Richard H. Clayton

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.

Evidence for Multiple Mechanisms in Human Ventricular Fibrillation

Background— The mechanisms that sustain ventricular fibrillation (VF) in the human heart remain unclear. Experimental models have demonstrated either a periodic source (mother rotor) or multiple wavelets as the mechanism underlying VF. The aim of this study was to map electrical activity from the entire ventricular epicardium of human hearts to establish the relative roles of these mechanisms in sustaining early human VF. Methods and Results— In 10 patients undergoing cardiac surgery, VF was induced by burst pacing, and 20 to 40 seconds of epicardial activity was sampled (1 kHz) with a sock containing 256 unipolar contact electrodes connected to a UnEmap system. Signals were interpolated from the electrode sites to a fine regular grid (100×100 points), and dominant frequencies (DFs) were calculated with a fast Fourier transform with a moving 4096-ms window (10-ms increments). Epicardial phase was calculated at each grid point with the Hilbert transform, and phase singularities and activation wavefronts were identified at 10-ms intervals. Early human VF was sustained by large coherent wavefronts punctuated by periods of disorganized wavelet behavior. The initial fitted DF intercept was 5.11±0.25 (mean±SE) Hz (P<0.0001), and DF increased at a rate of 0.018±0.005 Hz/s (P<0.01) during VF, whereas combinations of homogeneous, heterogeneous, static, and mobile DF domains were observed for each of the patients. Epicardial reentry was present in all fibrillating hearts, typically with low numbers of phase singularities. In some cases, persistent phase singularities interacted with multiple complex wavelets; in other cases, VF was driven at times by a single reentrant wave that swept the entire epicardium for several cycles. Conclusions— Our data support both the mother rotor and multiple wavelet mechanisms of VF, which do not appear to be mutually exclusive in the human heart.

Effects of aerobic exercise training and yoga on the baroreflex in healthy elderly persons.

It is unclear whether the age‐associated reduction in baroreflex sensitivity is modifiable by exercise training. The effects of aerobic exercise training and yoga, a non‐aerobic control intervention, on the baroreflex of elderly persons was determined. Baroreflex sensitivity was quantified by the α‐index, at high frequency (HF; 0.15–0.35 Hz, reflecting parasympathetic activity) and mid‐frequency (MF; 0.05–0.15 Hz, reflecting sympathetic activity as well), derived from spectral and cross‐spectral analysis of spontaneous fluctuations in heart rate and blood pressure. Twenty‐six (10 women) sedentary, healthy, normotensive elderly (mean 68 years, range 62–81 years) subjects were studied. Fourteen (4 women) of the sedentary elderly subjects completed 6 weeks of aerobic training, while the other 12 (6 women) subjects completed 6 weeks of yoga. Heart rate decreased following yoga (69 ± 8 vs. 61 ± 7 min−1, P < 0.05) but not aerobic training (66 ± 8 vs. 63 ± 9 min−1, P = 0.29). VO2 max increased by 11% following yoga (P < 0.01) and by 24% following aerobic training (P < 0.01). No significant change in αMF (6.5 ± 3.5 vs. 6.2 ± 3.0 ms mmHg−1, P = 0.69) or αHF (8.5 ± 4.7 vs. 8.9 ± 3.5 ms mmHg−1, P = 0.65) occurred after aerobic training. Following yoga, αHF (8.0 ± 3.6 vs. 11.5 ± 5.2 ms mmHg−1, P < 0.01) but not αMF (6.5 ± 3.0 vs. 7.6 ± 2.8 ms mmHg−1, P = 0.29) increased. Short‐duration aerobic training does not modify the α‐index at αMF or αHF in healthy normotensive elderly subjects. αHF but not αMF increased following yoga, suggesting that these parameters are measuring distinct aspects of the baroreflex that are separately modifiable.

Whole heart action potential duration restitution properties in cardiac patients: a combined clinical and modelling study

Steep action potential duration (APD) restitution has been shown to facilitate wavebreak and ventricular fibrillation. The global APD restitution properties in cardiac patients are unknown. We report a combined clinical electrophysiology and computer modelling study to: (1) determine global APD restitution properties in cardiac patients; and (2) examine the interaction of the observed APD restitution with known arrhythmia mechanisms. In 14 patients aged 52–85 years undergoing routine cardiac surgery, 256 electrode epicardial mapping was performed. Activation–recovery intervals (ARI; a surrogate for APD) were recorded over the entire ventricular surface. Mono‐exponential restitution curves were constructed for each electrode site using a standard S1–S2 pacing protocol. The median maximum restitution slope was 0.91, with 27% of all electrode sites with slopes < 0.5, 29% between 0.5 and 1.0, and 20% between 1.0 and 1.5. Eleven per cent of restitution curves maintained slope > 1 over a range of diastolic intervals of at least 30 ms; and 0.3% for at least 50 ms. Activation–recovery interval restitution was spatially heterogeneous, showing regional organization with multiple discrete areas of steep and shallow slope. We used a simplified computer model of 2‐D cardiac tissue to investigate how heterogeneous APD restitution can influence vulnerability to, and stability of re‐entry. Our model showed that heterogeneity of restitution can act as a potent arrhythmogenic substrate, as well as influencing the stability of re‐entrant arrhythmias. Global epicardial mapping in humans showed that APD restitution slopes were organized into regions of shallow and steep slopes. This heterogeneous organization of restitution may provide a substrate for arrhythmia.

