Markov modeling of phase singularity interaction effects in human atrial and ventricular fibrillation.

Atrial and ventricular fibrillation (AF/VF) are characterized by the repetitive regeneration of topological defects known as phase singularities (PSs). The effect of PS interactions has not been previously studied in human AF and VF. We hypothesized that PS population size would influence the rate of PS formation and destruction in human AF and VF, due to increased inter-defect interaction. PS population statistics were studied in computational simulations (Aliev-Panfilov), human AF and human VF. The influence of inter-PS interactions was evaluated by comparison between directly modeled discrete-time Markov chain (DTMC) transition matrices of the PS population changes, and M/M/∞ birth-death transition matrices of PS dynamics, which assumes that PS formations and destructions are effectively statistically independent events. Across all systems examined, PS population changes differed from those expected with M/M/∞. In human AF and VF, the formation rates decreased slightly with PS population when modeled with the DTMC, compared with the static formation rate expected through M/M/∞, suggesting new formations were being inhibited. In human AF and VF, the destruction rates increased with PS population for both models, with the DTMC rate increase exceeding the M/M/∞ estimates, indicating that PS were being destroyed faster as the PS population grew. In human AF and VF, the change in PS formation and destruction rates as the population increased differed between the two models. This indicates that the presence of additional PS influenced the likelihood of new PS formation and destruction, consistent with the notion of self-inhibitory inter-PS interactions.

An audit of uncertainty in multi-scale cardiac electrophysiology models.

Models of electrical activation and recovery in cardiac cells and tissue have become valuable research tools, and are beginning to be used in safety-critical applications including guidance for clinical procedures and for drug safety assessment. As a consequence, there is an urgent need for a more detailed and quantitative understanding of the ways that uncertainty and variability influence model predictions. In this paper, we review the sources of uncertainty in these models at different spatial scales, discuss how uncertainties are communicated across scales, and begin to assess their relative importance. We conclude by highlighting important challenges that continue to face the cardiac modelling community, identifying open questions, and making recommendations for future studies. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Gaussian process manifold interpolation for probabilistic atrial activation maps and uncertain conduction velocity.

In patients with atrial fibrillation, local activation time (LAT) maps are routinely used for characterizing patient pathophysiology. The gradient of LAT maps can be used to calculate conduction velocity (CV), which directly relates to material conductivity and may provide an important measure of atrial substrate properties. Including uncertainty in CV calculations would help with interpreting the reliability of these measurements. Here, we build upon a recent insight into reduced-rank Gaussian processes (GPs) to perform probabilistic interpolation of uncertain LAT directly on human atrial manifolds. Our Gaussian process manifold interpolation (GPMI) method accounts for the topology of the atrium, and allows for calculation of statistics for predicted CV. We demonstrate our method on two clinical cases, and perform validation against a simulated ground truth. CV uncertainty depends on data density, wave propagation direction and CV magnitude. GPMI is suitable for probabilistic interpolation of other uncertain quantities on non-Euclidean manifolds. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Uncertainty and variability in models of the cardiac action potential: Can we build trustworthy models?

Cardiac electrophysiology models have been developed for over 50years, and now include detailed descriptions of individual ion currents and sub-cellular calcium handling. It is commonly accepted that there are many uncertainties in these systems, with quantities such as ion channel kinetics or expression levels being difficult to measure or variable between samples. Until recently, the original approach of describing model parameters using single values has been retained, and consequently the majority of mathematical models in use today provide point predictions, with no associated uncertainty. In recent years, statistical techniques have been developed and applied in many scientific areas to capture uncertainties in the quantities that determine model behaviour, and to provide a distribution of predictions which accounts for this uncertainty. In this paper we discuss this concept, which is termed uncertainty quantification, and consider how it might be applied to cardiac electrophysiology models. We present two case studies in which probability distributions, instead of individual numbers, are inferred from data to describe quantities such as maximal current densities. Then we show how these probabilistic representations of model parameters enable probabilities to be placed on predicted behaviours. We demonstrate how changes in these probability distributions across data sets offer insight into which currents cause beat-to-beat variability in canine APs. We conclude with a discussion of the challenges that this approach entails, and how it provides opportunities to improve our understanding of electrophysiology.

