Quantifying the uncertainty in model parameters using Gaussian process-based Markov chain Monte Carlo in cardiac electrophysiology

A review of uncertainty quantification in medical image analysis: Probabilistic and non-probabilistic methods

The comprehensive integration of machine learning healthcare models within clinical practice remains suboptimal, notwithstanding the proliferation of high-performing solutions reported in the literature. A predominant factor hindering widespread adoption pertains to an insufficiency of evidence affirming the reliability of the aforementioned models. Recently, uncertainty quantification methods have been proposed as a potential solution to quantify the reliability of machine learning models and thus increase the interpretability and acceptability of the results. In this review, we offer a comprehensive overview of the prevailing methods proposed to quantify the uncertainty inherent in machine learning models developed for various medical image tasks. Contrary to earlier reviews that exclusively focused on probabilistic methods, this review also explores non-probabilistic approaches, thereby furnishing a more holistic survey of research pertaining to uncertainty quantification for machine learning models. Analysis of medical images with the summary and discussion on medical applications and the corresponding uncertainty evaluation protocols are presented, which focus on the specific challenges of uncertainty in medical image analysis. We also highlight some potential future research work at the end. Generally, this review aims to allow researchers from both clinical and technical backgrounds to gain a quick and yet in-depth understanding of the research in uncertainty quantification for medical image analysis machine learning models.

Uncertainties in the Analysis of Heart Rate Variability: A Systematic Review

Heart rate variability (HRV) is an important metric with a variety of applications in clinical situations such as cardiovascular diseases, diabetes mellitus, and mental health. HRV data can be potentially obtained from electrocardiography and photoplethysmography signals, then computational techniques such as signal filtering and data segmentation are used to process the sampled data for calculating HRV measures. However, uncertainties arising from data acquisition, computational models, and physiological factors can lead to degraded signal quality and affect HRV analysis. Therefore, it is crucial to address these uncertainties and develop advanced models for HRV analysis. Although several reviews of HRV analysis exist, they primarily focus on clinical applications, trends in HRV methods, or specific aspects of uncertainties such as measurement noise. This paper provides a comprehensive review of uncertainties in HRV analysis, quantifies their impacts, and outlines potential solutions. To the best of our knowledge, this is the first study that presents a holistic review of uncertainties in HRV methods and quantifies their impacts on HRV measures from an engineer's perspective. This review is essential for developing robust and reliable models, and could serve as a valuable future reference in the field, particularly for dealing with uncertainties in HRV analysis.

Pacemaking function of two simplified cell models

Simplified nonlinear models of biological cells are widely used in computational electrophysiology. The models reproduce qualitatively many of the characteristics of various organs, such as the heart, brain, and intestine. In contrast to complex cellular ion-channel models, the simplified models usually contain a small number of variables and parameters, which facilitates nonlinear analysis and reduces computational load. In this paper, we consider pacemaking variants of the Aliev-Panfilov and Corrado two-variable excitable cell models. We conducted a numerical simulation study of these models and investigated the main nonlinear dynamic features of both isolated cells and 1D coupled pacemaker-excitable systems. Simulations of the 2D sinoatrial node and 3D intestine tissue as application examples of combined pacemaker-excitable systems demonstrated results similar to obtained previously. The uniform formulation for the conventional excitable cell models and proposed pacemaker models allows a convenient and easy implementation for the construction of personalized physiological models, inverse tissue modeling, and development of real-time simulation systems for various organs that contain both pacemaker and excitable cells.

EP-PINNs: Cardiac Electrophysiology Characterisation Using Physics-Informed Neural Networks

Accurately inferring underlying electrophysiological (EP) tissue properties from action potential recordings is expected to be clinically useful in the diagnosis and treatment of arrhythmias such as atrial fibrillation. It is, however, notoriously difficult to perform. We present EP-PINNs (Physics Informed Neural Networks), a novel tool for accurate action potential simulation and EP parameter estimation from sparse amounts of EP data. We demonstrate, using 1D and 2D in silico data, how EP-PINNs are able to reconstruct the spatio-temporal evolution of action potentials, whilst predicting parameters related to action potential duration (APD), excitability and diffusion coefficients. EP-PINNs are additionally able to identify heterogeneities in EP properties, making them potentially useful for the detection of fibrosis and other localised pathology linked to arrhythmias. Finally, we show EP-PINNs effectiveness on biological in vitro preparations, by characterising the effect of anti-arrhythmic drugs on APD using optical mapping data. EP-PINNs are a promising clinical tool for the characterisation and potential treatment guidance of arrhythmias.

