Studies in Complex Systems: Complex Networks with Hidden Layers & Modelling Atrial Fibrillation
Author(s)
Falkenberg McGillivray, Max
Type
Thesis
Abstract
This thesis, covering the broad theme of complexity science, is split into two parts.
In part 1, I discuss models of network growth with hidden network layers. First, I introduce the “k2 model”, based on linear preferential attachment, where the attachment probability is proportional to the number of nodes within two steps of a target node. The model generates time dependent degree distributions and attachment kernels, despite initially appearing to grow as linear preferential attachment. Subsequently, I focus on node copying models. Motivated by observations of asymmetric triadic closure in real networks, I introduce a model of heterogeneous copying, built using a hidden and observed network layer. Framed in a social context, these two layers represent a node’s inner social circle, and wider social circle, such that the model can bias copying probabilities towards, or against, a node’s inner circle of friends. Compared to homogeneous copying, this heterogeneous model suppresses power-laws, leads to unusually high clustering, and results in size-independent clique growth.
Part 2 discusses simple percolation-based models of atrial fibrillation (AF), the most common cardiac arrhythmia. First, I introduce a 3d-analogue of a previous 2d lattice model. The model highlights the unification of previous discrepant observations in the clinical literature, specifically, how asymmetry in the fibre structure between the inside and the outside of the heart leads to differences in the observed surface activation patterns. The 3d model is not representative of real atrial geometries. Hence, I subsequently introduce a further adaptation of the model in which signals propagate on a spatial network representation of the atria, which can be adapted for use with real imaging data. The model highlights how, as the atria become increasingly decoupled through the accumulation of interstitial fibrosis, the successful termination of fibrillation via ablation becomes increasingly difficult.
In part 1, I discuss models of network growth with hidden network layers. First, I introduce the “k2 model”, based on linear preferential attachment, where the attachment probability is proportional to the number of nodes within two steps of a target node. The model generates time dependent degree distributions and attachment kernels, despite initially appearing to grow as linear preferential attachment. Subsequently, I focus on node copying models. Motivated by observations of asymmetric triadic closure in real networks, I introduce a model of heterogeneous copying, built using a hidden and observed network layer. Framed in a social context, these two layers represent a node’s inner social circle, and wider social circle, such that the model can bias copying probabilities towards, or against, a node’s inner circle of friends. Compared to homogeneous copying, this heterogeneous model suppresses power-laws, leads to unusually high clustering, and results in size-independent clique growth.
Part 2 discusses simple percolation-based models of atrial fibrillation (AF), the most common cardiac arrhythmia. First, I introduce a 3d-analogue of a previous 2d lattice model. The model highlights the unification of previous discrepant observations in the clinical literature, specifically, how asymmetry in the fibre structure between the inside and the outside of the heart leads to differences in the observed surface activation patterns. The 3d model is not representative of real atrial geometries. Hence, I subsequently introduce a further adaptation of the model in which signals propagate on a spatial network representation of the atria, which can be adapted for use with real imaging data. The model highlights how, as the atria become increasingly decoupled through the accumulation of interstitial fibrosis, the successful termination of fibrillation via ablation becomes increasingly difficult.
Version
Open Access
Date Issued
2021-10
Date Awarded
2022-04
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Christensen, Kim
Sponsor
EPSRC
Grant Number
EP/N509486/1
Publisher Department
Department of Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)