Uncertainty and variability in computational and mathematical models of cardiac physiology.

KEY POINTS: Mathematical and computational models of cardiac physiology have been an integral component of cardiac electrophysiology since its inception, and are collectively known as the Cardiac Physiome. We identify and classify the numerous sources of variability and uncertainty in model formulation, parameters and other inputs that arise from both natural variation in experimental data and lack of knowledge. The impact of uncertainty on the outputs of Cardiac Physiome models is not well understood, and this limits their utility as clinical tools. We argue that incorporating variability and uncertainty should be a high priority for the future of the Cardiac Physiome. We suggest investigating the adoption of approaches developed in other areas of science and engineering while recognising unique challenges for the Cardiac Physiome; it is likely that novel methods will be necessary that require engagement with the mathematics and statistics community. ABSTRACT: The Cardiac Physiome effort is one of the most mature and successful applications of mathematical and computational modelling for describing and advancing the understanding of physiology. After five decades of development, physiological cardiac models are poised to realise the promise of translational research via clinical applications such as drug development and patient-specific approaches as well as ablation, cardiac resynchronisation and contractility modulation therapies. For models to be included as a vital component of the decision process in safety-critical applications, rigorous assessment of model credibility will be required. This White Paper describes one aspect of this process by identifying and classifying sources of variability and uncertainty in models as well as their implications for the application and development of cardiac models. We stress the need to understand and quantify the sources of variability and uncertainty in model inputs, and the impact of model structure and complexity and their consequences for predictive model outputs. We propose that the future of the Cardiac Physiome should include a probabilistic approach to quantify the relationship of variability and uncertainty of model inputs and outputs.

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.

Fibroblast mediated dynamics in diffusively uncoupled myocytes: a simulation study using 2-cell motifs.

In healthy hearts myocytes are typically coupled to nearest neighbours through gap junctions. Under pathological conditions such as fibrosis, or in scar tissue, or across ablation lines myocytes can uncouple from their neighbours. Electrical conduction may still occur via fibroblasts that not only couple proximal myocytes but can also couple otherwise unconnected regions. We hypothesise that such coupling can alter conduction between myocytes via introduction of delays or by initiation of premature stimuli that can potentially result in reentry or conduction blocks. To test this hypothesis we have developed several 2-cell motifs and investigated the effect of fibroblast mediated electrical coupling between uncoupled myocytes. We have identified various regimes of myocyte behaviour that depend on the strength of gap-junctional conductance, connection topology, and parameters of the myocyte and fibroblast models. These motifs are useful in developing a mechanistic understanding of long-distance coupling on myocyte dynamics and enable the characterisation of interaction between different features such as myocyte and fibroblast properties, coupling strengths and pacing period. They are computationally inexpensive and allow for incorporation of spatial effects such as conduction velocity. They provide a framework for constructing scar tissue boundaries and enable linking of cellular level interactions with scar induced arrhythmia.

Observable Atrial and Ventricular Fibrillation Episode Durations Are Conformant With a Power Law Based on System Size and Spatial Synchronization.

BACKGROUND: Atrial fibrillation (AF) and ventricular fibrillation (VF) episodes exhibit varying durations, with some spontaneously ending quickly while others persist. A quantitative framework to explain episode durations remains elusive. We hypothesized that observable self-terminating AF and VF episode lengths, whereby durations are known, would conform with a power law based on the ratio of system size and correlation length ([Formula: see text]. METHODS: Using data from computer simulations (2-dimensional sheet and 3-dimensional left-atrial), human ischemic VF recordings (256-electrode sock, n=12 patients), and human AF recordings (64-electrode basket-catheter, n=9 patients; 16-electrode HD-grid catheter, n=42 patients), conformance with a power law was assessed using the Akaike information criterion, Bayesian information criterion, coefficient of determination (R2, significance=P<0.05) and maximum likelihood estimation. We analyzed fibrillatory episode durations and [Formula: see text], computed by taking the ratio between system size ([Formula: see text], chamber/simulation size) and correlation length ([Formula: see text], measured from pairwise correlation coefficients over electrode/node distance). RESULTS: In all computer models, the relationship between episode durations and [Formula: see text] was conformant with a power law (Aliev-Panfilov R2: 0.90, P<0.001; Courtemanche R2: 0.91, P<0.001; Luo-Rudy R2: 0.61, P<0.001). Observable clinical AF/VF durations were also conformant with a power law relationship (VF R2: 0.86, P<0.001; AF basket R2: 0.91, P<0.001; AF grid R2: 0.92, P<0.001). [Formula: see text] also differentiated between self-terminating and sustained episodes of AF and VF (P<0.001; all systems), as well as paroxysmal versus persistent AF (P<0.001). In comparison, other electrogram metrics showed no statistically significant differences (dominant frequency, Shannon Entropy, mean voltage, peak-peak voltage; P>0.05). CONCLUSIONS: Observable fibrillation episode durations are conformant with a power law based on system size and correlation length.

