terminalis, main branch and roof bundle were considered as anisotropic. We have simulated normal and abnormal electrophysiology of the two nodes. In accordance with experimental findings: (i) during sinus rhythm, conduction occurs down the interatrial septum and into the atrioventricular node via the fast pathway (conduction down the crista terminalis and into the atrioventricular node via the slow pathway is slower); (ii) during atrial fibrillation, the sinoatrial node is protected from overdrive by its long refractory period; and (iii) during atrial fibrillation, the atrioventricular node reduces the frequency of action potentials reaching the ventricles. The model is able to simulate ventricular echo beats. In summary, a 3D anatomical model of the right atrium containing the cardiac conduction system is able to simulate a wide range of classical nodal behaviours.

BACKGROUND—: Ventricular arrhythmia is a leading cause of cardiac mortality. Most antiarrhythmics present paradoxical pro-arrhythmic side effects, culminating in a greater risk of sudden death. METHODS—: We describe a new regulatory mechanism linking mitogen-activated kinase kinase-7 (MKK7) deficiency with increased arrhythmia vulnerability in hypertrophied and failing hearts using mouse models harbouring MKK7 knockout or overexpression. The human relevance of this arrhythmogenic mechanism is evaluated in human induced pluripotent stem cells-derived cardiomyocytes (iPSC-CMs). Therapeutic potentials by targeting this mechanism are explored in the mouse models and human iPSC-CMs. RESULTS—: Mechanistically, hypertrophic stress dampens expression and phosphorylation of MKK7. Such MKK7 deficiency leaves histone deacetylase-2 (HDAC2) unphosphorylated and filamin-A (FLNA) accumulated in the nucleus to form a complex with Krϋppel-like factor-4 (KLF4). This complex leads to KLF4 disassociation from the promoter regions of multiple key potassium channel genes (Kv4.2, KChIP2, Kv1.5, ERG1 and Kir6.2) and reduction of their transcript levels. Consequent repolarization delays result in ventricular arrhythmias. Therapeutically, targeting the repressive function of the KLF4/HDAC2/FLNA complex with the HDAC2 inhibitor Valproic acid (VPA) restores K channel expression and alleviates ventricular arrhythmias in pathologically remodelled hearts. CONCLUSIONS—: Our findings unveil this new gene regulatory avenue as a new anti-arrhythmic target where repurposing of anti-epileptic drug VPA as an antiarrhythmic is supported.

Atrial fibrillation (AF) is the most common cardiac arrhythmia causing morbidity and mortality. Despite recent advances, developing effective and safe anti-AF pharmaceutical therapies remains challenging and is prone to adverse effects in the ventricles. Atrial-selective therapies are promising in managing AF. A better understanding of the role of the atrial-specific ion channels in the atrial arrhythmogenesis and contractility, as well as the anti-AF effects of blocking these channels is of interests. Also, a 3D ventricle-torso model capable of modelling ventricular electrical activities and the resulting electrocardiogram (ECG) is a valuable tool in evaluating the selectiveness and safety of an anti-AF pharmaceutical therapy. In part I, the role of an atrial-specific ion channel, IKur, in atrial electrical and mechanical activities and the potential of the current as a pharmaceutical target for anti-AF therapies were investigated in silico. The role of IKur in atrial arrhythmogenesis and mechanical contraction was revealed by elucidating the functional impacts of the KCNA5 mutations exerting either gain- or loss-in-function, on the atria. First, novel IKur models were developed and incorporated into multiscale biophysical models of human atrial electrophysiology to assess the effects of mutated IKur on atrial electrical dynamics. Then, a family of single cell human atrial electromechanical models was developed and incorporated into an updated 3D anatomical electromechanical model of human atria to clarify the effects of mutated IKur on the atrial contractile function. Finally, the antiarrhythmic effect of IKur block was assessed together with INa and other K+-current block. It was shown that the gain-of-function in IKur impaired atrial contractility and promoted atrial arrhythmogenesis by shortening the APD, whereas the down-regulated IKur exerted positive inotropic effects and increased the susceptibility of the atria to the genesis of early-afterdepolarisations. Both simulated IKur and INa block in human-AF demonstrated antiarrhythmic effects; the multi-channel block exerted synergistic anti-AF effects and enhanced the AF-selectivity of INa inhibitions.In Part II, a human ventricle-torso model was developed through proposing a new family of single cell ventricular models accounting for transmural, apicobasal and interventricular electrical heterogeneities and integrating an updated 3D biophysical and anatomical model of human ventricles with a heterogeneous anatomical model of a human torso. First, using the model, the role of heterogeneities in the genesis of T-wave was revealed. Then, ECG manifestations of bundle branch block and ventricular ischaemia were simulated. Finally, the platform was applied to investigate the impact of a long-QT-linked mutation (KCNQ1-G269S) on the ventricles and ECG. Good agreement between simulated and experimental/clinical ECG was reached under both normal and diseased conditions. It was shown that the apicobasal heterogeneity had a more pronounced effect on the T-wave than other heterogeneities. Simulations of the KCNQ1-G269S elucidated the causal link between the mutation and ECG manifestations of the patients.

