Abstract
Introduction
Deep vein thrombosis (DVT) is a significant source of morbidity and mortality [1,2]. Although many suffer from the consequences of DVT, the mechanisms of initiation, progression, and resolution remain poorly understood. Indeed, particularly scant is information on the evolving mechanical properties of a venous thrombus. Such properties are fundamental to the mechanical integrity of the thrombus, especially its ability to remain intact under hemodynamic loads [3–6]. There is, therefore, a pressing need for more information on thrombus biomechanics.
If not proteolytically resolved, venous thrombus can undergo several phases of maturation in which the initial fibrin mesh is infiltrated by inflammatory and mesenchymal cells that gradually lead to a thickening of extant fibrin fibers or replacement with other structural proteins, including collagens [7–9]. Of course, such remodeling and replacement of structural constituents within a thrombus alters its biomechanical properties [5]. Quantitative relationships between changes in composition, organization, and biomechanical properties remain incompletely characterized. Consequently, an improved understanding of venous thrombus remodeling, particularly changes in its nonlinear biomechanical properties, promises to contribute to our understanding of DVT and thereby help clinicians make better-informed decisions about the best course of treatment for their patients.
Because it is difficult to track the remodeling of thrombus in patients and because in vitro generated fibrin equivalents tend not to exhibit the stiffness or strength observed for in vivo explants [10], several animal models have been introduced to study DVT. For example, Deatrick et al. [11] developed a murine model wherein they ligated the inferior vena cava (IVC) to create a space filling thrombus. Notwithstanding the challenge of working with such small vessels, murine models offer the added advantages of diverse genetic manipulations and the wide availability of antibodies.
Although different animal models have increased our understanding tremendously, there has yet to be a correlation of evolving histological changes with biomechanical properties. The primary goal of the present study, therefore, was to initiate such a correlation. We employed the IVC ligation model in mice for it yields a nearly cylindrical thrombus that is amenable both to standard uniaxial mechanical testing and subsequent immunohistological examination. Data collected over 4 weeks of thrombus evolution revealed a progressive remodeling from a fibrin-based towards a fibrin–collagen composite structure that was accompanied by a marked stiffening of the material response. We submit that this murine model holds considerable promise for understanding better the evolving histomechanical properties of venous thrombus.
Materials and methods
Mouse model
All animal protocols were approved by the Yale University Institutional Animal Care and Use Committee. Briefly, we used intraperitoneal injections of ketamine (100 mg/kg) and xylazine (20 mg/kg) to anesthetize ∼8 week old male C57BL/6 mice. While under deep anesthesia, and using aseptic techniques, we surgically exposed and then ligated with 7-0 silk suture the IVC and its major branches just beneath the left renal vein. The incision was then closed and the animal was allowed to recover with appropriate analgesics as well as normal food and drink supplied ad libitum. For more details on this type of procedure, see [11,12]. Two and four weeks after surgery, we euthanized the mice with an intraperitoneal injection of Beuthanasia-D. Immediately thereafter, we harvested the IVC containing an intraluminal thrombus and immediately placed samples of 2 mm length or longer in phosphate buffered saline until testing. The wall of the IVC was gently removed, thus leaving a nearly cylindrical sample of intraluminal thrombus for mechanical testing.
Uniaxial tests
We impaled each end of the thrombus with a custom glass cannula and secured the ends with a drop of cyanoacrylate before mounting them within a custom mechanical testing system [13]. The system comprised two precision motors to uniaxially extend the sample in opposing directions, which maintained the center within the same field of view of a video microscope. An axial force transducer recorded the reaction forces while custom software based on an edge-detection algorithm monitored changes in diameter in the sample center. All tests were performed in physiologic solution at 37°C.
Before collecting data for analysis, we preconditioned the specimens by loading them four times from 0 to
Histology
Fixed samples were cut into distal and proximal halves, embedded in paraffin, and sectioned at 5 µm thicknesses. Sections from the sample center were stained with Movat’s pentachrome to identify fibrin and collagen and with picrosirius red to identify different thickness collagen fibers. Additional sections were immuno-stained for α-smooth muscle actin (
We acquired all histological images with an Olympus BX51TF microscope and an Olympus DP70 camera using bright-field imaging, except for the picrosirius red stained sections, which were acquired using polarizing optics and dark-field imaging. Both bright-field and dark-field images were taken at 10× and 20× magnification. We performed quantitative measurements using ImageJ (NIH) and an in-house Matlab image processing software.
Mechanical characterization
To quantify the mechanical behavior of the thrombi under cyclic uniaxial loading, we transformed the force-displacement data sets into Cauchy stress–stretch data and attempted to fit the data with several different well established constitutive relations for soft tissues. For each model fit, we assumed the thrombus to be (pseudo)elastic; that is, we ignored any hysteresis remaining after preconditioning and focused on loading cycles alone. Of the models examined, which included standard phenomenological models such as the Fung-exponential, the microstructural model proposed by Hurschler et al. [14] yielded the best fit. Specifically, their model represents the Cauchy stress in the loading direction,
Finally, note that we assumed that the fibers did not have any compressive stiffness. Thus, the integral expression in Eq. (1) describes the material stress response as the sum of infinitesimal tensile stress contributions by each neo-Hookean fiber, individually activated at a recruitment stretch
The model parameters were determined via nonlinear regression of the experimental uniaxial data. Specifically, identifications were accomplished using the Levenberg–Marquardt algorithm implemented in Matlab R2013b.
We compared samples at 2 and 4 weeks using the independent, two-tailed student t-test. Furthermore, computed values of material stiffness at 2 and 4 weeks, for all ten loading protocols each, were compared using 2-way ANOVA. Alpha levels for both tests were set to 0.05. All data are reported as means ± 1 standard deviation unless indicated otherwise.
Results
The animal studies yielded an IVC thrombus in 17 mice at the two time points of interest. Of these 17 thrombi, 11 were long enough to be studied under uniaxial extension testing:

