A method for investigating spatiotemporal growth patterns at cell and tissue levels during C-looping in the embryonic chick heart.

We developed a workflow using multi-scale and multi-disciplinary experimental and computational approaches to analyze C-looping (the first phase of cardiac looping) of the chick across four developing hearts. We provide the first 3D datasets for the C-looping heart with cell to organism level information, including datasets of heart images and segmented myocardial cells within the heart. We used these datasets to investigate, as a proof-of-concept, the differential spatiotemporal patterns of growth at both the cellular and tissue levels, and demonstrate how geometrical changes of C-looping at the tissue level are linked to growth features at the cellular level. Our methodological pipeline provides preliminary results for qualitative and quantitative evidence of various cellular and tissue features as potential candidates regarding the mechanism of C-looping. This pipeline can be used and extended in future studies to include larger specimen samples for detailed analyses of, and potentially new insights into, cardiac C-looping.

Efficient estimation of load-free left ventricular geometry and passive myocardial properties using principal component analysis.

Models of cardiac mechanics require a well-defined reference geometry from which deformations and hence myocardial strain and stress can be calculated. In the in vivo beating heart, the load-free (LF) geometry generally cannot be measured directly, since, in many cases, there is no stage at which the lumen pressures and contractile state are all zero. Therefore, there is a need for an efficient method to estimate the LF geometry, which is essential for an accurate mechanical simulation of left ventricular (LV) mechanics, and for estimations of passive and contractile constitutive parameters of the heart muscle. In this paper, we present a novel method for estimating both the LF geometry and the passive stiffness of the myocardium. A linear combination of principal components from a population of diastolic displacements is used to construct the LF geometry. For each estimate of the LF geometry and tissue stiffness, LV inflation is simulated, and the model predictions are compared with surface data at multiple stages during passive diastolic filling. The feasibility of this method was demonstrated using synthetically deformation data that were generated using LV models derived from clinical magnetic resonance image data, and the identifiability of the LF geometry and passive stiffness parameters were analysed using Hessian metrics. Applications of this method to clinical data would improve the accuracy of constitutive parameter estimation and allow a better simulation of LV wall strains and stresses.

Enabling Detailed, Biophysics-Based Skeletal Muscle Models on HPC Systems.

Realistic simulations of detailed, biophysics-based, multi-scale models often require very high resolution and, thus, large-scale compute facilities. Existing simulation environments, especially for biomedical applications, are typically designed to allow for high flexibility and generality in model development. Flexibility and model development, however, are often a limiting factor for large-scale simulations. Therefore, new models are typically tested and run on small-scale compute facilities. By using a detailed biophysics-based, chemo-electromechanical skeletal muscle model and the international open-source software library OpenCMISS as an example, we present an approach to upgrade an existing muscle simulation framework from a moderately parallel version toward a massively parallel one that scales both in terms of problem size and in terms of the number of parallel processes. For this purpose, we investigate different modeling, algorithmic and implementational aspects. We present improvements addressing both numerical and parallel scalability. In addition, our approach includes a novel visualization environment which is based on the MegaMol framework and is capable of handling large amounts of simulated data. We present the results of a number of scaling studies at the Tier-1 supercomputer HazelHen at the High Performance Computing Center Stuttgart (HLRS). We improve the overall runtime by a factor of up to 2.6 and achieve good scalability on up to 768 cores.

Left Ventricular Diastolic Myocardial Stiffness and End-Diastolic Myofibre Stress in Human Heart Failure Using Personalised Biomechanical Analysis.

