There is a clear need for improved methods (e.g. computer modelling, imaging) to characterize the substrate of abnormal rhythms like ventricular tachycardia (VT) developed by patients who have suffered a heart attack. Progress leading to improved disease management and treatment planning (based on predictive models) as well as outcomes assessment will have immediate impact on the quality of life in this large patient population. Prior to integration into clinical applications, the predictive models have to be properly validated using experimental techniques selected to reflect the electrophysiological phenomena at spatio-temporal scales similar to those considered in simulations. This thesis advanced us toward this goal by addressing the challenge of building more accurate models of electrophysiology for individual hearts. A novel construction of a realistic 3D cardiac model from Magnetic Resonance Images (MRI), with a long-term aim to predict propagation of the electrical impulse in normal and pathologic large hearts (translatable to human hearts), and associated inducibility of VT is described. To parameterize the model, an original evaluation method of electrophysiological (EP) characteristics of the heart tissue was used. The method combined state-of-the-art experimental physiology tools like optical fluorescence imaging using voltage-sensitive dyes and a CARTO electro-anatomical system, with a cardiac computer model generated from high resolution MR scans of explanted normal and pathologic porcine hearts. Several input model parameters (e.g., conductivity, anisotropy, restitution) were successfully adjusted using the ex-vivo measurements of action potential to yield close correspondence between model output and experiments. Moreover, a simple, fast, and macroscopic mathematical model was used with computation times less than 1h, attractive for clinical EP applications.

There is a clear need for improved methods (e.g. computer modelling, imaging) to characterize the substrate of abnormal rhythms like ventricular tachycardia (VT) developed by patients who have suffered a heart attack. Progress leading to improved disease management and treatment planning (based on predictive models) as well as outcomes assessment will have immediate impact on the quality of life in this large patient population. Prior to integration into clinical applications, the predictive models have to be properly validated using experimental techniques selected to reflect the electrophysiological phenomena at spatio-temporal scales similar to those considered in simulations. This thesis advanced us toward this goal by addressing the challenge of building more accurate models of electrophysiology for individual hearts. A novel construction of a realistic 3D cardiac model from Magnetic Resonance Images (MRI), with a long-term aim to predict propagation of the electrical impulse in normal and pathologic large hearts (translatable to human hearts), and associated inducibility of VT is described. To parameterize the model, an original evaluation method of electrophysiological (EP) characteristics of the heart tissue was used. The method combined state-of-the-art experimental physiology tools like optical fluorescence imaging using voltage-sensitive dyes and a CARTO electro-anatomical system, with a cardiac computer model generated from high resolution MR scans of explanted normal and pathologic porcine hearts. Several input model parameters (e.g., conductivity, anisotropy, restitution) were successfully adjusted using the ex-vivo measurements of action potential to yield close correspondence between model output and experiments. Moreover, a simple, fast, and macroscopic mathematical model was used with computation times less than 1h, attractive for clinical EP applications.

