In silico pace-mapping: prediction of left vs. right outflow tract origin in idiopathic ventricular arrhythmias with patient-specific electrophysiological simulations.

AIMS: A pre-operative non-invasive identification of the site of origin (SOO) of outflow tract ventricular arrhythmias (OTVAs) is important to properly plan radiofrequency ablation procedures. Although some algorithms based on electrocardiograms (ECGs) have been developed to predict left vs. right ventricular origins, their accuracy is still limited, especially in complex anatomies. The aim of this work is to use patient-specific electrophysiological simulations of the heart to predict the SOO in OTVA patients. METHODS AND RESULTS: An in silico pace-mapping procedure was designed and used on 11 heart geometries, generating for each case simulated ECGs from 12 clinically plausible SOO. Subsequently, the simulated ECGs were compared with patient ECG data obtained during the clinical tachycardia using the 12-lead correlation coefficient (12-lead ρ). Left ventricle (LV) vs. right ventricle (RV) SOO was estimated by computing the LV/RV ratio for each patient, obtained by dividing the average 12-lead ρ value of the LV- and RV-SOO simulated ECGs, respectively. Simulated ECGs that had virtual sites close to the ablation points that stopped the arrhythmia presented higher correlation coefficients. The LV/RV ratio correctly predicted LV vs. RV SOO in 10/11 cases; 1.07 vs. 0.93 P < 0.05 for 12-lead ρ. CONCLUSION: The obtained results demonstrate the potential of the developed in silico pace-mapping technique to complement standard ECG for the pre-operative planning of complex ventricular arrhythmias.

Factors affecting basket catheter detection of real and phantom rotors in the atria: A computational study.

Anatomically based procedures to ablate atrial fibrillation (AF) are often successful in terminating paroxysmal AF. However, the ability to terminate persistent AF remains disappointing. New mechanistic approaches use multiple-electrode basket catheter mapping to localize and target AF drivers in the form of rotors but significant concerns remain about their accuracy. We aimed to evaluate how electrode-endocardium distance, far-field sources and inter-electrode distance affect the accuracy of localizing rotors. Sustained rotor activation of the atria was simulated numerically and mapped using a virtual basket catheter with varying electrode densities placed at different positions within the atrial cavity. Unipolar electrograms were calculated on the entire endocardial surface and at each of the electrodes. Rotors were tracked on the interpolated basket phase maps and compared with the respective atrial voltage and endocardial phase maps, which served as references. Rotor detection by the basket maps varied between 35-94% of the simulation time, depending on the basket's position and the electrode-to-endocardial wall distance. However, two different types of phantom rotors appeared also on the basket maps. The first type was due to the far-field sources and the second type was due to interpolation between the electrodes; increasing electrode density decreased the incidence of the second but not the first type of phantom rotors. In the simulations study, basket catheter-based phase mapping detected rotors even when the basket was not in full contact with the endocardial wall, but always generated a number of phantom rotors in the presence of only a single real rotor, which would be the desired ablation target. Phantom rotors may mislead and contribute to failure in AF ablation procedures.

Three-dimensional cardiac computational modelling: methods, features and applications.

The combination of computational models and biophysical simulations can help to interpret an array of experimental data and contribute to the understanding, diagnosis and treatment of complex diseases such as cardiac arrhythmias. For this reason, three-dimensional (3D) cardiac computational modelling is currently a rising field of research. The advance of medical imaging technology over the last decades has allowed the evolution from generic to patient-specific 3D cardiac models that faithfully represent the anatomy and different cardiac features of a given alive subject. Here we analyse sixty representative 3D cardiac computational models developed and published during the last fifty years, describing their information sources, features, development methods and online availability. This paper also reviews the necessary components to build a 3D computational model of the heart aimed at biophysical simulation, paying especial attention to cardiac electrophysiology (EP), and the existing approaches to incorporate those components. We assess the challenges associated to the different steps of the building process, from the processing of raw clinical or biological data to the final application, including image segmentation, inclusion of substructures and meshing among others. We briefly outline the personalisation approaches that are currently available in 3D cardiac computational modelling. Finally, we present examples of several specific applications, mainly related to cardiac EP simulation and model-based image analysis, showing the potential usefulness of 3D cardiac computational modelling into clinical environments as a tool to aid in the prevention, diagnosis and treatment of cardiac diseases.