The intracellular Ca2+ handling system in a cardiac myocyte is of crucial importance. It regulates the contraction and relaxation of the myocyte during the excitation-contraction (EC) coupling. A normal intracellular Ca2+ handling system keeps the contraction of the heart orderly, which represents a powerful force to pump blood to the whole body. However, disarrayed or remodelled cellular structure associated with the intracellular Ca2+ handling system at the subcellular level, such as loss of T-tubule network in diseased conditions, may promote abnormal cardiac EC coupling, leading to genesis of cardiac arrhythmias impairing cardiac mechanical functions. Up to date, it is still incompletely understood how the intracellular Ca2+ handling system is altered by changes in subcellular structures of Ca2+ handling systems. In this thesis, biophysically detailed computational models for the intracellular Ca2+ handling system of a cardiac cell were developed, providing a powerful platform to investigate the spatio-temporal complexity associated with the intracellular Ca2+ handling, and its role in generating abnormal cardiac EC coupling. First, a well-validated single cell model was used to investigate how the diastolic and systolic Ca2+ concentration responded to alterations in the model parameters related to the Ca2+ handling system, from which the mechanisms underlying the rate-dependence of EC coupling were analysed. Then, a novel single cell model, with a 2D presentation of the spatial structures of subcellular Ca2+ handling and membrane action potential, of a sheep atrial myocyte was developed for simulating the abnormal intracellular Ca2+ regulation system due to the loss of T-tubules during atrial fibrillation. Variant scenarios of T-tubule loss were considered to investigate the role of the T-tubule in affecting the intracellular Ca2+ regulation. Furthermore, membrane currents’ alterations due to the electrical remodelling arising from atrial fibrillation were considered together with the loss of T-tubule. Three typical types of abnormal Ca2+ cycling phenomenon, namely intracellular Ca2+ alternans, spontaneous Ca2+ sparks and intracellular Ca2+ waves were observed in AF conditions. The relationship between T-tubule loss, AF-remodelling and the genesis of delayed afterdepolarizations (DADs) was also investigated. It was shown that the loss of T-tubule in AF condition played an important role in disturbing the Ca2+ regulation system, which increases the risk for a cell to generate impaired contraction.

The heart is the most important organ in the human body. Without an optimally functioningheart, other organs soon fail and death ensues. Cardiovascular disease is theleading cause of death globally, accounting to 17.3 million deaths every year and thisnumber is expected to reach 23.6 million by 2030. A huge amount of resources arepooled annually for the study of the heart in order to gain a better understanding of theunderlying mechanisms involved in its function.Over the course of this project, a biophysically detailed, 3D computational modelof the rabbit atria has been developed. Previously published single cell models of therabbit atria served as a starting point and tissue heterogeneity was expanded by incorporatingnew experimental data and single cell models. Furthermore, a highly detailedanatomical reconstruction of the rabbit atria based on micro-CT imaging techniques aswell as realistic fibre orientation data extracted from this high resolution dataset wereincorporated into the 3D model. The project was successful in accurately representingthe physiology of the rabbit atrial function.Furthermore, a high resolution anatomical reconstruction of the atria from a rabbitwith experimental heart failure was used to study the effects of tissue hypertrophy,fibre disorganisation, tissue heterogeneity and ionic remodelling in cardiac function.It was found that tissue hypertrophy is a major contributor towards the increased riskassociated with heart failure through the promotion of re-entrant waves in the atria.Lastly, the role of the atrial septum in cardiac conduction was investigated. Throughthe use of 3D computational modelling, analysis of realistic fibre data extracted fromhigh resolution CT imaging as well as histological data, it was found that structures inthe atrial septum could play an important role in the propagation of electrical signalsfrom the atria towards the ventricles.

