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.

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.

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.

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.

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.

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.

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.

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.

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.

Re-entrant cardiac arrhythmias in computational models of long QT myocardium.

The long QT syndrome (LQTS) is an inherited disorder in which repolarization of cardiac ventricular cells is prolonged. Patients with the LQTS are at an increased risk of ventricular cardiac arrhythmias. Two phenotypes of the inherited LQTS are caused by defects in K(+)channels (LQT1 and LQT2) and one by defects in Na(+)channels (LQT3). Patients with LQT1 are more likely to have self-terminating arrhythmias than those with LQT3. The aim of this computational study was to propose an explanation for this finding by comparing the vulnerability of normal and LQT tissue to re-entry, and estimating the likelihood of self-termination by motion of re-entrant waves to an inexcitable boundary in simulated LQT1, LQT2 and LQT3 tissue. We modified a model of mammalian cardiac cells to simulate LQT1 by reducing maximal I(K(s))conductance, LQT2 by reducing maximal I(K(r))conductance, and LQT3 by preventing complete inactivation of I(Na)channels. Each simulated phenotype was incorporated into a computational model of action potential propagation in one- and two-dimensional homogeneous tissue. Simulated LQT tissue was no more vulnerable to re-entry than simulated normal tissue, but the motion of re-entrant waves in simulated LQT1 tissue was between 2 and 5 times greater than the motion of re-entrant waves in simulated LQT2 and LQT3 tissue. These findings suggest that LQT arrhythmias do not result from increased vulnerability to re-entry, and that re-entry once initiated is more likely to self-terminate by moving to an inexcitable tissue boundary in LQT1 than in LQT2 and LQT3. This finding is consistent with clinical observations.

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.

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.

Reproducibility of three different methods of measuring baroreflex sensitivity in normal subjects.

1. Baroreflex sensitivity is a useful tool for investigating cardiovascular reflexes in a number of clinical settings. Several different methods of measuring baroreflex sensitivity are available. In order to determine a clinically useful non-invasive method of measuring baroreflex sensitivity we compared two methods (spectral analysis and the Valsalva manoeuvre) with regard to reproducibility, agreement with a standard invasive method (phenylephrine infusion) and failure rate.2.Twenty-six healthy subjects aged 22 to 63 years attended on three separate occasions for measurement of baroreflex sensitivity using the different methods. The effect of a recent head-up tilt on baroreflex sensitivity was measured.3. Reproducibility was best for the low-frequency component of the spectral method [coefficient of variation 25.0% (range 3.5-42.4%)] and worst for the Valsalva method [coefficient of variation 29.3% (range 13.8-93.1%)]. Both non-invasive methods overestimated values compared with the phenylephrine method [bias of low-frequency component of the spectral method, 1.17 (0.38-3.6); bias of the Valsalva method, 1.13 (0.19-6.7)]. The high-frequency component of the spectral method did not agree with the phenylephrine method.4. The spectral analysis method had the fewest failures (seven subjects with a failure on at least one occasion), and the phenylephrine method the most (16 subjects with a failure on at least one occasion). A short head-up tilt did not affect the subsequent non-invasive measurement of baroreflex sensitivity.5. It was concluded that the low-frequency component of the spectral method was the most clinically useful non-invasive measurement of baroreflex sensitivity.

Baroreflex function in sedentary and endurance-trained elderly people.