Understanding the aetiology of heart failure with preserved (HFpEF) and reduced (HFrEF) ejection fraction requires knowledge of biomechanical factors such as diastolic myocardial stiffness and stress. Cine CMR images and intra-ventricular pressure recordings were acquired in 8 HFrEF, 11 HFpEF and 5 control subjects. Diastolic myocardial stiffness was estimated using biomechanical models and found to be greater in HFrEF (6.4 ± 1.2 kPa) than HFpEF (2.7 ± 0.6 kPa, p < 0.05) and also greater than control (1.2 ± 0.4 kPa, p < 0.005). End-diastolic mid-ventricular myofibre stress derived from the personalised biomechanics model was higher in HFrEF (2.9 ± 0.3 kPa) than control (0.9 ± 0.3 kPa, p < 0.01). Chamber stiffness, measured from the slope of the diastolic pressure-volume relationship, is determined by the intrinsic tissue properties as well as the size and shape of the heart, and was unable to distinguish between any of the three groups (p > 0.05). Personalised biomechanical analysis may provide more specific information about myocardial mechanical behaviour than global chamber indices, which are confounded by variations in ventricular geometry.

Spatio-temporal Organization During Ventricular Fibrillation in the Human Heart.

In this paper, we present a novel approach to quantify the spatio-temporal organization of electrical activation during human ventricular fibrillation (VF). We propose three different methods based on correlation analysis, graph theoretical measures and hierarchical clustering. Using the proposed approach, we quantified the level of spatio-temporal organization during three episodes of VF in ten patients, recorded using multi-electrode epicardial recordings with 30 s coronary perfusion, 150 s global myocardial ischaemia and 30 s reflow. Our findings show a steady decline in spatio-temporal organization from the onset of VF with coronary perfusion. We observed transient increases in spatio-temporal organization during global myocardial ischaemia. However, the decline in spatio-temporal organization continued during reflow. Our results were consistent across all patients, and were consistent with the numbers of phase singularities. Our findings show that the complex spatio-temporal patterns can be studied using complex network analysis.

Effect of global cardiac ischemia on human ventricular fibrillation: insights from a multi-scale mechanistic model of the human heart.

Acute regional ischemia in the heart can lead to cardiac arrhythmias such as ventricular fibrillation (VF), which in turn compromise cardiac output and result in secondary global cardiac ischemia. The secondary ischemia may influence the underlying arrhythmia mechanism. A recent clinical study documents the effect of global cardiac ischaemia on the mechanisms of VF. During 150 seconds of global ischemia the dominant frequency of activation decreased, while after reperfusion it increased rapidly. At the same time the complexity of epicardial excitation, measured as the number of epicardical phase singularity points, remained approximately constant during ischemia. Here we perform numerical studies based on these clinical data and propose explanations for the observed dynamics of the period and complexity of activation patterns. In particular, we study the effects on ischemia in pseudo-1D and 2D cardiac tissue models as well as in an anatomically accurate model of human heart ventricles. We demonstrate that the fall of dominant frequency in VF during secondary ischemia can be explained by an increase in extracellular potassium, while the increase during reperfusion is consistent with washout of potassium and continued activation of the ATP-dependent potassium channels. We also suggest that memory effects are responsible for the observed complexity dynamics. In addition, we present unpublished clinical results of individual patient recordings and propose a way of estimating extracellular potassium and activation of ATP-dependent potassium channels from these measurements.

A finite-element approach to the direct computation of relative cardiovascular pressure from time-resolved MR velocity data.

The evaluation of cardiovascular velocities, their changes through the cardiac cycle and the consequent pressure gradients has the capacity to improve understanding of subject-specific blood flow in relation to adjacent soft tissue movements. Magnetic resonance time-resolved 3D phase contrast velocity acquisitions (4D flow) represent an emerging technology capable of measuring the cyclic changes of large scale, multi-directional, subject-specific blood flow. A subsequent evaluation of pressure differences in enclosed vascular compartments is a further step which is currently not directly available from such data. The focus of this work is to address this deficiency through the development of a novel simulation workflow for the direct computation of relative cardiovascular pressure fields. Input information is provided by enhanced 4D flow data and derived MR domain masking. The underlying methodology shows numerical advantages in terms of robustness, global domain composition, the isolation of local fluid compartments and a treatment of boundary conditions. This approach is demonstrated across a range of validation examples which are compared with analytic solutions. Four subject-specific test cases are subsequently run, showing good agreement with previously published calculations of intra-vascular pressure differences. The computational engine presented in this work contributes to non-invasive access to relative pressure fields, incorporates the effects of both blood flow acceleration and viscous dissipation, and enables enhanced evaluation of cardiovascular blood flow.