Artificial Intelligence framework with traditional computer vision and deep learning approaches for optimal automatic segmentation of left ventricle with scar.

Automatic segmentation of the cardiac left ventricle with scars remains a challenging and clinically significant task, as it is essential for patient diagnosis and treatment pathways. This study aimed to develop a novel framework and cost function to achieve optimal automatic segmentation of the left ventricle with scars using LGE-MRI images. To ensure the generalization of the framework, an unbiased validation protocol was established using out-of-distribution (OOD) internal and external validation cohorts, and intra-observation and inter-observer variability ground truths. The framework employs a combination of traditional computer vision techniques and deep learning, to achieve optimal segmentation results. The traditional approach uses multi-atlas techniques, active contours, and k-means methods, while the deep learning approach utilizes various deep learning techniques and networks. The study found that the traditional computer vision technique delivered more accurate results than deep learning, except in cases where there was breath misalignment error. The optimal solution of the framework achieved robust and generalized results with Dice scores of 82.8 ± 6.4% and 72.1 ± 4.6% in the internal and external OOD cohorts, respectively. The developed framework offers a high-performance solution for automatic segmentation of the left ventricle with scars using LGE-MRI. Unlike existing state-of-the-art approaches, it achieves unbiased results across different hospitals and vendors without the need for training or tuning in hospital cohorts. This framework offers a valuable tool for experts to accomplish the task of fully automatic segmentation of the left ventricle with scars based on a single-modality cardiac scan.

Automatic development of 3D anatomical models of border zone and core scar regions in the left ventricle.

Patients with myocardial infarction are at elevated risk of sudden cardiac death, and scar tissue arising from infarction is known to play a role. The accurate identification of scars therefore is crucial for risk assessment, quantification and guiding interventions. Typically, core scars and grey peripheral zones are identified by radiologists and clinicians based on cardiac late gadolinium enhancement magnetic resonance images (LGE-MRI). Scar regions from LGE-MRI vary in size, shape, heterogeneity, artifacts, and image resolution. Thus, manual segmentation is time consuming, and influenced by the observer's experience (bias effect). We propose a fully automatic framework that develops 3D anatomical models of the left ventricle with border zone and core scar regions that are free from bias effect. Our myocardium (SOCRATIS), border scar and core scar (BZ-SOCRATIS) segmentation pipelines were evaluated using internal and external validation datasets. The automatic myocardium segmentation framework performed a Dice score of 81.9% and 70.0% in the internal and external validation dataset. The automatic scar segmentation pipeline achieved a Dice score of 60.9% for the core scar segmentation and 43.7% for the border zone scar segmentation in the internal dataset and in the external dataset a Dice score of 44.2% for the core scar segmentation and 54.8% for the border scar segmentation respectively. To the best of our knowledge, this is the first study outlining a fully automatic framework to develop 3D anatomical models of the left ventricle with border zone and core scar regions. Our method exhibits high performance without the need for training or tuning in an unseen cohort (unsupervised).

Quantifying the impact of shape uncertainty on predicted arrhythmias.

