Digital Twinning of Cardiac Electrophysiology Models From the Surface ECG: A Geodesic Backpropagation Approach

The eikonal equation has become an indispensable tool for modeling cardiac electrical activation accurately and efficiently. In principle, by matching clinically recorded and eikonal-based electrocardiograms (ECGs), it is possible to build patient-specific models of cardiac electrophysiology in a purely non-invasive manner. Nonetheless, the fitting procedure remains a challenging task. The present study introduces a novel method, Geodesic-BP, to solve the inverse eikonal problem. Geodesic-BP is well-suited for GPU-accelerated machine learning frameworks, allowing us to optimize the parameters of the eikonal equation to reproduce a given ECG. We show that Geodesic-BP can reconstruct a simulated cardiac activation with high accuracy in a synthetic test case, even in the presence of modeling inaccuracies. Furthermore, we apply our algorithm to a publicly available dataset of a biventricular rabbit model, with promising results. Given the future shift towards personalized medicine, Geodesic-BP has the potential to help in future functionalizations of cardiac models meeting clinical time constraints while maintaining the physiological accuracy of state-of-the-art cardiac models.

Synchronization of repolarization after cardiac resynchronization therapy: a combined clinical and modeling study

Introduction

The changes in ventricular repolarization after cardiac resynchronization therapy (CRT) are poorly understood. This knowledge gap is addressed using a multimodality approach including electrocardiographic and echocardiographic measurements in patients and using patient‐specific computational modeling.

Methods

In 33 patients electrocardiographic and echocardiographic measurements were performed before and at various intervals after CRT, both during CRT‐ON and temporary CRT‐OFF. T‐wave area was calculated from vectorcardiograms, and reconstructed from the 12‐lead electrocardiography (ECG). Computer simulations were performed using a patient‐specific eikonal model of cardiac activation with spatially varying action potential duration (APD) and repolarization rate, fit to a patient's ECG.

Results

During CRT‐ON T‐wave area diminished within a day and remained stable thereafter, whereas QT‐interval did not change significantly. During CRT‐OFF T‐wave area doubled within 5 days of CRT, while QT‐interval and peak‐to‐end T‐wave interval hardly changed. Left ventricular (LV) ejection fraction only increased significantly increased after 1 month of CRT. Computer simulations indicated that the increase in T‐wave area during CRT‐OFF can be explained by changes in APD following chronic CRT that are opposite to the change in CRT‐induced activation time. These APD changes were associated with a reduction in LV dispersion in repolarization during chronic CRT.

Conclusion

T‐wave area during CRT‐OFF is a sensitive marker for adaptations in ventricular repolarization during chronic CRT that may include a reduction in LV dispersion of repolarization.

Synchronization of repolarization after cardiac resynchronization therapy: time course and relation to reverse remodeling

Funding Acknowledgements

Type of funding sources: None.

Background

The changes in ventricular repolarization after cardiac resynchronization therapy (CRT) are poorly understood.

Objective

Address this knowledge gap using a multimodality approach including electrocardiographic and echocardiographic measurements in patients and patient-specific computational modeling.

Methods

In a cohort of consecutive CRT patients, electrocardiographic and echocardiographic measurements were performed before and at various intervals after CRT, both during CRT-ON and temporary CRT-OFF. T-wave area was calculated from vectorcardiograms, reconstructed from the 12-lead ECG. Computer simulations were performed using a patient-specific eikonal model of cardiac activation with spatially varying action potential duration (APD) and repolarization rate, based on a patient’s ECG and MRI-based chest and cardiac anatomy.

Results

In 33 patients T-wave area during CRT-OFF doubled within 5 days of CRT (left figure) while other repolarization markers like QT-interval and peak-to-end T-wave interval hardly changed. Patients with T-wave area increase above the median increase showed a significantly larger increase in left ventricular ejection fraction than those with smaller T-wave area increase (+11±8% vs. +6±6%, respectively; p<0.05, n=76). Computer simulations (figure, right) show the sequence of depolarization and repolarization before CRT, obtained by the patient-specific model (BL LBBB) and following Acute CRT. Repolarization after chronic CRT-OFF was obtained by matching the measured CRT-OFF ECG with that provided by the model. The best match was obtained by changes in APD following chronic CRT that are opposite to the change in CRT-induced activation time. Such APD changes were associated with a reduction in right and left ventricular dispersion in repolarization during chronic CRT-ON compared with acute CRT-ON.

