A constitutive model for a maturing fibrin network

Shear Elastic Coefficient of Normal and Fibrinogen-Deficient Clotting Plasma Obtained with a Sphere-Motion-Based Acoustic-Radiation-Force Approach

Blood coagulation is a process involving several chemical reactions governed by coagulation factors, during which the shear elastic coefficient, μ, varies as the medium transitions from liquid to gel phase. This work used ultrasound to measure μ during the clotting of human plasma samples by tracking the motion of a glass sphere located inside a cuvette filled with the plasma. A 2.03 MHz ultrasonic system generated an impulsive acoustic radiation force acting on the sphere, and a 4.89 MHz pulse-echo ultrasonic system tracked the sphere displacement induced by that force. Measurements of μ were determined by fitting a μ-dependent theoretical model to the motion waveform of the sphere immersed in clotting normal plasma and plasma samples with fibrinogen (FI) concentrations of 1.2 (FI-deficiency) and 3.6 (FI-normal) g/L. For normal plasma, μ started at 14.22 Pa and increased rapidly until 2 min, then slowly until it reached 210.23 Pa at 35 min after the clotting process started. A similar trend was exhibited in plasma samples with FI concentrations of 1.2 and 3.6 g/L, with μ reaching 120.55 and 679.42 Pa, respectively. A theoretical model, related to the kinetics of clot-structure formation, describes the time changes of μ for the clotting plasma samples. The sphere-motion-based acoustic-radiation-force approach allowed us to measure the shear elastic coefficient during the coagulation process of plasma samples with normal and deficient FI concentrations. Our results suggest that the method used in this study is capable of being used to detect bleeding disorders.

Dynamic assessment of plasma clotting in samples with distinct fibrinogen concentrations using impulsive acoustic radiation force

While some diseases reduce fibrinogen concentration, others increase the amount of this clotting factor in the blood. Some studies have shown that the fibrinogen concentration in the blood is related to the stiffness of the formed clot. Hence, the aim of this study was to employ an ultrasonic method based on impulsive acoustic radiation force (IARF) to identify the fibrinogen concentration (coagulation factor I) in a plasma sample by means of peak-displacement (PD), time of peak-displacement (TPD), and shear modulus (μ) as well as to identify the change of plasma samples during the clot formation process. The IARF-based ultrasonic system transmitted bursts with a frequency of 2.03 MHz, duration of 246.31 µs, amplitude of 118 VPP, and pulse with 1.25 Hz repetition frequency to generate an IARF on a glass sphere (2.99 mm in diameter and 2500 kg/m3 in density) embedded in a plasma sample, causing a displacement that was monitored by a pulse-echo system with a center frequency of 4.89 MHz. The values of the shear moduli were 124.14 ± 3.02, 556.99 ± 11.76, and 670.39 ± 9.77 Pa, for fibrinogen concentrations of 1.2, 2.4, and 3.6 g/L 20 to 36 min after the beginning of the coagulation process. The TPD values obtained in the same period were 5.28 ± 0.09, 3.03 ± 0.02, and 2.83 ± 0.01 s. The results indicate that an IARF-based ultrasonic system can be used clinically because it uses small amounts of plasma and has the ability to detect differences in PD, TPD, and μ as a function of fibrinogen concentrations.

Filamentous and step-like behavior of gelling coarse fibrin networks revealed by high-frequency microrheology

By a micro-experimental methodology, we study the ongoing molecular process inside coarse fibrin networks by means of microrheology. We made these networks gelate around a probe microbead, allowing us to observe a temporal evolution compatible with the well-known molecular formation of fibrin networks in four steps: monomer, protofibril, fiber and network. Thanks to the access that optical-trapping interferometry provides to the short-time scale on the bead's Brownian motion, we observe a Kelvin-Voigt mechanical behavior from low to high frequencies, range not available in conventional rheometry. We exploit that mechanical model for obtaining the characteristic lengths of the filamentous structures composing these fibrin networks, whose obtained values are compatible with a non-affine behavior characterized by bending modes. At very long gelation times, a ω^7/8 power-law is observed in the loss modulus, theoretically related with the longitudinal response of the molecular structures.