Automatic and interpretable prediction of the site of origin in outflow tract ventricular arrhythmias: machine learning integrating electrocardiograms and clinical data.

The treatment of outflow tract ventricular arrhythmias (OTVA) through radiofrequency ablation requires the precise identification of the site of origin (SOO). Pinpointing the SOO enhances the likelihood of a successful procedure, reducing intervention times and recurrence rates. Current clinical methods to identify the SOO are based on qualitative analysis of pre-operative electrocardiograms (ECG), heavily relying on physician's expertise. Although computational models and machine learning (ML) approaches have been proposed to assist OTVA procedures, they either consume substantial time, lack interpretability or do not use clinical information. Here, we propose an alternative strategy for automatically predicting the ventricular origin of OTVA patients using ML. Our objective was to classify ventricular (left/right) origin in the outflow tracts (LVOT and RVOT, respectively), integrating ECG and clinical data from each patient. Extending beyond differentiating ventricle origin, we explored specific SOO characterization. Utilizing four databases, we also trained supervised learning models on the QRS complexes of the ECGs, clinical data, and their combinations. The best model achieved an accuracy of 89%, highlighting the significance of precordial leads V1-V4, especially in the R/S transition and initiation of the QRS complex in V2. Unsupervised analysis revealed that some origins tended to group closer than others, e.g., right coronary cusp (RCC) with a less sparse group than the aortic cusp origins, suggesting identifiable patterns for specific SOOs.

Digital twinning of the human ventricular activation sequence to Clinical 12-lead ECGs and magnetic resonance imaging using realistic Purkinje networks for in silico clinical trials.

Cardiac in silico clinical trials can virtually assess the safety and efficacy of therapies using human-based modelling and simulation. These technologies can provide mechanistic explanations for clinically observed pathological behaviour. Designing virtual cohorts for in silico trials requires exploiting clinical data to capture the physiological variability in the human population. The clinical characterisation of ventricular activation and the Purkinje network is challenging, especially non-invasively. Our study aims to present a novel digital twinning pipeline that can efficiently generate and integrate Purkinje networks into human multiscale biventricular models based on subject-specific clinical 12-lead electrocardiogram and magnetic resonance recordings. Essential novel features of the pipeline are the human-based Purkinje network generation method, personalisation considering ECG R wave progression as well as QRS morphology, and translation from reduced-order Eikonal models to equivalent biophysically-detailed monodomain ones. We demonstrate ECG simulations in line with clinical data with clinical image-based multiscale models with Purkinje in four control subjects and two hypertrophic cardiomyopathy patients (simulated and clinical QRS complexes with Pearson's correlation coefficients > 0.7). Our methods also considered possible differences in the density of Purkinje myocardial junctions in the Eikonal-based inference as regional conduction velocities. These differences translated into regional coupling effects between Purkinje and myocardial models in the monodomain formulation. In summary, we demonstrate a digital twin pipeline enabling simulations yielding clinically consistent ECGs with clinical CMR image-based biventricular multiscale models, including personalised Purkinje in healthy and cardiac disease conditions.

Enhanced optimization-based method for the generation of patient-specific models of Purkinje networks.