Conclusions

T-wave area during CRT-OFF is a sensitive marker for adaptations in ventricular repolarization after CRT that are related to CRT-induced reverse remodeling and may involve an inverse relation between activation time and APD, coinciding with lower right and left ventricular dispersion of repolarization and with larger increases in LV ejection fraction during chronic CRT.

Fast Characterization of Inducible Regions of Atrial Fibrillation Models With Multi-Fidelity Gaussian Process Classification

Computational models of atrial fibrillation have successfully been used to predict optimal ablation sites. A critical step to assess the effect of an ablation pattern is to pace the model from different, potentially random, locations to determine whether arrhythmias can be induced in the atria. In this work, we propose to use multi-fidelity Gaussian process classification on Riemannian manifolds to efficiently determine the regions in the atria where arrhythmias are inducible. We build a probabilistic classifier that operates directly on the atrial surface. We take advantage of lower resolution models to explore the atrial surface and combine seamlessly with high-resolution models to identify regions of inducibility. We test our methodology in 9 different cases, with different levels of fibrosis and ablation treatments, totalling 1,800 high resolution and 900 low resolution simulations of atrial fibrillation. When trained with 40 samples, our multi-fidelity classifier that combines low and high resolution models, shows a balanced accuracy that is, on average, 5.7% higher than a nearest neighbor classifier. We hope that this new technique will allow faster and more precise clinical applications of computational models for atrial fibrillation. All data and code accompanying this manuscript will be made publicly available at: https://github.com/fsahli/AtrialMFclass.

Space-time shape uncertainties in the forward and inverse problem of electrocardiography

In electrocardiography, the "classic" inverse problem is the reconstruction of electric potentials at a surface enclosing the heart from remote recordings at the body surface and an accurate description of the anatomy. The latter being affected by noise and obtained with limited resolution due to clinical constraints, a possibly large uncertainty may be perpetuated in the inverse reconstruction. The purpose of this work is to study the effect of shape uncertainty on the forward and the inverse problem of electrocardiography. To this aim, the problem is first recast into a boundary integral formulation and then discretised with a collocation method to achieve high convergence rates and a fast time to solution. The shape uncertainty of the domain is represented by a random deformation field defined on a reference configuration. We propose a periodic-in-time covariance kernel for the random field and approximate the Karhunen-Loève expansion using low-rank techniques for fast sampling. The space-time uncertainty in the expected potential and its variance is evaluated with an anisotropic sparse quadrature approach and validated by a quasi-Monte Carlo method. We present several numerical experiments on a simplified but physiologically grounded two-dimensional geometry to illustrate the validity of the approach. The tested parametric dimension ranged from 100 up to 600. For the forward problem, the sparse quadrature is very effective. In the inverse problem, the sparse quadrature and the quasi-Monte Carlo method perform as expected, except for the total variation regularisation, where convergence is limited by lack of regularity. We finally investigate an H1/2 regularisation, which naturally stems from the boundary integral formulation, and compare it to more classical approaches.

Synergistic antiarrhythmic effect of inward rectifier current inhibition and pulmonary vein isolation in a 3D computer model for atrial fibrillation

AIMS

Recent clinical studies showed that antiarrhythmic drug (AAD) treatment and pulmonary vein isolation (PVI) synergistically reduce atrial fibrillation (AF) recurrences after initially successful ablation. Among newly developed atrial-selective AADs, inhibitors of the G-protein-gated acetylcholine-activated inward rectifier current (IKACh) were shown to effectively suppress AF in an experimental model but have not yet been evaluated clinically. We tested in silico whether inhibition of inward rectifier current or its combination with PVI reduces AF inducibility.

METHODS AND RESULTS

We simulated the effect of inward rectifier current blockade (IK blockade), PVI, and their combination on AF inducibility in a detailed three-dimensional model of the human atria with different degrees of fibrosis. IK blockade was simulated with a 30% reduction of its conductivity. Atrial fibrillation was initiated using incremental pacing applied at 20 different locations, in both atria. IK blockade effectively prevented AF induction in simulations without fibrosis as did PVI in simulations without fibrosis and with moderate fibrosis. Both interventions lost their efficacy in severe fibrosis. The combination of IK blockade and PVI prevented AF in simulations without fibrosis, with moderate fibrosis, and even with severe fibrosis. The combined therapy strongly decreased the number of fibrillation waves, due to a synergistic reduction of wavefront generation rate while the wavefront lifespan remained unchanged.

CONCLUSION

Newly developed blockers of atrial-specific inward rectifier currents, such as IKAch, might prevent AF occurrences and when combined with PVI effectively supress AF recurrences in human.

