Rheology of fibrin clots. v. shear modulus,creep, and creep recovery of fine unligated clots

Creep and creep recovery in small shearing deformations have been studied in fibrin clots at pH 8.5 and ionic strength 0.45, where the fine, transparent clot is formed with very little lateral aggregation of protofibrils. The initial shear modulus G₁ was measured 25 s after deformation on clots aged long enough for complete development of structure. For both human and bovine fibrin, the data were approximately described by log G₁ = 1.45 + 1.90 log c, where c is concentration in $\text{g}\text{l}$ and G₁ is in $\text{dyn}\text{cm}{}^2$, over a range of c from 4 to 13 $\text{g}\text{l}$. For bovine clots with completely developed structure, creep and creep recovery showed substantial irrecoverable deformation but the differential modulus G_Δ measured at intervals agreed with G₁ and did not change during the course of the experiment; it also agreed with the value calculated from the initial recovery after removal of stress. Moreover, several tests showed that the course of recovery conformed closely to the Boltzmann superposition principle. Thus the irrecoverable strain was associated with a structural rearrangement which caused no permanent damage. The irrecoverable deformation relative to the initial deformation was proportional to the elapsed time during creep in the early stages with a proportionality constant that decreased somewhat with increasing clot age prior to imposition of stress; it corresponded to a pseudo-viscosity of the order of 10⁷ poise. However, the irrecoverable deformation does not represent viscous flow and appears to approach a limiting value at long times. Experiments on clots without completely developed structure, i.e., with imposition of stress at an earlier clot age, showed an increase in the differential modulus G_Δ during creep. The irrecoverable deformation was greater and a portion of it could be attributed to the balance between two structures formed in the unstrained and strained states. However, unlike the case of ligated clots strained before complete development of structure, where the irrecoverable deformation is entirely due to a two-structure balance, there is also a contribution from structural rearrangement. Experiments with reverse creep and creep recovery showed that the structural rearrangement is symmetrical with respect to direction of deformation. The interpretation of these results in terms of clot structure and internal motions of protofibrils is discussed.     

Rheology of fibrin clots. I. Dynamic viscoelastic properties and fluid permeation

The storage and loss shear moduli (G', G″) of human fibrin clots have been measured in small oscillating deformations over a frequency range of 0.01 to 160 Hz with the modified Birnboim transducer apparatus. Most clots were prepared by the action of thrombin on purified fibrinogen, under various conditions of pH and ionic strength to produce networks ranging from coarse to fine structure; some were liaated by fibrinoligase. The fine, unligated clot showed very little mechanical loss or frequency dependence of G' over the experimental frequency range, though loss mechanisms evidently appear at higher frequencies; G' was proportional to the 1.5 power of fibrin concentration. The coarse, unligated clot showed a slight increase of G' with frequency, reflecting some relaxation mechanisms with time constants whose reciprocals lie in the experimental frequency range. Ligation did not greatly affect the magnitude of G'. However, clots prepared by dilution of solutions of fibrin monomer in 1 M sodium bromide had smaller moduli by a factor of ten than corresponding clots prepared by the action of thrombin of fibrinogen. Oscillatory measurements in the Birnboim apparatus with closed-end (annular pumping) geometry revealed a low-frequency anomaly which was shown to be due to permeation of fluid through the clot structure, and from these measurements the Darcy constants for coarse clots were calculated. From the Darcy constants, the average thicknesses of the fibrous elements of the structures were estimated to be from 300 to 700 A.     

Rheology of fibrin clots: III. Shear creep and creep recovery of fine ligated and coarse unligated clots

