A guide to modelling cardiac electrical activity in anatomically detailed ventricles.

One of the most recent trends in cardiac electrophysiology is the development of integrative anatomically accurate models of the heart, which include description of cardiac activity from sub-cellular and cellular level to the level of the whole organ. In order to construct this type of model, a researcher needs to collect a wide range of information from books and journal articles on various aspects of biology, physiology, electrophysiology, numerical mathematics and computer programming. The aim of this methodological article is to survey recent developments in integrative modelling of electrical activity in the ventricles of the heart, and to provide a practical guide to the resources and tools that are available for work in this exciting and challenging area.

Organization of ventricular fibrillation in the human heart: experiments and models.

Sudden cardiac death is a major health problem in the industrialized world. The lethal event is typically ventricular fibrillation (VF), during which the co-ordinated regular contraction of the heart is overthrown by a state of mechanical and electrical anarchy. Understanding the excitation patterns that sustain VF is important in order to identify potential therapeutic targets. In this paper, we studied the organization of human VF by combining clinical recordings of electrical excitation patterns on the epicardial surface during in vivo human VF with simulations of VF in an anatomically and electrophysiologically detailed computational model of the human ventricles. We find both in the computational studies and in the clinical recordings that epicardial surface excitation patterns during VF contain around six rotors. Based on results from the simulated three-dimensional excitation patterns during VF, which show that the total number of electrical sources is 1.4 +/- 0.12 times greater than the number of epicardial rotors, we estimate that the total number of sources present during clinically recorded VF is 9.0 +/- 2.6. This number is approximately fivefold fewer compared with that observed during VF in dog and pig hearts, which are of comparable size to human hearts. We explain this difference by considering differences in action potential duration dynamics across these species. The simpler spatial organization of human VF has important implications for treatment and prevention of this dangerous arrhythmia. Moreover, our findings underline the need for integrated research, in which human-based clinical and computational studies complement animal research.

Improved biomechanical metrics of cerebral vasospasm identified via sensitivity analysis of a 1D cerebral circulation model.

Cerebral vasospasm (CVS) is a life-threatening condition that occurs in a large proportion of those affected by subarachnoid haemorrhage and stroke. CVS manifests itself as the progressive narrowing of intracranial arteries. It is usually diagnosed using Doppler ultrasound, which quantifies blood velocity changes in the affected vessels, but has low sensitivity when CVS affects the peripheral vasculature. The aim of this study was to identify alternative biomarkers that could be used to diagnose CVS. We used a 1D modelling approach to describe the properties of pulse waves that propagate through the cardiovascular system, which allowed the effects of different types of vasospasm on waveforms to be characterised at several locations within a simulated cerebral network. A sensitivity analysis empowered by the use of a Gaussian process statistical emulator was used to identify waveform features that may have strong correlations with vasospasm. We showed that the minimum rate of velocity change can be much more effective than blood velocity for stratifying typical manifestations of vasospasm and its progression. The results and methodology of this study have the potential not only to improve the diagnosis and monitoring of vasospasm, but also to be used in the diagnosis of many other cardiovascular diseases where cardiovascular waves can be decoded to provide disease characterisation.

Phase singularities and filaments: simplifying complexity in computational models of ventricular fibrillation.

In the whole heart, millions of cardiac cells are involved in ventricular fibrillation (VF). Experimental studies indicate that VF is sustained by re-entrant activity, and that each re-entrant wave rotates around a filament of phase singularity. Filaments act as organising centres, and offer a way to simplify and quantify the complex spatio-temporal behaviour observed in VF. Where a filament touches the surface of fibrillating myocardium re-entrant activity can be observed, however the behaviour of filaments within bulk ventricular myocardium is difficult to observe directly using present experimental techniques. Large scale computational simulations of VF in three-dimensional (3D) tissue offer a tool to investigate the properties and behaviour of filaments, and the aim of this paper is to review recent advances in this area as well as to compare recent computational studies of fibrillation in whole ventricle geometries.