Reconstruction of three-dimensional biventricular activation based on the 12-lead electrocardiogram via patient-specific modelling

Aims

Non-invasive imaging of electrical activation requires high-density body surface potential mapping. The nine electrodes of the 12-lead electrocardiogram (ECG) are insufficient for a reliable reconstruction with standard inverse methods. Patient-specific modelling may offer an alternative route to physiologically constraint the reconstruction. The aim of the study was to assess the feasibility of reconstructing the fully 3D electrical activation map of the ventricles from the 12-lead ECG and cardiovascular magnetic resonance (CMR).

Methods and results

Ventricular activation was estimated by iteratively optimizing the parameters (conduction velocity and sites of earliest activation) of a patient-specific model to fit the simulated to the recorded ECG. Chest and cardiac anatomy of 11 patients (QRS duration 126–180 ms, documented scar in two) were segmented from CMR images. Scar presence was assessed by magnetic resonance (MR) contrast enhancement. Activation sequences were modelled with a physiologically based propagation model and ECGs with lead field theory. Validation was performed by comparing reconstructed activation maps with those acquired by invasive electroanatomical mapping of coronary sinus/veins (CS) and right ventricular (RV) and left ventricular (LV) endocardium. The QRS complex was correctly reproduced by the model (Pearson’s correlation r = 0.923). Reconstructions accurately located the earliest and latest activated LV regions (median barycentre distance 8.2 mm, IQR 8.8 mm). Correlation of simulated with recorded activation time was very good at LV endocardium (r = 0.83) and good at CS (r = 0.68) and RV endocardium (r = 0.58).

Conclusion

Non-invasive assessment of biventricular 3D activation using the 12-lead ECG and MR imaging is feasible. Potential applications include patient-specific modelling and pre-/per-procedural evaluation of ventricular activation.

Automatic reconstruction of the left atrium activation from sparse intracardiac contact recordings by inverse estimate of fibre structure and anisotropic conduction in a patient-specific model

AIMS

Electric conduction in the atria is direction-dependent, being faster in fibre direction, and possibly heterogeneous due to structural remodelling. Intracardiac recordings of atrial activation may convey such information, but only with high-quality data. The aim of this study was to apply a patient-specific approach to enable such assessment even when data are scarce, noisy, and incomplete.

METHODS AND RESULTS

Contact intracardiac recordings in the left atrium from nine patients who underwent ablation therapy were collected before pulmonary veins isolation and retrospectively included in the study. The Personalized Inverse Eikonal Model from cardiac Electro-Anatomical Maps (PIEMAP), previously developed, has been used to reconstruct the conductivity tensor from sparse recordings of the activation. Regional fibre direction and conduction velocity were estimated from the fitted conductivity tensor and extensively cross-validated by clustered and sparse data removal. Electrical conductivity was successfully reconstructed in all patients. Cross-validation with respect to the measurements was excellent in seven patients (Pearson correlation r > 0.93) and modest in two patients (r = 0.62 and r = 0.74). Bland-Altman analysis showed a neglectable bias with respect to the measurements and the limit-of-agreement at -22.2 and 23.0 ms. Conduction velocity in the fibre direction was 82 ± 25 cm/s, whereas cross-fibre velocity was 46 ± 7 cm/s. Anisotropic ratio was 1.91±0.16. No significant inter-patient variability was observed. Personalized Inverse Eikonal model from cardiac Electro-Anatomical Maps correctly predicted activation times in late regions in all patients (r = 0.88) and was robust to a sparser dataset (r = 0.95).

CONCLUSION

Personalized Inverse Eikonal model from cardiac Electro-Anatomical Maps offers a novel approach to extrapolate the activation in unmapped regions and to assess conduction properties of the atria. It could be seamlessly integrated into existing electro-anatomic mapping systems. Personalized Inverse Eikonal model from cardiac Electro-Anatomical Maps also enables personalization of cardiac electrophysiology models.

GEASI: Geodesic-based earliest activation sites identification in cardiac models

The identification of the initial ventricular activation sequence is a critical step for the correct personalization of patient-specific cardiac models. In healthy conditions, the Purkinje network is the main source of the electrical activation, but under pathological conditions the so-called earliest activation sites (EASs) are possibly sparser and more localized. Yet, their number, location and timing may not be easily inferred from remote recordings, such as the epicardial activation or the 12-lead electrocardiogram (ECG), due to the underlying complexity of the model. In this work, we introduce GEASI (Geodesic-based Earliest Activation Sites Identification) as a novel approach to simultaneously identify all EASs. To this end, we start from the anisotropic eikonal equation modeling cardiac electrical activation and exploit its Hamilton-Jacobi formulation to minimize a given objective function, for example, the quadratic mismatch to given activation measurements. This versatile approach can be extended to estimate the number of activation sites by means of the topological gradient, or fitting a given ECG. We conducted various experiments in 2D and 3D for in-silico models and an in-vivo intracardiac recording collected from a patient undergoing cardiac resynchronization therapy. The results demonstrate the clinical applicability of GEASI for potential future personalized models and clinical intervention.

