Coupled agent‐based and hyperelastic modelling of the left ventricle post‐myocardial infarction

Figures

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  Figure 1. A, The left ventricle (LV) geometry with 28‐mm‐long axis, internal radius of 5 mm and external radius of 10 mm at the base, and a block cut from the LV wall. The ratio between the LV wall thickness and the internal radius is chosen to be 1 following Omens and Fung.20 The basis vectors at the reference configuration are (c 0, l 0, n 0) for local coordinates, where c 0, l 0, and n 0 are the local circumferential, longitudinal, and transmural unit vectors. The basis vectors at the reference configuration are (X, Y, Z) for global Cartesian coordinates, with origin O at the LV apex. B, The fibre structure through the thickness of the LV wall. C, Five longitudinal–circumferential sections through the wall thickness. Collagen fibres lie in the c 0 − l 0 plane

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  Figure 2. The resultant cue that represents the mean fibroblast direction is computed from a weighted combination of all cues (left). The von Mises distribution of the fibroblast orientation (right)

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  Figure 3. The shaded areas show the range of Σ of stretched collagen fibres within −π2<θ<π2 for selected scenarios (dash line denotes I 4 = 1): A, Case 1, C 23 > 0. B, Case 2, C 33 − 1 > 0,Δ ≤ 0. C, Case 2, C 33 − 1 > 0,Δ > 0. D, Case 2, C 33 − 1 < 0,Δ > 0

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  Figure 4. Flowchart for the coupled agent‐based and FE LV model computation. FE, finite element; LV, left ventricle; MI, myocardial infarction

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  Figure 5. The finite element models of A, a transmural circular cryoinfarct with r 0≈5.5 mm and X c = (10.12,2.82,0.81), and B, a transmural elliptical cryoinfarct (with long axis ≈ 15 mm, short axis ≈ 5 mm, and X c = (10.12,2.82,0.81), in the anterior wall

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  Figure 6. Comparison of estimated infarct collagen volume evolution with the measurements16 (black dots with error bars). MI, myocardial infarction

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  Figure 7. The evolution of collagen fibre structure for a circular myocardial infarction (MI): A,‐D, 0, 1, 2 and 3 weeks. E, The overlap of estimated fibre structure with the experimental measurements 5 weeks post‐MI16

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  Figure 8. A, The mean angle for the circular and elliptical myocardial infarctions (MIs). B, The kurtosis of the fibre structure

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  Figure 9. Evolution of the collagen structure at the epicardial surface of the circular infarcted zone. The red lines define the mean angles of the overall fibre structure, while the blue lines indicate the mean fibre vectors over smaller local clusters

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  Figure 10. Evolution of the first principal stress distribution for the circular myocardial infarction (MI); its location is indicated by the arrow. The bottom right‐hand figure is a three‐dimensional (3D) plot at 5 weeks post‐MI

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  Figure 11. Evolution of A, radial stress; B, circumferential stress; C, longitudinal stress, for the circular myocardial infarction (MI)

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  Figure 12. Strain evolution over time: preferential accumulation in the circumferential direction reduces the anisotropy. The predicted strain trends agree reasonably with the experimentally measured strains 5 weeks after cryoinfarction16