Load Transfer along Continuous Collagen Fibers Reduces the Importance of Wall Thickness Variations

The mechanical response of biological soft tissues is influenced by wall heterogeneity, including spatial variations in wall thickness. Traditional models for homogeneous soft tissues under uniaxial loading predict higher stretch and stress in thinner regions. In fact, large gradients in stretch and stress are predicted to be induced by spatial variations in wall thickness. In prior studies, the role of collagen fibers in regions of thickness transition has been largely neglected or only considered in terms of their effect on anisotropy. Here, we explore the role of collagen fibers as primary load-bearing components across regions of varying wall thickness, using a three-dimensional representative volume element (RVE) model incorporating explicit collagen fiber architecture and a gradual thickness gradient. We examined two distinct collagen fiber configurations across the thickness transition: one featuring abrupt fiber termination and another with fiber continuity. Finite element analysis (FEA) under uniaxial tension revealed that load transfer by continuous fibers across the specimen markedly reduced the importance of the change in wall thickness, with stretch differentials dropping from ~20% (fiber-termination network) to 0.68% (continuous fibers) and stress differentials dropping from ~65% (fiber-termination network) to 2.3% (continuous fibers). Fiber tortuosity delayed the point at which mechanical response was governed by fiber structure. These findings demonstrate the critical role of fiber continuity in reducing stretch and stress gradients across regions of varying wall thickness and clarify the importance of accurately representing fiber architecture when modeling soft tissues with heterogeneous wall thickness.

💡 Research Summary

This paper investigates how collagen fiber continuity across regions of varying wall thickness influences the mechanical response of soft biological tissues, using a three‑dimensional meso‑scale representative volume element (RVE) and finite element analysis (FEA). Two extreme fiber architectures are compared: (1) an abrupt‑termination network in which fibers end at the thickness transition, and (2) a continuous‑fiber network in which fibers traverse the transition without interruption. Both models share identical overall collagen volume fraction (35.5 %), matrix material (nearly incompressible neo‑Hookean), and overall geometry—a rectangular block (500 µm × 500 µm) whose thickness varies smoothly from 200 µm to 100 µm along the loading direction, defined by a sigmoid function.

The authors embed 1‑D rod elements representing collagen within 8‑node hexahedral solid elements for the matrix, employing kinematic constraints to ensure affine deformation of fibers relative to the surrounding matrix. Fiber orientation follows a Gaussian distribution with a 10° standard deviation around the primary loading axis, and fiber diameter is set to 1.28 µm. To capture the effect of fiber waviness, three recruitment stretch values (λ_r = 1.01, 1.25, 1.5) are examined, representing increasing initial tortuosity.

Uniaxial tensile loading is applied by prescribing a uniform displacement on the thin face while roller constraints prevent rigid body motion. Simulations are quasi‑static with 2000 load steps, and mesh convergence is verified (<2 % variation).

Results show that in the abrupt‑termination network, the thinner region experiences a stretch differential of roughly 20 % and a von Mises stress differential of about 65 % relative to the thick region, confirming classical expectations that reduced cross‑sectional area leads to higher deformation and stress. In stark contrast, the continuous‑fiber network reduces the stretch differential to 0.68 % and the stress differential to 2.3 %, demonstrating that load transfer through uninterrupted fibers dramatically homogenizes the mechanical field across the thickness gradient.

Parametric studies further reveal that (i) increasing the steepness of the thickness gradient amplifies the differences in the abrupt network but has minimal impact on the continuous network; (ii) widening the fiber orientation angle (30°, 45°, 60°) slightly diminishes the load‑sharing efficiency of continuous fibers yet the homogenizing effect persists; and (iii) mixed networks with varying ratios of continuous to abrupt fibers exhibit a smooth transition in mechanical response, with the homogenization becoming pronounced once continuous fibers exceed ~50 % of the total population.

Fiber tortuosity, represented by higher λ_r values, delays the onset of fiber recruitment, causing the matrix to bear more load initially and thereby reducing the immediate benefit of continuity. Nonetheless, once fibers are recruited, the continuous architecture again dominates the load transfer, confirming that both fiber geometry and material recruitment are critical determinants of tissue mechanics.

The study underscores a key limitation of conventional continuum anisotropic models that assume uniform thickness or ignore discrete fiber continuity: they may over‑predict stress concentrations in regions where fibers are actually continuous, and under‑predict them where fibers are disrupted (e.g., near micro‑calcifications in aneurysms). By explicitly modeling discrete fibers and their continuity, the authors provide a more physiologically realistic framework for predicting mechanical behavior in heterogeneous soft tissues, with direct implications for assessing rupture risk in vascular pathologies and for designing biomimetic scaffolds that exploit fiber continuity to mitigate stress concentrations.