Verification of cardiac tissue electrophysiology simulators using an N-version benchmark

Ongoing developments in cardiac modelling have resulted, in particular, in the development of advanced and increasingly complex computational frameworks for simulating cardiac tissue electrophysiology. The goal of these simulations is often to represent the detailed physiology and pathologies of the heart using codes that exploit the computational potential of high-performance computing architectures. These developments have rapidly progressed the simulation capacity of cardiac virtual physiological human style models; however, they have also made it increasingly challenging to verify that a given code provides a faithful representation of the purported governing equations and corresponding solution techniques. This study provides the first cardiac tissue electrophysiology simulation benchmark to allow these codes to be verified. The benchmark was successfully evaluated on 11 simulation platforms to generate a consensus gold-standard converged solution. The benchmark definition in combination with the gold-standard solution can now be used to verify new simulation codes and numerical methods in the future.

Whole heart APD restitution properties in cardiac patients: a combined clinical and modelling study

Steep action potential duration (APD) restitution has been shown to facilitate wavebreak and ventricular fibrillation. The global APD restitution properties in cardiac patients are unknown. We report a combined clinical electrophysiology and computer modelling study to: (1) determine global APD restitution properties in cardiac patients; and (2) examine the interaction of the observed APD restitution with known arrhythmia mechanisms. In 14 patients aged 52–85 years undergoing routine cardiac surgery, 256 electrode epicardial mapping was performed. Activation–recovery intervals (ARI; a surrogate for APD) were recorded over the entire ventricular surface. Mono‐exponential restitution curves were constructed for each electrode site using a standard S1–S2 pacing protocol. The median maximum restitution slope was 0.91, with 27% of all electrode sites with slopes < 0.5, 29% between 0.5 and 1.0, and 20% between 1.0 and 1.5. Eleven per cent of restitution curves maintained slope > 1 over a range of diastolic intervals of at least 30 ms; and 0.3% for at least 50 ms. Activation–recovery interval restitution was spatially heterogeneous, showing regional organization with multiple discrete areas of steep and shallow slope. We used a simplified computer model of 2‐D cardiac tissue to investigate how heterogeneous APD restitution can influence vulnerability to, and stability of re‐entry. Our model showed that heterogeneity of restitution can act as a potent arrhythmogenic substrate, as well as influencing the stability of re‐entrant arrhythmias. Global epicardial mapping in humans showed that APD restitution slopes were organized into regions of shallow and steep slopes. This heterogeneous organization of restitution may provide a substrate for arrhythmia.

Recognition of ventricular fibrillation using neural networks

VENTRICULAR FIBRILLATION (VF) is a lethal cardiac arrhythmia which can be stopped by prompt application of a DC shock (defibrillation). On the electrocardiogram (ECG), VF appears as an irregular, undulating waveform. (Fig. 1) ECG monitoring systems and automatic defibrillators attempt to reduce delays in recognising VF by incorporating automatic detection algorithms. However, electrode artifact and other cardiac arrhythmias can produce VF-like ECG signals which lead to false positive detections. In addition, the ECG waveform during VF is poorly characterised and this can lead to false negative detections. Development and testing of VF detection algorithms has relied on a limited database of VF recordings because VF is unpredictable, and hence rarely recorded in a form suitable for analysis. Although many VF detection techniques have been developed and claim good performance (JAKOBSSEN e t al., 1990), independent evaluation has shown that some techniques are not optimal (CLAYTON et al., 1993). There is clearly room for further development. One approach with potential lies in the area of neural computing. Neural computing is a rapidly growing field (MILLER et al., 1992; BEALE and JACKSON, 1990). Simple processing units (neurons) are linked together by weighted connections. Each neuron processes its weighted inputs according to its activation function, and the output is then passed on to the inputs of the next layer of neurons. The remarkable feature of a neural network lies in its flexibility. By allocating appropriate values to the weights, a network can perform specific and complicated operations on its inputs. A network can hence be trained to perform a particular operation, using a set of training data comprising a series of input patterns for which the correct output is known. Each training pattern is repeatedly presented to the inputs. The network weights, orginally set to random values, are progressively optimised using a training algorithm which attempts to produce the correct output for the training patterns. Training continues until the errors associated with

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 (TCl); 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, TCl 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 TCl 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 TCl 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.

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.

Regional differences in APD restitution can initiate wavebreak and re-entry in cardiac tissue: a computational study.

BackgroundRegional differences in action potential duration (APD) restitution in the heart favour arrhythmias, but the mechanism is not well understood.MethodsWe simulated a 150 × 150 mm 2D sheet of cardiac ventricular tissue using a simplified computational model. We investigated wavebreak and re-entry initiated by an S1S2S3 stimulus protocol in tissue sheets with two regions, each with different APD restitution. The two regions had a different APD at short diastolic interval (DI), but similar APD at long DI. Simulations were performed twice; once with both regions having steep (slope > 1), and once with both regions having flat (slope < 1) APD restitution.ResultsWavebreak and re-entry were readily initiated using the S1S2S3 protocol in tissue sheets with two regions having different APD restitution properties. Initiation occurred irrespective of whether the APD restitution slopes were steep or flat. With steep APD restitution, the range of S2S3 intervals resulting in wavebreak increased from 1 ms with S1S2 of 250 ms, to 75 ms (S1S2 180 ms). With flat APD restitution, the range of S2S3 intervals resulting in wavebreak increased from 1 ms (S1S2 250 ms), to 21 ms (S1S2 340 ms) and then 11 ms (S1S2 400 ms).ConclusionRegional differences in APD restitution are an arrhythmogenic substrate that can be concealed at normal heart rates. A premature stimulus produces regional differences in repolarisation, and a further premature stimulus can then result in wavebreak and initiate re-entry. This mechanism for initiating re-entry is independent of the steepness of the APD restitution curve.