Foam-like compression behavior of fibrin networks

Flow affects the structural and mechanical properties of the fibrin network in plasma clots

The fibrin network is one of the main components of thrombi. Altered fibrin network properties are known to influence the development and progression of thrombotic disorders, at least partly through effects on the mechanical stability of fibrin. Most studies investigating the role of fibrin in thrombus properties prepare clots under static conditions, missing the influence of blood flow which is present in vivo. In this study, plasma clots in the presence and absence of flow were prepared inside a Chandler loop. Recitrated plasma from healthy donors were spun at 0 and 30 RPM. The clot structure was characterized using scanning electron microscopy and confocal microscopy and correlated with the stiffness measured by unconfined compression testing. We quantified fibrin fiber density, pore size, and fiber thickness and bulk stiffness at low and high strain values. Clots formed under flow had thinner fibrin fibers, smaller pores, and a denser fibrin network with higher stiffness values compared to clots formed in absence of flow. Our findings indicate that fluid flow is an essential factor to consider when developing physiologically relevant in vitro thrombus models used in researching thrombectomy outcomes or risk of embolization.

Fibrin clots from patients with acute-on-chronic liver failure are weaker than those from healthy individuals and patients with sepsis without underlying liver disease

BACKGROUND

Previous studies identified decreased clot permeability, without differences in fibrin fiber density in clots, from patients with cirrhosis compared with those from healthy controls (HCs). Fibrinogen hypersialylation could be the reason for this discrepancy.

OBJECTIVES

The aim of this work was to study mechanical properties of clots and reassess clot permeability in relation to hypersialylation in patients with stable cirrhosis, acute decompensation, and acute-on-chronic liver failure (ACLF). Sepsis patients without liver disease were included to distinguish between liver-specific and inflammation-driven phenotypes.

METHODS

Pooled plasma was used for rheology and permeability experiments. Permeability was assessed with compression using a rheometer and by liquid permeation. Purified fibrinogen treated with neuraminidase was used to study the effects of fibrinogen hypersialylation on liquid permeation.

RESULTS

Mechanical properties of clots from patients with stable cirrhosis and acute decompensation were similar to those of clots from HCs, but clots from patients with ACLF were softer and ruptured at lower shear stress. Clots from sepsis patients without liver disease were stiffer than those from the other groups, but this effect disappeared after adjusting for increased plasma fibrinogen concentrations. Permeability was similar between clots under compression from HCs and clots under compression from patients but decreased with increasing disease severity in liquid permeation. Removal of fibrinogen sialic acid residues increased permeability more in patients than in controls.

CONCLUSION

Clots from patients with ACLF have weak mechanical properties despite unaltered fibrin fiber density. Previous liquid permeation experiments may have erroneously concluded that clots from patients with ACLF are prothrombotic as fibrinogen hypersialylation leads to underestimation of clot permeability in this setting, presumably due to enhanced water retention.

Combined computational modeling and experimental study of the biomechanical mechanisms of platelet-driven contraction of fibrin clots

While blood clot formation has been relatively well studied, little is known about the mechanisms underlying the subsequent structural and mechanical clot remodeling called contraction or retraction. Impairment of the clot contraction process is associated with both life-threatening bleeding and thrombotic conditions, such as ischemic stroke, venous thromboembolism, and others. Recently, blood clot contraction was observed to be hindered in patients with COVID-19. A three-dimensional multiscale computational model is developed and used to quantify biomechanical mechanisms of the kinetics of clot contraction driven by platelet-fibrin pulling interactions. These results provide important biological insights into contraction of platelet filopodia, the mechanically active thin protrusions of the plasma membrane, described previously as performing mostly a sensory function. The biomechanical mechanisms and modeling approach described can potentially apply to studying other systems in which cells are embedded in a filamentous network and exert forces on the extracellular matrix modulated by the substrate stiffness.

