Diversity and complexity of the cavotricuspid isthmus in rabbits: A novel scheme for classification and geometrical transformation of anatomical structures.

The aim of this study was to describe the morphology of the cavotricuspid isthmus (CTI) in detail and introduce a comprehensive scheme to describe the topology of this region based on functional considerations. This may lead to a better understanding of isthmus-dependent flutter and fibrillation and to improved intervention strategies. We used images of the cavotricuspid isthmus from 52 rabbits of both sexes with a median weight of 3.40 ± 0.93 kg. The area of the CTI was 124.25 ± 42.14 mm2 with 53.28 ± 21.13 mm2 covered by pectinate muscles connecting the terminal crest and the vestibule. Isthmus length decreased from inferolateral (13.09 ±2.14 mm) to central (9.85 ± 2.14 mm) to paraseptal (4.88 ± 1.96 mm) resembling the overall human geometry. Ramification sites of pectinate muscles were identified and six levels dividing the CTI from posterior to anterior were introduced. This allowed the classification of pectinate muscle segments based on the connected ramification level. To account for the high inter-individual variations in size and shape, the CTI was projected onto a normalized reference frame using bilinear transformation. Furthermore, two measures of complexity were introduced: (i) the ramification index, which reflects the total number of muscle segments connected to a ramification site and (ii) the complexity index, which reflects the type of ramification (branching or merging site). Topological analysis showed that the complexity of the pectinate muscle network decreases from inferolateral to paraseptal and that the number of electrically uncoupled parallel pathways increases in the central section between the terminal crest and the vestibule which introduces potential reentry pathways.

Automated Texture Analysis and Determination of Fibre Orientation of Heart Tissue: A Morphometric Study.

The human heart has a heterogeneous structure, which is characterized by different cell types and their spatial configurations. The physical structure, especially the fibre orientation and the interstitial fibrosis, determines the electrical excitation and in further consequence the contractility in macroscopic as well as in microscopic areas. Modern image processing methods and parameters could be used to describe the image content and image texture. In most cases the description of the texture is not satisfying because the fibre orientation, detected with common algorithms, is biased by elements such as fibrocytes or endothelial nuclei. The goal of this work is to figure out if cardiac tissue can be analysed and classified on a microscopic level by automated image processing methods with a focus on an accurate detection of the fibre orientation. Quantitative parameters for identification of textures of different complexity or pathological attributes inside the heart were determined. The focus was set on the detection of the fibre orientation, which was calculated on the basis of the cardiomyocytes' nuclei. It turned out that the orientation of these nuclei corresponded with a high precision to the fibre orientation in the image plane. Additionally, these nuclei also indicated very well the inclination of the fibre.

An efficient finite element approach for modeling fibrotic clefts in the heart.

Advanced medical imaging technologies provide a wealth of information on cardiac anatomy and structure at a paracellular resolution, allowing to identify microstructural discontinuities which disrupt the intracellular matrix. Current state-of-the-art computer models built upon such datasets account for increasingly finer anatomical details, however, structural discontinuities at the paracellular level are typically discarded in the model generation process, owing to the significant costs which incur when using high resolutions for explicit representation. In this study, a novel discontinuous finite element (dFE) approach for discretizing the bidomain equations is presented, which accounts for fine-scale structures in a computer model without the need to increase spatial resolution. In the dFE method, this is achieved by imposing infinitely thin lines of electrical insulation along edges of finite elements which approximate the geometry of discontinuities in the intracellular matrix. Simulation results demonstrate that the dFE approach accounts for effects induced by microscopic size scale discontinuities, such as the formation of microscopic virtual electrodes, with vast computational savings as compared to high resolution continuous finite element models. Moreover, the method can be implemented in any standard continuous finite element code with minor effort.

Electroanatomical characterization of atrial microfibrosis in a histologically detailed computer model.

Fibrosis is thought to play an important role in the formation and maintenance of atrial fibrillation (AF). The propensity of fibrosis to increase AF vulnerability depends not only on its amount, its texture plays a crucial role as well. While the detection of fibrotic tissue patches in the atria with extracellular recordings is feasible based on the analysis of electrogram fractionation, as used in clinical practice to identify ablation targets, the classification of fibrotic texture is a more challenging problem. This study seeks to establish a method for the electroanatomical characterization of the fibrotic textures based on the analysis of electrogram fractionation. The proposed method exploits the dependence of fractionation patterns on the incidence direction of wavefronts which differs significantly as a function of texture. A histologically detailed computer model of the right atrial isthmus was developed for testing the method. A stimulation protocol was conceived which generated various incidence directions for any given recording site where electrograms were computed. A classification method is derived then for discriminating three types of fibrosis, no fibrosis (control), diffuse, and patchy fibrosis. Simulation results showed that electrogram fractionation and amplitudes and their dependence upon incidence direction allow a robust discrimination between different classes of fibrosis. Finally, to minimize the technical effort, sensitivity analysis was performed to identify a minimum number of incidence directions required for robust classification.