Creep and creep recovery of human fibrin clots in small shearing deformations have been investigated over a time scale from 24 to 10⁴ s. Coarse, unligated dots and fine dots ligated by fibrinoligase in the presence of calcium ions were studied to suppllement previous data on coarse ligated and fine unligated clots. Stress was found to be proportional to strain up to at least a maximum shear strain (in torsion geometry) of 2.6%. The initial modulus (25 s after imposition of stress) is proportional to approximately the 1.5 power of concentration for fine ligated and coarse unligated clots. For fine unligated clots, there is comparatively little creep subsequent to the initial deformation; ligation (in this case involving mostly the γ chains) reduces the creep to nearly zero. For coarse unligated dots, there is substantially more creep under constant stress, and creep recovery is not complete. legation (in this casa involving both γ and α chains) largely suppresses the creep and causes the recovery to be complete. If the structure is fully formed before creep begins, tests of creep recovery by the Boltzmann superposition principle show adherence to linear viscoelastic behavior for all four clot types. Otherwise, the Boltzmann test fails and the recovery is much less than calculated. For fine ligated clots, the observed recovery agrees well with that calculated on the basis of a dual structure model in which an additional independent structure is built up in the deformed state, so that the state of ease after removal of stress is a balance between two structures deformed in opposite senses, it is postulated that the coherence and elastic modulus of the fine ligated dot are largely due to steric blocking of long protofibrils with a high flexural stiffness. In the coarse clot, it is proposed that the structure involves extensive branching of thick bundles of protofibrils, which become permanently secured by the ligation of the α chains of the fibrin.     

Modification of shear modulus and creep compliance of fibrin clots by fibronectin

Shear moduli and creep compliances have been measured for four types of clots of human fibrin (about 7 $\text{mg}\text{ml}$) clotted with and without human plasma fibronectin (usually 1.2 $\text{mg}\text{ml}$). Fine clots (with little lateral aggregation of the fibrin protofibrils) were formed at pH 8.5, ionic strength 0.45 ; coarse clots (with substantial lateral aggregation) were formed at pH 7.5, ionic strength 0.15; in both cases with and without ligation by fibrinougase. In fine clots, the addition of fibronectin without ligation scarcely affected the shear modulus; with ligation, the modulus was decreased by a factor of 0.48. In coarse clots, the shear modulus was increased by addition of fibronectin. The increase was by a factor of 2.0 without ligation and by a factor of 2.4 with ligation. Creep and creep recovery in clots formed with and without fibronectin were similar except for the scale factor represented by the change in modulus.     

Rheology of fibrin clots. IV. Darcy constants and fiber thickness.

Measurements of small oscillatory deformations of a fibrin clot by axial motion of a rod in a closed tube reveal an anomalous mechanical loss due to permeation of fluid through the clot structure. The Darcy constant for permeation can be calculated from data at the frequency where the apparent storage and loss shear moduli are equal, without the necessity of measurements at much lower frequencies as previously employed. From the Darcy constant, the average number of fibrin monomer units (v) per cross-section of a fibrous element of the clot can be calculated; it ranges from 4 to several hundred. In the range of fibrin concentration(c) from 3 to 14 milligrams, v is approximately proportional to c-2 for clots of coarse structure and to c-0.5 for clots of fine structure.     

Rheological studies of creep and creep recovery of unligated fibrin clots: comparison of clots prepared with thrombin and ancrod

Mechanical creep and creep recovery in small shearing deformations have been studied in unligated clots formed with both thrombin and ancrod. In thrombin clots, both A binding sites (which interact with “a” sites to link monomer units within a protofibril) and B sites (which interact with “b” sites to form links between protofibrils) are exposed to enable formation of linkages; in ancrod clots, only the A sites are exposed. Fine clots (with minimal lateral aggregation of protofibrils), coarse clots (with substantial aggregation of fibril bundles), and clots of intermediate coarseness were compared. Fine thrombin clots showed less creep at short times but more creep at long times than coarse or intermediate clots and had more irrecoverable deformation relative to the initial elastic deformation. Ancrod clots had greater irrecoverable deformation than the corresponding thrombin clots, both fine and coarse. The permanent deformation in fine ancrod clots was enormous, corresponding almost to fluid character; the rate of permanent deformation was larger than that in fine thrombin clots by more than two orders of magnitude. For all types of clots, differential measurements of compliance (or its reciprocal, elastic modulus), as well as the applicability of the Boltzmann superposition principle to calculation of creep recovery, showed that the overall density of structure remained constant throughout the mechanical history; i.e., if structural elements were breaking, they were reforming at the same rate in different configurations. The possibility that the weakness of ancrod clots is attributable to partial degradation of α-chains rather than absence of Bb linkages was eliminated by comparisons of clots made with thrombin, ancrod, and ancrod plus thrombin; the last two showed identical partial degradation of α-chains (by gel electrophoresis), but the first and third had essentially identical initial elastic moduli and creep behavior. Two alternative mechanisms for irrecoverable deformation in fine clots are discussed, involving rupture of protofibrils and slippage of twisted segments, respectively.     

