Incorporating Inductances in Tissue-Scale Models of Cardiac Electrophysiology

In standard models of cardiac electrophysiology, including the bidomain and monodomain models, local perturbations can propagate at infinite speed. We address this unrealistic property by developing a hyperbolic bidomain model that is based on a generalization of Ohm's law with a Cattaneo-type model for the fluxes. Further, we obtain a hyperbolic monodomain model in the case that the intracellular and extracellular conductivity tensors have the same anisotropy ratio. In one spatial dimension, the hyperbolic monodomain model is equivalent to a cable model that includes axial inductances, and the relaxation times of the Cattaneo fluxes are strictly related to these inductances. A purely linear analysis shows that the inductances are negligible, but models of cardiac electrophysiology are highly nonlinear, and linear predictions may not capture the fully nonlinear dynamics. In fact, contrary to the linear analysis, we show that for simple nonlinear ionic models, an increase in conduction velocity is obtained for small and moderate values of the relaxation time. A similar behavior is also demonstrated with biophysically detailed ionic models. Using the Fenton-Karma model along with a low-order finite element spatial discretization, we numerically analyze differences between the standard monodomain model and the hyperbolic monodomain model. In a simple benchmark test, we show that the propagation of the action potential is strongly influenced by the alignment of the fibers with respect to the mesh in both the parabolic and hyperbolic models when using relatively coarse spatial discretizations. Accurate predictions of the conduction velocity require computational mesh spacings on the order of a single cardiac cell. We also compare the two formulations in the case of spiral break up and atrial fibrillation in an anatomically detailed model of the left atrium, and [...].Comment: 20 pages, 12 figure

Investigating Perceptual Congruence Between Data and Display Dimensions in Sonification

The relationships between sounds and their perceived meaning and connotations are complex, making auditory perception an important factor to consider when designing sonification systems. Listeners often have a mental model of how a data variable should sound during sonification and this model is not considered in most data:sound mappings. This can lead to mappings that are difficult to use and can cause confusion. To investigate this issue, we conducted a magnitude estimation experiment to map how roughness, noise and pitch relate to the perceived magnitude of stress, error and danger. These parameters were chosen due to previous findings which suggest perceptual congruency between these auditory sensations and conceptual variables. Results from this experiment show that polarity and scaling preference are dependent on the data:sound mapping. This work provides polarity and scaling values that may be directly utilised by sonification designers to improve auditory displays in areas such as accessible and mobile computing, process-monitoring and biofeedback

A method for incorporating three-dimensional residual stretches/stresses into patient-specific finite element simulations of arteries

The existence of residual stresses in human arteries has long been shown experimentally. Researchers have also demonstrated that residual stresses have a significant effect on the distribution of physiological stresses within arterial tissues, and hence on their development, e.g., stress-modulated remodeling. Through progress in medical imaging, image analysis and finite element (FE) meshing tools it is now possible to construct in vivo patient-specific geometries and thus to study specific, clinically relevant problems in arterial mechanics via FE simulations. Classical continuum mechanics and FE methods assume that constitutive models and the corresponding simulations start from unloaded, stress-free reference configurations while the boundary-value problem of interest represents a loaded geometry and includes residual stresses. We present a pragmatic methodology to simultaneously account for both (i) the three-dimensional (3-D) residual stress distributions in the arterial tissue layers, and (ii) the equilibrium of the in vivo patient-specific geometry with the known boundary conditions. We base our methodology on analytically determined residual stress distributions (Holzapfel and Ogden, 2010, J. R. Soc. Interface 7, 787-799) and calibrate it using data on residual deformations (Holzapfel et al., 2007, Ann. Biomed. Eng. 35, 530-545). We demonstrate our methodology on three patient-specific FE simulations calibrated using experimental data. All data employed here are generated from human tissues - both the aorta and thrombus, and their respective layers - including the geometries determined from magnetic resonance images, and material properties and 3-D residual stretches determined from mechanical experiments. We study the effect of 3-D residual stresses on the distribution of physiological stresses in the aortic layers (intima, media, adventitia) and the layers of the intraluminal thrombus (luminal, medial, abluminal) by comparing three types of FE simulations: (i) conventional calculations; (ii) calculations accounting only for prestresses; (iii) calculations including both 3-D residual stresses and prestresses. Our results show that including residual stresses in patient-specific simulations of arterial tissues significantly impacts both the global (organ-level) deformations and the stress distributions within the arterial tissue (and its layers). Our method produces circumferential Cauchy stress distributions that are more uniform through the tissue thickness (i.e., smaller stress gradients in the local radial directions) compared to both the conventional and prestressing calculations. Such methods, combined with appropriate experimental data, aim at increasing the accuracy of classical FE analyses for patient-specific studies in computational biomechanics and may lead to increased clinical application of simulation tools.publisher: Elsevier articletitle: A method for incorporating three-dimensional residual stretches/stresses into patient-specific finite element simulations of arteries journaltitle: Journal of the Mechanical Behavior of Biomedical Materials articlelink: http://dx.doi.org/10.1016/j.jmbbm.2015.03.024 content_type: article copyright: Copyright © 2015 Elsevier Ltd. All rights reserved.status: publishe