Fast Posterior Estimation of Cardiac Electrophysiological Model Parameters via Bayesian Active Learning

Probabilistic estimation of cardiac electrophysiological model parameters serves an important step toward model personalization and uncertain quantification. The expensive computation associated with these model simulations, however, makes direct Markov Chain Monte Carlo (MCMC) sampling of the posterior probability density function (pdf) of model parameters computationally intensive. Approximated posterior pdfs resulting from replacing the simulation model with a computationally efficient surrogate, on the other hand, have seen limited accuracy. In this study, we present a Bayesian active learning method to directly approximate the posterior pdf function of cardiac model parameters, in which we intelligently select training points to query the simulation model in order to learn the posterior pdf using a small number of samples. We integrate a generative model into Bayesian active learning to allow approximating posterior pdf of high-dimensional model parameters at the resolution of the cardiac mesh. We further introduce new acquisition functions to focus the selection of training points on better approximating the shape rather than the modes of the posterior pdf of interest. We evaluated the presented method in estimating tissue excitability in a 3D cardiac electrophysiological model in a range of synthetic and real-data experiments. We demonstrated its improved accuracy in approximating the posterior pdf compared to Bayesian active learning using regular acquisition functions, and substantially reduced computational cost in comparison to existing standard or accelerated MCMC sampling.

Uncertainty Quantification of Regional Cardiac Tissue Properties in Arrhythmogenic Cardiomyopathy Using Adaptive Multiple Importance Sampling

Introduction: Computational models of the cardiovascular system are widely used to simulate cardiac (dys)function. Personalization of such models for patient-specific simulation of cardiac function remains challenging. Measurement uncertainty affects accuracy of parameter estimations. In this study, we present a methodology for patient-specific estimation and uncertainty quantification of parameters in the closed-loop CircAdapt model of the human heart and circulation using echocardiographic deformation imaging. Based on patient-specific estimated parameters we aim to reveal the mechanical substrate underlying deformation abnormalities in patients with arrhythmogenic cardiomyopathy (AC). Methods: We used adaptive multiple importance sampling to estimate the posterior distribution of regional myocardial tissue properties. This methodology is implemented in the CircAdapt cardiovascular modeling platform and applied to estimate active and passive tissue properties underlying regional deformation patterns, left ventricular volumes, and right ventricular diameter. First, we tested the accuracy of this method and its inter- and intraobserver variability using nine datasets obtained in AC patients. Second, we tested the trueness of the estimation using nine in silico generated virtual patient datasets representative for various stages of AC. Finally, we applied this method to two longitudinal series of echocardiograms of two pathogenic mutation carriers without established myocardial disease at baseline. Results: Tissue characteristics of virtual patients were accurately estimated with a highest density interval containing the true parameter value of 9% (95% CI [0-79]). Variances of estimated posterior distributions in patient data and virtual data were comparable, supporting the reliability of the patient estimations. Estimations were highly reproducible with an overlap in posterior distributions of 89.9% (95% CI [60.1-95.9]). Clinically measured deformation, ejection fraction, and end-diastolic volume were accurately simulated. In presence of worsening of deformation over time, estimated tissue properties also revealed functional deterioration. Conclusion: This method facilitates patient-specific simulation-based estimation of regional ventricular tissue properties from non-invasive imaging data, taking into account both measurement and model uncertainties. Two proof-of-principle case studies suggested that this cardiac digital twin technology enables quantitative monitoring of AC disease progression in early stages of disease.