Identification of fibrin oligomers in sonicated fibrin clots

Clots of bovine fibrin, with both coarse and fine structure, and ligated to different extents by fibrinoligase, have been broken up by ultrasonic agitation and the sonicates have been examined by ultracentrifugal sedimentation. Sonication is followed by gross aggregation of the fragments unless guanidine hydrochloride is introduced (order of 1 M). In that case, sonicates of gamma-ligated fine clots contain two species whose sedimentation coefficients correspond to fibrin monomer and an oligomer with twice the monomer cross-section area and at least 20 monomer units, presumably with the structure of lateral dimerization with staggered overlapping. If the gamma ligation is incomplete, shorter oligomers are identified. The monomer and oligomer with degree of polymerization greater than 20 appear also in sonicates of coarse clots, but in smaller amounts, the principal product consisting of larger aggregates. The implications of these results with respect to metastability of the fine clot and the pattern of polymerization are discussed.     

Linear viscoelastic properties of bovine brain tissue in shear

We report the results from a series of rheological tests of fresh bovine brain tissue. Using a standard Bohlin VOR shear rheometer, shear relaxation and oscillating strain sweep experiments were performed on disks of brain tissue 30 mm in diameter, with a thickness of 1.5–2 mm. The strain sweep experiment showed that the viscoelastic strain limit is of the order of 0.1% strain. Shear relaxation data do not indicate the presence of a long-term elastic modulus, indicating fluid-like behavior. A relaxation spectrum was calculated by inverting the experimental data and used to predict oscillatory response, which agreed well with measured data.     

Incorporation of thrombospondin into fibrin clots

Thrombospondin is a major platelet glycoprotein which is released from platelets during blood coagulation. We examined the interaction of thrombospondin with polymerizing fibrin. Thrombospondin, purified from human platelets and labeled with 125I, became incorporated into clots formed from both plasma and purified fibrinogen. Plasma clots contained somewhat less thrombospondin than clots formed from equivalent concentrations of fibrinogen. In plasma clots and fibrin clots formed in the presence of factor XIII, thrombospondin was cross-linked in the clot; thrombospondin in the supernatant remained largely monomeric. Cross-linking of thrombospondin by factor XIII, however, only slightly increased the amount of thrombospondin which was incorporated into the clot. In contrast, incorporation of 125I-fibronectin into clots was dependent upon cross-linking. Most of the incorporation of 125I-thrombospondin occurred during fibrin polymerization as judged by parallel studies of the incorporation of 125I-fibrinogen. The amount of thrombospondin incorporated into a clot was directly related to thrombospondin concentration and was only weakly dependent on fibrinogen concentration. Incorporation was not saturated at thrombospondin:fibrin (mol/mol) ratios as high as 2/1. Thrombospondin, however, modified the final structure of fibrin clots in a concentration-dependent manner as monitored by opacity. When tryptic digests of 125I-thrombospondin were studied, the 270-kilodalton core became incorporated into fibrin whereas the 30-kilodalton heparin binding fragment was excluded. These results indicate that thrombospondin specifically co-polymerizes with fibrin during blood coagulation and may be an important modulator of clot structure.     

Interaction of fibrinogen-binding tetrapeptides with fibrin oligomers and fine fibrin clots

The polymerization of fibrin, at pH 8.5 and ionic strength 0.45, and under conditions where the action of thrombin on fibrinogen was the rate-determining step, was interrupted by inactivating thrombin with p-nitrophenyl-p′-guanidinobenzoate (NPGB). Addition of the tetrapeptide Gly-Pro-Arg-Pro (GPRP) partially dissociated the fibrin oligomers as shown by subsequent ligation with Factor XIIIa and calcium ion followed by denaturation and gel electrophoresis; polyacrylamide gel electrophoresis with reduction showed a decrease in the proportion of γ-γ ligation compared with controls untreated by GPRP, and agarose gel electrophoresis showed a shift in the distribution of oligomer sizes. The dissociation was accomplished within 15 min and its extent was consistent with establishment of an equilibrium in which two molecules of GPRP react to sever an oligomer. When GPRP was introduced into fine unligated fibrin clots by diffusion, there was some dissociation as shown by differences in the degree of γ-γ ligation after treatment by Factor XIIIa; but the action of GPRP was much slower and less complete than on soluble oligomers. However, even a small amount of dissociation affected the mechanical properties of fine clots profoundly. The shear modulus (measured 25 s after application of stress) decreased progressively with increasing concentration of GPRP introduced by diffusion. The rate of shear creep under constant stress and the proportion of irrecoverable deformation also increased enormously. If the steadystate creep rate is interpreted in terms of an effective viscosity, the latter is decreased by up to three orders of magnitude by the presence of GPRP. In terms of transient network theories of viscoelasticity, the average lifetime of a network strand is greatly diminished. However, the total density of strands remains constant during creep and creep recovery as shown by constancy of the differential modulus or compliance. Removal of GPRP by diffusion only partially restores the original shear modulus and creep behavior of the original clot. Some limited data on the effect of the tetrapeptide Gly-His-Arg-Pro are also reported.     