Constituting 90-95% of the cardiac non-myocyte cell population, cardiac fibroblasts can electrically couple to cardiac myocytes by forming gap junctions. The electrical interaction between cardiac myocytes and fibroblasts plays a vital role in cardiac fibrosis and arrhythmia related heart disease. In this thesis, cellular models of fibroblast-myocyte coupling in the rabbit sinoatrial node (SAN) and atrium were developed to explore the mechanism underlying the coupling. The effects of coupling fibroblast number and coupling strength between fibroblast and myocyte on electrical activities of the coupled myocyte were also investigated. 2D SAN-atrium tissue models with fibroblasts coupled in different ways were then developed to investigate the effects of the coupling fibroblast number and coupling strength on action potential initiation and propagation in cardiac tissue.Our simulation found that the coupling exerts significant effects on the action potential (AP) waveform of coupled myocyte in the SAN centre under weak coupling (the gap junction conductance (Ggap) is less than 0.2 nS), showing a smaller action potential amplitude (APA), a less negative maximum diastolic potential (MDP), a shortened APD90, and a decreased dV/dtmax after coupling with a larger Ggap or more fibroblasts. Moreover, the spontaneous activity in the SAN centre is abolished under strong coupling (Ggap > 1 nS). In contrast, there is no significant changes in AP characteristics of coupled myocytes in the SAN periphery and atrium under weak coupling. The APD90 increases along with the coupling fibroblast number or Ggap in atrium and SAN periphery under strong coupling. In the 2D tissue model, the conduction velocity (CV) increases in coupling regions after coupling with a larger Ggap or more fibroblasts in the attachment models. However, it increases in the SAN centre and decreases in the SAN periphery and atrium in the insertion models. Conduction blocks can be observed in both models after coupling with a certain number of fibroblasts. Therefore, fibroblasts are not only able to modulate the electrical activities of individual cells but also can modify the pacemaking activities and the AP conduction in cardiac tissue. However, the extent of changes is highly dependent on the electrophysiological properties of coupled myocytes, coupling fibroblast number and coupling strength between the myocyte and the fibroblast. N/A N/A

The sinoatrial node is the primary cardiac pacemaker, which is responsible for generating spontaneous depolarisation of cellular membranes, leading to pacemaking action potentials that control the initiation and regulation of the rhythms of the heart. Previous studies in experimental electrophysiology have gathered a large amount of experimental data about the mechanisms of cardiac pacemaking activities at the molecular, ionic and cellular levels, however, the precise mechanisms underlying the genesis of spontaneous pacemaking action potentials still remain controversial. Mathematical models of the electrophysiology provide a unique alternative tool complimentary to experimental investigations, enabling us to analyse the fundamental physiological mechanisms of cardiac pacemaking activities in an efficient way that would be more difficult to conduct in experimental approaches. In this thesis, an integrated model, incorporating the detailed cellular ion channel kinetics, multi-compartment intracellular Ca2+ handling system and cell morphology, was developed for simulating the spontaneous pacemaking action potentials as well as the stochastic nature of local Ca2+ dynamics in the murine SA node cells. By using the model, the ionic mechanisms underlying the automaticity of primary cardiac pacemaking cells were investigated, the individual role of the ‘membrane clock’ (the cell membrane events) and ‘Ca2+ clock’ (intracellular Ca2+ activities) on generating the pacemaking action potentials were examined. In addition, the model also considered the regulation of the autonomic nervous systems on cardiac pacemaking action potentials. For the first time, competitive regulation of electrical action potentials of the murine SA node cells by the circadian sympathetic and parasympathetic systems during 24-hours were investigated. Furthermore, the individual role of the neurotransmitters, ACh- and ISO-induced actions on variant ion channel and Ca2+ handling in regulating cardiac pacemaking action potentials were also analysed. At the tissue level, an anatomically detailed 2D model of the intact SA node and atrium was developed to investigate the ionic mechanisms underlying sinus node dysfunctions in variant genetic defect conditions. Effects of these genetic defects in impairing cardiac pacemaker ability in pacing and driving the surrounding atrium as seen in the sinus node dysfunction were investigated.