Human ventricular fibrillation during global ischemia and reperfusion: paradoxical changes in activation rate and wavefront complexity.

BACKGROUND: Ischemic ventricular fibrillation in experimental models has been shown to progress through a series of stages. Progression of ischemic VF in the in vivo human heart has not been determined. METHODS AND RESULTS: We studied 10 patients undergoing cardiac surgery. Ventricular fibrillation was induced by burst pacing. After 30 seconds, global myocardial ischemia was induced by aortic cross-clamp and maintained for 2.5 minutes, followed by coronary reflow. Epicardial activity was sampled (1 kHz) with a sock that contained 256 unipolar contact electrodes. Dominant frequencies were calculated with a fast Fourier transform with a moving window. The locations of phase singularities and activation wavefronts were identified at 10-ms intervals. Preischemic (perfused) ventricular fibrillation was maintained by a disorganized mix of large and small wavefronts. During global myocardial ischemia, mean dominant frequencies decreased from 6.4 to 4.7 Hz at a rate of -0.011±0.002 Hz s(-1) (P<0.001) and then increased rapidly to 7.4 Hz within 30 seconds of reflow. In contrast, the average number of epicardial phase singularities increased during ischemia from 7.7 to 9.7 at a rate of 0.013±0.005 phase singularities per second (P<0.01) and remained unchanged during reflow, at 10.3. The number of wavefronts showed a similar time course to the number of phase singularities. CONCLUSIONS: In human ventricular fibrillation, we found an increase in complexity of electric activation patterns during global myocardial ischemia, and this was not reversed during reflow despite an increase in activation rate.

FieldML: concepts and implementation.

The field modelling language FieldML is being developed as a standard for modelling and interchanging field descriptions in software, suitable for a wide range of computation techniques. It comprises a rich set of operators for defining generalized fields as functions of other fields, starting with basic domain fields including sets of discrete objects and coordinate systems. It is extensible by adding new operators and by their arbitrary combination in expressions, making it well suited for describing the inherent complexity of biological materials and organ systems. This paper describes the concepts behind FieldML, including a simple example of a spatially varying finite-element field. It outlines current implementations in established, open source computation and visualization software, both drawing on decades of bioengineering modelling software development experience.

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 (100x100 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.

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.

Imaging electrocardiographic dispersion of depolarization and repolarization during ischemia: simultaneous body surface and epicardial mapping.

BACKGROUND: Myocardial ischemia creates abnormal electrophysiological substrates that result in life-threatening ventricular arrhythmias. Identifying patients at risk of such abnormalities by use of body surface electrical measures is controversial. We investigated the sensitivity of torso measures, recorded simultaneously with epicardial electrograms, to changes in dispersion of depolarization and repolarization during localized ventricular ischemia. METHODS AND RESULTS: Ventricular epicardial electrograms were recorded from 5 anesthetized pigs with a 127-electrode sock. A controllable suture snare was used to ligate the left anterior descending coronary artery (LAD). The chest was reclosed, and a vest with 256 ECG electrodes was fitted to the torso. Simultaneous arrays of epicardial electrograms and torso ECGs were recorded during LAD occlusion and reperfusion. Activation-recovery intervals (ARIs), QTu and RTu dispersion (where u indicates upstroke), and QRST integrals were calculated, and these data were fitted to anatomically customized computational models of the swine ventricular epicardium and torso. LAD occlusion caused the epicardial ARI dispersion to steadily increase, whereas the location of shortest ARI shifted from the posterobasal ventricular tissue (control) to the anteroapical myocardium, distal to the suture snare. These changes were associated with a steady increase in the torso RTu dispersion as the shortest RTu interval moved from the right shoulder (control) to the sternum. QTu and RTu dispersion determined from the 12-lead ECG did not consistently reflect the myocardial changes. CONCLUSIONS: Although changes in myocardial repolarization dispersion resulting from localized ischemia are not reliably reflected in temporal indices derived from the 12-lead ECG, they can be readily identified with high-resolution torso ECG mapping.