A fiber-reinforced composite model of the viscoelastic behavior of the brainstem in shear.

Brainstem trauma occurs frequently in severe head injury, often resulting in fatal lesions due to importance of brainstem in crucial neural functions. Structurally, the brainstem is composed of bundles of axonal fibers distinctly oriented in a longitudinal direction surrounded by an extracellular matrix. We hypothesize that the oriented structure and architecture of the brainstem dictates this mechanical response and results in its selective vulnerability in rotational loading. In order to understand the relationship between the biologic architecture and the mechanical response and provide further insight into the high vulnerability of this region, a structural and mathematical model was created. A fiber-reinforced composite model composed of viscoelastic fibers surrounded by a viscoelastic matrix was used to relate the biological architecture of the brainstem to its anisotropic mechanical response. Relevant model parameters measured include the brainstem's composite complex moduli and relative fraction of matrix and fiber. The model predicted that the fiber component is three times stiffer and more viscous than the matrix. The fiber modulus predictions were compared with experimental tissue measurements. The optic nerve, a bundle of tightly packed longitudinally arranged myelinated fibers with little matrix, served as a surrogate for the brainstem fiber component. Model predictions agreed with experimental measures, offering a validation of the model. This approach provided an understanding of the relationship between the specific biologic architecture of the brainstem and the anisotropic mechanical response and allowed insight into reasons for the selective vulnerability of this region in rotational head injury.     

Adherence of Candida species to fibrin clots in vitro

The adherence of six Candida species to fibrin clots was studied using a simple, in vitro technique. Yeast suspensions were incubated with fibrin clots and the number of adherent organisms quantified as follows: after washing, the clots were subjected to vortex mixing and the number of CPU's which subsequently grew on Sabourauds medium were counted. Adhesion was directly proportional to the concentration of Candida species in the suspension (r=0.99 p<0.001). C. albicans and C. tropicalis exhibited marked adherence whereas C. krusei, C. gulliermondi and C. glabrata adhered less readily. C. parapsilosis was intermediate in its ability to adhere.     

Fibrinogen Dusart: electron microscopy of molecules, fibers and clots, and viscoelastic properties of clots.

Ultrastructural perturbations resulting from defects in polymerization of fibrinogen Dusart, a congenital dysfibrinogenemia with the amino acid substitution A alpha 554 arginine to cysteine, were investigated by a variety of electron microscope studies. Polymerization of this mutant fibrinogen on addition of thrombin is impaired, producing clots with decreased porosity and increased resistance to fibrinolysis, resulting in thrombotic complications in the family members with this dysfibrinogenemia. Electron microscopy of rotary-shadowed individual molecules revealed that, in contrast to control fibrinogen, most of the alpha C domains of fibrinogen or fibrin Dusart appeared to be free-swimming appendages that do not exhibit intra- or intermolecular interactions either with each other or with the central domains. The location of albumin on the alpha C domains was demonstrated by electron microscopy using anti-albumin antibodies. Electron microscopy of negatively contrasted fibrin Dusart fibers indicated that they were less ordered than control fibers and had additional mass visible. Electron microscopy of freeze-dried, unidirectionally shadowed fibers showed that they were twisted with a shorter pitch. Scanning electron microscopy revealed that intact clots were made up of thin fibers with many branch points and very small pore sizes. The viscoelastic properties of Dusart fibrin clots measured with a torsion pendulum indicated a marked increase in stiffness consistent with the structural observations.     