Alteration in the tone of pulmonary arteries may lead to disease such as pulmonary hypertension often associated with major cardiac complications. This dysfunction is partly in the pulmonary arterial smooth muscle cells (PASMCs) where the excitation-contraction coupling is modified by ion channel behaviour to increase the contractile force. Mathematical models of systemic smooth muscle cells (SMCs) that incorporate electrophysiological and chemomechanical mechanisms to understand the underlying cellular physiology have been successfully employed. Models of pulmonary arterial smooth muscle cells (PASMCs) are only beginning to emerge. Mathematical model prototyping with available experimental data and model investigation from different parameter values is a time-consuming and complex process.This thesis is concerned with the development and validation of mathematical models of excitation-contraction coupling in three types of PASMCs of the rat species, one homogeneous type originating from the distal pulmonary arteries and two from proximal pulmonary arteries. Some key novel additions from previous vascular SMC models include the distinct modelling of Ca2+ in the subplasmalemmal cytosolic region, incorporation of subunit-specific currents from the K+ channel family and a generic G-protein receptor model able to reproduce complex Ca2+ profiles. The main pulmonary and systemic arteries statistically differ in its response to phenylephrine in a wire myograph. The ionic currents of the models were validated against experimental data largely from rat species. The models replicate the recordings of Ca2+ and the resting potential (Em) profiles arising from agonist-induced cytosolic Ca2+ ([Ca2+]i) stimulation (G-protein activation), nifedipine, ryanodine, caffeine and niflumic acid. The distal PASMC model was sensitive to an increase in [Ca2+]i from G-protein activation although were less likely to reproduce Ca2+ oscillations than proximal PASMCs. The proximal models determined the likely proximal PASMC type in literature experiments recording [Ca2+]i and Em. I have developed software that enables other users to simulate Ca2+ and Em changes in SMC studies and the ability to parse a master file describing the mathematical model into different language formats to increase productivity. These models provide a foundation for further studies to better understand PASMC function in the context of normal physiology as well as pathological conditions.

Cardiovascular disease is a leading cause of death in developed countries, and places a huge demand on healthcare services and economies across the globe. In this thesis computational models of the rabbit and mouse whole heart were developed and used to investigate a variety of phenomena related to cardiac electrophysiology.In part I, a heterogeneous family of single cell models was developed for the rabbit ventricles. The models were incorporated into a 3D anatomical reconstruction, and subsequently used to study the relationship between ventricular heterogeneity and the electrocardiographic T-wave. It was found that, in order of significance, apico-basal, inter-ventricular and transmural heterogeneity had a lead-dependent effect on the T-wave of the 12-lead electrocardiogram. Subsequently, a detailed model of the rabbit whole heart was developed using image data from X-ray computed tomography, from which detailed anatomical structures were segmented and myocardial architecture determined. The developed 3D whole heart model exhibited physiological fibre structure and experimentally justified patterns of activation.In part II, a mathematical model of the mouse atrioventricular node was developed. The model was validated by its ability to show physiological pacemaking and response to ion channel blocking. The model was subsequently adapted to consider the heterogeneous nature of the atrioventricular node, and incorporated into a 2D simplistic tissue model of the whole heart. The developed model exhibited physiological atrioventricular conduction, and provided insights into the nature of dual-pathway electrophysiology and the role of the funny current. Finally, an optimisation study was carried out for contrast enhancement of X-ray computed tomography, specifically for imaging the mouse heart, the results of which may be used to facilitate future high-throughput imaging of cardiac tissue.

