Gregory B. Sands

Three-dimensional transmural organization of perimysial collagen in the heart

There is strong support for the view that the ventricular myocardium has a laminar organization in which myocytes are grouped into branching layers separated by cleavage planes. However, understanding of the extent and functional implications of this architecture has been limited by the lack of a systematic three-dimensional description of the organization of myocytes and associated perimysial collagen. We imaged myocytes and collagen across the left ventricular wall at high resolution in seven normal rat hearts using extended volume confocal microscopy. We developed novel reconstruction and segmentation techniques necessary for the quantitative analysis of three-dimensional myocyte and perimysial collagen organization. The results confirm that perimysial collagen has an ordered arrangement and that it defines a laminar organization. Perimysial collagen is composed of three distinct forms: extensive meshwork on laminar surfaces, convoluted fibers connecting adjacent layers, and longitudinal cords. While myolaminae are the principal form of structural organization throughout most of the wall, they are not seen in the subepicardium, where perimysial collagen is present only as longitudinal cords.

Laminar arrangement of ventricular myocytes influences electrical behavior of the heart.

The response of the heart to electrical shock, electrical propagation in sinus rhythm, and the spatiotemporal dynamics of ventricular fibrillation all depend critically on the electrical anisotropy of cardiac tissue. A long-held view of cardiac electrical anisotropy is that electrical conductivity is greatest along the myocyte axis allowing most rapid propagation of electrical activation in this direction, and that conductivity is isotropic transverse to the myocyte axis supporting a slower uniform spread of activation in this plane. In this context, knowledge of conductivity in two directions, parallel and transverse to the myofiber axis, is sufficient to characterize the electrical action of the heart. Here we present new experimental data that challenge this view. We have used a novel combination of intramural electrical mapping, and experiment-specific computer modeling, to demonstrate that left ventricular myocardium has unique bulk conductivities associated with three microstructurally-defined axes. We show that voltage fields induced by intramural current injection are influenced by not only myofiber direction, but also the transmural arrangement of muscle layers or myolaminae. Computer models of these experiments, in which measured 3D tissue structure was reconstructed in-silico, best matched recorded voltages with conductivities in the myofiber direction, and parallel and normal to myolaminae, set in the ratio 4:2:1, respectively. These findings redefine cardiac tissue as an electrically orthotropic substrate and enhance our understanding of how external shocks may act to successfully reset the fibrillating heart into a uniform electrical state. More generally, the mechanisms governing the destabilization of coordinated electrical propagation into ventricular arrhythmia need to be evaluated in the light of this discovery.

Three Distinct Directions of Intramural Activation Reveal Nonuniform Side-to-Side Electrical Coupling of Ventricular Myocytes

Background—The anisotropy of cardiac tissue is a key determinant of 3D electric propagation and the stability of activation wave fronts in the heart. The electric properties of ventricular myocardium are widely assumed to be axially anisotropic, with activation propagating most rapidly in the myofiber direction and at uniform velocity transverse to this. We present new experimental evidence that contradicts this view. Methods and Results—For the first time, high-density intramural electric mapping (325 electrodes at ≈4×4×1-mm spacing) from pig left ventricular tissue was used to reconstruct 3D paced activation surfaces projected directly onto 3D tissue structure imaged throughout the same left ventricular volume. These data from 5 hearts demonstrate that ventricular tissue is electrically orthotropic with 3 distinct propagation directions that coincide with local microstructural axes defined by the laminar arrangement of ventricular myocytes. The maximum conduction velocity of 0.67±0.019 ms−1 was aligned with the myofiber axis. However, transverse to this, the maximum conduction velocity was 0.30±0.010 ms−1, parallel to the myocyte layers and 0.17±0.004 ms−1 normal to them. These orthotropic conduction velocities give rise to preferential activation pathways across the left ventricular free wall that are not captured by structurally detailed computer models, which incorporate axially anisotropic electric properties. Conclusions—Our findings suggest that current views on uniform side-to-side electric coupling in the heart need to be revised. In particular, nonuniform laminar myocardial architecture and associated electric orthotropy should be included in future models of initiation and maintenance of ventricular arrhythmia.

A deformable finite element derived finite difference method for cardiac activation problems.

