A Matched-Filter-Based Algorithm for Subcellular Classification of T-System in Cardiac Tissues.

In mammalian ventricular cardiomyocytes, invaginations of the surface membrane form the transverse tubular system (T-system), which consists of transverse tubules (TTs) that align with sarcomeres and Z-lines as well as longitudinal tubules (LTs) that are present between Z-lines in some species. In many cardiac disease etiologies, the T-system is perturbed, which is believed to promote spatially heterogeneous, dyssynchronous Ca2+ release and inefficient contraction. In general, T-system characterization approaches have been directed primarily at isolated cells and do not detect subcellular T-system heterogeneity. Here, we present MatchedMyo, a matched-filter-based algorithm for subcellular T-system characterization in isolated cardiomyocytes and millimeter-scale myocardial sections. The algorithm utilizes "filters" representative of TTs, LTs, and T-system absence. Application of the algorithm to cardiomyocytes isolated from rat disease models of myocardial infarction (MI), dilated cardiomyopathy induced via aortic banding, and sham surgery confirmed and quantified heterogeneous T-system structure and remodeling. Cardiomyocytes from post-MI hearts exhibited increasing T-system disarray as proximity to the infarct increased. We found significant (p < 0.05, Welch's t-test) increases in LT density within cardiomyocytes proximal to the infarct (12 ± 3%, data reported as mean ± SD, n = 3) versus sham (4 ± 2%, n = 5), but not distal to the infarct (7 ± 1%, n = 3). The algorithm also detected decreases in TTs within 5° of the myocyte minor axis for isolated aortic banding (36 ± 9%, n = 3) and MI cardiomyocytes located intermediate (37 ± 4%, n = 3) and proximal (34 ± 4%, n = 3) to the infarct versus sham (57 ± 12%, n = 5). Application of bootstrapping to rabbit MI tissue revealed distal sections comprised 18.9 ± 1.0% TTs, whereas proximal sections comprised 10.1 ± 0.8% TTs (p < 0.05), a 46.6% decrease. The matched-filter approach therefore provides a robust and scalable technique for T-system characterization from isolated cells through millimeter-scale myocardial sections.

Confocal microscopy-based estimation of intracellular conductivities in myocardium for modeling of the normal and infarcted heart.

Ventricular arrhythmias are the leading cause of mortality in patients with ischemic heart diseases, such as myocardial infarction (MI). Computational simulation of cardiac electrophysiology provides insights into these arrhythmias and their treatment. However, only sparse information is available on crucial model parameters, for instance, the anisotropic intracellular electrical conductivities. Here, we introduced an approach to estimate these conductivities in normal and MI hearts. We processed and analyzed images from confocal microscopy of left ventricular tissue of a rabbit MI model to generate 3D reconstructions. We derived tissue features including the volume fraction of myocytes (Vmyo), gap junctions-containing voxels (Vgj), and fibrosis (Vfibrosis). We generated models of the intracellular space and intercellular coupling. Applying numerical methods for solving Poisson's equation for stationary electrical currents, we calculated normal (σmyo,n), longitudinal (σmyo,l), and transverse (σmyo,t) intracellular conductivities. Using linear regression analysis, we assessed relationships of conductivities to tissue features. Vgj and Vmyo were reduced in MI vs. control, but Vfibrosis was increased. Both σmyo,l and σmyo,n were lower in MI than in control. Differences of σmyo,t between control and MI were not significant. We found strong positive relationships of σmyo,l with Vmyo and Vgj, and a strong negative relationship with Vfibrosis. The relationships of σmyo,n with these tissue features were similar but less pronounced. Our study provides quantitative insights into the intracellular conductivities in the normal and MI heart. We suggest that our study establishes a framework for the estimation of intracellular electrical conductivities of myocardium with various pathologies.

Etiology-Specific Remodeling in Ventricular Tissue of Heart Failure Patients and Its Implications for Computational Modeling of Electrical Conduction.

With an estimated 64.3 million cases worldwide, heart failure (HF) imposes an enormous burden on healthcare systems. Sudden death from arrhythmia is the major cause of mortality in HF patients. Computational modeling of the failing heart provides insights into mechanisms of arrhythmogenesis, risk stratification of patients, and clinical treatment. However, the lack of a clinically informed approach to model cardiac tissues in HF hinders progress in developing patient-specific strategies. Here, we provide a microscopy-based foundation for modeling conduction in HF tissues. We acquired 2D images of left ventricular tissues from HF patients (n = 16) and donors (n = 5). The composition and heterogeneity of fibrosis were quantified at a sub-micrometer resolution over an area of 1 mm2. From the images, we constructed computational bidomain models of tissue electrophysiology. We computed local upstroke velocities of the membrane voltage and anisotropic conduction velocities (CV). The non-myocyte volume fraction was higher in HF than donors (39.68 ± 14.23 vs. 22.09 ± 2.72%, p < 0.01), and higher in ischemic (IC) than nonischemic (NIC) cardiomyopathy (47.2 ± 16.18 vs. 32.16 ± 6.55%, p < 0.05). The heterogeneity of fibrosis within each subject was highest for IC (27.1 ± 6.03%) and lowest for donors (7.47 ± 1.37%) with NIC (15.69 ± 5.76%) in between. K-means clustering of this heterogeneity discriminated IC and NIC with an accuracy of 81.25%. The heterogeneity in CV increased from donor to NIC to IC tissues. CV decreased with increasing fibrosis for longitudinal (R 2 = 0.28, p < 0.05) and transverse conduction (R 2 = 0.46, p < 0.01). The tilt angle of the CV vectors increased 2.1° for longitudinal and 0.91° for transverse conduction per 1% increase in fibrosis. Our study suggests that conduction fundamentally differs in the two etiologies due to the characteristics of fibrosis. Our study highlights the importance of the etiology-specific modeling of HF tissues and integration of medical history into electrophysiology models for personalized risk stratification and treatment planning.