Enabling forward uncertainty quantification and sensitivity analysis in cardiac electrophysiology by reduced order modeling and machine learning

We present a new, computationally efficient framework to perform forward uncertainty quantification (UQ) in cardiac electrophysiology. We consider the monodomain model to describe the electrical activity in the cardiac tissue, coupled with the Aliev-Panfilov model to characterize the ionic activity through the cell membrane. We address a complete forward UQ pipeline, including both: (i) a variance-based global sensitivity analysis for the selection of the most relevant input parameters, and (ii) a way to perform uncertainty propagation to investigate the impact of intra-subject variability on outputs of interest depending on the cardiac potential. Both tasks exploit stochastic sampling techniques, thus implying overwhelming computational costs because of the huge amount of queries to the high-fidelity, full-order computational model obtained by approximating the coupled monodomain/Aliev-Panfilov system through the finite element method. To mitigate this computational burden, we replace the full-order model with computationally inexpensive projection-based reduced-order models (ROMs) aimed at reducing the state-space dimensionality. Resulting approximation errors on the outputs of interest are finally taken into account through artificial neural network (ANN)-based models, enhancing the accuracy of the whole UQ pipeline. Numerical results show that the proposed physics-based ROMs outperform regression-based emulators relying on ANNs built with the same amount of training data, in terms of both numerical accuracy and overall computational efficiency.

Markov chain Monte Carlo with Gaussian processes for fast parameter estimation and uncertainty quantification in a 1D fluid-dynamics model of the pulmonary circulation

The past few decades have witnessed an explosive synergy between physics and the life sciences. In particular, physical modelling in medicine and physiology is a topical research area. The present work focuses on parameter inference and uncertainty quantification in a 1D fluid-dynamics model for quantitative physiology: the pulmonary blood circulation. The practical challenge is the estimation of the patient-specific biophysical model parameters, which cannot be measured directly. In principle this can be achieved based on a comparison between measured and predicted data. However, predicting data requires solving a system of partial differential equations (PDEs), which usually have no closed-form solution, and repeated numerical integrations as part of an adaptive estimation procedure are computationally expensive. In the present article, we demonstrate how fast parameter estimation combined with sound uncertainty quantification can be achieved by a combination of statistical emulation and Markov chain Monte Carlo (MCMC) sampling. We compare a range of state-of-the-art MCMC algorithms and emulation strategies, and assess their performance in terms of their accuracy and computational efficiency. The long-term goal is to develop a method for reliable disease prognostication in real time, and our work is an important step towards an automatic clinical decision support system.

Effects of Anti-Diabetic Drugs on Fracture Risk: A Systematic Review and Network Meta-Analysis

PURPOSE

Available data on the effects of anti-diabetic drugs on fracture risk are contradictory. Therefore, our study aimed to analyze all available data on the effects of anti-diabetic drugs on fracture risk in type 2 diabetes mellitus (T2DM) patients.

METHODS

Embase, Medline, ClinicalTrials.gov, and Cochrane CENTRAL were searched for relevant trials. All data analyses were performed with STATA (12.0) and R language (3.6.0). Risk ratio (RR) with its 95% confidence interval (CI) was calculated by combining data for the fracture effects of anti-diabetic drugs, including sodium-glucose co-transporter 2 (SGLT2) inhibitors, dipeptidyl peptidase-4 (DPP-4) inhibitors, glucagon-like peptide-1 (GLP-1) receptor agonists, meglitinides, α-glucosidase inhibitors, thiazolidinediones, biguanides, insulin, and sulfonylureas.

RESULTS

One hundred seventeen eligible randomized controlled trials (RCTs) with 221,364 participants were included in this study. Compared with placebo, trelagliptin (RR 3.51; 1.58-13.70) increased the risk of fracture, whereas albiglutide (RR 0.29; 0.04-0.93) and voglibose (RR 0.03; 0-0.11) decreased the risk of fracture. Other medications were comparable in terms of their effects on fracture risk, and no statistical significance was observed. In terms of fractures, voglibose (0.01%) may be the safest option, and trelagliptin (13.64%) may be the worst. Sensitivity analysis results were consistent with those of the main analysis. No statistically significant differences were observed in the regression coefficients of age (1.03; 0.32-2.1), follow-up duration (0.79; 0.27-1.64), and sex distribution (0.63; 0.15-1.56).

CONCLUSIONS

We found varied results on the association between the use of anti-diabetic drugs and fracture risk. Specifically, trelagliptin raised the risk of fracture, whereas voglibose and albiglutide showed benefit with statistical difference. Other drugs were comparable in terms of their effects on fracture risk. Some drugs (omarigliptin, sitagliptin, vildagliptin, saxagliptin, empagliflozin, ertugliflozin, rosiglitazone, pioglitazone, and nateglinide) may increase the risk of fracture, while others (such as dulaglutide, exenatide, liraglutide, semaglutide, lixisenatide, linagliptin, alogliptin, canagliflozin, dapagliflozin, glipizide, gliclazide, glibenclamide, glimepiride, metformin, and insulin) may show benefits. The risk of fracture was independent of age, sex distribution, and the duration of exposure to anti-diabetic drugs. When developing individualized treatment strategies, the clinical efficacy of anti-diabetic drugs must be weighed against their benefits and risks brought about by individual differences of patients.