Sympathetic reinnervation and heart rate variability after cardiac transplantation.

BACKGROUND: Heart rate variability is thought to measure autonomic modulation, but the relation has never been demonstrated directly in humans. AIM: To test the hypothesis that increased low frequency heart rate variability reflects sympathetic reinnervation after cardiac transplantation. PATIENTS: 24 cardiac transplant recipients at the time of routine surveillance coronary angiography two or more years after cardiac transplantation, and 10 controls with normal coronary arteries undergoing angiography for investigation of chest pain. SETTING: Regional cardiothoracic centre. METHODS: Sympathetic effector function at the sinus node was assessed by measuring the fall in cycle length for two minutes after injection of tyramine to the artery supplying the sinus node. Heart rate variability was measured from three-minute RR interval sequences at rest, during metronomic respiration, and before and after atropine. RESULTS: The logarithm of the low frequency component of heart rate variability during metronomic respiration was linearly related to the logarithm of the change in cycle length after injection of tyramine (R2 = 0.28, P = 0.007). Absolute units more accurately reflected sympathetic effector function than did normalised units or the ratio of low frequency to high frequency. Atropine did not affect high frequency heart rate variability in transplant recipients. CONCLUSIONS: The low frequency component of heart rate variability is directly related to sympathetic reinnervation to the sinus node.

Comparative assessment of the ventricular fibrillation detection algorithms in five semi-automatic or advisory defibrillators.

The sensitivity and specificity of ventricular fibrillation (VF) detection in three semi-automatic defibrillators (Laerdal Heartstart 3000, Spacelabs First Medic 610, Physio-Control Lifepak 300) and two advisory defibrillators (S&W DMS940, Marquette Responder 1500) were assessed with 25 ECG recordings, each of length 40 s. Of the 25 ECG recordings, 12 contained VF requiring defibrillation, three contained a tachyarrhythmia with a waveform similar to VF but which self-terminated, and 10 were selected from abnormal rhythms and artefacts which contained some features similar to VF. Sensitivity was assessed from the VF data. Specificity was assessed from both the rhythm preceding VF or the tachyarrhythmias, and from the VF-like data. The response to a changing rhythm was assessed from the self-terminating tachyarrhythmias. Each recording was replayed to the defibrillators at three signal amplitudes (normal, half and double). For each defibrillator, requests to check the patient and advice to shock were noted separately. The sensitivity for recommending a shock when a shock was required varied from 81 to 97%. The sensitivity for drawing attention to VF, either through requesting the patient to be checked or advising a shock, varied from 92% to 100%. There were no false detections in the rhythms preceding VF or the tachyarrhythmias (specificity with good quality signals 100%). The specificity with the VF-like data ranged from 63 to 90% for recommending a shock, and from 63% to 70% for requesting the patient be checked or shocked. There was no difference between the defibrillators for VF detection, but there was a significant difference between the semi-automatic and advisory defibrillators (P < 0.05) for the specificity of the final recommendation.

Assessment of the ventricular fibrillation detection algorithm in the semi-automatic Cardio-Aid defibrillator.

The sensitivity and specificity of ventricular fibrillation (VF) detection in the semi-automatic Cardio-Aid defibrillator was assessed with 25 ECG recordings, each of length 40 s. Of the 25 ECG recordings, 12 contained VF requiring defibrillation, 3 contained a tachyarrhythmia with a waveform similar to VF but which self-terminated, and 10 were selected from abnormal rhythms and artefacts which contained some features similar to VF. Sensitivity was assessed from the VF data. Specificity was assessed from both the rhythm preceding VF or the tachyarrhythmias, and from the VF-like data. The response to a changing rhythm was assessed from the self-terminating tachyarrhythmias. Each recording was replayed to the defibrillators at 3 signal amplitudes (normal, half and double). Request to analyse the ECG because of possible VF and advice to shock were noted separately. The sensitivity for recommending a shock when a shock was required was 92%. The sensitivity for drawing attention to VF, through requesting analysis was 97%. There were no false detections in the rhythms preceding VF or the tachyarrhythmias (specificity with good quality signals 100%). The specificity with the VF-like data ws 90%. There was significant difference between this defibrillator and other semi-automated defibrillators previously assessed.