Extended Bidomain Modeling of Defibrillation: Quantifying Virtual Electrode Strengths in Fibrotic Myocardium.

Defibrillation is a well-established therapy for atrial and ventricular arrhythmia. Here, we shed light on defibrillation in the fibrotic heart. Using the extended bidomain model of electrical conduction in cardiac tissue, we assessed the influence of fibrosis on the strength of virtual electrodes caused by extracellular electrical current. We created one-dimensional models of rabbit ventricular tissue with a central patch of fibrosis. The fibrosis was incorporated by altering volume fractions for extracellular, myocyte and fibroblast domains. In our prior work, we calculated these volume fractions from microscopic images at the infarct border zone of rabbit hearts. An average and a large degree of fibrosis were modeled. We simulated defibrillation by application of an extracellular current for a short duration (5 ms). We explored the effects of myocyte-fibroblast coupling, intra-fibroblast conductivity and patch length on the strength of the virtual electrodes present at the borders of the normal and fibrotic tissue. We discriminated between effects on myocyte and fibroblast membranes at both borders of the patch. Similarly, we studied defibrillation in two-dimensional models of fibrotic tissue. Square and disk-like patches of fibrotic tissue were embedded in control tissue. We quantified the influence of the geometry and fibrosis composition on virtual electrode strength. We compared the results obtained with a square and disk shape of the fibrotic patch with results from the one-dimensional simulations. Both, one- and two-dimensional simulations indicate that extracellular current application causes virtual electrodes at boundaries of fibrotic patches. A higher degree of fibrosis and larger patch size were associated with an increased strength of the virtual electrodes. Also, patch geometry affected the strength of the virtual electrodes. Our simulations suggest that increased fibroblast-myocyte coupling and intra-fibroblast conductivity reduce virtual electrode strength. However, experimental data to constrain these modeling parameters are limited and thus pinpointing the magnitude of the reduction will require further understanding of electrical coupling of fibroblasts in native cardiac tissues. We propose that the findings from our computational studies are important for development of patient-specific protocols for internal defibrillators.

Confocal Microscopy-Based Estimation of Parameters for Computational Modeling of Electrical Conduction in the Normal and Infarcted Heart.

Computational modeling is an important tool to advance our knowledge on cardiac diseases and their underlying mechanisms. Computational models of conduction in cardiac tissues require identification of parameters. Our knowledge on these parameters is limited, especially for diseased tissues. Here, we assessed and quantified parameters for computational modeling of conduction in cardiac tissues. We used a rabbit model of myocardial infarction (MI) and an imaging-based approach to derive the parameters. Left ventricular tissue samples were obtained from fixed control hearts (animals: 5) and infarcted hearts (animals: 6) within 200 µm (region 1), 250-750 µm (region 2) and 1,000-1,250 µm (region 3) of the MI border. We assessed extracellular space, fibroblasts, smooth muscle cells, nuclei and gap junctions by a multi-label staining protocol. With confocal microscopy we acquired three-dimensional (3D) image stacks with a voxel size of 200 × 200 × 200 nm. Image segmentation yielded 3D reconstructions of tissue microstructure, which were used to numerically derive extracellular conductivity tensors. Volume fractions of myocyte, extracellular, interlaminar cleft, vessel and fibroblast domains in control were (in %) 65.03 ± 3.60, 24.68 ± 3.05, 3.95 ± 4.84, 7.71 ± 2.15, and 2.48 ± 1.11, respectively. Volume fractions in regions 1 and 2 were different for myocyte, myofibroblast, vessel, and extracellular domains. Fibrosis, defined as increase in fibrotic tissue constituents, was (in %) 21.21 ± 1.73, 16.90 ± 9.86, and 3.58 ± 8.64 in MI regions 1, 2, and 3, respectively. For control tissues, image-based computation of longitudinal, transverse and normal extracellular conductivity yielded (in S/m) 0.36 ± 0.11, 0.17 ± 0.07, and 0.1 ± 0.06, respectively. Conductivities were markedly increased in regions 1 (+75, +171, and +100%), 2 (+53, +165, and +80%), and 3 (+42, +141, and +60%). Volume fractions of the extracellular space including interlaminar clefts strongly correlated with conductivities in control and MI hearts. Our study provides novel quantitative data for computational modeling of conduction in normal and MI hearts. Notably, our study introduces comprehensive statistical information on tissue composition and extracellular conductivities on a microscopic scale in the MI border zone. We suggest that the presented data fill a significant gap in modeling parameters and extend our foundation for computational modeling of cardiac conduction.