SYSTEMATIC REVIEW REGISTRATION

This Systematic Review was prospectively registered on the PROSPERO (https://www.crd.york.ac.uk/PROSPERO/, registration number CRD42020189464).

Deep learning-based reduced order models in cardiac electrophysiology

Predicting the electrical behavior of the heart, from the cellular scale to the tissue level, relies on the numerical approximation of coupled nonlinear dynamical systems. These systems describe the cardiac action potential, that is the polarization/depolarization cycle occurring at every heart beat that models the time evolution of the electrical potential across the cell membrane, as well as a set of ionic variables. Multiple solutions of these systems, corresponding to different model inputs, are required to evaluate outputs of clinical interest, such as activation maps and action potential duration. More importantly, these models feature coherent structures that propagate over time, such as wavefronts. These systems can hardly be reduced to lower dimensional problems by conventional reduced order models (ROMs) such as, e.g., the reduced basis method. This is primarily due to the low regularity of the solution manifold (with respect to the problem parameters), as well as to the nonlinear nature of the input-output maps that we intend to reconstruct numerically. To overcome this difficulty, in this paper we propose a new, nonlinear approach relying on deep learning (DL) algorithms—such as deep feedforward neural networks and convolutional autoencoders—to obtain accurate and efficient ROMs, whose dimensionality matches the number of system parameters. We show that the proposed DL-ROM framework can efficiently provide solutions to parametrized electrophysiology problems, thus enabling multi-scenario analysis in pathological cases. We investigate four challenging test cases in cardiac electrophysiology, thus demonstrating that DL-ROM outperforms classical projection-based ROMs.

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'.

Creation and application of virtual patient cohorts of heart models

Patient-specific cardiac models are now being used to guide therapies. The increased use of patient-specific cardiac simulations in clinical care will give rise to the development of virtual cohorts of cardiac models. These cohorts will allow cardiac simulations to capture and quantify inter-patient variability. However, the development of virtual cohorts of cardiac models will require the transformation of cardiac modelling from small numbers of bespoke models to robust and rapid workflows that can create large numbers of models. In this review, we describe the state of the art in virtual cohorts of cardiac models, the process of creating virtual cohorts of cardiac models, and how to generate the individual cohort member models, followed by a discussion of the potential and future applications of virtual cohorts of cardiac models. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Quantifying atrial anatomy uncertainty from clinical data and its impact on electro-physiology simulation predictions

Patient-specific computational models of structure and function are increasingly being used to diagnose disease and predict how a patient will respond to therapy. Models of anatomy are often derived after segmentation of clinical images or from mapping systems which are affected by image artefacts, resolution and contrast. Quantifying the impact of uncertain anatomy on model predictions is important, as models are increasingly used in clinical practice where decisions need to be made regardless of image quality. We use a Bayesian probabilistic approach to estimate the anatomy and to quantify the uncertainty about the shape of the left atrium derived from Cardiac Magnetic Resonance images. We show that we can quantify uncertain shape, encode uncertainty about the left atrial shape due to imaging artefacts, and quantify the effect of uncertain shape on simulations of left atrial activation times.

Computational models in cardiology

The treatment of individual patients in cardiology practice increasingly relies on advanced imaging, genetic screening and devices. As the amount of imaging and other diagnostic data increases, paralleled by the greater capacity to personalize treatment, the difficulty of using the full array of measurements of a patient to determine an optimal treatment seems also to be paradoxically increasing. Computational models are progressively addressing this issue by providing a common framework for integrating multiple data sets from individual patients. These models, which are based on physiology and physics rather than on population statistics, enable computational simulations to reveal diagnostic information that would have otherwise remained concealed and to predict treatment outcomes for individual patients. The inherent need for patient-specific models in cardiology is clear and is driving the rapid development of tools and techniques for creating personalized methods to guide pharmaceutical therapy, deployment of devices and surgical interventions.

