A multiscale discrete fiber model of failure in heterogeneous tissues: Applications to remodeled cerebral aneurysms

Abstract

Damage-accumulation failure models are broadly used to examine tissue property changes caused by mechanical loading. However, damage accumulation models are purely phenomenological. The underlying justification in using this type of model is often that damage occurs to the extracellular fibers and/or cells which changes the fundamental mechanical behavior of the system. In this work, we seek to align damage accumulation models with microstructural models to predict alterations in the mechanical behavior of biological materials that arise from structural heterogeneity associated with nonuniform remodeling of tissues. Further, we seek to extend this multiscale model toward assessing catastrophic failure events such as cerebral aneurysm rupture. First, we demonstrate that a model made up of linear elastin and actin and nonlinear collagen fibers can replicate bot the pre-failure and failure tissue-scale mechanics of uniaxially-stretched cerebral aneurysms. Next, we investigate how mechanical heterogeneities, like those observed in cerebral aneurysms, influence fiber and tissue failure. Notably, we find that failure occurs and the interface between regions of high and low material stiffness, suggesting that spatial mechanical heterogeneity influences aneurysm failure behavior. This model system is a step toward linking structural changes in growth and remodeling to failure properties.

Fig. 1.

A. Representative hexahedral finite element with microstructural network at each Gauss integration point. B. Fiber stress-stretch behavior with ultimate failure indicated with an X.

Fig. 2.

A. Finite element model of uniaxial extension to failure of a representative cerebral aneurysm geometry. B. Heterogeneous local stress field in the sample during stretch. C. Stress-stretch behavior with varied network properties altered by changing the radius of collagen and cytoskeletal stress fibers compared to Robertson, A.M. et al. (2015) for cerebral aneurysm (CA) and normal basilar/internal carotid artery (BA/ICA). The purple, red, and yellow lines are varied fiber radii scales of 0.5, 0.7, and 1.0 respectively. The solid lines are the average behavior and the dashed lines are the traces of every Gauss point network. The data shown in black is experimental data from Robertson, A.M. et al. (2015). The data points are for CA samples with the error bars showing standard deviations. The final point represented as a black X is the failure point of the tissue. Failure strength for the non-aneurysmal basilar artery and internal carotid artery (BA/ICA) is the grey shaded region with the black dashed lines showing the upper and lower standard deviation. When compared to the CA data of Robertson et al, for 1.0×R, r² = −1.62, for 0.7×R, r² = 0.747, and for 0.5×R, r² = 0.674.

Fig. 3.

Representative behavior of cerebral artery model in biaxial extension. A. Initial geometry with material domains defined by the relative radius of collagen and cytoskeletal stress fibers. B. Bulk behavior of flat plate in biaxial extension. C. Local first principal stretches following failure. The arrow denotes the element used in Fig. 4 below. D. Direction vectors of first principal stretch scaled by magnitude.

Fig. 4.

Demonstration of the failure process in networks. A. Stretched network immediately prior to failure. B. Initial network failure in collagen. C. Network failure proceeds with failure of elastin. The first column shows the collagen structure, the second column the elastin structure, the third column the actin structure and the fourth and fifth column the composite network structure. All network images for A, B, and C are on the same scale.

Fig. 5.

Failure metrics for the average of ten simulations mapped onto the undeformed domain with material boundaries shown in light blue. A. First principal stretch at failure. B. Percentage of collagen fibers failed. C. Percentage of elastin fibers failed. D. Percentage of cytoskeletal stress fibers failed. Element failure is defined as an element principal stretch exceeding 1.5x the applied stretch.