Computational models of normal and abnormal action potential propagation in cardiac tissue: linking experimental and clinical cardiology.

Computational models have the potential to make a huge impact on our understanding of normal and abnormal cardiac function. The aim of this article is to review tools that have been developed to simulate the electrophysiology of cardiac cells and tissue, and to show how computational models have been used to gain insight into normal and abnormal action potential propagation. Some of the practical problems experienced in the development and application of these models are described, and examples are given.

Coherence between body surface ECG leads and intracardiac signals increases during the first 10 s of ventricular fibrillation in the human heart.

Ventricular fibrillation (VF) in the human heart is not well understood. The aim of this study was to measure changes in the phase relationship between the body surface ECG and intracardiac electrograms recorded during the first 10 s of human VF. We studied 11 episodes of VF and measured the coherence of (a) ECG lead I and ECG lead V1, (b) ECG lead V1 and the right ventricular apex (RVA) electrogram, and (c) ECG lead V1 and the smoothed RVA electrogram. Each coherence measurement was the average of the magnitude squared coherence function in the range 0-60 Hz, and measurements were made 1, 3, 5, 7 and 9 s after the onset of VF. Overall, the mean (SD) coherence was 31(6)% between ECG leads I and V1, 17(3)% between ECG lead V1 and the RVA electrogram, and 20(4)% between ECG lead V1 and the smoothed RVA electrogram. All three measurements of coherence increased significantly between 1 and 9 s with mean (SD) rates of 0.97(1.01)% s(-1), 0.8(1.18)% s(-1) and 0.82(1.19)% s(-1) respectively. These results show that propagation in human VF becomes more organized during the first 10 s of VF. This may be an optimal window for defibrillation.

Measurement of baroreflex gain from heart rate and blood pressure spectra: a comparison of spectral estimation techniques.

The baroreflex is the physiological control system linking blood pressure and heart rate. Baroreflex gain, alpha, can be estimated from the ratio of heart rate and blood pressure spectra. The aim of this study was to quantify differences in estimates of alpha incurred by using four different spectral analysis techniques. ECG and blood pressure were recorded from 10 healthy subjects. Spectra were estimated using fast Fourier transform (FFT), zero-padded FFT (FFTZ), FFT of the windowed autocovariance function (ACVF), and maximum-entropy (ME) methods. For each subject a mean value of alpha was calculated in the MF (0.05-0.15 Hz) and HF (0.15-0.35 Hz) bands. Mean alpha MF varied between subjects (range 2-10 ms mmHg-1) as did mean alpha HF (range 4-12 ms mmHg-1). Mean differences in alpha MF and alpha HF estimated with different techniques were small. Differences in alpha MF ranged from 0.074 ms mmHg-1 (FFTZ against ME) to 0.298 ms mmHg-1 (FFT against ACVF) and those in alpha HF ranged from 0.057 ms mmHg-1 (FFT against FFTZ) to 0.342 ms mmHg-1 (ACVF against ME). None of these differences were significant. The use of different spectral analysis techniques does not significantly affect estimates of alpha.

Simplified body-surface electrocardiographic maps with depolarization magnitude and direction.

A new technique is presented for extracting the magnitude and direction of ventricular depolarization at the body surface from surface electrocardiographic (ECG) map data. Bipolar electrocardiograms were obtained from 36 sites on the chest surface in five normal subjects. The direction and magnitude of depolarization as seen from the chest surface were calculated for 18 body-surface areas centred between electrode positions V1 and V6. Each area was bounded by three electrodes with an electrode spacing of 5 cm. A major depolarization component could be calculated for all triangular areas, with 48% of areas having a smaller second component. The area with the greatest magnitude in each subject had a depolarization vector pointing downwards and to the left, with an average angle to the horizontal of 55 degrees. This was consistent with an average angle of 51 degrees obtained from the subjects' 12-lead electrocardiograms. There was more variability in vector angle between adjacent areas on the right-hand side. At the V5/V6 areas, close to the cardiac apex, the vector component had an upwards orientation in all subjects, opposing the overall downward component of ventricular depolarization. The technique was able to determine local depolarization directions which were in agreement with the normal cardiac vector derived from standard electrocardiography. Reversal of the vector direction close to the cardiac apex and the collision of depolarization components from different directions could be detected. This simple form of body-surface mapping can reduce the essential features of depolarization to a single map, and provide information not directly available from a 12-lead electrocardiogram.