How personalized heart modeling can help treatment of lethal arrhythmias: A focus on ventricular tachycardia ablation strategies in post-infarction patients

Precision Cardiology is a targeted strategy for cardiovascular disease prevention and treatment that accounts for individual variability. Computational heart modeling is one of the novel approaches that have been developed under the umbrella of Precision Cardiology. Personalized computational modeling of patient hearts has made strides in the development of models that incorporate the individual geometry and structure of the heart as well as other patient-specific information. Of these developments, one of the potentially most impactful is the research aimed at noninvasively predicting the targets of ablation of lethal arrhythmia, ventricular tachycardia (VT), using patient-specific models. The approach has been successfully applied to patients with ischemic cardiomyopathy in proof-of-concept studies. The goal of this paper is to review the strategies for computational VT ablation guidance in ischemic cardiomyopathy patients, from model developments to the intricacies of the actual clinical application. To provide context in describing the road these computational modeling applications have undertaken, we first review the state of the art in VT ablation in the clinic, emphasizing the benefits that personalized computational prediction of ablation targets could bring to the clinical electrophysiology practice. This article is characterized under: Analytical and Computational Methods > Computational Methods Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models Translational, Genomic, and Systems Medicine > Translational Medicine.

Differences between models of partial thickness and subendocardial ischaemia in terms of sensitivity analyses of ST-segment epicardial potential distributions

Mathematical modelling is a useful technique to help elucidate the connection between non-transmural ischaemia and ST elevation and depression of the ECG. Generally, models represent non-transmural ischaemia using an ischaemic zone that extends from the endocardium partway to the epicardium. However, recent experimental work has suggested that ischaemia typically arises within the heart wall. This work examines the effect of modelling cardiac ischaemia in the left ventricle using two different models: subendocardial ischaemia and partial thickness ischaemia, representing the first and second scenarios, respectively. We found that it is possible, only in the model of subendocardial ischaemia, to see a single minimum on the epicardial surface above the ischaemic region, and this only occurs for low ischaemic thicknesses. This may help to explain the rarity of ST depression that is located over the ischaemic region. It was also found that, in both models, the epicardial potential distribution is most sensitive to the proximity of the ischaemic region to the epicardium, rather than to the thickness of the ischaemic region. Since proximity does not indicate the thickness of the ischaemic region, this suggests a reason why it may be difficult to determine the degree of ischaemia using the ST segment of the ECG.

ML and MAP estimation of parameters for the Kalman filter and smoother applied to electrocardiographic imaging

In electrocardiographic imaging (ECGI), one solves the inverse problem of electrocardiography (ECG) to reconstruct equivalent cardiac sources based on the body surface potential measurements and a mathematical model of the torso. Due to attenuation and spatial smoothing within the torso, this inverse problem is ill-posed. Among many regularization approaches used in the ECG literature to overcome this ill-posedness, statistical techniques have received great attention because of their flexibility to represent the data, and ability to provide performance evaluation tools for quantification of uncertainties and errors in the model. However, despite their potential to accurately reconstruct the equivalent cardiac sources, one major challenge in these methods is how to best utilize the prior information available in terms of training data. In this paper, we address the question of how to define the prior probability distributions (pdf) of the sources and the error terms so that we can obtain more accurate and robust inverse solutions. We employ two methods, maximum likelihood (ML) and maximum a posteriori (MAP), for estimating the model parameters such as the prior pdfs, error pdfs, and the state-transition matrix, based on the same training data. These model parameters are then used for the state-space representation and estimation of the epicardial potentials, which constitute the equivalent cardiac sources in this study. The performances of ML- and MAP-based model parameter estimation methods are evaluated qualitatively and quantitatively at various noise levels and geometric disturbances using two different simulated datasets. Bayesian MAP estimation, which is also a well-known statistical inversion technique, and Tikhonov regularization, which can be formulated as a special and simplified version of Bayesian MAP estimation, have been included here for comparison with the Kalman filtering method. Our results show that the state-space approach outperforms Bayesian MAP estimation in all cases; ML yields accurate results when the test and training beats come from the same physiological model, but MAP is superior to ML, especially if the test and training beats are from different physiological models. Graphical Abstract ML and MAP estimation of parameters for the Kalman filter and smoother applied to electrocardiographic imaging.