Atrial fibrillation (AF), the most common sustained arrhythmia, is associated with abnormal intracellular Ca2+ handling. Understanding AF requires comprehensive understanding of ionic currents, Ca2+ handling, phosphorylation regulation and related signalling pathways, but appropriate models are limited. The aim of this thesis is to develop an ionic model of the mouse atrial myocyte to investigate the cellular proarrhythmic mechanisms. We have developed the first mouse atrial myocyte model that incorporates mathematically detailed ion channels, cellular Ca2+ and Na+ handling and their regulation by Ca2+-calmodulin-dependent protein kinase II (CaMKII) and protein kinase A. For the first time, the inositol 1,4,5-trisphosphate (IP3) production system and its effects on excitation-contraction coupling have also been described. The validated model predicted that: 1) hyperactivity of CaMKII and elevated intracellular Na+ concentration are the crucial factors that induce sarcoplasmic reticulum (SR) Ca2+ spontaneous release and delayed afterdepolarisations; 2) β-adrenergic stimulation may have proarrhythmic effects by exacerbating Ca2+ overload; and 3) enhanced activity in ryanodine receptors during IP3-induced Ca2+ release is the major cause of the arrhythmogenesis in IP3 signalling.

Heart Failure is a common long term progressive and serious medical condition with high mortality and costly health services in the UK. By the year of 2010, there were around 90,000 people in the UK suffered from heart failure and in 2008, 10,000 heart failure patients were recorded death. Treatments of heart failure cost the National Health Service around £625 million every year. Although heart failure is highly pro-arrhythmic, the underlying mechanisms of the pro-arrhythmic effects of heart failure are not completely understood. Heart failure is associated with electrical remodelling of the properties and kinetics of some ionic channels responsible for the action potential of cardiac cells. However, it is still unclear whether this ionic channel remodelling can account for the pro-arrhythmic effects of heart failure as the complexity of the heart impedes a detailed experimental analysis. Biophysically detailed computational models have been developed in the last two decades, enabling the evaluation of experimental data. The aim of this thesis is to use arrhythmic mechanisms to investigate the pro-arrhythmic effects of heart failure-induced remodelling on the cardiac action potentials and Purkinje-ventricular junction. Single canine Purkinje fibre and ventricular cell models were developed to investigate the effects of heart failure-remodelled ionic channel currents on cell action potentials and identify optimal options for the potential clinical treatments. One-dimensional strand tissue model and three-dimensional wedge model were developed to further explore the effects of heart failure-induced remodelling in propagation of the canine Purkinje fibre, ventricle and Purkinje-ventricular junction. It was found that heart failure-induced remodelling on the Purkinje fibre and ventricle reduced the conduction safety and increased tissue’s vulnerability to the genesis of the unidirectional conduction block, especially at the Purkinje-ventricular junction, which may cause conduction failure, re-entry or both.

The recently identified genetic short QT syndrome is characterised by abbreviated QT intervals on the electrocardiogram, an increased risk of atrial and ventricular arrhythmias, and an increased risk of sudden death. Although the short QT syndrome has been suggested to provide a paradigm for increasing understanding of the role of potassium channels in ventricular fibrillation, the basis for arrhythmogenesis in the short QT syndrome is incompletely understood. There are no animal models that accurately reproduce a short QT phenotype, and whilst in vitro electrophysiology of short QT mutant channels provides a route to greater understanding of the effects of short QT mutants on action potential repolarisation, on its own, this approach is insufficient to explain how arrhythmias arise and are maintained at the tissue level. Consequently, this thesis is concerned with the use of the viable alternative; in silico (computational) modelling to elucidate how the short QT syndrome facilitates the genesis and maintenance of ventricular arrhythmias and its effects on ventricular contraction. Using extant biophysical data on changes induced by the short QT mutations and data from BHF-funded in vitro electrophysiology, three novel mathematical models of the first three variants of the short QT syndrome were developed; a Markov chain model for short QT variant 1, a Markov chain model for short QT variant 2 and a Hodgkin-Huxley model for short QT variant 3. These models were incorporated into single cell and anatomically detailed tissue and organ computer models to elucidate how these variants lead to ventricular arrhythmias. The developed short QT models were then incorporated into electromechanically coupled single cell and tissue models to investigate the effects of the short QT mutants on ventricular contraction. It was found that each short QT variant uniquely increased the transmural dispersion of action potential duration across the ventricular wall, increased the temporal window of tissue vulnerability to premature excitation stimulus, leading to increased susceptibility to re-entrant arrhythmia.