Cardiac Purkinje networks are a fundamental part of the conduction system and are known to initiate a variety of cardiac arrhythmias. However, patient-specific modeling of Purkinje networks remains a challenge due to their high morphological complexity. This work presents a novel method based on optimization principles for the generation of Purkinje networks that combines geometric and activation accuracy in branch size, bifurcation angles, and Purkinje-ventricular-junction activation times. Three biventricular meshes with increasing levels of complexity are used to evaluate the performance of our approach. Purkinje-tissue coupled monodomain simulations are executed to evaluate the generated networks in a realistic scenario using the most recent Purkinje/ventricular human cellular models and physiological values for the Purkinje-ventricular-junction characteristic delay. The results demonstrate that the new method can generate patient-specific Purkinje networks with controlled morphological metrics and specified local activation times at the Purkinje-ventricular junctions.

Exocyst is involved in polarized cell migration and cerebral cortical development.

Neuronal migration is essential for proper development of the cerebral cortex. As a first step, a postmitotic cell extends its leading process, presumably by adding new membrane at the growing tip, which would enable directed locomotion. The goal of the present study was to determine if biosynthetic exocytic pathway is polarized in migrating cells and whether polarized exocytosis promotes directed cell migration. A promising candidate for controlling the spatial sites of vesicle tethering and fusion at the plasma membrane is a protein complex called the exocyst. We found that cell migration in a wound assay, as well as cortical neuronal migration during embryonic development was impaired when the exocyst was disturbed. By combining TIRF microscopy and a stochastic model of exocytosis, we found that vesicle exocytosis is preferentially distributed close to the leading edge of polarized cells, that the exocytic process is organized into hotspots, and that the polarized delivery of vesicles and their clustering in hotspots depend on the intact exocyst complex. The exocyst complex seems to achieve this spatial regulation by determining the sites at the membrane where secretory vesicles tether. Thus, our study supports the notion that polarized membrane traffic regulated by the exocyst is an essential component of cell migration and that its deficit may lead to cortical abnormalities involving cortical neuronal malpositioning.

Training machine learning models with synthetic data improves the prediction of ventricular origin in outflow tract ventricular arrhythmias.

In order to determine the site of origin (SOO) in outflow tract ventricular arrhythmias (OTVAs) before an ablation procedure, several algorithms based on manual identification of electrocardiogram (ECG) features, have been developed. However, the reported accuracy decreases when tested with different datasets. Machine learning algorithms can automatize the process and improve generalization, but their performance is hampered by the lack of large enough OTVA databases. We propose the use of detailed electrophysiological simulations of OTVAs to train a machine learning classification model to predict the ventricular origin of the SOO of ectopic beats. We generated a synthetic database of 12-lead ECGs (2,496 signals) by running multiple simulations from the most typical OTVA SOO in 16 patient-specific geometries. Two types of input data were considered in the classification, raw and feature ECG signals. From the simulated raw 12-lead ECG, we analyzed the contribution of each lead in the predictions, keeping the best ones for the training process. For feature-based analysis, we used entropy-based methods to rank the obtained features. A cross-validation process was included to evaluate the machine learning model. Following, two clinical OTVA databases from different hospitals, including ECGs from 365 patients, were used as test-sets to assess the generalization of the proposed approach. The results show that V2 was the best lead for classification. Prediction of the SOO in OTVA, using both raw signals or features for classification, presented high accuracy values (>0.96). Generalization of the network trained on simulated data was good for both patient datasets (accuracy of 0.86 and 0.84, respectively) and presented better values than using exclusively real ECGs for classification (accuracy of 0.84 and 0.76 for each dataset). The use of simulated ECG data for training machine learning-based classification algorithms is critical to obtain good SOO predictions in OTVA compared to real data alone. The fast implementation and generalization of the proposed methodology may contribute towards its application to a clinical routine.

Deciphering subcellular processes in live imaging datasets via dynamic probabilistic networks.

