Model-based Analysis of Temporal Patterns in Atrioventricular Node Conduction During Atrial Fibrillation

The lifetime risk of developing atrial fibrillation (AF) is estimated to be between 1in 3 to 1 in 4 individuals, making it the most common arrhythmia in the world.For persistent AF, rate control drugs with the purpose to affect the conduction properties of the atrioventricular (AV) node are the most common treatment. The drug of choice varies between β-blockers and calcium channel blockers, often chosen empirically. This can lead to long periods of time before sufficient treatment is found. However, due to the physiological differences between the drug types, it could be possible to predict the effect of the drugs and thus assist in treatment selection. The main focus of this thesis is therefore to assess drug-dependent differences in the AV node, using non-invasive measurements. This thesis comprises an introduction to the subject as well as two papers. The first paper proposes a framework for assessing the conduction properties of the AV node non-invasively using a mathematical model of the AV node in combination with a genetic algorithm.The second paper is a continuation of the work in paper I, where the proposed workflow was adapted to assess the drug-dependent effect on the AV node of four different rate control drugs during a period of 24 hours.The methods presented in this thesis have made it possible to assess both the refractory period and the conduction delay in the AV node in a robust way using ECG, and by doing so found population-related differences in AV node conduction properties between drug types

ECG-based estimation of respiratory modulation of AV nodal conduction during atrial fibrillation

Information about autonomic nervous system (ANS) activity may be valuable for personalized atrial fibrillation (AF) treatment but is not easily accessible from the ECG. In this study, we propose a new approach for ECG-based assessment of respiratory modulation in AV nodal refractory period and conduction delay. A 1-dimensional convolutional neural network (1D-CNN) was trained to estimate respiratory modulation of AV nodal conduction properties from 1-minute segments of RR series, respiration signals, and atrial fibrillatory rates (AFR) using synthetic data that replicates clinical ECG-derived data. The synthetic data were generated using a network model of the AV node and 4 million unique model parameter sets. The 1D-CNN was then used to analyze respiratory modulation in clinical deep breathing test data of 28 patients in AF, where a ECG-derived respiration signal was extracted using a novel approach based on periodic component analysis. We demonstrated using synthetic data that the 1D-CNN can predict the respiratory modulation from RR series alone ($\rho$ = 0.805) and that the addition of either respiration signal ($\rho$ = 0.830), AFR ($\rho$ = 0.837), or both ($\rho$ = 0.855) improves the prediction. Results from analysis of clinical ECG data of 20 patients with sufficient signal quality suggest that respiratory modulation decreased in response to deep breathing for five patients, increased for five patients, and remained similar for ten patients, indicating a large inter-patient variability.Comment: 20 pages, 7 figures, 5 table

An atrioventricular node model incorporating autonomic tone

The response to atrial fibrillation (AF) treatment is differing widely among patients, and a better understanding of the factors that contribute to these differences is needed. One important factor may be differences in the autonomic nervous system (ANS) activity. The atrioventricular (AV) node plays an important role during AF in modulating heart rate. To study the effect of the ANS-induced activity on the AV nodal function in AF, mathematical modelling is a valuable tool. In this study, we present an extended AV node model that incorporates changes in autonomic tone. The extension was guided by a distribution-based sensitivity analysis and incorporates the ANS-induced changes in the refractoriness and conduction delay. Simulated RR series from the extended model driven by atrial impulse series obtained from clinical tilt test data were qualitatively evaluated against clinical RR series in terms of heart rate, RR series variability and RR series irregularity. The changes to the RR series characteristics during head-down tilt were replicated by a 10% decrease in conduction delay, while the changes during head-up tilt were replicated by a 5% decrease in the refractory period and a 10% decrease in the conduction delay. We demonstrate that the model extension is needed to replicate ANS-induced changes during tilt, indicating that the changes in RR series characteristics could not be explained by changes in atrial activity alone

Systolic ejection murmurs and the left ventricular outflow tract in boxer dogs

Turbulence of various genesis in the left ventricular outflow tract (LVOT) causes systolic ejection murmurs. The prevalence of murmurs in adult boxer dogs is 50-80%, the majority of which are of low intensity. Some of the murmurs are caused by aortic stenosis (AS), while the origin of the others is unclear. The aim of this thesis was to study the physiology and clinical evaluation of systolic ejection murmurs and their relation to the development of the LVOT in boxers with and without AS. Growing and adult boxer dogs were examined by the standard methods cardiac auscultation, ECG, phonocardiography and echocardiography. Additionally, the complementary methods time-frequency and complexity analyses of heart murmurs and contrast echocardiography were evaluated. Studies on inter-observer variation in cardiac auscultation proved the importance of experience in detection and grading of low intensity ejection murmurs. Excitement of the dogs by exercise or noise stimulation (barking dog and squeaky toy) caused higher murmur grades, longer murmur duration and increased aortic flow velocities. No differences were found between diameters measured at different levels of the LVOT in growing boxers. Contrast echocardiography enhanced Doppler signals, but did not allow evaluation of myocardial blood flow. Using time-frequency analysis, duration of murmur frequency >200 Hz proved useful for differentiation between dogs with mild AS and dogs without. Combining assessment of murmur duration >200 Hz and complexity analysis using the correlation dimension (T2), a sensitivity of 94% and a specificity of 82% for differentiation between dogs with and without AS was achieved. The variability in presence and intensity of low intensity murmurs during growth was high. None of the young dogs developed AS, whereas 3 out of 16 individuals developed mild-moderate aortic insufficiency. Aortic or pulmonic flow velocities did not differ significantly between growing dogs with or without low intensity murmurs. In conclusion, the variability in presence and intensity of low intensity ejection murmurs in boxers is high during growth with no obvious progression. Both in young and adult boxers the murmur grade increased during excitement, which may be due to rapid flow in a comparatively small LVOT that has been suggested for the boxer breed. Experience is important in cardiac auscultation of low intensity murmurs. Therefore, assessment of murmur duration > 200 Hz combined with T2 analysis may be a useful complementary method for diagnosis of cardiovascular function in dogs