OBJECTIVE: to determine the differences associated with age and endurance exercise training on the baroreflex function of healthy subjects. DESIGN: cross-sectional study. SETTING: university research department. PARTICIPANTS: 26 (10 female) sedentary, healthy, normotensive elderly subjects (mean age 67 years, range 62-81), eight (two female) elderly endurance-trained athletes (66 years, 62-69) and eight (two female) young (30 years, 25-34) subjects. MEASUREMENTS: baroreflex sensitivity was quantified by the alpha-index, at high frequency (HF, 0.15-0.35 Hz) and mid frequency (MF, 0.05-0.15 Hz), derived from spectral and cross-spectral analysis of spontaneous fluctuations in heart rate and blood pressure. RESULTS: resting heart rate was significantly lower in endurance-trained athletes than sedentary elderly people (58 +/- 12 versus 68 +/- 11 min(-1), P < 0.05) but not different to that in healthy young subjects (63 +/- 9 min[-1]). alpha(HF) in sedentary elderly subjects (8.1 +/- 4.2 ms.mm Hg[-1]) was lower than both endurance-trained elderly athletes (14.8 +/- 4.8 ms.mm Hg(-1), P < 0.05) and healthy young subjects (28.3 +/- 21.8 ms.mm Hg(-1), P < 0.05) and was not significantly different between endurance-trained elderly athletes and healthy young subjects (P = 0.10). alpha(MF) in healthy young subjects (15.4 +/- 8.8 ms.mm Hg[-1]) was greater than in sedentary elderly subjects (6.5 +/- 3.2 ms.mm Hg(-1), P < 0.01) and endurance-trained elderly athletes (6.9 +/- 2.0 ms.mmHg(-1), P < 0.01), while there was no significant difference between the two elderly groups (P = 0.66). CONCLUSIONS: both components of the baroreflex measured by the alpha-index show a decrease with age. Elderly endurance-trained athletes have less reduction in the high, but not mid, frequency component of the alpha-index compared with sedentary elderly subjects. Some of the age-related changes in baroreflex sensitivity may be related to physical fitness and activity levels.

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.

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 alpha-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 alpha MF (6.5 +/- 3.5 vs. 6.2 +/- 3.0 ms mmHg-1, P = 0.69) or alpha HF (8.5 +/- 4.7 vs. 8.9 +/- 3.5 ms mmHg-1, P = 0.65) occurred after aerobic training. Following yoga, alpha HF (8.0 +/- 3.6 vs. 11.5 +/- 5.2 ms mmHg-1, P < 0.01) but not alpha MF (6.5 +/- 3.0 vs. 7.6 +/- 2.8 ms mmHg-1, P = 0.29) increased. Short-duration aerobic training does not modify the alpha-index at alpha MF or alpha HF in healthy normotensive elderly subjects. alpha HF but not alpha MF increased following yoga, suggesting that these parameters are measuring distinct aspects of the baroreflex that are separately modifiable.

Analysis of the body surface ECG measured in independent leads during ventricular fibrillation in humans.

The degree of myocardial electrical organization during ventricular fibrillation remains unknown. The aim of this study was to compare the characteristics of the surface ECG on three independent and approximately orthogonal leads. Ten recordings of ventricular fibrillation, each induced at electrophysiology study and successfully terminated by direct current shock, were analyzed. Each recording was divided into 1-second epochs for analysis. Frequency analysis using the Fast Fourier Transform showed that the frequency of the dominant spectral peak increased significantly from a mean of 4.1 +/- 0.8 Hz to 5.2 +/- 0.7 Hz during the first 5 seconds of ventricular fibrillation. In 95% of the epochs analyzed, a similar dominant frequency was observed on either two or three ECG leads. Frequency agreement tended to increase as ventricular fibrillation evolved. This study shows that the rate of ventricular fibrillation increases rapidly during the first 5 seconds but only gradually thereafter, and that similar signal characteristics are observed on independent ECG leads. These findings are not compatible with the traditional view of incoherent myocardial activity during ventricular fibrillation.

Evidence for electrical organization during ventricular fibrillation in the human heart.

INTRODUCTION: Ventricular fibrillation is a most dangerous cardiac arrhythmia that has received considerable attention, yet its pattern of electrical activation remains controversial. The aim of this study was to investigate the degree of organization during the clinical arrhythmia and to examine the phase relationship between deflections in independent ECG leads. METHODS AND RESULTS: Ten recordings of ventricular fibrillation were examined. Each had been provoked during routine electrophysiological study. The mean duration of ventricular fibrillation was 21 seconds (range 11 to 34). Independent and approximately orthogonal ECG leads I, aVF, and V2 were recorded to computer at a sampling rate of 250 Hz. The phase relationship of each ECG lead pair was measured from the lag of peaks in their cross-correlation function (CCF). In 61% of the 1-second ECG epochs analyzed, CCF peak lag changed by < 20 msec compared to the previous epoch. Thus, the overall phase relationship was stable most of the time. Changes in CCF peak lag tended to be either gradual or to punctuate periods of stability. CONCLUSIONS: This study provides evidence of organized myocardial activation during human ventricular fibrillation.