AbstractWe present a finite element (FE) derived finite difference (FD) technique for solving cardiac activation problems over deforming geometries using a bidomain framework. The geometry of the solution domain is defined by a FE mesh and over these FEs a high resolution FD mesh is generated. The difference points are located at regular intervals in the normalized material space within each of the FEs. The bidomain equations are then transformed to the embedded FD mesh which provides a solution space that is both regular and orthogonal. The solution points move in physical space with any deformation of the solution domain, but the equations are set up in such a way that the solution is invariant as it is constructed in material space. The derivation of this new solution technique is presented along with a series of examples that demonstrate the accuracy of this bidomain framework.

An image-based model of atrial muscular architecture: Effects of structural anisotropy on electrical activation

Background— Computer models that capture key features of the heterogeneous myofiber architecture of right and left atria and interatrial septum provide a means of investigating the mechanisms responsible for atrial arrhythmia. The data necessary to implement such models have not previously been available. The aims of this study were to characterize surface geometry and myofiber architecture throughout the atrial chambers and to investigate the effects of this structure on atrial activation. Methods and Results— Atrial surface geometry and myofiber orientations were reconstructed in 3D at 50×50×50-&mgr;m3 resolution from serial images acquired throughout the sheep atrial chambers. Myofiber orientations were determined by Eigen-analysis of the structure tensor. These data have been incorporated into an anatomic model that provides the first quantitative representation of myofiber architecture throughout the atrial chambers. By simulating activation on this 3D structure, we have confirmed the roles of specialized myofiber tracts such as the crista terminalis, pectinate muscles, and the Bachman bundle on the spread of activation from the sinus node. We also demonstrate how the complex myocyte arrangement in the posterior left atrium contributes to activation time dispersion adjacent to the pulmonary veins and increased vulnerability to rhythm disturbance generated by ectopic stimuli originating in the pulmonary vein sleeves. Conclusions— We have developed a structurally detailed, image-based model of atrial anatomy that provides deeper understanding of the role that myocyte architecture plays in normal and abnormal atrial electric function.Background— Computer models that capture key features of the heterogeneous myofiber architecture of right and left atria and interatrial septum provide a means of investigating the mechanisms responsible for atrial arrhythmia. The data necessary to implement such models have not previously been available. The aims of this study were to characterize surface geometry and myofiber architecture throughout the atrial chambers and to investigate the effects of this structure on atrial activation. Methods and Results— Atrial surface geometry and myofiber orientations were reconstructed in 3D at 50×50×50-μm3 resolution from serial images acquired throughout the sheep atrial chambers. Myofiber orientations were determined by Eigen-analysis of the structure tensor. These data have been incorporated into an anatomic model that provides the first quantitative representation of myofiber architecture throughout the atrial chambers. By simulating activation on this 3D structure, we have confirmed the roles of specialized myofiber tracts such as the crista terminalis, pectinate muscles, and the Bachman bundle on the spread of activation from the sinus node. We also demonstrate how the complex myocyte arrangement in the posterior left atrium contributes to activation time dispersion adjacent to the pulmonary veins and increased vulnerability to rhythm disturbance generated by ectopic stimuli originating in the pulmonary vein sleeves. Conclusions— We have developed a structurally detailed, image-based model of atrial anatomy that provides deeper understanding of the role that myocyte architecture plays in normal and abnormal atrial electric function.

High-Resolution 3-Dimensional Reconstruction of the Infarct Border Zone Impact of Structural Remodeling on Electrical Activation

