Stress-Swelling Finite Element Modeling of Cervical Response With Homeostatic Collagen Fiber Distributions

Abstract

During pregnancy, the cervix experiences significant mechanical property change due to tissue swelling, and to ongoing changes in the collagen content. In this paper, we model how these two effects contribute to cervical deformation as the pressure load on top of the cervix increases. The cervix and its surrounding supporting ligaments are taken into consideration in the resulting mechanical analysis. The cervix itself is treated as a multilayered tube-like structure, with layer-specific collagen orientation. The cervical tissue in each layer is treated in terms of a collagen constituent that remodels with time within a ground substance matrix that experiences swelling. The load and swelling are taken to change sufficiently slowly so that the collagen properties at any instant can be regarded as being in a state of homeostasis. Among other things, the simulations show how the luminal cross-sectional area varies along its length as a function of pressure and swelling. In general, an increase in pressure causes an overall shortening of the lumen while an increase in swelling has the opposite effect.

Growth-profile configuration for specific deformations of tubular organs: A study of growth-induced thinning and dilation of the human cervix

“…The size of the cervix from each woman was different, and the average of these data is employed as the geometrical parameters of the cervix in this article; more particularly, R 1 = 4 mm, R 2 = 8 mm, R 3 = 16 mm, and R 4 = 20 mm. The cervical length is 50 mm [ 19 , 38 ], but is unchanged according to the deformation defined in Eq (5) . For the stiffness parameters [ 19 , 58 ], μ = 1650 Pa, and γ = 1000 Pa (estimated).…”

“…The cervical length is 50 mm [ 19 , 38 ], but is unchanged according to the deformation defined in Eq (5) . For the stiffness parameters [ 19 , 58 ], μ = 1650 Pa, and γ = 1000 Pa (estimated). To elucidate how cervical wall thinning and dilation are associated with the growth parameters g r , g θ , and g z , we study the deformation results for isotropic growth ( g r = g θ = g z ) and anisotropic growth by varying one growth parameter while fixing the other two parameters.…”

Bulging initiation and propagation in fiber-reinforced swellable Mooney–Rivlin membranes

“…The first two terms on the right-hand side of ( 18) define the isotropic behavior of the ground substance material, in which the fibers are embedded, and they describe a swellable modification of the classical Mooney-Rivlin material (see, e.g., [16]). The material parameters μ 1 and μ 2 are taken to be independent of the swelling, and we refer to works such as [24,25] that discuss the changes of the material stiffness with the amount of swelling. The last two terms on the right-hand side of equation ( 18) account for the anisotropic material behavior due to the two fiber families.…”

“…In this case, the strain energy density function is formulated in terms of both I 4 and I 5 . Figure 7 shows combinations for k 1 ≥ 0 and k 2 ≥ 0 that fulfill the bulging condition (20) for λ = 2 with f I 1 given by (21a), f I 2 = 0, and f I 4 and f I 5 given by (25) and (26), respectively, with λ z = 1.1, three swelling values v = 1, v = 1.1, and v = 1.2 and different values of β. Fiber winding angle values β = π/6 and β = π/4 are used in Fig.…”

“…The recent work by Topol et al [24] models the interaction between soft tissue swelling of a ground substance material and strain stabilization of collagenous fiber to enzymatic degradation. This effect has been further investigated in the finite element study by Gou et al [25] for fiber remodeling homeostasis in swelling cervical soft tissue. The recent works by Demirkoparan and Merodio [12,26] study the swelling-induced bulging in hyperelastic fibrous tubes.…”