A novel constitutive model for passive right ventricular myocardium: evidence for myofiber-collagen fiber mechanical coupling

Abstract

The function of right ventricle (RV) is recognized to play a key role in the development of many cardiopulmonary disorders, such as pulmonary arterial hypertension (PAH). Given the strong link between tissue structure and mechanical behavior, there remains a need for a myocardial constitutive model that accurately accounts for right ventricular myocardium architecture. Moreover, most available myocardial constitutive models approach myocardium at the length scale of mean fiber orientation and do not explicitly account for different fibrous constituents and possible interactions among them. In the present work, we developed a fiber-level constitutive model for the passive mechanical behavior of the right ventricular free wall (RVFW). The model explicitly separates the mechanical contributions of myofiber and collagen fiber ensembles, and accounts for the mechanical interactions between them. To obtain model parameters for the healthy passive RVFW, the model was informed by transmural orientation distribution measurements of myo- and collagen fibers and was fit to the mechanical testing data, where both sets of data were obtained from recent experimental studies on non-contractile, but viable, murine RVFW specimens. Results supported the hypothesis that in the low-strain regime, the behavior of the RVFW is governed by myofiber response alone, which does not demonstrate any coupling between different myofiber ensembles. At higher strains, the collagen fibers and their interactions with myofibers begin to gradually contribute and dominate the behavior as recruitment proceeds. Due to the use of viable myocardial tissue, the contribution of myofibers was significant at all strains with the predicted tensile modulus of [Formula: see text]32 kPa. This was in contrast to earlier reports (Horowitz et al. 1988) where the contribution of myofibers was found to be insignificant. Also, we found that the interaction between myo- and collagen fibers was greatest under equibiaxial strain, with its contribution to the total stress not exceeding 20 %. The present model can be applied to organ-level computational models of right ventricular dysfunction for efficient diagnosis and evaluation of pulmonary hypertension disorder.

Figure 1

(a) Isolated rat heart and right ventricular free wall (RVFW), showing outline of RVFW (blue dots) and square slab excised for histological measurements (dashed lines). (b) An example of Gomori-stained histological section used to quantify fiber orientation angle (pink indicates myofibers.) The histological study was limited within the dashed squared box. The mechanical and histological data were measured in the rectangular Cartesian basis {e₁,e₂,e₃} and $\{{\mathbf{e}}_1^{\prime },{\mathbf{e}}_2^{\prime },{\mathbf{e}}_3^{\prime }\}$, respectively. The directions ${\mathbf{e}}_1^{\prime }$ and ${\mathbf{e}}_3={\mathbf{e}}_3^{\prime }$ are parallel to inter-ventricular septum and normal to the wall, respectively. The directions e₁ and e₂ are approximately aligned with mean fiber and cross-fiber directions, respectively.

Figure 2

A schematic illustration of an ensemble of myo- and collagen fibers with uniform (planar) orientations, characterized by unit vectors n^m and n^c, respectively.

Figure 3

Microscopic images of myocardium. (a) Numerous myofibers (m) and large collagen fibers (colored strands). Note the presence of a dense network of fine collagen fibers (within orange box). Confocal image. (b) Mesh-like arrangement of fine collagen fiber network (m: myfiber lacunae, cl: capillary lacunae). SEM. Bar = 10 µm. From Macchiarelli (2002). (c) Polarized collagen demonstrating undulated structure. Polarized image of picrosirius red stained myocardium.

Figure 4

An example of the collagen fiber ensemble response under equibiaxial loading condition (E_ens = E₁₁ = E₂₂, ${\mathrm{S}}_{\text{ens}}^{\mathrm{c}}={\mathrm{S}}_{11}^{\mathrm{c}}+{\mathrm{S}}_{22}^{\mathrm{c}}$.), and the associated recruitment function.

Figure 5

(a) A representative example of the bicubic Hermite surface that allows us to interpolate the stress values for the equibiaxial loading path (solid line) from other biaxial protocols (markers). (b) A representative example of fitting the myofiber response to the interpolated tissue response in low strain regime under equibiaxial loading condition (E_ens = E₁₁ = E₂₂, S_ens = S₁₁ + S₂₂.)

Figure 6

3D distribution of fiber orientation in RVFW. (a, b) Quantified (planar) orientation distribution for myo- and collagen together with the Beta-distribution fit fiber at ten transmural sections. (c, d) Average surface fit to transmural distributions of myo- and collagen fibers.

Figure 7

Statistical measurements of the fitted transmural distribution for myo- and collagen fibers as functions of the wall depth. (a) Mean. (b) Standard deviation.

Figure 8

A representative fit of our constitutive model to the RVFW response (Specimen No. 1). (a) Results for S₁₁ as functions of E₁₁. (b) Results for S₂₂ as functions of E₂₂. Corresponding biaxial strain protocols are included in Part (b). The stress and strain components are given relative to the basis {e_i} shown in Fig. 1.

Figure 9

Predictions of our constitutive model (quantified only through the interpolated equibiaxial response) for the RVFW response under non-equibiaxial loading protocols (Specimen No. 2). (a) Results for S₁₁ as functions of E₁₁. (b) Results for S₂₂ as functions of E₂₂. Corresponding biaxial strain protocols are included in Part (b).

Figure 10

The effect of including the interaction term in the constitutive model (7) under (nearly) equibiaxial and non-equibiaxial loading conditions. (a) Results for S₁₁ as functions of E₁₁. (b) Results for S₂₂ as functions of E₂₂.

Figure 11

Prediction of our model for contributions of myo- and collagen fibers and interaction among them in the total energy density as function of applied strain under Equibiaxial loading path. Note that each contributions includes the respective volume fraction term as defined in relation (6). The results correspond to the estimated values of Specimen No. 3 in Table 1.

Figure 12

Predictions of our model for contributions of myo- and collagen fibers and interaction among them in the total stress as functions of applied strain. The results correspond to Specimen No. 3 in Table 1. (a, b) Equibiaxial loading path. (c, d) Loading path E₁₁ = 2E₂₂. (e, f) Loading path E₂₂ = 0.5E₁₁.

Figure 13

Contour plots of total potential ${\mathrm{\Psi }}_{\text{ens}}^{\text{Aniso}}({\mathrm{I}}^{\mathrm{m}},{\mathrm{I}}^{\mathrm{c}})$ for material parameters of Specimen No. 3.

Figure 14

Comparisons between the results of our model (incorporating transmural fiber orientation distributions) for stress-strain behavior of the RVFW with the corresponding results based on “average” fiber orientation. The results correspond to the estimated values of Specimen No. 3 in Table 1.