Rationale: Slow nonuniform electric propagation in the border zone (BZ) of a healed myocardial infarct (MI) can give rise to reentrant arrhythmia. The extent to which this is influenced by structural rather than cellular electric remodeling is unclear. Objective: To determine whether structural remodeling alone in the infarct BZ could provide a substrate for re-entry by (i) characterizing the 3-dimensional (3D) structure of the myocardium surrounding a healed MI at high spatial resolution and (ii) modeling electric activation on this structure. Methods and Results: Anterior left ventricular (LV) infarcts were induced in 2 rats by coronary artery ligation. Three-dimensional BZ volume (4.1 mm3 and 5.6 mm3) were imaged at 14 days using confocal microscopy. Viable myocytes were identified, and their connectivity and orientation were quantified. Preserved cell networks were observed in the subendocardium and subepicardium of the infarct. Myocyte tracts traversed the BZ, and there was heavy infiltration of collagen into the adjacent myocardium. Myocyte connectivity decreased by ≈65% over 250 &mgr;m across the BZ. This structure was incorporated into 3D network models on which activation was simulated using Luo–Rudy membrane dynamics assuming normal cellular electric properties. Repetitive stimulation was imposed at selected BZ sites. Stimulus site-specific unidirectional propagation occurred in the BZ with rate-dependent slowing and conduction block, and reentry was demonstrated in one substrate. Activation times were prolonged because of tract path length and local slowing. Conclusions: We have used a detailed image-based model of the infarct BZ to demonstrate that structural heterogeneity provides a dynamic substrate for electric reentry.Rationale: Slow nonuniform electric propagation in the border zone (BZ) of a healed myocardial infarct (MI) can give rise to reentrant arrhythmia. The extent to which this is influenced by structural rather than cellular electric remodeling is unclear. Objective: To determine whether structural remodeling alone in the infarct BZ could provide a substrate for re-entry by (i) characterizing the 3-dimensional (3D) structure of the myocardium surrounding a healed MI at high spatial resolution and (ii) modeling electric activation on this structure. Methods and Results: Anterior left ventricular (LV) infarcts were induced in 2 rats by coronary artery ligation. Three-dimensional BZ volume (4.1 mm3 and 5.6 mm3) were imaged at 14 days using confocal microscopy. Viable myocytes were identified, and their connectivity and orientation were quantified. Preserved cell networks were observed in the subendocardium and subepicardium of the infarct. Myocyte tracts traversed the BZ, and there was heavy infiltration of collagen into the adjacent myocardium. Myocyte connectivity decreased by ≈65% over 250 μm across the BZ. This structure was incorporated into 3D network models on which activation was simulated using Luo–Rudy membrane dynamics assuming normal cellular electric properties. Repetitive stimulation was imposed at selected BZ sites. Stimulus site-specific unidirectional propagation occurred in the BZ with rate-dependent slowing and conduction block, and reentry was demonstrated in one substrate. Activation times were prolonged because of tract path length and local slowing. Conclusions: We have used a detailed image-based model of the infarct BZ to demonstrate that structural heterogeneity provides a dynamic substrate for electric reentry. # Novelty and Significance {#article-title-38}

Cardiac electrophysiology and tissue structure: bridging the scale gap with a joint measurement and modelling paradigm

Significant tissue structures exist in cardiac ventricular tissue that are of supracellular dimension. It is hypothesized that these tissue structures contribute to the discontinuous spread of electrical activation, may contribute to arrhymogenesis and also provide a substrate for effective cardioversion. However, the influences of these mesoscale tissue structures in intact ventricular tissue are difficult to understand solely on the basis of experimental measurement. Current measurement technology is able to record at both the macroscale tissue level and the microscale cellular or subcellular level, but to date it has not been possible to obtain large volume, direct measurements at the mesoscales. To bridge this scale gap in experimental measurements, we use tissue‐specific structure and mathematical modelling. Our models have enabled us to consider key hypotheses regarding discontinuous activation. We also consider the future developments of our intact tissue experimental programme.

