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

Abstract

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.

Keywords: cardiac modeling; cardiac tissue; electrical conduction; myocardial infarction; tissue conductivity.

Figure 1

Distribution of (A) WGA, (E) DAPI, (I) Cx43, (M) α-SMA, and (Q) vimentin in a single slice of an image stack from MI heart. Scar to region farthest from scar is shown from left to right. Zoom-in of regions identified in panel (A) are shown for each channel. Scale bar in (A) 50 μm. Applies to (E,I,M,Q). Scale bar in (B) 20 μm. Applies to (C,D, F–H, J–L, N–P, R–T).

Figure 2

Intensity profiles of DAPI, Cx43, WGA, α-SMA, and vimentin through MI to MI border zone to distal tissue. The profiles were generated from the image stacks represented in Figure 1.

Figure 3

3D reconstruction of control myocardium with (A) cardiomyocytes, (B) complementary tissue constituents, (C) extracellular space, (D) fibroblasts, and (E) vessels. Volume fractions of tissue constituents are shown in (F). The reconstruction has a size of 204.8 × 204.8 × 41.2 μm.

Figure 4

3D reconstruction of tissue in region 1 with (A) cardiomyocytes, (B) complementary tissue constituents, (C) extracellular space, (D) fibroblasts, (E) myofibroblasts, and (F) vessels. Volume fractions of tissue constituents are shown in (G). The reconstruction has a size of 204.8 × 204.8 × 41.2 μm.

Figure 5

3D reconstruction of tissue in region 3 with (A) cardiomyocytes, (B) complementary tissue constituents, (C) extracellular space, (D) fibroblasts, (E) myofibroblasts, and (F) vessels. Volume fractions of tissue constituents are shown in (G). The reconstruction has a size of 204.8 × 204.8 × 41.2 μm.

Figure 6

Pie charts of volume fractions in (A) control, (B) region 1, (C) region 2, and (D) region 3. For statistical information and significance of differences see Table 1.

Figure 7

Evaluation of fibrosis. (A) Sum of fractional volumes of domains contributing to fibrosis. (B) Degree of fibrosis in proximal, adjacent and distal regions to the MI calculated based on Equation (1). Brackets mark significant differences between groups.

Figure 8

Image-based computation of extracellular conductivity tensor for control tissue. 3D-reconstructions of the extracellular space with modeled electrodes for applying voltages in (A) x, (B) y, and (C) z-direction. Only half of the image stacks is shown. (D–F) Calculated potential distribution corresponding to (A–C). (G–I) Calculated current density corresponding to (D–F).

Figure 9

Image-based computation of extracellular conductivity tensor for tissue in region 1. 3D-reconstructions of the extracellular space with modeled electrodes for applying voltages in (A) x, (B) y, and (C) z-direction. Only half of the image stacks is shown. (D–F) Calculated potential distribution corresponding to (A–C). (G–I) Calculated current density corresponding to (D–F).

Figure 10

Image-based computation of extracellular conductivity tensor for tissue in region 3. 3D-reconstructions of the extracellular space with modeled electrodes for applying voltages in (A) x, (B) y, and (C) z-direction. Only half of the image stacks is shown. (D–F) Calculated potential distribution corresponding to (A–C). (G–I) Calculated current density corresponding to (D–F).

Figure 11

Statistical analyses of the relationship between volume fractions of tissue constituents and calculated conductivities. Each symbol represents an image-based computation of conductivity. Linear regression modeled the relationship between V_e and (A) σ_e,l, (B) σ_e,t and (C) σ_e,n, V_e–V_cleft and (D) σ_e,l, (E) σ_e,t and (F) σ_e,n as well as between V_cleft and (G) σ_e,l, (H) σ_e,t, and (I) σ_e,n.