Learning atrial fiber orientations and conductivity tensors from intracardiac maps using physics-informed neural networks

Electroanatomical maps are a key tool in the diagnosis and treatment of atrial fibrillation. Current approaches focus on the activation times recorded. However, more information can be extracted from the available data. The fibers in cardiac tissue conduct the electrical wave faster, and their direction could be inferred from activation times. In this work, we employ a recently developed approach, called physics informed neural networks, to learn the fiber orientations from electroanatomical maps, taking into account the physics of the electrical wave propagation. In particular, we train the neural network to weakly satisfy the anisotropic eikonal equation and to predict the measured activation times. We use a local basis for the anisotropic conductivity tensor, which encodes the fiber orientation. The methodology is tested both in a synthetic example and for patient data. Our approach shows good agreement in both cases and it outperforms a state of the art method in the patient data. The results show a first step towards learning the fiber orientations from electroanatomical maps with physics-informed neural networks.

Short P-Wave Duration is a Marker of Higher Rate of Atrial Fibrillation Recurrences after Pulmonary Vein Isolation: New Insights into the Pathophysiological Mechanisms Through Computer Simulations

Background Short ECG P-wave duration has recently been demonstrated to be associated with higher risk of atrial fibrillation (AF). The aim of this study was to assess the rate of AF recurrence after pulmonary vein isolation in patients with a short P wave, and to mechanistically elucidate the observation by computer modeling. Methods and Results A total of 282 consecutive patients undergoing a first single-pulmonary vein isolation procedure for paroxysmal or persistent AF were included. Computational models studied the effect of adenosine and sodium conductance on action potential duration and P-wave duration (PWD). About 16% of the patients had a PWD of 110 ms or shorter (median PWD 126 ms, interquartile range, 115 ms-138 ms; range, 71 ms-180 ms). At Cox regression, PWD was significantly associated with AF recurrence (P=0.012). Patients with a PWD <110 ms (hazard ratio [HR], 2.20; 95% CI, 1.24-3.88; P=0.007) and patients with a PWD ≥140 (HR, 1.87, 95% CI, 1.06-3.30; P=0.031) had a nearly 2-fold increase in risk with respect to the other group. In the computational model, adenosine yielded a significant reduction of action potential duration 90 (52%) and PWD (7%). An increased sodium conductance (up to 200%) was robustly accompanied by an increase in conduction velocity (26%), a reduction in action potential duration 90 (28%), and PWD (22%). Conclusions One out of 5 patients referred for pulmonary vein isolation has a short PWD which was associated with a higher rate of AF after the index procedure. Computer simulations suggest that shortening of atrial action potential duration leading to a faster atrial conduction may be the cause of this clinical observation.

Epicardial Fibrosis Explains Increased Endo-Epicardial Dissociation and Epicardial Breakthroughs in Human Atrial Fibrillation

Background

Atrial fibrillation (AF) is accompanied by progressive epicardial fibrosis, dissociation of electrical activity between the epicardial layer and the endocardial bundle network, and transmural conduction (breakthroughs). However, causal relationships between these phenomena have not been demonstrated yet. Our goal was to test the hypothesis that epicardial fibrosis suffices to increase endo–epicardial dissociation (EED) and breakthroughs (BT) during AF.

Methods

We simulated the effect of fibrosis in the epicardial layer on EED and BT in a detailed, high-resolution, three-dimensional model of the human atria with realistic electrophysiology. The model results were compared with simultaneous endo–epicardial mapping in human atria. The model geometry, specifically built for this study, was based on MR images and histo-anatomical studies. Clinical data were obtained in four patients with longstanding persistent AF (persAF) and three patients without a history of AF.

Results

The AF cycle length (AFCL), conduction velocity (CV), and EED were comparable in the mapping studies and the simulations. EED increased from 24.1 ± 3.4 to 56.58 ± 6.2% (p < 0.05), and number of BTs per cycle from 0.89 ± 0.55 to 6.74 ± 2.11% (p < 0.05), in different degrees of fibrosis in the epicardial layer. In both mapping data and simulations, EED correlated with prevalence of BTs. Fibrosis also increased the number of fibrillation waves per cycle in the model.