Statistical field theory for nonlinear elasticity of polymer networks with excluded volume interactions

Polymer networks formed by cross linking flexible polymer chains are ubiquitous in many natural and synthetic soft-matter systems. Current micromechanics models generally do not account for excluded volume interactions except, for instance, through imposing a phenomenological incompressibility constraint at the continuum scale. This work aims to examine the role of excluded volume interactions on the mechanical response. The approach is based on the framework of the self-consistent statistical field theory of polymers, which provides an efficient mesoscale approach that enables the accounting of excluded volume effects without the expense of large-scale molecular modeling. A mesoscale representative volume element is populated with multiple interacting chains, and the macroscale nonlinear elastic deformation is imposed by mapping the end-to-end vectors of the chains by this deformation. In the absence of excluded volume interactions, it recovers the closed-form results of the classical theory of rubber elasticity. With excluded volume interactions, the model is solved numerically in three dimensions using a finite element method to obtain the energy, stresses, and linearized moduli under imposed macroscale deformation. Highlights of the numerical study include: (i) the linearized Poisson's ratio is very close to the incompressible limit without a phenomenological imposition of incompressibility; (ii) despite the harmonic Gaussian chain as a starting point, there is an emergent strain-softening and strain-stiffening response that is characteristic of real polymer networks, driven by the interplay between the entropy and the excluded volume interactions; and (iii) the emergence of a deformation-sensitive localization instability at large excluded volumes.

Fracture toughness of fibrin gels as a function of protein volume fraction: Mechanical origins

The mechanical stability of blood clots necessary for their functions is provided by fibrin, a fibrous gel. Rupture of clots leads to life-threatening thrombotic embolization, which is little understood. Here, we combine experiments and simulations to determine the toughness of plasma clots as a function of fibrin content and correlate toughness with fibrin network structure characterized by confocal and scanning electron microscopy. We develop fibrin constitutive laws that scale with fibrin concentration and capture the force-stretch response of cracked clot specimens using only a few material parameters. Toughness is calculated from the path-independent J* integral that includes dissipative effects due to fluid flow and uses only the constitutive model and overall stretch at crack propagation as input. We show that internal fluid motion, which is not directly measurable, contributes significantly to clot toughness, with its effect increasing as fibrin content increases, because the reduced gel porosity at higher density results in greater expense of energy in fluid motion. Increasing fibrin content (1→10mg/mL) results in a significant increase in clot toughness (3→15 N/m) in accordance with a power law relation reminiscent of cellular solids and elastomeric gels. These results provide a basis for understanding and predicting the tendency for thrombotic embolization. STATEMENT OF SIGNIFICANCE: Fibrin, a naturally occurring biomaterial, is the major determinant of the structural and mechanical integrity of blood clots. We determined that increasing the fibrin content in clots, as in some thrombi and fibrin-based anti-bleeding sealants, results in an increase in clot toughness. Toughness corresponds to the ability to resist rupturing in the presence of a defect. We couple bulk mechanical testing, microstructural measurements, and finite element modeling to capture the force-stretch response of fibrin clots and compute toughness. We show that increased fibrin content in clots reduces porosity and limits fluid motion and that fluid motion drastically alters the clot toughness. These results provide a fundamental understanding of blood clot rupture and could help in rational design of fibrin-containing biomaterials.

Effect of hyaluronic acid on microscale deformations of collagen gels

As fibrous collagen is the most abundant protein in mammalian tissues, gels of collagen fibers have been extensively used as an extracellular matrix scaffold to study how cells sense and respond to cues from their microenvironment. Other components of native tissues, such as glycosaminoglycans like hyaluronic acid, can affect cell behavior in part by changing the mechanical properties of the collagen gel. Prior studies have quantified the effects of hyaluronic acid on the mechanical properties of collagen gels in experiments of uniform shear or compression at the macroscale. However, there remains a lack of experimental studies of how hyaluronic acid changes the mechanical properties of collagen gels at the scale of a cell. Here, we studied how addition of hyaluronic acid to gels of collagen fibers affects the local field of displacements in response to contractile loads applied on length scales similar to those of a contracting cell. Using spherical poly(N-isopropylacrylamide) particles, which contract when heated, we induced displacement in gels of collagen and collagen with hyaluronic acid. Displacement fields were quantified using a combination of confocal microscopy and digital image correlation. Results showed that hyaluronic acid suppressed the distance over which displacements propagated, suggesting that it caused the network to become more linear. Additionally, hyaluronic acid had no statistical effect on heterogeneity of the displacement fields, but it did make the gels more elastic by substantially reducing the magnitude of permanent deformations. Lastly, we examined the effect of hyaluronic acid on fiber remodeling due to localized forces and found that hyaluronic acid partially - but not fully - inhibited remodeling. This result is consistent with prior studies suggesting that fiber remodeling is associated with a phase transition resulting from an instability caused by nonlinearity of the collagen gel.