A three-dimensional phase-field model for multiscale modeling of thrombus biomechanics in blood vessels

Mechanical interactions between flowing and coagulated blood (thrombus) are crucial in dictating the deformation and remodeling of a thrombus after its formation in hemostasis. We propose a fully-Eulerian, three-dimensional, phase-field model of thrombus that is calibrated with existing in vitro experimental data. This phase-field model considers spatial variations in permeability and material properties within a single unified mathematical framework derived from an energy perspective, thereby allowing us to study effects of thrombus microstructure and properties on its deformation and possible release of emboli under different hemodynamic conditions. Moreover, we combine this proposed thrombus model with a particle-based model which simulates the initiation of the thrombus. The volume fraction of a thrombus obtained from the particle simulation is mapped to an input variable in the proposed phase-field thrombus model. The present work is thus the first computational study to integrate the initiation of a thrombus through platelet aggregation with its subsequent viscoelastic responses to various shear flows. This framework can be informed by clinical data and potentially be used to predict the risk of diverse thromboembolic events under physiological and pathological conditions.

Structure, mechanical properties, and modeling of cyclically compressed pulmonary emboli

Pulmonary embolism occurs when blood flow to a part of the lungs is blocked by a venous thrombus that has traveled from the lower limbs. Little is known about the mechanical behavior of emboli under compressive forces from the surrounding musculature and blood pressure. We measured the stress-strain responses of human pulmonary emboli under cyclic compression, and showed that emboli exhibit a hysteretic stress-strain curve. The fibrin fibers and red blood cells (RBCs) are damaged during the compression process, causing irreversible changes in the structure of the emboli. We showed using electron and confocal microscopy that bundling of fibrin fibers occurs due to compression, and damage is accumulated as more cycles are applied. The stress-strain curves depend on embolus structure, such that variations in composition give quantitatively different responses. Emboli with a high fibrin component demonstrate higher normal stress compared to emboli that have a high RBC component. We compared the compression response of emboli to that of whole blood clots containing various volume fractions of RBCs, and found that RBCs rupture at a certain critical stress. We describe the hysteretic response characteristic of foams, using a model of phase transitions in which the compressed foam is segregated into coexisting rarefied and densified phases whose fractions change during compression. Our model takes account of the rupture of RBCs in the compressed emboli and stresses due to fluid flow through their small pores. Our results can help in classifying emboli as rich in fibrin or rich in red blood cells, and can help in understanding what responses to expect when stresses are applied to thrombi in vivo.

Mass spectrometry-based molecular mapping of native FXIIIa cross-links in insoluble fibrin clots

The roles of factor XIIIa-specific cross-links in thrombus formation, regression, or probability for embolization are largely unknown. A molecular understanding of fibrin architecture at the level of these cross-links could inform the development of therapeutic strategies to prevent the sequelae of thromboembolism. Here, we present an MS-based method to map native factor XIIIa cross-links in the insoluble matrix component of whole-blood or plasma-fibrin clots and in in vivo thrombi. Using a chaotrope-insoluble digestion method and quantitative cross-linking MS, we identified the previously mapped fibrinogen peptides that are responsible for covalent D-dimer association, as well as dozens of novel cross-links in the αC region of fibrinogen α. Our findings expand the known native cross-linked species from one to over 100 and suggest distinct antiparallel registries for interprotofibril association and covalent attachment of serpins that regulate clot dissolution.

Three-phase Model of Visco-elastic Incompressible Fluid Flow and its Computational Implementation

Energetic Variational Approach is used to derive a novel thermodynamically consistent three-phase model of a mixture of Newtonian and visco-elastic fluids. The model which automatically satisfies the energy dissipation law and is Galilean invariant, consists of coupled Navier-Stokes and Cahn-Hilliard equations. Modified General Navier Boundary Condition with fluid elasticity taken into account is also introduced for using the model to study moving contact line problems. Energy stable numerical scheme is developed to solve system of model equations efficiently. Convergence of the numerical scheme is verified by simulating a droplet sliding on an inclined plane under gravity. The model can be applied for studying various biological or biophysical problems. Predictive abilities of the model are demonstrated by simulating deformation of venous blood clots with different visco-elastic properties and experimentally observed internal structures under different biologically relevant shear blood flow conditions.