Remodeling thrombus changes appearance over time from red to white and undergoes contraction. Representative (A), (B) in situ images of the inferior vena cava containing thrombus (dashed lines) and (C), (D) in vitro images of thrombus following excision and isolation from the venous wall, both for 2 and 4 weeks post-surgery. Comparison of mean values of isolated thrombus (E) length and (F) outer diameter (OD) at 2 (

Remodeling thrombus undergoes replacement of fibrin with collagen from the periphery inwards, while
Staining with Movat’s pentachrome revealed an accumulation of fibrin in the center of the thrombi at 2 weeks, which tended to disappear by 4 weeks (Fig. 2(A) and (B)). This qualitative observation was supported by a significant (
Staining for

Macrophages and neutrophils increased in density and invaded the remodeling thrombus from the periphery inwards. (A), (B) CD68 positive staining revealed the presence of macrophages whereas (C), (D) Ly6b positive staining revealed neutrophils. Both cell types increased in concentration from 2 to 4 weeks: (E) CD68 positive cells and (F) Ly6b positive cells. ∗∗
Figure 4(A) and (B) shows images of the central region of a representative sample while mounted within the mechanical testing device and loaded to

Thrombus samples exhibited nonlinear uniaxial Cauchy stress–stretch responses, with hysteresis and a Mullin’s type damage behavior. Video-capture images during uniaxial testing show representative thrombus geometries at a load of (A)
Note: Symbols are the shear modulus μ, the shape parameter β, the location parameter γ and the scale parameter δ.