Several studies have been carried out recently with the aim of achieving cardiac modelling of the whole heart for a full heartbeat. However, within the context of the Galerkin method, those simulations require high computational demand, ranging from 16 - 200 CPUs, and long calculation time, lasting from 1 h - 50 h. To solve this problem, this research proposes to make use of a Reduced Order Method (ROM) called the Proper Orthogonal Decomposition with Interpolation method (PODI) to achieve real-time modelling with an adequate level of solution accuracy. The idea behind this method is to first construct a database of pre-computed full-scale solutions using the Element-free Galerkin method (EFG) and then project a selected subset of these solutions to a low dimensional space. Using the Moving Least Square method (MLS), an interpolation is carried out for the problem-at-hand, before the resulting coefficients are projected back to the original high dimensional solution space. The aim of this project is to tackle real-time modelling of a patient-specific heart for a full heartbeat in different stages, namely: modelling (i) the diastolic filling with variations of material properties, (ii) the isovolumetric contraction (IVC), ejection and isovolumetric relation (IVR) with arbitrary time evolutions, and (iii) variations in heart anatomy. For the diastolic filling, computations are carried out on a bi-ventricle model (BV) to investigate the performance and accuracy for varying the material parameters. The PODI calculations of the LV are completed within 14 s on a normal desktop machine with a relative L₂-error norm of 6x10⁻³. These calculations are about 2050 times faster than EFG, with each displacement step generated at a calculation frequency of 1074 Hz. An error sensitivity analysis is consequently carried out to find the most sensitive parameter and optimum dataset to be selected for the PODI calculation. In the second phase of the research, a so-called "time standardisation scheme" is adopted to model a full heartbeat cycle. This is due to the simulation of the IVC, ejection, and IVR phases being carried out using a displacement-driven calculation method which does not use uniform simulation steps across datasets. Generated results are accurate, with the PODI calculations being 2200 faster than EFG. The PODI method is, in the third phase of this work, extended to deal with arbitrary heart meshes by developing a method called "Degrees of freedom standardisation" (DOFS). DOFS consists of using a template mesh over which all dataset result fields are projected. Once the result fields are standardised, they are consequently used for the PODI calculation, before the PODI solution is projected back to the mesh of the problem-at-hand. The first template mesh to be considered is a cube mesh. However, it is found to produce results with high errors and non-physical behaviour. The second template mesh used is a heart template. In this case, a preprocessing step is required where a non-rigid transformation based on the coherent point drift method is used to transform all dataset hearts onto the heart template. The heart template approach generated a PODI solution of higher accuracy at a relatively low computational time. Following these encouraging results, a final investigation is carried out where the PODI method is coupled with a computationally expensive gradient-based optimisation method called the Levenberg- Marquardt (PODI-LVM) method. It is then compared against the full-scale simulation one where the EFG is used with the Levenberg-Marquardt method (EFG-LVM). In this case, the PODI-LVM simulations are 1025 times faster than the EFG-LVM, while its error is less than 1%. It is also observed that since the PODI database is built using EFG simulations, the PODI-LVM behaves similarly to the EFG-LVM one.

Cardiovascular disease remains the leading cause of death in the developed world. In this thesis computational modelling techniques were used to study the mechanisms and genesis of atrial arrhythmias. It is separated into 2 parts: (1) The mechanistic links between mutations of the fast Na+ channel (INa) and the ability of the sinoatrial node to pace the surrounding atrial muscle were investigated. The mutations were separated into two groups, one for the mutations affecting the steady-state activation, and the other for those affecting steady-state inactivation. On the single cell level it was found that all mutations slowed the pacing rate of the sinoatrial node in a similar way, but at the 2D level the two mutation groups modulated the excitation of the tissue differently. One caused a conduction block between the sinoatrial node and atrium, where the other abolished pacemaking all together. (2) A new set of mathematical models were then developed for the sheep atria. This was incorporated into an anatomically detailed 3D geometry of the whole sheep atria to form a platform suitable for the study of clinical atrial fibrillation, and other atrial arrhythmias. Due to the lack of single cell electrophysiology data available, a method of cross-species modelling was utilised. A biophysically detailed model of the 3D sheep atria was created, and used in a preliminary study into the susceptibility of tissue to atrial fibrillation from the rapid pacing of the pulmonary vein area. It was found that both electrical heterogeneity and the complex fibre structure of the atria need to be considered for sustained atrial fibrillation to be seen.

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.

The aim of this work is to propose an algorithm to segment and track the myocardium using the level-set formalism. The myocardium is first approximated by a geometric model (hyperquadrics) which allows to handle asymetric shapes such as the myocardium while avoiding a learning step. This representation is then embedded into the level-set formalism as a shape prior for the joint segmentation of the endocardial and epicardial borders. This shape prior term is coupled with a local data attachment term and a thickness term that prevents both contours from merging. The algorithm is validated on a dataset of 80 images at end diastolic and end systolic phase with manual references from 3 cardiologists. In a second step, we propose to segment whole sequences using motion information. To this end, we apply a level conservation constraint on the implicit function associated to the level-set and express this contraint as an energy term in a variational framework. This energy is then added to the previously described algorithm in order to constrain the temporal evolution of the contour. Finally the algorithm is validated on 20 echocardiographic sequences with manual references of 2 experts (corresponding to approximately 1200 images).