Conclusion

A realistic 3D computer model of AF in which epicardial fibrosis was increased, in the absence of other pathological changes, showed increases in EED and epicardial BT comparable to those in longstanding persAF. Thus, epicardial fibrosis can explain both phenomena.

The influence of scar on the spatio-temporal relationship between electrical and mechanical activation in heart failure patients

Aims

The aim of this study was to determine the relationship between electrical and mechanical activation in heart failure (HF) patients and whether electromechanical coupling is affected by scar.

Methods and results

Seventy HF patients referred for cardiac resynchronization therapy or biological therapy underwent endocardial anatomo-electromechanical mapping (AEMM) and delayed-enhancement magnetic resonance (CMR) scans. Area strain and activation times were derived from AEMM data, allowing to correlate mechanical and electrical activation in time and space with unprecedented accuracy. Special attention was paid to the effect of presence of CMR-evidenced scar. Patients were divided into a scar (n = 43) and a non-scar group (n–27). Correlation between time of electrical and mechanical activation was stronger in the non-scar compared to the scar group [R = 0.84 (0.72–0.89) vs. 0.74 (0.52–0.88), respectively; P = 0.01]. The overlap between latest electrical and mechanical activation areas was larger in the absence than in presence of scar [72% (54–81) vs. 56% (36–73), respectively; P = 0.02], with smaller distance between the centroids of the two regions [10.7 (4.9–17.4) vs. 20.3 (6.9–29.4) % of left ventricular radius, P = 0.02].

Conclusion

Scar decreases the association between electrical and mechanical activation, even when scar is remote from late activated regions.

Fast uncertainty quantification of activation sequences in patient-specific cardiac electrophysiology meeting clinical time constraints

We present a fast, patient-specific methodology for uncertainty quantification in electrophysiology, aimed at meeting the time constraints of clinical practitioners. We focus on computing the statistics of the activation map, given the uncertainties associated with the conductivity tensor modeling the fiber orientation in the heart. We use a fast parallel solution method implemented on a graphics processing unit for the eikonal approximation, in order to compute the activation map and to sample the random fiber field with correlation on the basis of geodesic distances. While this enables to perform uncertainty quantification studies with a manageable computational effort, the required time frame still exceeds clinically suitable time expectations. In order to reduce it further by 2 orders of magnitude, we rely on Bayesian multifidelity methods. In particular, we propose a low-fidelity model that is patient-specific and free from the additional training cost associated with reduced models. This is achieved by a sound physics-based simplification of the full eikonal model. The low-fidelity output is then corrected by the standard multifidelity framework. In practice, the complete procedure only requires approximately 100 new runs of our eikonal graphics processing unit solver for producing the sought estimates and their associated credible intervals, enabling a full online analysis in less than 5 minutes.

Solid tumors are poroelastic solids with a chemo-mechanical feedback on growth

The experimental evidence that a feedback exists between growth and stress in tumors poses challenging questions. First, the rheological properties (the "constitutive equations") of aggregates of malignant cells are still a matter of debate. Secondly, the feedback law (the "growth law") that relates stress and mitotic-apoptotic rate is far to be identified. We address these questions on the basis of a theoretical analysis of in vitro and in vivo experiments that involve the growth of tumor spheroids. We show that solid tumors exhibit several mechanical features of a poroelastic material, where the cellular component behaves like an elastic solid. When the solid component of the spheroid is loaded at the boundary, the cellular aggregate grows up to an asymptotic volume that depends on the exerted compression. Residual stress shows up when solid tumors are radially cut, highlighting a peculiar tensional pattern. By a novel numerical approach we correlate the measured opening angle and the underlying residual stress in a sphere. The features of the mechanobiological system can be explained in terms of a feedback of mechanics on the cell proliferation rate as modulated by the availability of nutrient, that is radially damped by the balance between diffusion and consumption. The volumetric growth profiles and the pattern of residual stress can be theoretically reproduced assuming a dependence of the target stress on the concentration of nutrient which is specific of the malignant tissue.