The sinoatrial node (SAN) is the primary pacemaker in mammalian hearts and is vital to cardiac function. Genetic mutations in SAN can result in lose-of-function of ion channels, consequently arouse sinus node dysfunction (SND), Brugada syndrome (BrS) and progressive cardiac conduction disease (PCCD). The mechanisms underlying the he pathogenesis for cardiac pacemaker dysfunctions associated with genetic mutations has not been defined. In this project, by using computer modeling, mechanisms by which the HCN4 mutations impair cardiac pacemaking and possible pro-arrhythmic effects of ivabradine were investigated. Action potential (AP) models for rabbit sinoatrial node cells were modified to incorporate experimentally reported If changes induced by HCN4 gene mutations. At both the cellular and intact SAN-atrium tissue level, If reduction due to the HCN4 mutations slowed down pacemaking. At the tissue level, these mutations compromised the AP conduction across the SAN-atrium, leading to a possible sinus arrest or SAN exit block. Moreover, vagal nerve activity could amplify the bradycardiac effects of the HCN4 gene mutations, leading to sinus arrest and SAN exit block that was not observed with the mutations or ACh alone. Similarly, SND associated with SCN5A mutations and acquired cardiac conditions were studied. 1) Mathematical models of rabbit SAN cells and 2D tissue models were modified to investigate SAN function and intracardiac conduction in a murine model of long QT syndrome type 3. A prolonged tail current INa,L was introduced and incorporated with a normal INa,T to test the SAN pacemaker function and AP conduction from the SAN to atrial septum. Simulation results showed that a combined reduction in INa,T and introduction of INa,L achieved alterations in both pacemaking rate and conduction. 2) Mathematical models of mouse SAN cells were modified to investigate the mechanisms underlies the SAN associated with SCN5A deficiency and aging. A coupled SAN-atrium cell model was developed to replicate the experimentally observed slowing of SAN conduction with aging and SCN5A-disruption The modelling studies reconstructed the physiological mechanisms by which both aging and SCN5A-disruption lead to SND, thereby drawing parallels between these and similar conduction changes in the ventricle that occur in the possibly related condition of PCCD. At last, a 2D anatomically based model of the SAN-atrium was constructed. This model successfully reproduced the effects of vagal nerve stimulation and SCN5A-E161K gene mutation on spontaneous activity of the SAN and AP conduction across the SAN-atrium.

During excitation-contraction coupling, Ca2+ transient induced by the depolarization of membrane potential is the trigger of mechanical contraction in cardiac myocytes, which is responsible for the pumping function of the heart. However, mechanisms underlying intracellular Ca2+ regulation and the coupling between Ca2+ transient and membrane potential are not completely understood. Abnormalities in intracellular Ca2+ regulation have been observed during heart failure and cardiac arrhythmias, such as intracellular Ca2+ alternans and T-tubule disorganization. In this project, intracellular Ca2+ dynamics in different types of cardiac myocytes were investigated by using computer modelling. For atrial myocytes, a biophysically detailed computer model was developed to describe the observations of Ca2+ alternans and Ca2+ wave propagation in cardiac myocytes lacking T-tubules. The model was validated by its ability to reproduce experimental observed Ca2+ wave propagation under normal condition and the influences on spatial Ca2+ distribution by modifying various aspects of Ca2+ cycling, such as Ca2+ influx, SR Ca2+ uptake and SR Ca2+ release in cardiac myocytes lacking T-tubules. Mechanisms underlying the genesis of Ca2+ alternans in this type of cell were investigated by the model. Furthermore, a spontaneous second Ca2+ release was observed in response to a single voltage stimulus pulse with enhanced Ca2+ influx as well as SR Ca2+ overload. For the ventricular myocytes, an existing canine model was used to study the genesis of APD and intracellular Ca2+ alternans under various conditions. The genesis of Ca2+ alternans was investigated by analyzing the relationship between systolic Ca2+ concentration and SR Ca2+ content. On the other side, the roles of SR Ca2+ regulation and action potential restitution in the genesis of intracellular Ca2+ and APD alternans were also examined under various conditions. In addition, it was shown that spatially discordant Ca2+ alternans was generated when the Ca2+-dependent inactivation of ICa,L was strong. It tended to be concordant for weak Ca2+-dependent inactivation of ICa,L. For the sinoatrial node cells, a mathematical model was developed to simulate stochastic opening of unitary L-type Ca2+ channel and single RyR channel, thereby reproducing experimental observed local Ca2+ release during diastolic depolarization phase of the action potential. Simulation results of ionic channel block and modifications of SR Ca2+ regulation suggested a limited role of intracellular Ca2+ in the automaticity of central SA node cells.