Model predictions of deformation, embolization and permeability of partially obstructive blood clots under variable shear flow

Thromboembolism, one of the leading causes of morbidity and mortality worldwide, is characterized by formation of obstructive intravascular clots (thrombi) and their mechanical breakage (embolization). A novel two-dimensional multi-phase computational model is introduced that describes active interactions between the main components of the clot, including platelets and fibrin, to study the impact of various physiologically relevant blood shear flow conditions on deformation and embolization of a partially obstructive clot with variable permeability. Simulations provide new insights into mechanisms underlying clot stability and embolization that cannot be studied experimentally at this time. In particular, model simulations, calibrated using experimental intravital imaging of an established arteriolar clot, show that flow-induced changes in size, shape and internal structure of the clot are largely determined by two shear-dependent mechanisms: reversible attachment of platelets to the exterior of the clot and removal of large clot pieces. Model simulations predict that blood clots with higher permeability are more prone to embolization with enhanced disintegration under increasing shear rate. In contrast, less permeable clots are more resistant to rupture due to shear rate-dependent clot stiffening originating from enhanced platelet adhesion and aggregation. These results can be used in future to predict risk of thromboembolism based on the data about composition, permeability and deformability of a clot under specific local haemodynamic conditions.

Structure, Mechanics, and Instability of Fibrin Clot Infected with Staphylococcus epidermidis

Health care-associated infection, over half of which can be attributed to indwelling medical devices, is a strong risk factor for thromboembolism. Although most experimental models of medical device infection draw upon isolated bacterial biofilms, in fact there is no infection without host protein contribution. Here we study, to our knowledge, a new model for medical device infection-that of an infected fibrin clot-and show that the common blood-borne pathogen Staphylococcus epidermidis influences this in vitro model of a blood clot mechanically and structurally on both microscopic and macroscopic scales. Bacteria present during clot formation produce a visibly disorganized microstructure that increases clot stiffness and triggers mechanical instability over time. Our results provide insight into the observed correlation between medical device infection and thromboembolism; the increase in model clot heterogeneity shows that S. epidermidis can rupture a fibrin clot. The resultant embolization of the infected clot can contribute to the systemic dissemination of the pathogen.

Interplay of Platelet Contractility and Elasticity of Fibrin/Erythrocytes in Blood Clot Retraction

Blood clot contraction (retraction) is driven by platelet-generated forces propagated by the fibrin network and results in clot shrinkage and deformation of erythrocytes. To elucidate the mechanical nature of this process, we developed a model that combines an active contractile motor element with passive viscoelastic elements. Despite its importance for thrombosis and wound healing, clot contraction is poorly understood. This model predicts how clot contraction occurs due to active contractile platelets interacting with a viscoelastic material, rather than to the poroelastic nature of fibrin, and explains the observed dynamics of clot size, ultrastructure, and measured forces. Mechanically passive erythrocytes and fibrin are present in series and parallel to active contractile cells. This mechanical interplay induces compressive and tensile resistance, resulting in increased contractile force and a reduced extent of contraction in the presence of erythrocytes. This experimentally validated model provides the fundamental mechanical basis for understanding contraction of blood clots.

Recombinant fibrinogen reveals the differential roles of α- and γ-chain cross-linking and molecular heterogeneity in fibrin clot strain-stiffening

Essentials Fibrinogen circulates in human plasma as a complex mixture of heterogeneous molecular variants. We measured strain-stiffening of recombinantly produced fibrinogen upon clotting. Factor XIII and molecular heterogeneity alter clot elasticity at the protofibril and fiber level. This highlights the hitherto unknown role of molecular composition in fibrin clot mechanics.