A microstructurally-inspired material model fit well the loading responses of 2 and 4 week thrombi and revealed that mean material stiffness increased over time and with increasing load in remodeling thrombus. (A) Loading data from representative samples at 2 (circles) and 4 (squares) weeks post-surgery that were subjected to increasingly greater loads (
We employed an established in vivo mouse model of venous thrombus that naturally yields samples that are convenient for standard mechanical testing without the need to cut or shape the samples. Hence, this model allows one to begin to correlate the evolving composition and mechanical properties while quantifying spatial distributions and concentrations of the different cell types thought to remodel thrombus. Our results, for two times of development, represent the first mechanical characterization of this thrombus model. Preliminary tests revealed that the thrombus was not sufficiently stiff at 1 week post-surgery to permit the collection of robust uniaxial data using our current device; in contrast, data at 2 and 4 weeks post-surgery revealed a dramatic evolution in both composition and material stiffness. Whereas thrombi at 2 weeks consisted primarily of fibrin, with some collagen fibers near the periphery, thrombi at 4 weeks were highly collagenous throughout the cross-section. Indeed, these thrombi sustained extremely high stresses without gross failure (Figs 4 and 5). The infiltration of α-smooth muscle positive cells, presumably myofibroblasts but possibly fibrocytes, into the peripheral regions of the thrombus at 2 weeks but throughout the thrombus at 4 weeks strongly suggests a primary role for these cells in the synthesis and organization of collagen during the radially-directed, inward remodeling process. Similar findings were reported before, though evolving mechanical properties were not reported [7,8,15]. The observed increased deposition of collagen was accompanied by a reduction in thrombus size (Fig. 1), consistent with the phenomenon of wound contraction that is aided by contractile myofibroblasts [16]. Associated increases in neutrophils and macrophages from 2 to 4 weeks suggested, however, that continued thrombus remodeling may still have been driven largely by inflammation at 4 weeks. That macrophages secrete transforming growth factor beta, among many other cytokines, is consistent with the differentiation of fibroblasts to myofibroblasts under the influence of mechanical stress [17], thus supporting a potentially important paracrine interaction between these two cell types. Although we did not measure fibrin degradation products, the inflammatory cells also likely contributed to the degradation of the fibrin that allowed it to be replaced with collagen. Future studies should explore thrombus remodeling in this model at times beyond 4 weeks.
The material behavior of the thrombi did not change qualitatively between the younger and older samples. Both showed a nonlinear stress–stretch response, with hysteresis and a Mullin’s type damage phenomenon that was reflected by notable shifts in the material response along the stretch-axis as the load was increased. Nevertheless, significant quantitative changes in structural composition were accompanied by quantitative changes in mechanical properties from 2 to 4 weeks of development.
To correlate the quantitative changes in mechanical properties with changes in structural composition, we fit the collected stress–stretch data with a number of material models for soft tissue. We found that the microstructurally-inspired material model by Hurschler et al. [14] provided the best fit, with the added benefit of requiring only 4 parameters. Based on this material model and the identified parameters, we were able to derive continuous, analytical expressions not only for Cauchy stress as a function of stretch, but also for the material stiffness. Given these expressions, we found a statistically significant difference in material stiffness between 2 and 4 weeks – with the mean stiffness higher at 4 weeks compared to 2 weeks for each load level – consistent with the significant change from a fibrin-dominated to collagenous thrombus (cf. Fig. 2). Notwithstanding large specimen-to-specimen variability, as expected of an evolving disease process, the observed increase in mean material stiffness with increasing thrombus age is qualitatively consistent with reports on the mechanical properties of thrombi of various levels of maturity explanted from human AAAs [18]. We emphasize, however, that the present data are the first for a relatively early (weeks rather than years) maturation of a venous, not arterial, clot. Given the goodness of fit provided by the microstructurally-inspired material model, we submit that the model and identified parameters will lend themselves well for future studies of thrombus mechanics in general, though with site-specific values of parameters.
To the best of our knowledge, this is the first time that a Mullin’s type damage behavior has been reported for relatively early thrombus. While the observed behavior is not, strictly speaking, the same as the classical Mullin’s effect in elastomers, it shows remarkable resemblance [19]. Our finding may nevertheless be of particular interest as this phenomenon could result in damage-induced anisotropy, and perhaps help explain the directionally-dependent material properties that have been reported for intraluminal thrombus in aneurysms [18].
Interestingly, the transition from a fibrin-dominated mesh to a more mature, collagen-dominated network was not accompanied by a quantitative reduction of characteristics that are typically associated with viscoelasticity, including hysteresis and load-history dependence [20,21]. We speculate that the total occlusion of the IVC and associated failure to replenish important coagulation factors from the flowing blood, such as factor VIII, may have prevented complete cross-linking of the fibrin and collagen fibers within the central region of the thrombus that was tested. Such non-cross-linked meshes have been shown to exhibit pronounced viscoelastic responses [22], as observed here. Thus, thrombi formed under isolated, stagnant flow conditions may present with mechanical properties different from those that form under non-obstructive flow conditions, as, for example, those discussed in [12,23,24]. This limitation should be kept in mind before extrapolating the present mechanical data to thrombi formed under different conditions. Furthermore, thrombi are complex, three-dimensional biomaterials with a heterogeneous microstructure. Importantly, in our current model we assumed that thrombus can be represented by a constrained homogenous mixture, thus our mechanical modeling represents only the bulk behavior of the material, not that of its individual spatially distributed (radially or axially) constituents or their interactions.
Conclusion
We showed that an established mouse model of venous thrombus naturally yields specimens that are convenient for uniaxial testing, and thus can be used to correlate histological and biomechanical changes in remodeling thrombus. We demonstrated that 2- to 4-week old thrombus can undergo drastic remodeling from a fibrin-dominated mesh to a collagen-dominated microstructure and that these changes are accompanied by marked increases in stiffness. That a simple microstructurally-inspired constitutive relation described well the associated data suggests that in vivo changes could be predicted. There is, however, a need for similar data covering additional times, with quantification of the biomechanics of earlier thrombus (days rather than weeks) remaining a technical challenge due to its extreme compliance.
Footnotes
Acknowledgement
This work was supported, in part, by NIH Grants R03 EB010109, R01 HL086418 and U01 HL116323 to Yale University.