Cardiovascular disease is a leading cause of death throughout the world. In order to understand the mechanisms by which the heart functions, computational models of a variety of cardiac myocytes have been developed. Although these models provide substantial information on the activity of single heart cells, there is limited understanding of the interactions of these cells at the tissue level. This thesis is concerned with the integration of such single cell models into larger, more complex tissue structures. Firstly, this thesis introduces and reviews a number of single cell models. These individual models were integrated into a structurally detailed 2D slice of heart with a histological geometry. This model was used to investigate the cardiac sequence of a rabbit heart, and a number of biophysical parameters were compared with, and found to closely reproduce experimental data. To further investigate, a 3D rabbit heart geometry was obtained and segmented into atrial, sino-atrial nodal, atrio-ventricular nodal, Purkinje fibre and ventricular tissue, with each ventricle divided into endocardial, epicardial and mid-myocardial regions, with an aim to investigate the effect of a number of pro- and anti-arrhythmic effects on the rabbit heart. Analysis of the 3D model predicted huge computational load related to the resolution of millions of cells. Currently, large scale computational simulations of cardiac activity are carried out using dedicated supercomputing facilities, but such solutions can be costly and unwieldy. To overcome this, investigation was carried out into the use of graphical programming to decrease the computational time required to resolve such equations. Investigation was carried out into the problem size at which graphical computation outperforms traditional computation, and found to give up to a hundred-fold increase in computational speed at 10^6 cells. These results pave the way for a new style of cardiac programming, allowing quick and detailed investigation into a multitude of problems using cheap, easily available hardware.

Cardiac fibroblasts are by number the largest component of the non-myocytes, providing structural support for the heart by regulating the synthesis and degradation of extracellular matrix components. Experimental studies suggested that they are electrically coupled to myocytes and participate in the electrical activity. The aim of this study was to provide insights into the electrophysiological role of fibroblasts in cardiac pacemaking activity at single cell level by using mathematical models and computational simulations. The simulations in the central SAN showed that the myocyte-fibroblast coupling 1) shortened action potential duration, 2) shortened cycle length, 3) decreased the maximum upstroke velocity, 4) produced more hyperpolarised maximum diastolic potential, and 5) reduced the peak value of the action potential. Since the coupling in the centre of the SAN was sensitive to the gap junctional conductance, myocytes could just couple to a fibroblast with a junctional conductance less than 0.169 nS. The coupling in the peripheral SAN showed that 1) at weak coupling (0.13 nS), there was a reduction in the peak value of the action potential and the maximum upstroke velocity, and an increase in the cycle length and a more hyperpolarised maximum diastolic potential, resulting in a slowing down in the firing rate. Whether the pacemaking rate was accelerated or decelerated, the driving ability was actually impaired as the maximum upstroke velocity and the amplitude of potential were decreased in both cases.

Cardiovascular disease is prevalent across the western world and is a major cause of morbidity and mortality, accounting for approximately a third of all fatalities. Investigating the heart by simulating its electrophysiology via the aid of mathematical models has advanced significantly over the past 60 years and is now a well established field. While much of the research focus is placed on the ventricles, the study of the atria is in comparison neglected. Therefore this Thesis is focused on the genesis and maintenance of atrial fibrillation (AF). A series of case studies are performed whereby established biophysically detailed mathematical models are implemented and modified to incorporate electrophysical alterations of atrial cells resulting from a variety of external conditions. The opening section of this Thesis is dedicated to developing a background to the field, including a discussion into the clinical aspect of the diagnosis and management of AF. The suitability of two atrial cell models is discussed and the development of single cell, 1D, 2D, and 3D multi-scale simulation protocols are described in detail. In addition measurements taken to quantify the arrhythmogenic properties of the cells susceptibility to AF are outlined. The second section is focused on the incorporation of conditions thought to enhance atrial tissues ability to initiate and maintain the genesis of AF. Included is a case study into the missence S140G gene mutation, and elevated physiological levels of the hormone Homocystein. The third section investigates the effectiveness of well established and widely used pharmacological treatments such as Beta-Blockers. In addition possible avenues of investigations for the development of atrial specific drugs are explored. These include blocking of the ultra rapid potassium channel and a more novel target for therapy via the targeting of 5HT4 receptors; which is transcribed solely in the atria and alters the electrophysical properties of the L-type Calcium current. The final part of this Thesis is dedicated to the development of a 2D atrial sheet model which includes electrical and spatial heterogeneities via the inclusion of multiple cell types and basic fiber orientation respectively. This allows for an investigation into the role that heterogeneities play in role genesis and maintenance of AF. The main finding of this Thesis is that alterations to the electrophysiology of atrial cells, due to external factors, can be successfully simulated via the implementation of mathematically detailed atrial cell models. It is concluded that simulations of the KENQ1 mutation and elevated levels of Homocystein successfully reproduce conditions which increase the onset of AF. Established treatments such as Beta-Blockers are found to have limited effectiveness. Possible theoretical treatments, such as the blocking of IKur, are found to provide a small amount of therapeutic benefit. In contrast, investigations into the effects of Serotonin were inconclusive. The study into the 2D atria indicated the importance that heterogeneities play in atria. The conclusions show that models provide a powerful tool when investigating how changes to electrophysiology of cells are manifested at a multi-scale level. The models also have their limitations and require further advancement to improve their accuracy.