BACKGROUND: Personalised computer models are increasingly used to diagnose cardiac arrhythmias and tailor treatment. Patient-specific models of the left atrium are often derived from pre-procedural imaging of anatomy and fibrosis. These images contain noise that can affect simulation predictions. There are few computationally tractable methods for propagating uncertainties from images to clinical predictions. METHOD: We describe the left atrium anatomy using our Bayesian shape model that captures anatomical uncertainty in medical images and has been validated on 63 independent clinical images. This algorithm describes the left atrium anatomy using Nmodes=15 principal components, capturing 95% of the shape variance and calculated from 70 clinical cardiac magnetic resonance (CMR) images. Latent variables encode shape uncertainty: we evaluate their posterior distribution for each new anatomy. We assume a normally distributed prior. We use the unscented transform to sample from the posterior shape distribution. For each sample, we assign the local material properties of the tissue using the projection of late gadolinium enhancement CMR (LGE-CMR) onto the anatomy to estimate local fibrosis. To test which activation patterns an atrium can sustain, we perform an arrhythmia simulation for each sample. We consider 34 possible outcomes (31 macro-re-entries, functional re-entry, atrial fibrillation, and non-sustained arrhythmia). For each sample, we determine the outcome by comparing pre- and post-ablation activation patterns following a cross-field stimulus. RESULTS: We create patient-specific atrial electrophysiology models of ten patients. We validate the mean and standard deviation maps from the unscented transform with the same statistics obtained with 12,000 Monte Carlo (ground truth) samples. We found discrepancies <3% and <2% for the mean and standard deviation for fibrosis burden and activation time, respectively. For each patient case, we then compare the predicted outcome from a model built on the clinical data (deterministic approach) with the probability distribution obtained from the simulated samples. We found that the deterministic approach did not predict the most likely outcome in 80% of the cases. Finally, we estimate the influence of each source of uncertainty independently. Fixing the anatomy to the posterior mean and maintaining uncertainty in fibrosis reduced the prediction of self-terminating arrhythmias from ≃14% to ≃7%. Keeping the fibrosis fixed to the sample mean while retaining uncertainty in shape decreased the prediction of substrate-driven arrhythmias from ≃33% to ≃18% and increased the prediction of macro-re-entries from ≃54% to ≃68%. CONCLUSIONS: We presented a novel method for propagating shape uncertainty in atrial models through to uncertainty in numerical simulations. The algorithm takes advantage of the unscented transform to compute the output distribution of the outcomes. We validated the unscented transform as a viable sampling strategy to deal with anatomy uncertainty. We then showed that the prediction computed with a deterministic model does not always coincide with the most likely outcome. Finally, we found that shape uncertainty affects the predictions of macro-re-entries, while fibrosis uncertainty affects the predictions of functional re-entries.

A computational model of auxin and pH dynamics in a single plant cell.

Directed cell-to-cell movement of the plant growth hormone auxin is often referred to as polar auxin transport, and has gained much interest since its discovery at the beginning of the 20th century, both by biologists and theoreticians. Computational modelling of auxin transport at tissue and whole plant scales has given valuable insights into the feedback dynamics between auxin and its transport, which often leads to cell polarisation. However, one cellular feedback mechanism that has been overlooked so far in previous models is the interplay between auxin and pH during auxin transport, even though this is well known from biology. We propose a kinetic model of such a feedback mechanism, linking knowledge about auxin-induced acidification of cell wall compartments to the chemiosmotic hypothesis of auxin transport. Our results suggest that proton fluxes may play a significant role in auxin transport. Since active auxin transport relies on the proton motive force over the cellular membrane, allocation of auxin is linked to its effects on compartmental pH. Our auxin/pH feedback model predicts enhanced accumulation of auxin in cells and increases in both auxin influx and efflux when this feedback is in effect. These results were robust in all simulations and consistent with biological evidence, thus providing a framework for generating and testing hypotheses of auxin-related polarisation events at a cellular level.

Characterization of persistent atrial fibrillation with non-contact charge density mapping and relationship to voltage.