Dynamic remodeling of fiber networks with stiff inclusions under compressive loading

The ability of tissues to sustain and withstand mechanical stress is critical to tissue development and healthy tissue maintenance. The mechanical properties of tissues are typically considered to be dominated by the fibrous extracellular matrix (ECM) component of tissues. Fiber network mechanics can capture certain mechanical features of tissues, such as shear strain stiffening, but is insufficient in describing the compressive response of certain tissues and blood clots that are rich in extracellular matrix. To understand the mechanical response of tissues, we employ a contemporary mechanical model, a fibrous network of fibrin embedded with inert bead inclusions that preserve the volume-conserving constraints of cells in tissues. Combining bulk mechanical rheology and a custom imaging device, we show that the presence of inclusions alters the local dynamic remodeling of the networks undergoing uniaxial compressive strains and demonstrate non-affine correlated motion within a fiber-bead network, predicted to stretch fibers in the network and lead to the ability of the network to stiffen under compression, a key feature of real tissues. These findings have important implications for understanding how local structural properties of cells and ECM fibers impact the bulk mechanical response of real tissues. STATEMENT OF SIGNIFICANCE: To understand why real tissue stiffens under compression, we study a model tissue system which also stiffens: a fibrin network embedded with stiff beads. We design a device that images compression of both fiber and fiber-bead networks. Distinct from previous imaging studies, this setup can dynamically capture network deformation on scales larger than single fibers. From the videos, we see fluid flow and network remodeling are both critical to compression behavior. The fiber-bead network has faster fluid flow, reduced network recovery, and correlated motion during network relaxation. We hypothesize that the beads hinder network relaxation of stretched fibers, thus retaining the applied stress and exhibiting stiffening. Our findings reveal important details for modeling tissue mechanics towards optimizing healthcare.

Biomechanical origins of inherent tension in fibrin networks

Blood clots form at the site of vascular injury to seal the wound and prevent bleeding. Clots are in tension as they perform their biological functions and withstand hydrodynamic forces of blood flow, vessel wall fluctuations, extravascular muscle contraction and other forces. There are several mechanisms that generate tension in a blood clot, of which the most well-known is the contraction/retraction caused by activated platelets. Here we show through experiments and modeling that clot tension is generated by the polymerization of fibrin. Our mathematical model is built on the hypothesis that the shape of fibrin monomers having two-fold symmetry and off-axis binding sites is ultimately the source of inherent tension in individual fibers and the clot. As the diameter of a fiber grows during polymerization the fibrin monomers must suffer axial twisting deformation so that they remain in register to form the half-staggered arrangement characteristic of fibrin protofibrils. This deformation results in a pre-strain that causes fiber and network tension. Our results for the pre-strain in single fibrin fibers is in agreement with experiments that measured it by cutting fibers and measuring their relaxed length. We connect the mechanics of a fiber to that of the network using the 8-chain model of polymer elasticity. By combining this with a continuum model of swellable elastomers we can compute the evolution of tension in a constrained fibrin gel. The temporal evolution and tensile stresses predicted by this model are in qualitative agreement with experimental measurements of the inherent tension of fibrin clots polymerized between two fixed rheometer plates. These experiments also revealed that increasing thrombin concentration leads to increasing internal tension in the fibrin network. Our model may be extended to account for other mechanisms that generate pre-strains in individual fibers and cause tension in three-dimensional proteinaceous polymeric networks.

Rheology of fibrous gels under compression

A number of biological tissues and synthetic gels consist of a fibrous network infused with liquid. There have been a few experimental studies of the rheological properties of such gels under applied compressive strain. Their results suggest that a plot of rheological moduli as a function of applied compressive strain has a long plateau flanked by a steeply increasing curve for large compressive strains and a slowly decreasing curve for small strains. In this paper we explain these trends in rheological properties using a chemo-elastic model characterized by a double-well strain energy function for the underlying fibrous network. The wells correspond to rarefied and densified phases of the fibrous network at low and high strains, respectively. These phases can co-exist across a movable transition front in the gel in order to accommodate overall applied compression. We find that the rheological properties of fibrous gels share similarities with a Kelvin-Voigt visco-elastic solid. The storage modulus has its origins in the elasticity of the fibrous network, while the loss modulus is determined by the dissipation caused by liquid flow through pores. The rheological properties can depend on the number of phase transition fronts present in a compressed sample. Our analysis may explain the dependence of storage and loss moduli of fibrin gels on the loading history. We also point to the need for combining rheological measurements on gels with a microstructural analysis that could shed light on various dissipation mechanisms.