MOTIVATION: Designing mathematical tools that can formally describe the dynamics of complex intracellular processes remains a challenge. Live cell imaging reveals changes in the cellular states, but current simple approaches extract only minimal information of a static snapshot. RESULTS: We implemented a novel approach for analyzing organelle behavior in live cell imaging data based on hidden Markov models (HMMs) and showed that it can determine the number and evolution of distinct cellular states involved in a biological process. We analyzed insulin-mediated exocytosis of single Glut4-vesicles, a process critical for blood glucose homeostasis and impaired in type II diabetes, by using total internal reflection fluorescence microscopy (TIRFM). HMM analyses of movie sequences of living cells reveal that insulin controls spatial and temporal dynamics of exocytosis via the exocyst, a putative tethering protein complex. Our studies have validated the proof-of-principle of HMM for cellular imaging and provided direct evidence for the existence of complex spatial-temporal regulation of exocytosis in non-polarized cells. We independently confirmed insulin-dependent spatial regulation by using static spatial statistics methods. CONCLUSION: We propose that HMM-based approach can be exploited in a wide avenue of cellular processes, especially those where the changes of cellular states in space and time may be highly complex and non-obvious, such as in cell polarization, signaling and developmental processes.

Clinically-Driven Virtual Patient Cohorts Generation: An Application to Aorta.

The combination of machine learning methods together with computational modeling and simulation of the cardiovascular system brings the possibility of obtaining very valuable information about new therapies or clinical devices through in-silico experiments. However, the application of machine learning methods demands access to large cohorts of patients. As an alternative to medical data acquisition and processing, which often requires some degree of manual intervention, the generation of virtual cohorts made of synthetic patients can be automated. However, the generation of a synthetic sample can still be computationally demanding to guarantee that it is clinically meaningful and that it reflects enough inter-patient variability. This paper addresses the problem of generating virtual patient cohorts of thoracic aorta geometries that can be used for in-silico trials. In particular, we focus on the problem of generating a cohort of patients that meet a particular clinical criterion, regardless the access to a reference sample of that phenotype. We formalize the problem of clinically-driven sampling and assess several sampling strategies with two goals, sampling efficiency, i.e., that the generated individuals actually belong to the target population, and that the statistical properties of the cohort can be controlled. Our results show that generative adversarial networks can produce reliable, clinically-driven cohorts of thoracic aortas with good efficiency. Moreover, non-linear predictors can serve as an efficient alternative to the sometimes expensive evaluation of anatomical or functional parameters of the organ of interest.

Estimation of Personalized Minimal Purkinje Systems From Human Electro-Anatomical Maps.

The Purkinje system is a heart structure responsible for transmitting electrical impulses through the ventricles in a fast and coordinated way to trigger mechanical contraction. Estimating a patient-specific compatible Purkinje Network from an electro-anatomical map is a challenging task, that could help to improve models for electrophysiology simulations or provide aid in therapy planning, such as radiofrequency ablation. In this study, we present a methodology to inversely estimate a Purkinje network from a patient's electro-anatomical map. First, we carry out a simulation study to assess the accuracy of the method for different synthetic Purkinje network morphologies and myocardial junction densities. Second, we estimate the Purkinje network from a set of 28 electro-anatomical maps from patients, obtaining an optimal conduction velocity in the Purkinje network of 1.95 ± 0.25 m/s, together with the location of their Purkinje-myocardial junctions, and Purkinje network structure. Our results showed an average local activation time error of 6.8±2.2 ms in the endocardium. Finally, using the personalized Purkinje network, we obtained correlations higher than 0.85 between simulated and clinical 12-lead ECGs.

Cardiac computational modelling.

Cardiovascular diseases currently have a major social and economic impact, constituting one of the leading causes of mortality and morbidity. Personalized computational models of the heart are demonstrating their usefulness both to help understand the mechanisms underlying cardiac disease, and to optimize their treatment and predict the patient's response. Within this framework, the Spanish Research Network for Cardiac Computational Modelling (VHeart-SN) has been launched. The general objective of the VHeart-SN network is the development of an integrated, modular and multiscale multiphysical computational model of the heart. This general objective is addressed through the following specific objectives: a) to integrate the different numerical methods and models taking into account the specificity of patients; b) to assist in advancing knowledge of the mechanisms associated with cardiac and vascular diseases; and c) to support the application of different personalized therapies. This article presents the current state of cardiac computational modelling and different scientific works conducted by the members of the network to gain greater understanding of the characteristics and usefulness of these models.