Linear and non-linear analysis of the surface electrocardiogram during human ventricular fibrillation shows evidence of order in the underlying mechanism.

Ventricular fibrillation (VF) is a poorly understood yet potentially lethal cardiac arrhythmia. The electrocardiogram (ECG) time series of VF is investigated by comparison of the linear and non-linear features of VF time series and surrogates in which internal correlations have been destroyed. From 40 ECG time series of human VF and 40 surrogate time series, three quantities are evaluated: the percentage of the linear time-frequency distribution (TFD) exceeding a threshold, the non-linear coarse-grained correlation dimension (Dcg), and the percentage of diagonal lines in the non-linear recurrence plot longer than 10 elements (D10). It is found that the mean (SD) percent threshold TFD and Dcg are higher for the surrogates (6.7% (1.3) and 5.3 (0.6)) than the VF time series (5.6% (0.7) and 3.8 (0.9)), whereas the mean D10 is higher for the VF time series (49% (13)) than the surrogates (32% (7)). All of these differences are significant (p < 0.0001) and indicate greater order in the VF time series than in the surrogates. It is therefore shown that both linear and non-linear signal analysis demonstrate order in the ECG time series of VF.

Comparison of four techniques for recognition of ventricular fibrillation from the surface ECG.

Four ventricular fibrillation (VF) detection techniques were assessed using recordings of VF to evaluate sensitivity and VF-like recordings to evaluate specificity. The recordings were obtained from Coronary Care Unit patients. The techniques were: threshold crossing intervals (TCI); peaks in the autocorrelation function (ACF); signal content outside the mean frequency (VF-filter); and signal spectrum shape (spectrum). Using 70 extracts, each 4 s long, from VF recordings, the VF filter achieved a sensitivity of 77 per cent; the ACF, TCI and spectrum algorithms had sensitivities of 67, 53 and 46 per cent, respectively. Susceptibility to false alarms was assessed using 40 extracts from VF-like recordings. The TCI algorithm was the most specific (93 per cent), while the spectrum, VF filter and ACF algorithms had specificities of 72, 55 and 38 per cent, respectively. The TCI algorithm achieved overall sensitivity of 93 per cent and specificity of 60 per cent. The spectrum, VF filter and ACF algorithms had overall sensitivities of 80, 93 and 87 per cent, and overall specificities of 60, 20 and 0 per cent, respectively.

Enhanced self-termination of re-entrant arrhythmias as a pharmacological strategy for antiarrhythmic action.

Ventricular tachycardia and fibrillation are potentially lethal cardiac arrhythmias generated by high frequency, irregular spatio-temporal electrical activity. Re-entrant propagation has been demonstrated as a mechanism generating these arrhythmias in computational and in vitro animal models of these arrhythmias. Re-entry can be idealised in homogenous isotropic virtual cardiac tissues as spiral and scroll wave solutions of reaction-diffusion equations. A spiral wave in a bounded medium can be terminated if its core reaches a boundary. Ventricular tachyarrhythmias in patients are sometimes observed to spontaneously self-terminate. One possible mechanism for self-termination of a spiral wave is meander of its core to an inexcitable boundary. We have previously proposed the hypothesis that the spatial extent of meander of a re-entrant wave in the heart can be directly related to its probability of self-termination, and so inversely related to its lethality. Meander in two-dimensional virtual ventricular tissues based on the Oxsoft family of cell models, with membrane excitation parameters simulating the inherited long Q-T syndromes has been shown to be consistent with this hypothesis: the largest meander is seen in the syndrome with the lowest probability of death per arrhythmic episode. Here we extend our previous results to virtual tissues based on the Luo-Rudy family of models. Consistent with our hypothesis, for both families of models, whose different ionic mechanisms produce different patterns of meander, the LQT virtual tissue with the larger meander simulates the syndrome with the lower probability of death per episode. Further, we search the parameter space of the repolarizing currents to find their conductance parameter values that give increased meander of spiral waves. These parameters may provide targets for antiarrhythmic drugs designed to act by increasing the likelihood of self-termination of re-entrant arrhythmias. (c) 2002 American Institute of Physics.