Atrial arrhythmias are the most prevalent sustained cardiac arrhythmias. Rates of hospitalisation and costs incurred to healthcare organisations are increasing in epidemic proportions. Despite this, the mechanisms of the transition from sinus rhythm to arrhythmic states are not well understood. The high level of regional electrical heterogeneity observed in the atria is thought to contribute towards the high prevalence of atrial arrhythmias. However, current computer models of the intact human atria only account for a small degree of this regional electrical heterogeneity, and do not include descriptions of the pacemaker regions of the sinoatrial node and the atrioventricular node. In this project, a new computational model of the intact 3D human atria is developed. First, a new single cell model to simulate the electrical action potential of the human atrial myocyte is developed. This model more accurately simulated the experimentally observed properties of human atrial action potentials than previous models. A family of electrically heterogeneous models describing the major regions within the atria is then developed, including those of the sinoatrial- and atrioventricular- nodes. This set of regional cell models represents the most expansive and complete set currently available. It is demonstrated that the large range of different electrical properties results in a large range of action potential morphology and duration within the atria. Models of the effect of sympathetic and parasympathetic regulation on the electrical AP of the models of the atrial working myocardium and the pacemaker regions were also incorporated. This demonstrated that sympathetic regulation can increase the pacing rate of the sinoatrial node and the atrio-ventricular node, and has a complex dose dependent effect on the atrial working myocardium. Four distinct models of the effects of atrial fibrillation induced remodelling on the atrial working myocardium are developed. These characterised the effect of remodelling of IKur on the overall changes in action potential morphology and duration observed. It is shown that the presence or absence of remodelling of this channel accounts for two distinct observed morphologies. A previous 3D anatomical model of the human atria is improved. First, detailed anatomical models for the sinoatrial node and the atrioventricular node are incorporated into the model. Second, it is further segmented to include regions for the pulmonary veins, atrio-ventricular ring, atrial septum and sinoatrial node block zone. This model is used to investigate the effects of sympathetic and parasympathetic regulation in the 3D atria. Finally, a detailed investigation of the underlying mechanisms of atrial fibrillation in the 3D atria, and the effect of electrical remodelling on the behaviour of atrial fibrillation, is performed using the detailed 3D model. This work represents a significant advance in 3D human atrial modelling. The anatomical model incorporates a greater level of complexity than previous models, and for the first time allowed investigation of the pacemaking mechanisms in the 3D intact human atria. The atrial fibrillation protocols are more physiologically relevant than previous models and have elucidated the roles that electrophysiological remodelling, electrical heterogeneity and structural anisotropy play in the development and maintenance of atrial fibrillation.

Cardiac motion is a highly complex and integrated process of vital importance as it sustains the primary function of the heart, that is pumping blood. Cardiac tissue microstructure, in particular the alignment of myocytes (also referred to as fibre direction) and their lateral organisation into laminae (or sheets), has been shown by both experimental and computational research to play an important role in the determination of cardiac motion patterns. However, current models of cardiac electromechanics, although already embedding structural information in the models equations, are not yet able to fully reproduce the connection between structural dynamics and cardiac deformation. The aim of this thesis was to develop an electromechanical modelling framework to investigate the impact of tissue structure on cardiac motion, focussing on left ventricular contraction in rat. The computational studies carried out were complemented with a preliminary validation study based on experimental data of tissue structure rearrangement during contraction from diffusion tensor MRI.