A novel method to correct repolarization time estimation from unipolar electrograms distorted by standard filtering.

Reliable patient-specific ventricular repolarization times (RTs) can identify regions of functional block or afterdepolarizations, indicating arrhythmogenic cardiac tissue and the risk of sudden cardiac death. Unipolar electrograms (UEs) record electric potentials, and the Wyatt method has been shown to be accurate for estimating RT from a UE. High-pass filtering is an important step in processing UEs, however, it is known to distort the T-wave phase of the UE, which may compromise the accuracy of the Wyatt method. The aim of this study was to examine the effects of high-pass filtering, and improve RT estimates derived from filtered UEs. We first generated a comprehensive set of UEs, corresponding to early and late activation and repolarization, that were then high-pass filtered with settings that mimicked the CARTO filter. We trained a deep neural network (DNN) to output a probabilistic estimation of RT and a measure of confidence, using the filtered synthetic UEs and their true RTs. Unfiltered ex-vivo human UEs were also filtered and the trained DNN used to estimate RT. Even a modest 2 Hz high-pass filter imposes a significant error on RT estimation using the Wyatt method. The DNN outperformed the Wyatt method in 62.75% of cases, and produced a significantly lower absolute error (p=8.99E-13), with a median of 16.91 ms, on 102 ex-vivo UEs. We also applied the DNN to patient UEs from CARTO, from which an RT map was computed. In conclusion, DNNs trained on synthetic UEs improve the RT estimation from filtered UEs, which leads to more reliable repolarization maps that help to identify patient-specific repolarization abnormalities.

Personalized Cardiac Computational Models: From Clinical Data to Simulation of Infarct-Related Ventricular Tachycardia.

In the chronic stage of myocardial infarction, a significant number of patients develop life-threatening ventricular tachycardias (VT) due to the arrhythmogenic nature of the remodeled myocardium. Radiofrequency ablation (RFA) is a common procedure to isolate reentry pathways across the infarct scar that are responsible for VT. Unfortunately, this strategy show relatively low success rates; up to 50% of patients experience recurrent VT after the procedure. In the last decade, intensive research in the field of computational cardiac electrophysiology (EP) has demonstrated the ability of three-dimensional (3D) cardiac computational models to perform in-silico EP studies. However, the personalization and modeling of certain key components remain challenging, particularly in the case of the infarct border zone (BZ). In this study, we used a clinical dataset from a patient with a history of infarct-related VT to build an image-based 3D ventricular model aimed at computational simulation of cardiac EP, including detailed patient-specific cardiac anatomy and infarct scar geometry. We modeled the BZ in eight different ways by combining the presence or absence of electrical remodeling with four different levels of image-based patchy fibrosis (0, 10, 20, and 30%). A 3D torso model was also constructed to compute the ECG. Patient-specific sinus activation patterns were simulated and validated against the patient's ECG. Subsequently, the pacing protocol used to induce reentrant VTs in the EP laboratory was reproduced in-silico. The clinical VT was induced with different versions of the model and from different pacing points, thus identifying the slow conducting channel responsible for such VT. Finally, the real patient's ECG recorded during VT episodes was used to validate our simulation results and to assess different strategies to model the BZ. Our study showed that reduced conduction velocities and heterogeneity in action potential duration in the BZ are the main factors in promoting reentrant activity. Either electrical remodeling or fibrosis in a degree of at least 30% in the BZ were required to initiate VT. Moreover, this proof-of-concept study confirms the feasibility of developing 3D computational models for cardiac EP able to reproduce cardiac activation in sinus rhythm and during VT, using exclusively non-invasive clinical data.

Optimization of Lead Placement in the Right Ventricle During Cardiac Resynchronization Therapy. A Simulation Study.