Far-infrared observations of a massive cluster forming in the Monoceros R2 filament hub⋆

We present far-infrared observations of Monoceros R2 (a giant molecular cloud at approximately 830 pc distance, containing several sites of active star formation), as observed at 70 μm, 160 μm, 250 μm, 350 μm, and 500 μm by the Photodetector Array Camera and Spectrometer (PACS) and Spectral and Photometric Imaging Receiver (SPIRE) instruments on the Herschel Space Observatory as part of the Herschel imaging survey of OB young stellar objects (HOBYS) Key programme. The Herschel data are complemented by SCUBA-2 data in the submillimetre range, and WISE and Spitzer data in the mid-infrared. In addition, C18O data from the IRAM 30-m Telescope are presented, and used for kinematic information. Sources were extracted from the maps with getsources, and from the fluxes measured, spectral energy distributions were constructed, allowing measurements of source mass and dust temperature. Of 177 Herschel sources robustly detected in the region (a detection with high signal-to-noise and low axis ratio at multiple wavelengths), including protostars and starless cores, 29 are found in a filamentary hub at the centre of the region (a little over 1% of the observed area). These objects are on average smaller, more massive, and more luminous than those in the surrounding regions (which together suggest that they are at a later stage of evolution), a result that cannot be explained entirely by selection effects. These results suggest a picture in which the hub may have begun star formation at a point significantly earlier than the outer regions, possibly forming as a result of feedback from earlier star formation. Furthermore, the hub may be sustaining its star formation by accreting material from the surrounding filaments.

Impact of mechanical deformation on pseudo-ECG: a simulation study

AIMS

Electrophysiological simulations may help to investigate causes and possible treatments of ventricular conduction disturbances. Most electrophysiological models do not take into account that the heart moves during the cardiac cycle. We used an electro-mechanical model to study the effect of mechanical deformation on the results of electrophysiological simulations.

METHODS AND RESULTS

Pseudo-electrocardiogram (ECG) were generated from the propagation of electrical signals in tissue slabs undergoing active mechanical deformation. We used the mono-domain equation for electrophysiology with the Bueno-Orovio ionic model and a fully incompressible Guccione-Costa hyperelastic law for the mechanics with the Nash-Panfilov model for the active force. We compared a purely electrophysiological approach (PE) with mono-directional (MD) and bi-directional (BD) electromechanical coupling strategies. The numerical experiments showed that BD and PE simulations led to different S- and T-waves. Mono-directional simulations generally approximated the BD ones, unless fibres were oriented along one short axis of the slab. When present, notching in the QRS-complex was larger in MD than in BD simulations.

CONCLUSIONS

Tissue deformation has to be taken into account when estimating the S- and T-wave of the ECG in electrophysiological simulations.

Evaluation of a Rapid Anisotropic Model for ECG Simulation

State-of-the-art cardiac electrophysiology models that are able to deliver physiologically motivated activation maps and electrocardiograms (ECGs) can only be solved on high-performance computing architectures. This makes it nearly impossible to adopt such models in clinical practice. ECG imaging tools typically rely on simplified models, but these neglect the anisotropic electric conductivity of the tissue in the forward problem. Moreover, their results are often confined to the heart-torso interface. We propose a forward model that fully accounts for the anisotropic tissue conductivity and produces the standard 12-lead ECG in a few seconds. The activation sequence is approximated with an eikonal model in the 3d myocardium, while the ECG is computed with the lead-field approach. Both solvers were implemented on graphics processing units and massively parallelized. We studied the numerical convergence and scalability of the approach. We also compared the method to the bidomain model in terms of ECGs and activation maps, using a simplified but physiologically motivated geometry and 6 patient-specific anatomies. The proposed methods provided a good approximation of activation maps and ECGs computed with a bidomain model, in only a few seconds. Both solvers scaled very well to high-end hardware. These methods are suitable for use in ECG imaging methods, and may soon become fast enough for use in interactive simulation tools.

Space-discretization error analysis and stabilization schemes for conduction velocity in cardiac electrophysiology

In cardiac electrophysiology, the propagation of the action potential may be described by a set of reaction-diffusion equations known as the bidomain model. The shape of the solution is determined by a balance of a strong reaction and a relatively weak diffusion, which leads to steep variations in space and time. From a numerical point of view, the sharp spatial gradients may be seen as particularly problematic, because computational grid resolution on the order of 0.1 mm or less is required, yielding considerable computational efforts on human geometries. In this paper, we discuss a number of well-known numerical schemes for the bidomain equation and show how the quality of the solution is affected by the spatial discretization. In particular, we study in detail the effect of discretization on the conduction velocity (CV), which is an important quantity from a physiological point of view. We show that commonly applied finite element techniques tend to overestimate the CV on coarse grids, while it tends to be underestimated by finite difference schemes. Furthermore, the choice of interpolation and discretization scheme for the nonlinear reaction term has a strong impact on the CV. Finally, we exploit the results of the error analysis to propose improved numerical methods, including a stabilized scheme that tends to correct the CV on coarse grids but converges to the correct solution as the grid is refined. Copyright © 2016 John Wiley & Sons, Ltd.

