We focus on the problem of shock wave formation in a model of blood flow along an elastic artery. We analyze the conditions under which this phenomenon can appear and we provide an estimation of the instant of shock formation. Numerical simulations of the model have been conducted using the Discontinuous Galerkin Finite Element Method. The results are consistent with certain phenomena observed by practitioners in patients with arteriopathies, and they could predict the possible formation of a shock wave in the aorta.
Cristóbal Rodero, J. Alberto Conejero and Ignacio García-Fernández. Shock wave formation in compliant arteries.Evolution Equations & Control Theory. Volume 8, issue 1. 2019. Full text.
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.
F. Barber, M. Lozano, I. García‐Fernández, R. Sebastián. Automatic Estimation of Purkinje-Myocardial Junction hot-spots from Noisy Endocardial Samples: A simulation study. International Journal for Numerical Methods in Biomedical Engineering. Volume 34, issue 7. Article e2988. 2018. PDF.
Introduction: Focal atrial tachycardia is commonly treated by radio frequency ablation with an acceptable long-term success. Although the location of ectopic foci tends to appear in specific hot-spots, they can be located virtually in any atrial region. Multi-electrode surface ECG systems allow acquiring dense body surface potential maps (BSPM) for non-invasive therapy planning of cardiac arrhythmia. However, the activation of the atria could be affected by fibrosis and therefore biomarkers based on BSPM need to take these effects into account. We aim to analyze the effect of fibrosis on a BSPM derived index, and its potential application to predict the location of ectopic foci in the atria.
Methodology: We have developed a 3D atrial model that includes 5 distributions of patchy fibrosis in the left atrium at 5 different stages. Each stage corresponds to a different amount of fibrosis that ranges from 2 to 40%. The 25 resulting 3D models were used for simulation of Focal Atrial Tachycardia (FAT), triggered from 19 different locations described in clinical studies. BSPM were obtained for all simulations, and the body surface potential integral maps (BSPiM) were calculated to describe atrial activations. A machine learning (ML) pipeline using a supervised learning model and support vector machine was developed to learn the BSPM patterns of each of the 475 activation sequences and relate them to the origin of the FAT source.
Results: Activation maps for stages with more than 15% of fibrosis were greatly affected, producing conduction blocks and delays in propagation. BSPiMs did not always cluster into non-overlapped groups since BSPiMs were highly altered by the conduction blocks. From stage 3 (15% fibrosis) the BSPiMs showed differences for ectopic beats placed around the area of the pulmonary veins. Classification results were mostly above 84% for all the configurations studied when a large enough number of electrodes were used to map the torso. However, the presence of fibrosis increases the area of the ectopic focus location and therefore decreases the utility for the electrophysiologist.
Conclusions: The results indicate that the proposed ML pipeline is a promising methodology for non-invasive ectopic foci localization from BSPM signal even when fibrosis is present.
Eduardo Jorge Godoy, Miguel Lozano, Ignacio Garcia-Fernandez, Ana Ferrer-Albero, Javier Saiz, Rafael Sebastian. Atrial fibrosis hampers non-invasive localization of atrial ectopic foci from multi-electrode signals: A 3D simulation study. Frontiers in Physiology. Volume 9. Article 404. 2018. PDF.
Conformation Constraints for Efficient Viscoelastic Fluid Simulation
The simulation of high viscoelasticity poses important computational chal-lenges. One is the difficulty to robustly measure strain and its derivativesin a medium without permanent structure. Another is the high stiffness ofthe governing differential equations. Solutions that tackle these challengesexist, but they are computationally slow. We propose a constraint-basedmodel of viscoelasticity that enables efficient simulation of highly viscousand viscoelastic phenomena. Our model reformulates, in a constraint-basedfashion, a constitutive model of viscoelasticity for polymeric fluids, whichdefines simple governing equations for a conformation tensor. The modelcan represent a diverse palette of materials, spanning elastoplastic, highlyviscous, and inviscid liquid behaviors. In addition, we have designed a con-strained dynamics solver that extends the position-based dynamics methodto handle efficiently both position-based and velocity-based constraints. Weshow results that range from interactive simulation of viscoelastic effects tolarge-scale simulation of high viscosity with competitive performance.
Publication:
Héctor Barreiro, Ignacio García-Fernández, Iván Alduán, Miguel A. Otaduy. Conformation Constraints for Efficient Viscoelastic Fluid Simulation. ACM Trans. on Graphics (Proc. of ACM SIGGRAPH Asia), Volume 36, Number 6 – 2017. PDF preprint, suplemental material, video.
Modeling the cardiac conduction system is a challenging problem in the context of computational cardiac electrophysiology. Its ventricular section, the Purkinje system, is responsible for triggering tissue electrical activation at discrete terminal locations, which subsequently spreads throughout the ventricles. In this paper, we present an algorithm that is capable of estimating the location of the Purkinje system triggering points from a set of random measurements on tissue. We present the properties and the performance of the algorithm under controlled synthetic scenarios. Results show that the method is capable of locating most of the triggering points in scenarios with a fair ratio between terminals and measurements. When the ratio is low, the method can locate the terminals with major impact in the overall activation map. Mean absolute errors obtained indicate that solutions provided by the algorithm are useful to accurately simulate a complete patient ventricular activation map.
A solution provided by the algorithm. Red dots are the signal source points (unknown to the algorithm) and blue points are the estimated source points. The estimated points are capable or reproducing the activation pattern measured at the crosses.