Visualization of Myocardial Strain Pattern Uniqueness with Respect to Activation Time and Contractility: A Computational Study

Speckle tracking echography is used to measure myocardial strain patterns in order to assess the state of myocardial tissue. Because electro-mechanical coupling in myocardial tissue is complex and nonlinear, and because of the measurement errors the uniqueness of strain patterns is questionable. In this study, the uniqueness of strain patterns was visualized in order to revel characteristics that may improve their interpretation. A computational model of sarcomere mechanics was used to generate a database of 1681 strain patterns, each simulated with a different set of sarcomere parameters: time of activation (TA) and contractility (Con). TA and Con ranged from −100 ms to 100 ms and 2% to 202% in 41 steps respectively, thus forming a two-dimensional 41 × 41 parameter space. Uniqueness of the strain pattern was assessed by using a cohort of similar strain patterns defined by a measurement error. The cohort members were then visualized in the parameter space. Each cohort formed one connected component (or blob) in the parameter space; however, large differences in the shape, size, and eccentricity of the blobs were found for different regions in the parameter space. The blobs were elongated along the TA direction (±50 ms) when contractility was low, and along the Con direction (±50%) when contractility was high. The uniqueness of the strain patterns can be assessed and visualized in the parameter space. The strain patterns in the studied database are not degenerated because a cohort of similar strain patterns forms only one connected blob in the parameter space. However, the elongation of the blobs means that estimations of TA when contractility is low and of Con when contractility is high have high uncertainty.

Impact of the Endocardium in a Parameter Optimization to Solve the Inverse Problem of Electrocardiography

Electrocardiographic imaging aims at reconstructing cardiac electrical events from electrical signals measured on the body surface. The most common approach relies on the inverse solution of the Laplace equation in the torso to reconstruct epicardial potential maps from body surface potential maps. Here we apply a method based on a parameter identification problem to reconstruct both activation and repolarization times. From an ansatz of action potential, based on the Mitchell-Schaeffer ionic model, we compute body surface potential signals. The inverse problem is reduced to the identification of the parameters of the Mitchell-Schaeffer model. We investigate whether solving the inverse problem with the endocardium improves the results or not. We solved the parameter identification problem on two different meshes: one with only the epicardium, and one with both the epicardium and the endocardium. We compared the results on both the heart (activation and repolarization times) and the torso. The comparison was done on validation data of sinus rhythm and ventricular pacing. We found similar results with both meshes in 6 cases out of 7: the presence of the endocardium slightly improved the activation times. This was the most visible on a sinus beat, leading to the conclusion that inclusion of the endocardium would be useful in situations where endo-epicardial gradients in activation or repolarization times play an important role.

Mathematical Modeling and Characterization of the Spread of Chikungunya in Colombia

The Chikungunya virus is the cause of an emerging disease in Asia and Africa, and also in America, where the virus was first detected in 2006. In this paper, we present a mathematical model of the Chikungunya epidemic at the population level that incorporates the transmission vector. The epidemic threshold parameter R 0 for the extinction of disease is computed using the method of the next generation matrix, which allows for insights about what are the most relevant model parameters. Using Lyapunov function theory, some sufficient conditions for global stability of the the disease-free equilibrium are obtained. The proposed mathematical model of the Chikungunya epidemic is used to investigate and understand the importance of some specific model parameters and to give some explanation and understanding about the real infected cases with Chikungunya virus in Colombia for data belonging to the year 2015. In this study, we were able to estimate the value of the basic reproduction number R 0 . We use bootstrapping and Markov chain Monte Carlo techniques in order to study parameters’ identifiability. Finally, important policies and insights are provided that could help government health institutions in reducing the number of cases of Chikungunya in Colombia.

A Common-Ground Review of the Potential for Machine Learning Approaches in Electrocardiographic Imaging Based on Probabilistic Graphical Models

Machine learning (ML) methods have seen an explosion in their development and application. They are increasingly being used in many different fields with considerable success. However, although the interest is growing, their impact in the field of electrocardiographic imaging (ECGI) remains limited. One of the main reasons that ML has yet to become more prevalent in ECGI is that the published literature is scattered and there is no common ground description and comparison of these methods in an ML framework. Here we address this limitation with a review of ECGI methods from the perspective of ML. We will use probabilistic modeling to provide a common ground framework to compare different methods and well known approaches. Finally, we will discuss which approaches have been used to do inference on these models and which alternatives could be utilized as the methods in ML become more mature.