Finite element simulations of the active stress in the imaginal disc of the Drosophila Melanogaster

During the larval stages of development, the imaginal disc of Drosphila Melanogaster is composed by a monolayer of epithelial cells, which undergo a strain actively produced by the cells themselves. The well-organized collective contraction produces a stress field that seemingly has a double morphogenetic role: it orchestrates the cellular organization towards the macroscopic shape emergence while simultaneously providing a local information on the organ size. Here we perform numerical simulations of such a mechanical control on morphogenesis at a continuum level, using a three-dimensional finite model that accounts for the active cell contraction. The numerical model is able to reproduce the (few) known qualitative characteristics of the tensional patterns within the imaginal disc of the fruit fly. The computed stress components slightly deviate from planarity, thus confirming the previous theoretical assumptions of a nonlinear elastic analytical model, and enforcing the hypothesis that the spatial variation of the mechanical stress may act as a size regulating signal that locally scales with the global dimension of the domain.

Verification of cardiac mechanics software: benchmark problems and solutions for testing active and passive material behaviour

Models of cardiac mechanics are increasingly used to investigate cardiac physiology. These models are characterized by a high level of complexity, including the particular anisotropic material properties of biological tissue and the actively contracting material. A large number of independent simulation codes have been developed, but a consistent way of verifying the accuracy and replicability of simulations is lacking. To aid in the verification of current and future cardiac mechanics solvers, this study provides three benchmark problems for cardiac mechanics. These benchmark problems test the ability to accurately simulate pressure-type forces that depend on the deformed objects geometry, anisotropic and spatially varying material properties similar to those seen in the left ventricle and active contractile forces. The benchmark was solved by 11 different groups to generate consensus solutions, with typical differences in higher-resolution solutions at approximately 0.5%, and consistent results between linear, quadratic and cubic finite elements as well as different approaches to simulating incompressible materials. Online tools and solutions are made available to allow these tests to be effectively used in verification of future cardiac mechanics software.

High-order finite element methods for cardiac monodomain simulations

Computational modeling of tissue-scale cardiac electrophysiology requires numerically converged solutions to avoid spurious artifacts. The steep gradients inherent to cardiac action potential propagation necessitate fine spatial scales and therefore a substantial computational burden. The use of high-order interpolation methods has previously been proposed for these simulations due to their theoretical convergence advantage. In this study, we compare the convergence behavior of linear Lagrange, cubic Hermite, and the newly proposed cubic Hermite-style serendipity interpolation methods for finite element simulations of the cardiac monodomain equation. The high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements. Additionally, we propose a dimensionless number, the cell Thiele modulus, as a more useful metric for determining solution convergence than element size alone. Finally, we use the cell Thiele modulus to examine convergence criteria for obtaining clinically useful activation patterns for applications such as patient-specific modeling where the total activation time is known a priori.

Active contraction of the cardiac ventricle and distortion of the microstructural architecture

The shortening of the myocardial fibers is the microstructural engine that produces the contraction of the cardiac muscle. The complex interplay between fibers shortening and elastic macroscopic strain is functional to the ejection of blood into the pulmonary and arterial networks. Here, we address the contraction of the left ventricle in a finite elasticity framework, adopting the 'prolate ellipsoid' geometry and the invariants-based strain energy proposed by Holzapfel and Ogden, where the mechanical role of fibers and sheets is accounted for. We show that a microstructurally motivated mathematical model of active strain type reproduces the main indicators of normal cardiac function along the whole PV-loop without introduction of any further ad hoc law. The bare-bones mathematical model depends on one measurable parameter only, that is, the shortening ratio of the sarcomere units, which we assume to be nearly independent on the prestretch. Strict enforcement of incompressibility and novel treatment of boundary conditions are shown to be crucial to simulate the correct muscle torsion.

High vitamin E plasma levels and low low-density lipoprotein oxidation are associated with the absence of atherosclerosis in octogenarians

OBJECTIVES

To identify the biological characteristics of older subjects with vascular successful aging (VASA), defined as the absence of instrumental signs and clinical symptoms of atherosclerosis in the extracoronary and coronary vessels.

DESIGN

A cross-sectional study.

SETTING

A university-affiliated outpatient clinic.

PARTICIPANTS

Sixty older subjects (30 with VASA and 30 controls with moderate carotid atherosclerosis (AG group)) from a sample of 705 subjects age 75 and older consecutively screened.