Decomposition of fractionated local electrograms using an analytic signal model based on sigmoid functions.

Microstructural heterogeneities in cardiac tissue, such as embedded connective tissue secondary to fibrosis, may lead to complex patterns of electrical activation that are reflected in the fractionation of extracellularly recorded electrograms. The decomposition of such electrograms into non-fractionated components is expected to provide additional information to allow a more precise classification of the microstructural properties adjacent to a given recording site. For the sake of this, an analytic signal model is introduced in this study that is capable of reliably identifying extracellular waveforms associated with sites of initiating, free-running, and terminating or colliding activation wavefronts. Using this signal model as a template, a procedure is developed for the automatic decomposition of complex fractionated electrograms into non-fractionated components. The decomposition method has been validated using electrograms obtained from one- and two-dimensional computer simulations in which all relevant intracellular and extracellular quantities are accessible at a very high spatiotemporal resolution and can be manipulated in a controlled manner. Fractionated electrograms were generated in these models by incorporating microstructural obstacles that mimicked inlays of connective tissue. Using this signal model, fractionated electrograms emerging from microstructural heterogeneities in the submillimeter range with latencies between components down to 0.6 ms can be decomposed.

Influence of ischemic core muscle fibers on surface depolarization potentials in superfused cardiac tissue preparations: a simulation study.

Thin-walled cardiac tissue samples superfused with oxygenated solutions are widely used in experimental studies. However, due to decreased oxygen supply and insufficient wash out of waste products in the inner layers of such preparations, electrophysiological functions could be compromised. Although the cascade of events triggered by cutting off perfusion is well known, it remains unclear as to which degree electrophysiological function in viable surface layers is affected by pathological processes occurring in adjacent tissue. Using a 3D numerical bidomain model, we aim to quantify the impact of superfusion-induced heterogeneities occurring in the depth of the tissue on impulse propagation in superficial layers. Simulations demonstrated that both the pattern of activation as well as the distribution of extracellular potentials close to the surface remain essentially unchanged. This was true also for the electrophysiological properties of cells in the surface layer, where most relevant depolarization parameters varied by less than 5.5 %. The main observed effect on the surface was related to action potential duration that shortened noticeably by 53 % as hypoxia deteriorated. Despite the known limitations of such experimental methods, we conclude that superfusion is adequate for studying impulse propagation and depolarization whereas repolarization studies should consider the influence of pathological processes taking place at the core of tissue sample.

A finite element approach for modeling micro-structural discontinuities in the heart.

The presence of connective tissue as well as interstitial clefts forms a natural barrier to the electrical propagation in the heart. At a microscopic scale, such uncoupling structures change the pattern of the electrical conduction from uniform towards complex and may play a role in the genesis of cardiac arrhythmias. The anatomical diversity of conduction structures and their topology at a microscopic size scale is overwhelming for experimental techniques. Mathematical models have been often employed to study the behavior of the electrical propagation at a sub-cellular level. However, very fine and computationally expensive meshes are required to capture all microscopic details found in the cardiac tissue. In this work, we present a numerical technique based on the finite element method which allows to reproduce the effects of microscopic conduction barriers caused by the presence of uncoupling structures without actually resolving these structures in a high resolution mesh, thereby reducing the computational costs significantly.

A 2D-computer model of atrial tissue based on histographs describes the electro-anatomical impact of microstructure on endocardiac potentials and electric near-fields.

In experiments with cardiac tissue, local conduction is described by waveform analysis of the derivative of the extracellular potential Φ(e) and by the loop morphology of the near-field strength E (the components of the electric field parallel and very close to the tissue surface). The question arises whether the features of these signals can be used to quantify the degree of fibrosis in the heart. A computer model allows us to study the behavior of electric signals at the endocardium with respect to known configurations of microstructure which can not be detected during the electrophysiological experiments. This work presents a 2D-computer model with sub-cellular resolution of atrial micro-conduction in the rabbit heart. It is based on the monodomain equations and digitized histographs from tissue slices obtained post-experimentum. It could be shown that excitation spread in densely coupled regions produces uniform and anisotropic conduction. In contrast, zones with parallel fibers separated by uncoupling interstitial space or connective tissue may show uniform or complex signals depending on pacing site. These results suggest that the analysis of Φ(e) and E combined with multi-site pacing could be used to characterize the type and the size of fibrosis.