An increasingly important research area within the field of cardiac modelling is the development and study of methods of model-based parameter estimation from clinical measurements of cardiac function. This provides a powerful approach for the quantification of cardiac function, with the potential to ultimately lead to the improved stratification and treatment of individuals with pathological myocardial mechanics. In particular, the diastolic function (i.e., blood filling) of left ventricle (LV) is affected by its capacity for relaxation, or the decay in residual active tension (AT) whose inhibition limits the relaxation of the LV chamber, which in turn affects its compliance (or its reciprocal, stiffness). The clinical determination of these two factors, corresponding to the diastolic residual AT and passive constitutive parameters (stiffness) in the cardiac mechanical model, is thus essential for assessing LV diastolic function. However these parameters are difficult to be assessed in vivo, and the traditional criterion to diagnose diastolic dysfunction is subject to many limitations and controversies. In this context, the objective of this study is to develop model-based applicable methodologies to estimate in vivo, from 4D imaging measurements and LV cavity pressure recordings, these clinically relevant parameters (passive stiffness and active diastolic residual tension) in computational cardiac mechanical models, which enable the quantification of key clinical indices characterising cardiac diastolic dysfunction. Firstly, a sequential data assimilation framework has been developed, covering various types of existing Kalman filters, outlined in chapter 3. Based on these developments, chapter 4 demonstrates that the novel reduced-order unscented Kalman filter can accurately retrieve the homogeneous and regionally varying constitutive parameters from the synthetic noisy motion measurements. This work has been published in Xi et al. 2011a. Secondly, this thesis has investigated the development of methods that can be applied to clinical practise, which has, in turn, introduced additional difficulties and opportunities. This thesis has presented the first study, to our best knowledge, in literature estimating human constitutive parameters using clinical data, and demonstrated, for the first time, that while an end-diastolic MR measurement does not constrain the mechanical parameters uniquely, it does provide a potentially robust indicator of myocardial stiffness. This work has been published in Xi et al. 2011b. However, an unresolved issue in patients with diastolic dysfunction is that the estimation of myocardial stiffness cannot be decoupled from diastolic residual AT because of the impaired ventricular relaxation during diastole. To further address this problem, chapter 6 presents the first study to estimate diastolic parameters of the left ventricle (LV) from cine and tagged MRI measurements and LV cavity pressure recordings, separating the passive myocardial constitutive properties and diastolic residual AT. We apply this framework to three clinical cases, and the results show that the estimated constitutive parameters and residual active tension appear to be a promising candidate to delineate healthy and pathological cases. This work has been published in Xi et al. 2012a. Nevertheless, the need to invasively acquire LV pressure measurement limits the wide application of this approach. Chapter 7 addresses this issue by analysing the feasibility of using two kinds of non-invasively available pressure measurements for the purpose of inverse parameter estimation. The work has been submitted for publication in Xi et al. 2012b.

Mathematical models have been used to capture the behaviour of biological systems, from low-level biochemical reactions to multi-scale whole-organ models. Models are typically based on experimentally-derived data, attempting to reproduce the observed behaviour through mathematical constructs, e.g. using Ordinary Differential Equations (ODEs) for spatially-homogeneous systems. These models are developed and published as mathematical equations, yet are of such complexity that they necessitate computational simulation. This computational model development is often performed in an ad hoc fashion by modellers who lack extensive software engineering experience, resulting in brittle, inefficient model code that is hard to extend and reuse. Several Domain Specific Languages (DSLs) exist to aid capturing such biological models, including CellML and SBML; however these DSLs are designed to facilitate model curation rather than simplify model development. We present research into the application of techniques from software engineering to this domain; starting with the design, development and implementation of a DSL, termed Ode, to aid the creation of ODE-based biological models. This introduces features beneficial to model development, such as model verification and reproducible results. We compare and contrast model development to large-scale software development, focussing on extensibility and reuse. This work results in a module system that enables the independent construction and combination of model components. We further investigate the use of software engineering processes and patterns to develop complex modular cardiac models. Model simulation is increasingly computationally demanding, thus models are often created in complex low-level languages such as C/C++. We introduce a highly-efficient, optimising native-code compiler for Ode that generates custom, model-specific simulation code and allows use of our structured modelling features without degrading performance. Finally, in certain contexts the stochastic nature of biological systems becomes relevant. We introduce stochastic constructs to the Ode DSL that enable models to use Stochastic Differential Equations (SDEs), the Stochastic Simulation Algorithm (SSA), and hybrid methods. These use our native-code implementation and demonstrate highly-efficient stochastic simulation, beneficial as stochastic simulation is highly computationally intensive. We introduce a further DSL to model ion channels declaratively, demonstrating the benefits of DSLs in the biological domain. This thesis demonstrates the application of software engineering methodologies, and in particular DSLs, to facilitate the development of both deterministic and stochastic biological models. We demonstrate their benefits with several features that enable the construction of large-scale, reusable and extensible models. This is accomplished whilst providing efficient simulation, creating new opportunities for biological model development, investigation and experimentation.