Patients suffering from heart failure and left bundle branch block show electrical ventricular dyssynchrony causing an abnormal blood pumping. Cardiac resynchronization therapy (CRT) is recommended for these patients. Patients with positive therapy response normally present QRS shortening and an increased left ventricle (LV) ejection fraction. However, around one third do not respond favorably. Therefore, optimal location of pacing leads, timing delays between leads and/or choosing related biomarkers is crucial to achieve the best possible degree of ventricular synchrony during CRT application. In this study, computational modeling is used to predict the optimal location and delay of pacing leads to improve CRT response. We use a 3D electrophysiological computational model of the heart and torso to get insight into the changes in the activation patterns obtained when the heart is paced from different regions and for different atrioventricular and interventricular delays. The model represents a heart with left bundle branch block and heart failure, and allows a detailed and accurate analysis of the electrical changes observed simultaneously in the myocardium and in the QRS complex computed in the precordial leads. Computational simulations were performed using a modified version of the O'Hara et al. action potential model, the most recent mathematical model developed for human ventricular electrophysiology. The optimal location for the pacing leads was determined by QRS maximal reduction. Additionally, the influence of Purkinje system on CRT response was assessed and correlation analysis between several parameters of the QRS was made. Simulation results showed that the right ventricle (RV) upper septum near the outflow tract is an alternative location to the RV apical lead. Furthermore, LV endocardial pacing provided better results as compared to epicardial stimulation. Finally, the time to reach the 90% of the QRS area was a good predictor of the instant at which 90% of the ventricular tissue was activated. Thus, the time to reach the 90% of the QRS area is suggested as an additional index to assess CRT effectiveness to improve biventricular synchrony.

Changes in the spatial distribution of the Purkinje network after acute myocardial infarction in the pig.

Purkinje cells (PCs) are more resistant to ischemia than myocardial cells, and are suspected to participate in ventricular arrhythmias following myocardial infarction (MI). Histological studies afford little evidence on the behavior and adaptation of PCs in the different stages of MI, especially in the chronic stage, and no quantitative data have been reported to date beyond subjective qualitative depictions. The present study uses a porcine model to present the first quantitative analysis of the distal cardiac conduction system and the first reported change in the spatial distribution of PCs in three representative stages of MI: an acute model both with and without reperfusion; a subacute model one week after reperfusion; and a chronic model one month after reperfusion. Purkinje cells are able to survive after 90 minutes of ischemia and subsequent reperfusion to a greater extent than cardiomyocytes. A decrease is observed in the number of PCs, which suffer reversible subcellular alterations such as cytoplasm vacuolization, together with redistribution from the mesocardium-the main localization of PCs in the heart of ungulate species-towards the endocardium and perivascular epicardial areas. However, these changes mainly occur during the first week after ischemia and reperfusion, and are maintained in the chronic stages. This anatomical substrate can explain the effectiveness of endo-epicardial catheter ablation of monomorphic ventricular tachycardias in the chronic scar after infarction, and sets a basis for further electrophysiological and molecular studies, and future therapeutic strategies.

A rule-based method to model myocardial fiber orientation in cardiac biventricular geometries with outflow tracts.

Rule-based methods are often used for assigning fiber orientation to cardiac anatomical models. However, existing methods have been developed using data mostly from the left ventricle. As a consequence, fiber information obtained from rule-based methods often does not match histological data in other areas of the heart such as the right ventricle, having a negative impact in cardiac simulations beyond the left ventricle. In this work, we present a rule-based method where fiber orientation is separately modeled in each ventricle following observations from histology. This allows to create detailed fiber orientation in specific regions such as the endocardium of the right ventricle, the interventricular septum, and the outflow tracts. We also carried out electrophysiological simulations involving these structures and with different fiber configurations. In particular, we built a modeling pipeline for creating patient-specific volumetric meshes of biventricular geometries, including the outflow tracts, and subsequently simulate the electrical wavefront propagation in outflow tract ventricular arrhythmias with different origins for the ectopic focus. The resulting simulations with the proposed rule-based method showed a very good agreement with clinical parameters such as the 10 ms isochrone ratio in a cohort of nine patients suffering from this type of arrhythmia. The developed modeling pipeline confirms its potential for an in silico identification of the site of origin in outflow tract ventricular arrhythmias before clinical intervention.