Hyper-viscoelastic damage modeling of whole blood clot under large deformation

Blood clots play a diametric role in our bodies as they are both vital as a wound sealant, as well as the source for many devastating diseases. In blood clots' physiological and pathological roles, their mechanics play a critical part. These mechanics are non-trivial owing to blood clots' complex nonlinear, viscoelastic behavior. Casting this behavior into mathematical form is a fundamental step toward a better basic scientific understanding of blood clots, as well as toward diagnostic and prognostic computational models. Here, we identify a hyper-viscoelastic damage model that we fit to original data on the nonlinear, viscoelastic behavior of blood clots. Our model combines the classic Ogden hyperelastic constitutive law, a finite viscoelastic model for large deformations, and a non-local, gradient-enhanced damage formulation. By fitting our model to cyclic tensile test data and extension-to-failure data, we inform the model's nine unknown material parameters. We demonstrate the predictability of our model by validating it against unseen cyclic tensile test and stress-relaxation data. Our original data, model formulation, and the identified constitutive parameters of this model are openly available for others to use, which will aid in developing accurate, quantitative simulations of blood clot mechanics.

Cells exploit a phase transition to mechanically remodel the fibrous extracellular matrix

Through mechanical forces, biological cells remodel the surrounding collagen network, generating striking deformation patterns. Tethers-tracts of high densification and fibre alignment-form between cells, thinner bands emanate from cell clusters. While tethers facilitate cell migration and communication, how they form is unclear. Combining modelling, simulation and experiment, we show that tether formation is a densification phase transition of the extracellular matrix, caused by buckling instability of network fibres under cell-induced compression, featuring unexpected similarities with martensitic microstructures. Multiscale averaging yields a two-phase, bistable continuum energy landscape for fibrous collagen, with a densified/aligned second phase. Simulations predict strain discontinuities between the undensified and densified phase, which localizes within tethers as experimentally observed. In our experiments, active particles induce similar localized patterns as cells. This shows how cells exploit an instability to mechanically remodel the extracellular matrix simply by contracting, thereby facilitating mechanosensing, invasion and metastasis.

Analysis of the foam-forming of non-woven lightweight fibrous materials using X-ray tomography

Abstract

Foam-forming has in the past predominantly been used to create two-dimensional sheet-like fibrous materials. Allowing the foam to drain freely and decay under gravity, rather than applying a vacuum to remove it rapidly, we can produce lightweight three-dimensional fibrous structures from cellulose fibres, of potential use for thermal and acoustic insulation. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document}μCT scanning of the fibrous materials enable us to determine both void size distributions and also distributions of fibre orientations. Through image analysis and uniaxial compression testing, we find that the orientation of the fibres, rather than the size of the voids, determine the compressive strength of the material. The fibrous samples display a layering of the fibres perpendicular to the direction of drainage of the precursor liquid foam. This leads to an anisotropy of the compressive behaviour of the samples. Varying the initial liquid fraction of the foam allows for tuning of the compressive strength. We show an increase in over seven times can be achieved for samples of the same density (13 kg.m^-3).

Graphic abstract

Fibrous gels modelled as fluid-filled continua with double-well energy landscape

Several biological materials are fibre networks infused with fluid, often referred to as fibrous gels. An important feature of these gels is that the fibres buckle under compression, causing a densification of the network that is accompanied by a reduction in volume and release of fluid. Displacement-controlled compression of fibrous gels has shown that the network can exist in a rarefied and a densified state over a range of stresses. Continuum chemo-elastic theories can be used to model the mechanical behaviour of these gels, but they suffer from the drawback that the stored energy function of the underlying network is based on neo-Hookean elasticity, which cannot account for the existence of multiple phases. Here we use a double-well stored energy function in a chemo-elastic model of gels to capture the existence of two phases of the network. We model cyclic compression/decompression experiments on fibrous gels and show that they exhibit propagating interfaces and hysteretic stress-strain curves that have been observed in experiments. We can capture features in the rate-dependent response of these fibrous gels without recourse to finite-element calculations. We also perform experiments to show that certain features in the stress-strain curves of fibrous gels predicted by our model can be found in the compression response of blood clots. Our methods may be extended to other tissues and synthetic gels that have a fibrous structure.