A multiscale model for collagen alignment in wound healing

It is thought that collagen alignment plays a significant part in scar tissue formation during dermal wound healing. We present a multiscale model for collagen deposition and alignment during this process. We consider fibroblasts as discrete units moving within an extracellular matrix of collagen and fibrin modelled as continua. Our model includes flux induced alignment of collagen by fibroblasts, and contact guidance of fibroblasts by collagen fibres. We can use the model to predict the effects of certain manipulations, such as varying fibroblast speed, or placing an aligned piece of tissue in the wound. We also simulate experiments which alter the TGF-β concentrations in a healing dermal wound and use the model to offer an explanation of the observed influence of this growth factor on scarring

Cancer modelling: Getting to the heart of the problem

Paradoxically, improvements in healthcare that have enhanced the life expectancy of humans in the Western world have, indirectly, increased the prevalence of certain types of cancer such as prostate and breast. It remains unclear whether this phenomenon should be attributed to the ageing process itself or the cumulative effect of prolonged exposure to harmful environmental stimuli such as ultraviolet light, radiation and carcinogens (Franks and Teich, 1988). Equally, there is also compelling evidence that certain genetic abnormalities can predispose individuals to specific cancers (Ilyas et al., 1999). The variety of factors that have been implicated in the development of solid tumours stems, to a large extent, from the fact that ‘cancer’ is a generic term, often used to characterize a series of disorders that share common features. At this generic level of description, cancer may be viewed as a cellular disease in which controls that usually regulate growth and maintain homeostasis are disrupted. Cancer is typically initiated by genetic mutations that lead to enhanced mitosis of a cell lineage and the formation of an avascular tumour. Since it receives nutrients by diffusion from the surrounding tissue, the size of an avascular tumour is limited to several millimeters in diameter. Further growth relies on the tumour acquiring the ability to stimulate the ingrowth of a new, circulating blood supply from the host vasculature via a process termed angiogenesis (Folkman, 1974). Once vascularised, the tumour has access to a vast nutrient source and rapid growth ensues. Further, tumour fragments that break away from the primary tumour, on entering the vasculature, may be transported to other organs in which they may establish secondary tumours or metastases that further compromise the host. Invasion is another key feature of solid tumours whereby contact with the tissue stimulates the production of enzymes that digest the tissue, liberating space into which the tumour cells migrate. Thus, cancer is a complex, multiscale process. The spatial scales of interest range from the subcellular level, to the cellular and macroscopic (or tissue) levels while the timescales may vary from seconds (or less) for signal transduction pathways to months for tumour doubling times The variety of phenomena involved, the range of spatial and temporal scales over which they act and the complex way in which they are inter-related mean that the development of realistic theoretical models of solid tumour growth is extremely challenging. While there is now a large literature focused on modelling solid tumour growth (for a review, see, for example, Preziosi, 2003), existing models typically focus on a single spatial scale and, as a result, are unable to address the fundamental problem of how phenomena at different scales are coupled or to combine, in a systematic manner, data from the various scales. In this article, a theoretical framework will be presented that is capable of integrating a hierarchy of processes occurring at different scales into a detailed model of solid tumour growth (Alarcon et al., 2004). The model is formulated as a hybrid cellular automaton and contains interlinked elements that describe processes at each spatial scale: progress through the cell cycle and the production of proteins that stimulate angiogenesis are accounted for at the subcellular level; cell-cell interactions are treated at the cellular level; and, at the tissue scale, attention focuses on the vascular network whose structure adapts in response to blood flow and angiogenic factors produced at the subcellular level. Further coupling between the different spatial scales arises from the transport of blood-borne oxygen into the tissue and its uptake at the cellular level. Model simulations will be presented to illustrate the effect that spatial heterogeneity induced by blood flow through the vascular network has on the tumour’s growth dynamics and explain how the model may be used to compare the efficacy of different anti-cancer treatment protocols

Damage-driven strain localisation in networks of fibres: A computational homogenisation approach

In many applications, such as textiles, fibreglass, paper and several kinds of biological fibrous tissues, the main load-bearing constituents at the micro-scale are arranged as a fibre network. In these materials, rupture is usually driven by micro-mechanical failure mechanisms, and strain localisation due to progressive damage evolution in the fibres is the main cause of macro-scale instability. We propose a strain-driven computational homogenisation formulationbased on Representative Volume Element (RVE), within a framework in which micro-scale fibre damage can lead to macro-scale localisation phenomena. The mechanical stiffness considered here for the fibrous structure system is due to: i) an intra-fibre mechanism in which each fibre is axially stretched, and as a result, it can suffer damage; ii) an inter-fibre mechanism in which the stiffness results from the variation of the relative angle between pairs of fibres. The homogenised tangent tensor, which comes from the contribution of these two mechanisms, is required to detect the so-called bifurcation point at the macro-scale, through the spectral analysis of the acoustic tensor. This analysis can precisely determine the instant at which the macro-scale problem becomes ill-posed. At such a point, the spectral analysis provides information about the macro-scale failure pattern (unit normal and crack-opening vectors). Special attention is devoted to present the theoretical fundamentals rigorously in the light of variational formulations for multi-scale models. Also, the impact of a recent derived more general boundary condition for fibre networks is assessed in the context of materials undergoing softening. Numerical examples showing the suitability of the present methodology are also shown and discussed