BACKGROUND: Despite studies using localized high density contact mapping and lower resolution panoramic approaches, the mechanisms that sustain human persistent atrial fibrillation (AF) remain unresolved. Voltage mapping is commonly employed as a surrogate of atrial substrate to guide ablation procedures. OBJECTIVE: To study the distribution and temporal stability of activation during persistent AF using a global non-contact charge density approach and compare the findings with bipolar contact mapping. METHODS: Patients undergoing either redo or de novo ablation for persistent AF underwent charge density and voltage mapping to guide the ablation procedure. Offline analysis was performed to measure the temporal stability of three specific charge density activation (CDA) patterns, and the degree of spatial overlap between CDA patterns and low voltage regions. RESULTS: CDA was observed in patient-specific locations that partially overlapped, comprising local rotational activity (18% of LA), local irregular activity (41% of LA), and focal activity (39% of LA). Local irregular activity had the highest temporal stability. LA voltage was similar in regions with and without CDA. CONCLUSION: In persistent AF, CDA patterns appear unrelated to low voltage areas but occur in varying locations with high temporal stability.

Calibrating cardiac electrophysiology models using latent Gaussian processes on atrial manifolds.

Models of electrical excitation and recovery in the heart have become increasingly detailed, but have yet to be used routinely in the clinical setting to guide personalized intervention in patients. One of the main challenges is calibrating models from the limited measurements that can be made in a patient during a standard clinical procedure. In this work, we propose a novel framework for the probabilistic calibration of electrophysiology parameters on the left atrium of the heart using local measurements of cardiac excitability. Parameter fields are represented as Gaussian processes on manifolds and are linked to measurements via surrogate functions that map from local parameter values to measurements. The posterior distribution of parameter fields is then obtained. We show that our method can recover parameter fields used to generate localised synthetic measurements of effective refractory period. Our methodology is applicable to other measurement types collected with clinical protocols, and more generally for calibration where model parameters vary over a manifold.

A governing equation for rotor and wavelet number in human clinical ventricular fibrillation: Implications for sudden cardiac death.

BACKGROUND: Ventricular fibrillation (VF) is characterized by multiple wavelets and rotors. No equation to predict the number of rotors and wavelets observed during fibrillation has been validated in human VF. OBJECTIVE: The purpose of this study was to test the hypothesis that a single equation derived from a Markov M/M/∞ birth-death process could predict the number of rotors and wavelets occurring in human clinical VF. METHODS: Epicardial induced VF (256-electrode) recordings obtained from patients undergoing cardiac surgery were studied (12 patients; 62 epochs). Rate constants for phase singularity (PS) (which occur at the pivot points of rotors) and wavefront (WF) formation and destruction were derived by fitting distributions to PS and WF interformation and lifetimes. These rate constants were combined in an M/M/∞ governing equation to predict the number of PS and WF in VF episodes. Observed distributions were compared to those predicted by the M/M/∞ equation. RESULTS: The M/M/∞ equation accurately predicted average PS and WF number and population distribution, demonstrated in all epochs. Self-terminating episodes of VF were distinguished from VF episodes requiring termination by a trend toward slower PS destruction, slower rates of PS formation, and a slower mixing rate of the VF process, indicated by larger values of the second largest eigenvalue modulus of the M/M/∞ birth-death matrix. The longest-lasting PS (associated with rotors) had shorter interactivation time intervals compared to shorter-lasting PS lasting <150 ms (∼1 PS rotation in human VF). CONCLUSION: The M/M/∞ equation explains the number of wavelets and rotors observed, supporting a paradigm of VF based on statistical fibrillatory dynamics.

The inspection paradox: An important consideration in the evaluation of rotor lifetimes in cardiac fibrillation.