Fibrinogen and Fibrin

Fibrinogen is a large glycoprotein, synthesized primarily in the liver. With a normal plasma concentration of 1.5-3.5 g/L, fibrinogen is the most abundant blood coagulation factor. The final stage of blood clot formation is the conversion of soluble fibrinogen to insoluble fibrin, the polymeric scaffold for blood clots that stop bleeding (a protective reaction called hemostasis) or obstruct blood vessels (pathological thrombosis). Fibrin is a viscoelastic polymer and the structural and mechanical properties of the fibrin scaffold determine its effectiveness in hemostasis and the development and outcome of thrombotic complications. Fibrin polymerization comprises a number of consecutive reactions, each affecting the ultimate 3D porous network structure. The physical properties of fibrin clots are determined by structural features at the individual fibrin molecule, fibrin fiber, network, and whole clot levels and are among the most important functional characteristics, enabling the blood clot to withstand arterial blood flow, platelet-driven clot contraction, and other dynamic forces. This chapter describes the molecular structure of fibrinogen, the conversion of fibrinogen to fibrin, the mechanical properties of fibrin as well as its structural origins and lastly provides evidence for the role of altered fibrin clot properties in both thrombosis and bleeding.

Continuum elastic models for force transmission in biopolymer gels

We review continuum elastic models for the transmission of both external forces and internal active cellular forces in biopolymer gels, and relate them to recent experiments. Rather than being exhaustive, we focus on continuum elastic models for small affine deformations and intend to provide a systematic continuum method and some analytical perspectives on the study of force transmission in biopolymer gels. We start from a very brief review of the nonlinear mechanics of individual biopolymers and a summary of constitutive models for the nonlinear elasticity of biopolymer gels. We next show that the simple 3-chain model can give predictions that fit well the shear experiments of some biopolymer gels, including the effects of strain-stiffening and negative normal stress. We then review continuum models for the transmission of internal active forces that are induced by a spherically contracting cell embedded in a three-dimensional biopolymer gel. Various scaling regimes for the decay of cell-induced displacements are identified for linear isotropic and anisotropic materials, and for biopolymer gels with nonlinear compressive-softening and strain-stiffening elasticity, respectively. After that, we present (using an energetic approach) the generic and unified continuum theory proposed in [D. Ben-Yaakov et al., Soft Matter, 2015, 11, 1412] about how the transmission of forces in the biogel matrix can mediate long-range interactions between cells with mechanical homeostasis. We show the predictions of the theory in a special hexagonal multicellular array, and relate them to recent experiments. Finally, we conclude this paper with comments on the limitations and outlook of continuum modeling, and highlight the need for complementary theoretical approaches, such as discrete network simulations, to force transmission in biopolymer gels and phenomenological active gel theories for multicellular systems.

Rupture of blood clots: Mechanics and pathophysiology

Fibrin is the three-dimensional mechanical scaffold of protective blood clots that stop bleeding and pathological thrombi that obstruct blood vessels. Fibrin must be mechanically tough to withstand rupture, after which life-threatening pieces (thrombotic emboli) are carried downstream by blood flow. Despite multiple studies on fibrin viscoelasticity, mechanisms of fibrin rupture remain unknown. Here, we examined mechanically and structurally the strain-driven rupture of human blood plasma-derived fibrin clots where clotting was triggered with tissue factor. Toughness, i.e., resistance to rupture, quantified by the critical energy release rate (a measure of the propensity for clot embolization) of physiologically relevant fibrin gels was determined to be 7.6 ± 0.45 J/m2. Finite element (FE) simulations using fibrin material models that account for forced protein unfolding independently supported this measured toughness and showed that breaking of fibers ahead the crack at a critical stretch is the mechanism of rupture of blood clots, including thrombotic embolization.

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.

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.

Poroelasticity of (bio)polymer networks during compression: theory and experiment

Soft living tissues like cartilage can be considered as biphasic materials comprising a fibrous complex biopolymer network and a viscous background liquid. Here, we show by a combination of experiment and theoretical analysis that both the hydraulic permeability and the elastic properties of (bio)polymer networks can be determined with simple ramp compression experiments in a commercial rheometer. In our approximate closed-form solution of the poroelastic equations of motion, we find the normal force response during compression as a combination of network stress and fluid pressure. Choosing fibrin as a biopolymer model system with controllable pore size, measurements of the full time-dependent normal force during compression are found to be in excellent agreement with the theoretical calculations. The inferred elastic response of large-pore (μm) fibrin networks depends on the strain rate, suggesting a strong interplay between network elasticity and fluid flow. Phenomenologically extending the calculated normal force into the regime of nonlinear elasticity, we find strain-stiffening of small-pore (sub-μm) fibrin networks to occur at an onset average tangential stress at the gel-plate interface that depends on the polymer concentration in a power-law fashion. The inferred permeability of small-pore fibrin networks scales approximately inverse squared with the fibrin concentration, implying with a microscopic cubic lattice model that the number of protofibrils per fibrin fiber cross-section decreases with protein concentration. Our theoretical model provides a new method to obtain the hydraulic permeability and the elastic properties of biopolymer networks and hydrogels with simple compression experiments, and paves the way to study the relation between fluid flow and elasticity in biopolymer networks during dynamical compression.