While premature birth is still one of the major clinical problems worldwide, theexact physiological mechanisms underlying myometrium activity during pregnancyremain unclear. In this thesis, a novel biophysically detailed model wasconstructed using available experimental data to simulate chemical, electrical andmechanical activity in a late pregnant rat uterine myocycte. The developed modelhas been used to elucidate the ionic mechanism underlying myometrium functionality,providing better insights in the function of the uterus during pregnancy. Themodel consisted of 15 membrane currents, intracellular calcium handling processcoupled with a sliding actin-myosin filament mechanical model to describe uterinebehaviour and contractile activity at the single myocyte level. Each of theionic currents were modelled using Hodgkin-Huxley-type equations. The simulatedcurrent traces and current-voltage curves were validated with experimentalrecordings and the model was further validated by the ability to produce a burstingaction potential (AP) during an external stimulus. The model replicated theeffects of estradiol during pregnancy, modulating the amplitude and activationproperties of individual Ca2+ and K+ currents, therefore altering the AP configurationto a tonic-like plateau. The model also reproduced the actions of drugsto inhibit certain channels to investigate their roles in myometrium. Sensitivityanalysis was performed to examine the model’s behaviour to changing parameters.A simple 1-D study was conducted to investigate how electrical signals propagatealong strand of cells. Although the model successfully replicated results similarto recordings seen in the experiments, limitations have to be addressed and morestudies have to be carried out to further improve the model.

Cardiovascular disease remains the primary cause of morbidity and mortality in the UK and EU, accounting for more than 2.0 million deaths per year across the EU. The economic consequences of cardiovascular disease are equally grave, with a total estimated annual health care expenditure of €109.7 billion in the EU, rising to €192.5 billion if informal health care costs and productivity losses are taken into account. The precise mechanisms underlying arrhythmogenesis in heart failure are not fully understood, however there is an increasing body of evidence identifying the Purkinje fibre (PF) network as both a major source and contributor to the sustenance of ventricular arrhythmias. Mathematical models of the electrical action potentials (APs), and their propagation through the cardiac conduction system, compliment, and present a unique alternative to, experimental observations and investigation. They enable fundamental physiological mechanisms to be dissected and theories rigorously tested in a consistent and efficient manner. In this thesis, a 3D wedge model of the canine Purkinje-ventricular junction (PVJ) is developed incorporating details of the transmural AP heterogeneity, tissue geometry, and fibre orientation of the left ventricular free wall, completed with a single PF entering the endocardium. The relationships between the tissue heterogeneity; AP conduction velocity; and the safety of conduction at the junction are explored and pharmacological effects on conduction through the junction are studied. A new mathematical model for the AP of the canine PF cell is developed to support the construction of the PVJ model and additionally, a new model for the AP of the human PF cell is developed. Biophysically detailed, species specific models are necessary for a complete understanding of the cardiac conduction system, yet PF models have been largely neglected since the early work of DiFrancesco & Noble in 1985. The models are proven in the analysis and dissection of the mechanisms underlying experimental phenomena including the Bowditch effect; rate dependence of the AP; and overdrive suppression.