Models of cardiac tissue electrophysiology are an important component of the Cardiac Physiome Project, which is an international effort to build biophysically based multi-scale mathematical models of the heart. Models of tissue electrophysiology can provide a bridge between electrophysiological cell models at smaller scales, and tissue mechanics, metabolism and blood flow at larger scales. This paper is a critical review of cardiac tissue electrophysiology models, focussing on the micro-structure of cardiac tissue, generic behaviours of action potential propagation, different models of cardiac tissue electrophysiology, the choice of parameter values and tissue geometry, emergent properties in tissue models, numerical techniques and computational issues. We propose a tentative list of information that could be included in published descriptions of tissue electrophysiology models, and used to support interpretation and evaluation of simulation results. We conclude with a discussion of challenges and open questions.
In this manuscript we review the state of cardiac cell modelling in the context of international initiatives such as the IUPS Physiome and Virtual Physiological Human Projects, which aim to integrate computational models across scales and physics. In particular we focus on the relationship between experimental data and model parameterisation across a range of model types and cellular physiological systems. Finally, in the context of parameter identification and model reuse within the Cardiac Physiome, we suggest some future priority areas for this field.
The interaction of spiral waves of excitation with atrial anatomy remains unclear. This simulation study isolates the role of atrial anatomical structures on spiral wave spontaneous drift in the human atrium. We implemented realistic and idealised 3D human atria models to investigate the functional impact of anatomical structures on the long-term ( approximately 40 s) behaviour of spiral waves. The drift of a spiral wave was quantified by tracing its tip trajectory, which was correlated to atrial anatomical features. The interaction of spiral waves with the following idealised geometries was investigated: (a) a wedge-like structure with a continuously varying atrial wall thickness; (b) a ridge-like structure with a sudden change in atrial wall thickness; (c) multiple bridge-like structures consisting of a bridge connected to the atrial wall. Spiral waves drifted from thicker to thinner regions and along ridge-like structures. Breakthrough patterns caused by pectinate muscles (PM) bridges were also observed, albeit infrequently. Apparent anchoring close to PM-atrial wall junctions was observed. These observations were similar in both the realistic and the idealised models. We conclude that spatially altering atrial wall thickness is a significant cause of drift of spiral waves. PM bridges cause breakthrough patterns and induce transient anchoring of spiral waves.
Atrial fibrillation (AF) is a common cardiac disease of genuine clinical concern with high rates of morbidity, leading to major personal and National Health Service costs. Computer modelling of AF using biophysically detailed cellular models with realistic 3D anatomical geometry allows investigation of the underlying ionic mechanisms in far more detail than with experimental physiology. We have developed a 3D virtual human atrium that combines detailed cellular electrophysiology including ion channel kinetics and homeostasis of ionic concentrations with anatomical details. The segmented anatomical structure and the multi- variable nature of the system make the 3D simulations of AF computationally large and intensive.
Investigating the mechanisms underlying the genesis and conduction of electrical excitation in the atria at physiological and pathological states is of great importance. To provide knowledge concerning the mechanisms of excitation, we constructed a biophysical detailed and anatomically accurate computer model of human atria that incorporates both structural and electrophysiological heterogeneities. The three-dimensional geometry was extracted from the visible female dataset. The sinoatrial node (SAN) and atrium, including crista terminalis (CT), pectinate muscles (PM), appendages (APG) and Bachmann's bundle (BB) were segmented in this work. Fibre orientation in CT, PM and BB was set to local longitudinal direction. Descriptions for all used cell types were based on modifications of the Courtemanche et al. model of a human atrial cell. Maximum conductances of Ito, IKr and ICa,L were modified for PM, CT, APG and atrioventricular ring to reproduce measured action potentials (AP). Pacemaker activity in the human SAN was reproduced by removing IK1, but including If, ICa,T, and gradients of channel conductances as described in previous studies for heterogeneous rabbit SAN. Anisotropic conduction was computed with a monodomain model using the finite element method. The transversal to longitudinal ratio of conductivity for PM, CT and BB was 1:9. Atrial working myocardium (AWM) was set to be isotropic. Simulation of atrial electrophysiology showed initiation of APs in the SAN centre. The excitation spread afterwards to the periphery near to the region of the CT and preferentially towards the atrioventricular region. The excitation extends over the right atrium along PM. Both CT and PM activated the right AWM. Earliest activation of the left atrium was through BB and excitation spread over to the APG. The conduction velocities were 0.6ms-1 for AWM, 1.2ms-1 for CT, 1.6ms-1 for PM and 1.1ms-1 for BB at a rate of 63bpm. The simulations revealed that bundles form dominant pathways for atrial conduction. The preferential conduction towards CT and along PM is comparable with clinical mapping. Repolarization is more homogeneous than excitation due to the heterogeneous distribution of electrophysiological properties and hence the action potential duration.