Background and Objective: Renewal theory is a statistical approach to model the formation and destruction of phase singularities (PS), which occur at the pivots of spiral waves. A common issue arising during observation of renewal processes is an inspection paradox, due to oversampling of longer events. The objective of this study was to characterise the effect of a potential inspection paradox on the perception of PS lifetimes in cardiac fibrillation. Methods: A multisystem, multi-modality study was performed, examining computational simulations (Aliev-Panfilov (APV) model, Courtmanche-Nattel model), experimentally acquired optical mapping Atrial and Ventricular Fibrillation (AF/VF) data, and clinically acquired human AF and VF. Distributions of all PS lifetimes across full epochs of AF, VF, or computational simulations, were compared with distributions formed from lifetimes of PS existing at 10,000 simulated commencement timepoints. Results: In all systems, an inspection paradox led towards oversampling of PS with longer lifetimes. In APV computational simulations there was a mean PS lifetime shift of +84.9% (95% CI, ± 0.3%) (p < 0.001 for observed vs overall), in Courtmanche-Nattel simulations of AF +692.9% (95% CI, ±57.7%) (p < 0.001), in optically mapped rat AF +374.6% (95% CI, ± 88.5%) (p = 0.052), in human AF mapped with basket catheters +129.2% (95% CI, ±4.1%) (p < 0.05), human AF-HD grid catheters 150.8% (95% CI, ± 9.0%) (p < 0.001), in optically mapped rat VF +171.3% (95% CI, ±15.6%) (p < 0.001), in human epicardial VF 153.5% (95% CI, ±15.7%) (p < 0.001). Conclusion: Visual inspection of phase movies has the potential to systematically oversample longer lasting PS, due to an inspection paradox. An inspection paradox is minimised by consideration of the overall distribution of PS lifetimes.

Hypoglycaemia combined with mild hypokalaemia reduces the heart rate and causes abnormal pacemaker activity in a computational model of a human sinoatrial cell.

Low blood glucose, hypoglycaemia, has been implicated as a possible contributing factor to sudden cardiac death (SCD) in people with diabetes but it is challenging to investigate in clinical studies. We hypothesized the effects of hypoglycaemia on the sinoatrial node (SAN) in the heart to be a candidate mechanism and adapted a computational model of the human SAN action potential developed by Fabbri et al., to investigate the effects of hypoglycaemia on the pacemaker rate. Using Latin hypercube sampling, we combined the effects of low glucose (LG) on the human ether-a-go-go-related gene channel with reduced blood potassium, hypokalaemia, and added sympathetic and parasympathetic stimulus. We showed that hypoglycaemia on its own causes a small decrease in heart rate but there was also a marked decrease in heart rate when combined with hypokalaemia. The effect of the sympathetic stimulus was diminished, causing a smaller increase in heart rate, with LG and hypokalaemia compared to normoglycaemia. By contrast, the effect of the parasympathetic stimulus was enhanced, causing a greater decrease in heart rate. We therefore demonstrate a potential mechanistic explanation for hypoglycaemia-induced bradycardia and show that sinus arrest is a plausible mechanism for SCD in people with diabetes.

MA-SOCRATIS: An automatic pipeline for robust segmentation of the left ventricle and scar.

Multi-atlas segmentation of cardiac regions and total infarct scar (MA-SOCRATIS) is an unsupervised automatic pipeline to segment left ventricular myocardium and scar from late gadolinium enhanced MR images (LGE-MRI) of the heart. We implement two different pipelines for myocardial and scar segmentation from short axis LGE-MRI. Myocardial segmentation has two steps; initial segmentation and re-estimation. The initial segmentation step makes a first estimate of myocardium boundaries by using multi-atlas segmentation techniques. The re-estimation step refines the myocardial segmentation by a combination of k-means clustering and a geometric median shape variation technique. An active contour technique determines the unhealthy and healthy myocardial wall. The scar segmentation pipeline is a combination of a Rician-Gaussian mixture model and full width at half maximum (FWHM) thresholding, to determine the intensity pixels in scar regions. Following this step a watershed method with an automatic seed-points framework segments the final scar region. MA-SOCRATIS was evaluated using two different datasets. In both datasets ground truths were based on manual segmentation of short axis images from LGE-MRI scans. The first dataset included 40 patients from the MS-CMRSeg 2019 challenge dataset (STACOM at MICCAI 2019). The second is a collection of 20 patients with scar regions that are challenging to segment. MA-SOCRATIS achieved robust and accurate performance in automatic segmentation of myocardium and scar regions without the need of training or tuning in both cohorts, compared with state-of-the-art techniques (intra-observer and inter observer myocardium segmentation: 81.9% and 70% average Dice value, and scar (intra-observer and inter observer segmentation: 70.5% and 70.5% average Dice value).

Corrigendum: Bayesian Calibration of Electrophysiology Models Using Restitution Curve Emulators.

[This corrects the article DOI: 10.3389/fphys.2021.693015.].