Gender differences in sleep patterns and sleep complaints of elite athletes.

OBJECTIVE: The present study aimed to investigate the gender differences for sleep complaints, patterns and disorders of elite athletes during preparation for the Rio 2016 Olympic Games. METHODS: The study included 146 athletes from the Brazilian Olympic Team (male: n=86; 59%; female: n=60; 41%). The assessment of the Olympic athletes' sleep took place in 2015, during the preparation period for the Rio Olympic Games. The athletes underwent a single polysomnography (PSG) evaluation. Sleep specialists evaluated the athletes and asked about their sleep complaints during a clinical consultation. In this evaluation week, the athletes did not take part in any training or competitions. RESULTS: The prevalence of sleep complaints was 53% of the athletes during the medical consultation, the most prevalent being insufficient sleep/waking up tired (32%), followed by snoring (21%) and insomnia (19.2%). In relation to the sleep pattern findings, the men had significantly higher sleep latency and wake after sleep onset than the women (p=0.004 and p=0.002, respectively). The sleep efficiency and sleep stages revealed that men had a lower percentage of sleep efficiency and slow wave sleep than the women (p=0.001 and p=0.05, respectively). CONCLUSION: Most athletes reported some sleep complaints, with men reporting more sleep complaints than women in the clinical evaluation. The PSG showed that 36% of all athletes had a sleep disorder with a greater reduction in sleep quality in men than in women.

Measuring spatiotemporal dependencies in bivariate temporal random sets with applications to cell biology.

Analyzing spatio-temporal dependencies between different types of events is highly relevant to numerous biological phenomena (e.g. signalling and trafficking) especially as advances in probes and microscopy have facilitated imaging of dynamic processes in living cells. For many types of events, the segmented areas can overlap spatially and temporally forming random clumps. In this paper, we model binary image sequences of two different event types as a realization of a bivariate temporal random set and propose a non-parametric approach to quantify spatial and spatio-temporal interrelations using the pair-correlation, cross-covariance and the Ripley IK functions. Based on these summary statistics we propose a randomization procedure to test independence between event types by applying random toroidal shifts and Monte Carlo tests. A simulation study assessed the performance of the proposed estimators and showed that these statistics capture the spatio-temporal dependencies accurately. The estimation of the spatio-temporal interval of interactions was also obtained. The method was successfully applied to analyze the interdependencies of several endocytic proteins using image sequences of living cells and validated the procedure as a new way to automatically quantify dependencies between proteins in a formal and robust manner.

Automatic estimation of Purkinje-Myocardial junction hot-spots from noisy endocardial samples: A simulation study.

The reconstruction of the ventricular cardiac conduction system (CCS) from patient-specific data is a challenging problem. High-resolution imaging techniques have allowed only the segmentation of proximal sections of the CCS from images acquired ex vivo. In this paper, we present an algorithm to estimate the location of a set of Purkinje-myocardial junctions (PMJs) from electro-anatomical maps, as those acquired during radio-frequency ablation procedures. The method requires a mesh representing the myocardium with local activation time measurements on a subset of nodes. We calculate the backwards propagation of the electrical signal from the measurement points to all the points in the mesh to define a set of candidate PMJs that is iteratively refined. The algorithm has been tested on several Purkinje network configurations, with simulated activation maps, subject to different error amplitudes. The results show that the method is able to build a set of PMJs that explain the observed activation map for different synthetic CCS configurations. In the tests, the average error in the predicted activation time is below the amplitude of the error applied to the data.