High-Resolution 3-Dimensional Reconstruction of the Infarct Border Zone

Rationale: Slow nonuniform electric propagation in the border zone (BZ) of a healed myocardial infarct (MI) can give rise to reentrant arrhythmia. The extent to which this is influenced by structural rather than cellular electric remodeling is unclear. Objective: To determine whether structural remodeling alone in the infarct BZ could provide a substrate for re-entry by (i) characterizing the 3-dimensional (3D) structure of the myocardium surrounding a healed MI at high spatial resolution and (ii) modeling electric activation on this structure. Methods and Results: Anterior left ventricular (LV) infarcts were induced in 2 rats by coronary artery ligation. Three-dimensional BZ volume (4.1 mm3 and 5.6 mm3) were imaged at 14 days using confocal microscopy. Viable myocytes were identified, and their connectivity and orientation were quantified. Preserved cell networks were observed in the subendocardium and subepicardium of the infarct. Myocyte tracts traversed the BZ, and there was heavy infiltration of collagen into the adjacent myocardium. Myocyte connectivity decreased by ≈65% over 250 &mgr;m across the BZ. This structure was incorporated into 3D network models on which activation was simulated using Luo–Rudy membrane dynamics assuming normal cellular electric properties. Repetitive stimulation was imposed at selected BZ sites. Stimulus site-specific unidirectional propagation occurred in the BZ with rate-dependent slowing and conduction block, and reentry was demonstrated in one substrate. Activation times were prolonged because of tract path length and local slowing. Conclusions: We have used a detailed image-based model of the infarct BZ to demonstrate that structural heterogeneity provides a dynamic substrate for electric reentry.Rationale: Slow nonuniform electric propagation in the border zone (BZ) of a healed myocardial infarct (MI) can give rise to reentrant arrhythmia. The extent to which this is influenced by structural rather than cellular electric remodeling is unclear. Objective: To determine whether structural remodeling alone in the infarct BZ could provide a substrate for re-entry by (i) characterizing the 3-dimensional (3D) structure of the myocardium surrounding a healed MI at high spatial resolution and (ii) modeling electric activation on this structure. Methods and Results: Anterior left ventricular (LV) infarcts were induced in 2 rats by coronary artery ligation. Three-dimensional BZ volume (4.1 mm3 and 5.6 mm3) were imaged at 14 days using confocal microscopy. Viable myocytes were identified, and their connectivity and orientation were quantified. Preserved cell networks were observed in the subendocardium and subepicardium of the infarct. Myocyte tracts traversed the BZ, and there was heavy infiltration of collagen into the adjacent myocardium. Myocyte connectivity decreased by ≈65% over 250 μm across the BZ. This structure was incorporated into 3D network models on which activation was simulated using Luo–Rudy membrane dynamics assuming normal cellular electric properties. Repetitive stimulation was imposed at selected BZ sites. Stimulus site-specific unidirectional propagation occurred in the BZ with rate-dependent slowing and conduction block, and reentry was demonstrated in one substrate. Activation times were prolonged because of tract path length and local slowing. Conclusions: We have used a detailed image-based model of the infarct BZ to demonstrate that structural heterogeneity provides a dynamic substrate for electric reentry. # Novelty and Significance {#article-title-38}

Image-Based Model of Atrial Anatomy and Electrical Activation: A Computational Platform for Investigating Atrial Arrhythmia

Computer models provide a powerful platform for investigating mechanisms that underlie atrial rhythm disturbances. We have used novel techniques to build a structurally-detailed, image-based model of 3-D atrial anatomy. A volume image of the atria from a normal sheep heart was acquired using serial surface macroscopy, then smoothed and down-sampled to 50 μm3 resolution. Atrial surface geometry was identified and myofiber orientations were estimated throughout by eigen-analysis of the 3-D image structure tensor. Sinus node, crista terminalis, pectinate muscle, Bachmans bundle, and pulmonary veins were segmented on the basis of anatomic characteristics. Heterogeneous electrical properties were assigned to this structure and electrical activation was simulated on it at 100 μm3 resolution, using both biophysically-detailed and reduced-order cell activation models with spatially-varying membrane kinetics. We confirmed that the model reproduced key features of the normal spread of atrial activation. Furthermore, we demonstrate that vulnerability to rhythm disturbance caused by structural heterogeneity in the posterior left atrium is exacerbated by spatial variation of repolarization kinetics across this region. These results provide insight into mechanisms that may sustain paroxysmal atrial fibrillation. We conclude that image-based computer models that incorporate realistic descriptions of atrial myofiber architecture and electrophysiologic properties have the potential to analyse and identify complex substrates for atrial fibrillation.

Rapid construction of a patient-specific torso model from 3D ultrasound for non-invasive imaging of cardiac electrophysiology

One of the main limitations in using inverse methods for non-invasively imaging cardiac electrical activity in a clinical setting is the difficulty in readily obtaining high-quality data sets to reconstruct accurately a patient-specific geometric model of the heart and torso. This issue was addressed by investigation into the feasibility of using a pseudo-3D ultrasound system and a hand-held laser scanner to reconstruct such a model. This information was collected in under 20 min prior to a catheter ablation or pacemaker study in the electrophysiology laboratory. Using the models created from these data, different activation field maps were computed using several different inverse methods. These were independently validated by comparison of the earliest site of activation with the physical location of the pacing electrodes, as determined from orthogonal fluoroscopy images. With an estimated average geometric error of approximately 8 mm, it was also possible to reconstruct the site of initial activation to within 17.3 mm and obtain a quantitatively realistic activation sequence. The study demonstrates that it is possible rapidly to construct a geometric model that can then be used non-invasively to reconstruct an activation field map of the heart.