Stiffening of individual fibrin fibers equitably distributes strain and strengthens networks

Abstract

As the structural backbone of blood clots, fibrin networks carry out the mechanical task of stemming blood flow at sites of vascular injury. These networks exhibit a rich set of remarkable mechanical properties, but a detailed picture relating the microscopic mechanics of the individual fibers to the overall network properties has not been fully developed. In particular, how the high strain and failure characteristics of single fibers affect the overall strength of the network is not known. Using a combined fluorescence/atomic force microscope nanomanipulation system, we stretched 2-D fibrin networks to the point of failure, while recording the strain of individual fibers. Our results were compared to a pair of model networks: one composed of linearly responding elements and a second of nonlinear, strain-stiffening elements. We find that strain-stiffening of the individual fibers is necessary to explain the pattern of strain propagation throughout the network that we observe in our experiments. Fiber strain-stiffening acts to distribute strain more equitably within the network, reduce strain maxima, and increase network strength. Along with its physiological implications, a detailed understanding of this strengthening mechanism may lead to new design strategies for engineered polymeric materials.

Figure 1

Experimental setup: (a and b) Side and bottom views depicting the AFM and a fibrin network suspended between ridges. (c–e) Three time point snapshots of a network undergoing deformation due to AFM manipulation. (f–h) Model network deformations at equivalent points to c–e.

Figure 2

Network strain measurements. (a–d) Images from a video of network deformation. (a) The original network geometry highlighting four fibers whose strain will be tracked throughout the network deformation (plotted in frames e–f). (b–d) Fiber nodes in the network were selectively tracked, and fiber strains were calculated using the distances between the nodes. The lines in c and d show tracking data, tracing the motion of network junctions throughout the deformation. (e) A plot of individual fiber strain versus AFM tip movement. Each trace represents the strain versus AFM tip movement for one fiber corresponding to frame a. (f) The strain fraction (derivative of strain with respect to tip movement, or slope, of plot in e). The circled data in the lower left of the plot in e indicates the stretching transition where fibers are reorienting and beginning to stretch. The other circles on the right side highlight a concave downward trend in the strain plot e) and the corresponding decrease in the strain fraction f for the most strained fiber (top trace). Note also that the strain fraction of the several lesser strained traces trends upward in the strain fraction plot (f) at high AFM tip movement. These trends indicate that as the most strained fiber stiffens, it transfers strain share to the less strained, softer fibers.

Figure 3

Experiment versus simulations. (a–c) Fiber strain traces for a particular experimental network and for simulations of equivalent WLC and linear model networks. (d–f) Plots of the strain fraction corresponding to a–c. The experimental strain and strain fraction data show a much closer correspondence to the WLC model than to the linear network particularly for the most strained fibers at high AFM tip movement. Two predominant features contrast the experiment and WLC model data from the linear model. First, the linear model shows much higher maximum strain (top trace. c) then either experiment (a) or WLC model (b). Second, within the strain fraction plots, the most strained fiber (top trace) shows a clear decrease above tip movement of 15 μm for both the experiment and WLC model, whereas the linear model shows no such decrease. The strain fractions of the fibers in the linear model approach constant and highly dispersed values indicating each fiber takes on constant and inequitable strain share. The strain fraction of the experimental and WLC model fibers converge into a much narrower range at high AFM tip movement indicating that strain share is transferring from the most strained to the lesser strained fibers, more equitably distributing strain throughout the network.

Figure 4

Single fibrin fiber force curve: Inset (a–d) depicts a single suspended fiber stretched to breaking (d) by an AFM tip. (Plot) The black points depict single fibrin fiber force-strain data determined by calibrated lateral AFM force measurement. The geometrical aspects of the measurement were taken into account to convert raw AFM force data to fiber tensile force. The strain of the fiber was determined from the calibrated video data. The line through the data depicts the WLC fit using two fitting parameters: the persistence and contour lengths.

Figure 5

Ligated network strain distributions. A compilation of model versus experimental strain distributions for nine different network geometries formed with FXIIIa ligation. Each dot in the plots indicates the strain of a fiber within a network. The shaded bars underneath the data points are simply guides to the eye to emphasize the strain ranges. Measurements were made after 15 μm of AFM movement (intermediate strain, top plot) and at the point of network failure (high strains, lower plot) (see inset). At intermediate strains there are clear variations, but no clear trends distinguish the experiment and models. At high strains, the linear model shows much higher maximum strain for all networks and lower minimum strain for all but two of the experimental networks. There is much closer correspondence between the experimental and WLC distributions (see Table 1 for statistical analysis).

Figure 6

Unligated network strain distributions. A compilation of model versus experimental strain distributions for nine network geometries formed without FXIIIa cross-linking.