Automatically generated, anatomically accurate meshes for cardiac electrophysiology problems.

Significant advancements in imaging technology and the dramatic increase in computer power over the last few years broke the ground for the construction of anatomically realistic models of the heart at an unprecedented level of detail. To effectively make use of high-resolution imaging datasets for modeling purposes, the imaged objects have to be discretized. This procedure is trivial for structured grids. However, to develop generally applicable heart models, unstructured grids are much preferable. In this study, a novel image-based unstructured mesh generation technique is proposed. It uses the dual mesh of an octree applied directly to segmented 3-D image stacks. The method produces conformal, boundary-fitted, and hexahedra-dominant meshes. The algorithm operates fully automatically with no requirements for interactivity and generates accurate volume-preserving representations of arbitrarily complex geometries with smooth surfaces. The method is very well suited for cardiac electrophysiological simulations. In the myocardium, the algorithm minimizes variations in element size, whereas in the surrounding medium, the element size is grown larger with the distance to the myocardial surfaces to reduce the computational burden. The numerical feasibility of the approach is demonstrated by discretizing and solving the monodomain and bidomain equations on the generated grids for two preparations of high experimental relevance, a left ventricular wedge preparation, and a papillary muscle.

Accuracy of local conduction velocity determination from non-fractionated cardiac activation signals.

Local velocity and direction of cardiac excitation spread can be estimated from four extra-cellular electric potential waveforms recorded simultaneously by closely-spaced electrodes. In this work, three methods for the determination of these parameters in case of non-fractionated electrograms were compared. Waveforms recorded during in-vitro experiments were analyzed in terms of their noise components. Noise according to the experimental environment was generated and added to noise-free waveforms obtained from computer simulations. For each of the three investigated methods the accuracy of the determined parameters velocity and direction was evaluated for three different noise levels and three types of propagation.

Oblique propagation of activation allows the detection of uncoupling microstructures from cardiac near field behavior.

Wave fronts of cardiac activation, when propagating oblique to the fiber axis, reveal small fractionations and distortions in extracellular potential waveforms Phi(e) as well as in parameters derived from Phi(e) like dPhi(e)/dt and the gradient of Phi(e), the cardiac near field E. dPhi(e)/dt shows multiple deflections and E changes its morphology forming abnormal or even two or multiple subsequent loops. We analyze segments of such irregular loops of E obtained from in-vitro experiments and from computer simulation of a 2D-tissue sheet with a longitudinal oriented obstacle. In computer simulations we found that the individual sections of E reflect fairly well individual pathways of activation separated and delayed by the presence of a structural obstacle similar to connective tissue embedded longitudinally in heart tissue. Electrophysiological experiments with papillary muscles confirm this near field behavior.

Contributions of Purkinje-myocardial coupling to suppression and facilitation of early afterdepolarization-induced triggered activity.

Electrical loading by ventricular myocardium modulates conduction system repolarization near Purkinje-ventricular junctions (PVJs). We investigated how that loading suppresses and facilitates early afterdepolarizations (EADs) under conditions where there is a high degree of functional coupling between tissue types, which is consistent with the anatomic arrangement at the peripheral conduction system-myocardial interface. Experiments were completed in eight rabbit right ventricular (RV) free wall preparations. Free-running Purkinje strands were locally superfused, and action potentials were recorded from strands. RV free walls were bathed in normal solution. Surface electrograms were recorded near strand insertions into downstream free wall myocardium. Detailed histology was performed to assemble a computer model with interspersed Purkinje and ventricular myocytes weakly coupled throughout the region. Delays from Purkinje upstrokes to downstream peripheral conduction system and myocardial activation were comparable between experiments and simulations, supporting model node-to-node electrical coupling, i.e., the functional coupling. Purkinje action potential duration (APD) prolongation with localized isoproterenol in experiments and calcium current enhancement in simulations failed to establish EADs. With myocardial APD prolongation by delayed rectifier potassium current inhibition or L-type calcium current enhancement accompanying Purkinje APD prolongation in simulations, however, EAD-induced triggered activity developed. Collectively, our findings suggest competing contributions of the myocardial sink when there is a high degree of functional coupling between tissue types, with the transition from suppression to facilitation of EAD-induced triggered activity depending critically upon myocardial APD prolongation.