Strain history dependence of the nonlinear stress response of fibrin and collagen networks

Abstract

We show that the nonlinear mechanical response of networks formed from un-cross-linked fibrin or collagen type I continually changes in response to repeated large-strain loading. We demonstrate that this dynamic evolution of the mechanical response arises from a shift of a characteristic nonlinear stress-strain relationship to higher strains. Therefore, the imposed loading does not weaken the underlying matrices but instead delays the occurrence of the strain stiffening. Using confocal microscopy, we present direct evidence that this behavior results from persistent lengthening of individual fibers caused by an interplay between fiber stretching and fiber buckling when the networks are repeatedly strained. Moreover, we show that covalent cross-linking of fibrin or collagen inhibits the shift of the nonlinear material response, suggesting that the molecular origin of individual fiber lengthening may be slip of monomers within the fibers. Thus, a fibrous architecture in combination with constituents that exhibit internal plasticity creates a material whose mechanical response adapts to external loading conditions. This design principle may be useful to engineer novel materials with this capability.

Keywords: ECM; blood clot; factor XIII; nonlinear rheology.

Fig. 1.

Evolution of the nonlinear viscoelastic stress response of fibrin (A–C) and collagen networks (D–F) in response to large amplitude strain cycles. (A) Sets of 10 strain oscillations with stepwise increasing strain amplitude (0.4, 0.6, 0.8, 1, 1.2) are imposed on a 1 mg/mL fibrin network free of covalent cross-links. (Upper Inset) Colored loops show the stress vs. strain response of half-cycles (sets of cycles at different amplitudes are represented by different colors; later cycles are indicated by darker shades of each color). (Lower Inset) Enlarged view of the evolution of the first set of cycles at a strain of 0.4; the stresses decrease with each subsequent cycle (vertical arrow), and the onset of nonlinearity occurs at higher strains (horizontal arrow). Gray lines represent the elastic midlines of each cycle; the intersect strain γ_char with the threshold stress σ_thresh is calculated for each midline (Inset in B). (B) Stress vs. strain loops from cycles at the same strain amplitude are replotted by subtracting Δγ_char, the increase of γ_char of each cycle with respect to γ_char of the first cycle at each strain amplitude. (C) All stress vs. strain loops are collapsed onto a single master curve by replotting each cycle subtracted by γ_char. (Inset) Collapse of the elastic midlines σ_el by replotting each curve subtracted by γ_char. Colors correspond to the viscoelastic loops in the main panel. (D–F) A similar strain protocol (0.06, 0.08, 0.1, 0.12, 0.14, 0.16, and 0.18 strain amplitude) is performed on a 0.9 mg/mL collagen network; this shows a similar shift of the material’s stress–strain response that can also be collapsed onto a single master curve. (All panels and Insets correspond to those in A–C.)

Fig. 2.

Structural changes of an un–cross-linked fibrin network held under shear deformation, and the effect of repeated stretching of an individual fibrin fiber. (A) A fluorescently labeled 1 mg/mL fibrin network free of covalent cross-links is polymerized in a custom-built shear cell consisting of two parallel glass plates. Its 3D network structure is imaged before (Left), during (Center), and after (Right) a shear deformation of a strain of 0.7 is applied for 1 h by translating the top plate horizontally while the bottom stays stationary. The colored lines highlight fibers in the direction of shear (right of red lines) and perpendicular to the direction of shear (left of blue lines). All images are x–z projections of a volume spanning 15 µm in the y direction. (Scale bar: 20 µm.) (B) An individual fibrin fiber suspended perpendicularly over a 20-µm–wide micropatterned channel is stretched 15 times for 5 s to 175% of its original length with a pulled glass capillary. With ongoing cycles, the fiber appears increasingly bowed, indicating that it becomes successively longer.

Fig. 3.

Lengthening of viscoelastic fibers due to stretching followed by buckling. (A) (I) Fibers oriented in the direction of shear (solid line) and fibers oriented perpendicular to it (dashed lines) behave differently when the bulk is sheared. (II) Upon shear, fibers in the direction of shear are stretched, putting them under tension (red line), whereas fibers perpendicular to it buckle. (III) The tension within the stretched fibers relaxes quickly due to internal viscoelastic processes, leading to an increase of their rest lengths. (IV) Upon return of the bulk deformation to the initial 0-strain position, lengthened fibers remain so, because they do not become compressed, but instead buckle. (V) When the network is sheared again, the lengthened fibers do not contribute to the bulk shear stress until they are pulled taut. (VI) Once the shear amplitude exceeds those of previous cycles, fibers contribute to the shear stress as before, which accounts for the observed shift of the bulk stress response to higher strains. (B) When an un–cross-linked fiber is put under tension, slip of protofibrils (blue lines) leads to a strong relaxation of the internal stress and causes the rest length of the fiber to increase. (C) By contrast, in a fiber fully cross-linked, adjacent protofibrils are covalently bound to one another (red links) and do not slip under tension leading to a suppressed relaxation; therefore, the fiber retains its initial rest length upon stress release.

Fig. 4.

Nonlinear viscoelastic stress response of covalently cross-linked fibrin and collagen networks in response to large-amplitude strain cycles. (A) The stress vs. strain loops of a 1 mg/mL fibrin network cross-linked by factor XIII all overlap and do not display a pronounced shift to larger strains as indicated by the strongly inhibited evolution of γ_char with cycles (Inset). (B) The stress response of a 0.9 mg/mL collagen network cross-linked by 0.2% glutaraldehyde displays a similarly suppressed working behavior. (Inset) Evolution of γ_char with cycles. (The strain protocols for both systems are identical to those in Fig. 1. The gray lines represent the midlines of the viscoelastic loops from which γ_char is determined for each cycle.)