MEASUREMENTS

Clinical examination; ultrasonographic examination of carotid, vertebral, abdominal aortic, iliac, and femoral arteries; electrocardiogram; and laboratory evaluation (lipid profile, lipophilic antioxidants, and markers of low-density lipoprotein (LDL) oxidation).

RESULTS

Compared with controls, there were more females in the VASA group (82% vs 50%, P <.01), and fewer previous smokers (20.5% vs 52.5%, P <.01). Vitamin E/total cholesterol levels both in plasma (4.81 vs 3.51 micromol/mmol, P <.001) and in isolated LDLs (2.71 vs 1.86 microg/mg LDL cholesterol (LDL-C), P <.01), were higher in the VASA group, as was the resistance of LDLs to in vitro oxidation (as indicated by a longer duration of the lag phase: 80.2 vs 65.6 minutes, P <.001). The level of fluorescent products of lipid peroxidation (FPLPs) in native LDLs was lower in the VASA group (13.5 vs 18.8 URF/mg LDL-C, P <.001). Multivariate logistic regression analysis showed that only plasma vitamin E level (odds ratio (OR) = 6.04, 95% confidence interval (CI) = 1.48-24.63) and FPLPs in LDLs (OR = 0.53, 95% CI = 0.31-0.91) were independently associated with VASA.

CONCLUSIONS

These results suggest that an appropriate level of vitamin E and a low level of LDL oxidation might be important for reaching advanced age without developing atherosclerosis.

Antioxidant profile and early outcome in stroke patients

BACKGROUND AND PURPOSE

Experimental studies provide evidence of an association between ischemic stroke and increased oxidative stress, but data in humans are still limited and controversial. The purpose of this study was to investigate the time course of plasma antioxidant changes in ischemic stroke patients.

METHODS

Plasma antioxidants, including water-soluble (vitamin C and uric acid) and lipid-soluble (vitamins A and E) compounds as well as antioxidant enzyme activities in plasma (superoxide dismutase [SOD] and glutathione peroxidase) and erythrocytes (SOD), were measured by high-performance liquid chromatography (antioxidant vitamins) and by spectrophotometry (antioxidant enzymes) in 38 subjects (25 men and 13 women aged 77.2+/-7.9 years) with acute ischemic stroke of recent onset (<24 hours) on admission, after 6 and 24 hours, and on days 3, 5, and 7. Antioxidant levels in patients on admission were compared with those of age- and sex-matched controls.

RESULTS

Mean antioxidant levels and activities in patients on admission were lower than those of controls and showed a gradual increase over time. Patients with the worst early outcome (death or functional decline) had higher vitamin A and uric acid plasma levels and lower vitamin C levels and erythrocyte SOD activity than those who remained functionally stable.

CONCLUSIONS

These results suggest that the majority of antioxidants are reduced immediately after an acute ischemic stroke, possibly as a consequence of increased oxidative stress. A specific antioxidant profile is associated with a poor early outcome.

Impact of the earthquake of September 26, 1997 in Umbria, Italy on the socioenvironmental and psychophysical conditions of an elderly population

The consequences of natural disasters on the social and health status of older people have not been deeply considered. The aim of this study was to evaluate the socioenvironmental and psychophysical conditions of an elderly population after a devastating earthquake. A randomly selected group of 332 older people (> or =64 years) was selected among 1548 eligible subjects living in the city of Nocera Umbra four months after an earthquake of 5.6 magnitude on the Richter scale. Three geriatricians evaluated the study subjects by means of a structured interview, and standardized scales, which considered physical and mental status, mood and anxiety, and self-perception of well-being, as well as the characteristics of family composition and social interactions. Of the study subjects, 11.1% lived alone, and 33.4% with the spouse only. Most were self-sufficient in the basic activities of daily life. Musculoskeletal diseases and hypertension were the most frequently observed pathologies in this geriatric population. In addition, 47.9% of the subjects lived in temporary houses; this group more frequently suffered from hypertension, and had a higher score of comorbidity as measured by Cumulative Illness Rating Scale (CIRS) compared to people who remained at home. People living in the pre-fabricated huts also showed a higher score on the Geriatric Depression Scale and the Hamilton scale for anxiety, and complained more often of their health status, evaluated as self-perception of well-being, when compared to the home dwellers. Although all the studied subjects suffered from the discomforts caused by the earthquake, the precariousness of living in temporary houses, whose structural characteristics do not take the needs of elderly subjects into account, could justify the higher distress experienced by persons housed in the huts. These observations suggest that, after natural disasters, emergency programs should be more adapted to elderly people, whose needs and expectations are often different from those of young adults.