Personalized computational modeling of left atrial geometry and transmural myofiber architecture

La fibrilación auricular (FA) es una taquiarritmia supraventricular caracterizada por la ausencia total de contracción auricular coordinada y se asocia con un aumento de la morbilidad y la mortalidad. La modelización computacional personalizada proporciona un marco novedoso para integrar e interpretar el papel de la electrofisiología auricular (EP), incluida la anatomía y la microestructura subyacente, en el desarrollo y el mantenimiento de la FA. Los datos de la angiografía de tomografía computarizada coronaria se segmentaron utilizando un enfoque estadístico y las representaciones de vóxeles suavizados se discretizaron en mallas de elementos finitos tetraédricos (FE) de alta resolución. Para estimar la compleja arquitectura de miofibra de la aurícula izquierda, se generaron campos de fibra individuales de acuerdo con los datos morfológicos de las superficies endo y epicárdica basados en soluciones locales de la ecuación de Laplace e interpolados transmutalmente a elementos tetraédricos. La influencia de las microestructuras transmurales variables se cuantificó a través de simulaciones EP en 3 pacientes usando 5 funciones de interpolación de fibras diferentes. Los modelos geométricos personalizados incluyeron la distribución de grosor heterogénea del miocardio auricular izquierdo y la posterior discretización condujo a mallas de FE tetraédricas de alta fidelidad. El novedoso algoritmo para la incorporación automatizada de la arquitectura de fibras de la aurícula izquierda proporcionó una estimación realista de la microestructura de la aurícula y fue capaz de capturar cualitativamente todos los haces de fibras importantes. Se predijeron tiempos máximos de activación local consistentes en las simulaciones de EP usando funciones individuales de interpolación de fibras transmurales para cada paciente, sugiriendo un efecto insignificante de la arquitectura de miofibra transmu- ral en el EP. La tubería de modelación establecida proporciona un marco robusto para el rápido desarrollo de cohortes de modelos personalizados que tienen en cuenta la anatomía y la microestructura detallada y facilita las simulaciones del EP auricular.Atrial fibrillation (AF) is a supraventricular tachyarrhythmia characterized by complete absence of co-ordinated atrial contraction and is associated with an increased morbidity and mortality. Personalized computational modeling provides a novel framework for integrating and interpreting the role of atrial electrophysiology (EP) including the underlying anatomy and microstructure in the development and sus- tenance of AF. Coronary computed tomography angiography data were segmented using a statistics-based approach and the smoothed voxel representations were discretized into high-resolution tetrahedral finite element (FE) meshes. To estimate the complex left atrial myofiber architecture, individual fiber fields were generated according to morphological data on the endo- and epicardial surfaces based on local solutions of Laplace’s equation and transmurally interpolated to tetrahedral elements. The influence of variable transmural microstructures was quantified through EP simulations on 3 patients using 5 differ- ent fiber interpolation functions. Personalized geometrical models included the heterogeneous thickness distribution of the left atrial myocardium and subsequent discretization led to high-fidelity tetrahedral FE meshes. The novel algorithm for automated incorporation of the left atrial fiber architecture provided a realistic estimate of the atrial microstructure and was able to qualitatively capture all important fiber bundles. Consistent maximum local activation times were predicted in EP simulations using individual transmural fiber interpolation functions for each patient suggesting a negligible effect of the transmu- ral myofiber architecture on EP. The established modeling pipeline provides a robust framework for the rapid development of personalized model cohorts accounting for detailed anatomy and microstructure and facilitates simulations of atrial EP.• UK Medical Research Council through Clinical Research Training Fellowship grant MR/N001877/1 • UK Medical Research Council through New Investigator grant MR/N011007/1 • Austrian Science Fund project grants F3210-N18 and I2760-B30 • UK Engineering and Physical Sciences Research Council through Intermediate Fellowship grant EP/F043929/1 and project grant EP/P01268X/1 • British Heart Foundation project grant PG/13/37/30280 • Award to Guy’s & St Thomas’ NHS Foundation Trust in partnership with King’s College London and King’s College Hospital NHS Foundation TrustpeerReviewe