Experiment-model interaction for analysis of epicardial activation during human ventricular fibrillation with global myocardial ischaemia.

We describe a combined experiment-modelling framework to investigate the effects of ischaemia on the organisation of ventricular fibrillation in the human heart. In a series of experimental studies epicardial activity was recorded from 10 patients undergoing routine cardiac surgery. Ventricular fibrillation was induced by burst pacing, and recording continued during 2.5 min of global cardiac ischaemia followed by 30 s of coronary reflow. Modelling used a 2D description of human ventricular tissue. Global cardiac ischaemia was simulated by (i) decreased intracellular ATP concentration and subsequent activation of an ATP sensitive K⁺ current, (ii) elevated extracellular K⁺ concentration, and (iii) acidosis resulting in reduced magnitude of the L-type Ca²âº current I(Ca,L). Simulated ischaemia acted to shorten action potential duration, reduce conduction velocity, increase effective refractory period, and flatten restitution. In the model, these effects resulted in slower re-entrant activity that was qualitatively consistent with our observations in the human heart. However, the flattening of restitution also resulted in the collapse of many re-entrant waves to several stable re-entrant waves, which was different to the overall trend we observed in the experimental data. These findings highlight a potential role for other factors, such as structural or functional heterogeneity in sustaining wavebreak during human ventricular fibrillation with global myocardial ischaemia.

Models of cardiac tissue electrophysiology: progress, challenges and open questions.

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.

Initiation of re-entry in an excitable medium: structural investigation of cardiac tissue using a genetic algorithm.

The detailed mechanisms by which re-entry and ventricular fibrillation are initiated in the heart remain poorly understood because they are difficult to investigate experimentally. We have used a simplified excitable media computational model of action potential propagation to systematically study how re-entry can be produced by diffuse regions of inexcitable tissue. Patterns of excitable and inexcitable tissue were generated using a genetic algorithm. The inexcitable tissue was modeled in two ways: (i) diffusive, electrically connected but inexcitable tissue, or (ii) zero-flux, areas of tissue electrically disconnected in the same way as zero-flux boundary conditions. We were able to evolve patterns of diffuse inexcitable tissue that favored re-entry, but no single structure or pattern emerged. Diffusive inexcitable regions were inherently less arrhythmogenic than zero-flux inexcitable ones.

Dynamical and cellular electrophysiological mechanisms of ECG changes during ischaemia.

The interpretation of normal and pathological electrocardiographic (ECG) patterns in terms of the underlying cellular and tissue electrophysiology is rudimentary, as the existing theories rely on geometrical aspects. We relate effects of sub-endocardial ischaemia on the ST-segment depression in ECG to patterns of transmural action potential propagation in a one-dimensional virtual ventricular wall. Our computational study exposes two electrophysiological mechanisms of ST depression: dynamic-predominantly positive spatial gradients in the membrane potential during abnormal repolarization of the wall, produced by action potential duration changes in the ischaemic region; and static-a negative spatial gradient of the resting membrane potential between the normal and ischaemic regions. Hyperkalaemia is the major contributor to both these mechanisms at the cellular level. These results complement simulations of the effects of cardiac geometry on the ECG, and dissect spatio-temporal and cellular electrophysiological mechanisms of ST depression seen in sub-endocardial ischaemia.