Continuous measurement of lysis of radioactively marked fibrin clots

Methods for continuous measurement of dissolution of experimentally induced radioactively labelled thrombi were described. They are suited for the use in artificial circulating systems and in animal experiments. The radioactivity can be measured continuously in a circulating system by fitting a flow through cell with a well scintillator. In order to measure thrombotic processes in vivo, we developed a specially adapted single hole collimator. By this device changes in radioactivity over a defined occluded area of the vessel could be detected. The usefulness of the methods was demonstrated by means of a thrombolytic agent.     

Dynamic changes of fibrin architecture during fibrin formation and intrinsic fibrinolysis of fibrin-rich clots

Clotting and fibrinolysis are initiated simultaneously in vivo, and fibrinolysis usually occurs without any individualized lysis front (intrinsic fibrinolysis). We have developed a novel model to assess whether morphological changes resulting from intrinsic fibrinolysis are similar to those previously reported at the lysis front using externally applied lytic agents. Fibrin assembly and fibrinolysis were followed in real-time by confocal microscopy using gold-labeled fibrinogen molecules. An increase in fiber absorbance (30%, p < 0.01) and a decrease in fiber diameter (60%, p < 0.01) due to the ongoing accumulation and packing of fibrin molecules were the most significant detectable features occurring during fibrin assembly. Similar features with a similar magnitude were observed during fibrin dissolution, but in the reverse order and with a 3-fold increase in duration. Then, lysing fibers were progressively transected laterally, and thinner fibers were cleaved at a 2.5-fold faster rate than thicker fibers (p < 0.001). Frayed lysing fibers were seen to interact progressively with adjoining fibers (agglomeration), leading to a 76 and 88% increase in the network pore diameter (p < 0.05) and fiber diameter (p < 0.01), respectively. At the maximum decrease in fiber absorbance (46%, p < 0.05), the network suddenly collapsed with the release of large fragments that gradually vanished. Morphological changes of fibrin that occur during intrinsic fibrinolysis are similar as those observed next to the lysis front, although they are not restricted spatially to the clot/surrounding milieu interface but are observed through the entire clot.     

Release kinetics of transforming growth factor-beta1 from fibrin clots

In any therapeutic model involving a tissue-engineering approach to the repair of partial-thickness articular cartilage defects, a chondrogenic differentiation factor is required to ensure tissue-specific healing. Transforming growth factor-beta1 (TGF-beta1) is known to act in this capacity, but at such high concentrations as to render its direct injection into the joint cavity inadvisable. This situation calls for a delivery system that can be applied directly to the defect site and that will release the drug gradually over a period of some weeks. Liposome encapsulation represents one such system, and has been recently implemented with some success in an animal model for cartilage repair. However, the kinetics of TGF-beta1 release have not been determined, it was the purpose of the present study to characterize these. The liberation of [(125)I]-labeled TGF-beta1 from fibrin matrices containing this agent in either a free or liposome-encapsulated form was monitored by liquid scintillation counting for 25 days in vitro. During the initial 5 days, fibrin clots containing liposome-encapsulated TGF-beta1 released this cytokine at a slower rate (2% to 4% per day) than did those containing the free molecules (10% to 20% per day); thereafter, the release rates were similar. At the end of the incubation period, only 40% of the liposome-encapsulated TGF-beta1 had been released from the fibrin clots, as compared with 68% from those containing the free molecules. Liposome encapsulation thus represents a suitable means of establishing a slow-delivery system in tissue-engineering approaches to articular cartilage repair.     

Truncated vitronectins: binding to immobilized fibrin and to fibrin clots, and their subsequent interaction with cells.

The plasminogen activator inhibitor-1 (PAI-1) is stabilized in its inhibitory conformation by binding to Vitronectin (Vn). The anchorage of PAI-1 to the fibrin fibers was recently shown to be mediated by Vn, and as such to modulate fibrinolysis. Here we report the mapping of the fibrin binding sites in Vn using truncated recombinant Vns, and show that two segments of Vn are involved: one at its carboxyl terminus (within residues 348-459) and one at its amino terminus (within residues 1-44). This mapping sets the stage for (i) the design of specific inhibitors for the Vn-fibrin interaction; (ii) for studying the role of this interaction in the anchoring of endothelial cells and platelets onto the fibrin clot; and (iii) for getting a deeper insight into the mechanism of the Vn-fibrin interaction in fibrinolysis. (c)2002 Elsevier Science.