Atrial fibrillation (AF) induced electrical remodelling of ionic channels shortens action potential duration and reduces atrial excitability. Experimental data of AF-induced electrical remodelling (AFER) from two previous studies on human atrial myocytes were incorporated into a human atrial cell computer model to simulate their effects on atrial electrical behaviour. The dynamical behaviors of excitation scroll waves in an anatomical 3D homogenous model of human atria were studied for control and AF conditions. Under control condition, scroll waves meandered in large area and became persistent when entrapped by anatomical obstacles. In this case, a mother rotor dominated atrial excitation. Action potentials from several sites behaved as if the atrium were paced rapidly. Under AF conditions, AFER increased the stability of re-entrant scroll waves by reducing meander. Scroll wave break up leads to wavelets underpinning sustained chronic AF. Our simulation results support the hypothesis that AF-induced electrical remodelling perpetuates and sustains AF.
Atrial fibrillation (AF) is a common cardiac disease with high rates of morbidity, leading to major personal and NHS costs. Computer modeling of AF using a detailed cellular model with realistic 3D anatomical geometry allows investigation of the underlying ionic mechanisms in far more detail than in a physiology laboratory. We have developed a 3D virtual human atrium that combines detailed cellular electrophysiology, including ion channel kinetics and homeostasis of ionic concentrations, with anatomical detail. The segmented anatomical structure and multi-variable nature of the system makes the 3D simulations of AF large and computationally intensive. The computational demands are such that a full problem solving environment requires access to resources of High Performance Computing (HPC), High Performance Visualization (HPV), remote data repositories and a backend infrastructure. This is a classic example of eScience and Gridenabled computing. Initial work has been carried out using multiple processor machines with shared memory architectures. As spatial resolution of anatomical models increases, requirement of HPC resources is predicted to increase many-fold ( ~ 1 10 teraflops). Distributed computing is essential, both through massively parallel systems (a single supercomputer) and multiple parallel systems made accessible through the Grid.
Anatomically realistic computational models provide a powerful platform for investigating mechanisms that underlie atrial rhythm disturbances. In recent years, novel techniques have been developed to construct structurally-detailed, image-based models of 3D atrial anatomy. However, computational models still do not contain full descriptions of the atrial intramural myofiber architecture throughout the entire atria. To address this, a semi-automatic rule-based method was developed for generating multi-layer myofiber orientations in the human atria. The rules for fiber generation are based on the careful anatomic studies of Ho, Anderson and co-workers using dissection, macrophotography and visual tracing of fiber tracts. Separately, a series of high color contrast images were obtained from sheep atria with a novel confocal surface microscopy method. Myofiber orientations in the normal sheep atria were estimated by eigen-analyis of the 3D image structure tensor. These data have been incorporated into an anatomical model that provides the quantitative representation of myofiber architecture in the atrial chambers. In this study, we attempted to compare the two myofiber generation approaches. We observed similar myo-bundle structure in the human and sheep atria, for example in Bachmann's bundle, atrial septum, pectinate muscles, superior vena cava and septo-pulmonary bundle. Our computational simulations also confirmed that the preferential propagation pathways of the activation sequence in both atrial models is qualitatively similar, largely due to the domination of the major muscle bundles.