SUMMARY

Background Fibrin plays a crucial role in haemostasis and wound healing by forming strain-stiffening fibrous networks that reinforce blood clots. The molecular origin of fibrin's strain-stiffening behavior remains poorly understood, primarily because plasma fibrinogen is a complex mixture of heterogeneous molecular variants and is often contaminated by plasma factors that affect clot properties. Objectives and methods To facilitate mechanistic dissection of fibrin nonlinear elasticity, we produced a homogeneous recombinant fibrinogen corresponding to the main variant in human plasma, termed rFib610. We characterized the structure of rFib610 clots using turbidimetry, microscopy and X-ray scattering. We used rheology to measure the strain-stiffening behavior of the clots and determined the fiber properties by modeling the clots as semi-flexible polymer networks. Results We show that addition of FXIII to rFib610 clots causes a dose-dependent stiffness increase at small deformations and renders the strain-stiffening response reversible. We find that γ-chain cross-linking contributes to clot elasticity by changing the force-extension behavior of the protofibrils, whereas α-chain cross-linking stiffens the fibers, as a consequence of tighter coupling between the constituent protofibrils. Interestingly, rFib610 protofibrils have a 25% larger bending rigidity than plasma-purified fibrin protofibrils and a delayed strain-stiffening, indicating that molecular heterogeneity influences clot mechanics at the protofibril scale. Conclusions Fibrinogen molecular heterogeneity and FXIII affect the mechanical function of fibrin clots by altering the nonlinear viscoelastic properties at the protofibril and fiber scale. This work provides a starting point to investigate the role of molecular heterogeneity of plasma fibrinogen in fibrin clot mechanics and haemostasis.

A constitutive model for developing blood clots with various compositions and their nonlinear viscoelastic behavior

The mechanical properties determine to a large extent the functioning of a blood clot. These properties depend on the composition of the clot and have been related to many diseases. However, the various involved components and their complex interactions make it difficult at this stage to fully understand and predict properties as a function of the components. Therefore, in this study, a constitutive model is developed that describes the viscoelastic behavior of blood clots with various compositions. Hereto, clots are formed from whole blood, platelet-rich plasma and platelet-poor plasma to study the influence of red blood cells, platelets and fibrin, respectively. Rheological experiments are performed to probe the mechanical behavior of the clots during their formation. The nonlinear viscoelastic behavior of the mature clots is characterized using a large amplitude oscillatory shear deformation. The model is based on a generalized Maxwell model that accurately describes the results for the different rheological experiments by making the moduli and viscosities a function of time and the past and current deformation. Using the same model with different parameter values enables a description of clots with different compositions. A sensitivity analysis is applied to study the influence of parameter variations on the model output. The relative simplicity and flexibility make the model suitable for numerical simulations of blood clots and other materials showing similar behavior.

A constitutive model for the time-dependent, nonlinear stress response of fibrin networks

Blood clot formation is important to prevent blood loss in case of a vascular injury but disastrous when it occludes the vessel. As the mechanical properties of the clot are reported to be related to many diseases, it is important to have a good understanding of their characteristics. In this study, a constitutive model is presented that describes the nonlinear viscoelastic properties of the fibrin network, the main structural component of blood clots. The model is developed using results of experiments in which the fibrin network is subjected to a large amplitude oscillatory shear (LAOS) deformation. The results show three dominating nonlinear features: softening over multiple deformation cycles, strain stiffening and increasing viscous dissipation during a deformation cycle. These features are incorporated in a constitutive model based on the Kelvin–Voigt model. A network state parameter is introduced that takes into account the influence of the deformation history of the network. Furthermore, in the period following the LAOS deformation, the stiffness of the networks increases which is also incorporated in the model. The influence of cross-links created by factor XIII is investigated by comparing fibrin networks that have polymerized for 1 and 2 h. A sensitivity analysis provides insights into the influence of the eight fit parameters. The model developed is able to describe the rich, time-dependent, nonlinear behavior of the fibrin network. The model is relatively simple which makes it suitable for computational simulations of blood clot formation and is general enough to be used for other materials showing similar behavior.