Elastic Anisotropy Governs the Range of Cell-Induced Displacements

The unique nonlinear mechanics of the fibrous extracellular matrix (ECM) facilitates long-range cell-cell mechanical communications that would be impossible for linear elastic substrates. Past research has described the contribution of two separated effects on the range of force transmission, including ECM elastic nonlinearity and fiber alignment. However, the relation between these different effects is unclear, and how they combine to dictate force transmission range is still elusive. Here, we combine discrete fiber simulations with continuum modeling to study the decay of displacements induced by a contractile cell in fibrous networks. We demonstrate that fiber nonlinearity and fiber reorientation both contribute to the strain-induced elastic anisotropy of the cell's local environment. This elastic anisotropy is a "lumped" parameter that governs the slow decay of displacements, and it depends on the magnitude of applied strain, either an external tension or an internal contraction, as a model of the cell. Furthermore, we show that accounting for artificially prescribed elastic anisotropy dictates the decay of displacements induced by a contracting cell. Our findings unify previous single effects into a mechanical theory that explains force transmission in fibrous networks. This work may provide insights into biological processes that involve communication of distant cells mediated by the ECM, such as those occurring in morphogenesis, wound healing, angiogenesis, and cancer metastasis. It may also provide design parameters for biomaterials to control force transmission between cells as a way to guide morphogenesis in tissue engineering.

Computational simulations of thrombolysis in acute stroke: Effect of clot size and location on recanalisation

Acute ischaemic stroke can be treated by intravenous thrombolysis whereby tissue plasminogen activator (tPA) is infused to dissolve clots that block blood supply to the brain. In this study, we aim to examine the influence of clot location and size on lysis pattern and recanalisation by using a recently developed computational modelling framework for thrombolysis under physiological flow conditions. An image-based patient-specific model is reconstructed which consists of the internal carotid bifurcation with the A1 segment of anterior cerebral arteries and M1 segment of middle cerebral arteries, and the M1 bifurcation containing the M2 segments. By varying the clot size and location, 7 scenarios are simulated mimicking thrombolysis of M1 and M2 occlusions. Our results show that initial breakthrough always occurs along the inner curvature of the occluded cerebral artery, due to prolonged tPA residence time in the recirculation zone. For a given occlusion site, lysis completion time appears to increase almost quadratically with the initial clot volume; whereas for a given clot volume, the simulated M2 occlusions take up to 30% longer for complete lysis compared to the corresponding M1 occlusions.

Fibrin as a Multipurpose Physiological Platform for Bone Tissue Engineering and Targeted Delivery of Bioactive Compounds

Although bone graft is still considered as the gold standard method, bone tissue engineering offers promising alternatives designed to mimic the extracellular matrix (ECM) and to guide bone regeneration process. In this attempt, due to their similarity to the ECM and their low toxicity/immunogenicity properties, growing attention is paid to natural polymers. In particular, considering the early critical role of fracture hematoma for bone healing, fibrin, which constitutes blood clot, is a candidate of choice. Indeed, in addition to its physiological roles in bone healing cascade, fibrin biochemical characteristics make it suitable to be used as a multipurpose platform for bioactive agents’ delivery. Thus, taking advantage of these key assets, researchers and clinicians have the opportunity to develop composite systems that might further improve bone tissue reconstruction, and more generally prevent/treat skeletal disorders.

Contribution of nascent cohesive fiber-fiber interactions to the non-linear elasticity of fibrin networks under tensile load

Fibrin is a viscoelastic proteinaceous polymer that determines the deformability and integrity of blood clots and fibrin-based biomaterials in response to biomechanical forces. Here, a previously unnoticed structural mechanism of fibrin clots' mechanical response to external tensile loads is tested using high-resolution confocal microscopy and recently developed three-dimensional computational model. This mechanism, underlying local strain-stiffening of individual fibers as well as global stiffening of the entire network, is based on previously neglected nascent cohesive pairwise interactions between individual fibers (crisscrossing) in fibrin networks formed under tensile load. Existence of fiber-fiber crisscrossings of reoriented fibers was confirmed using 3D imaging of experimentally obtained stretched fibrin clots. The computational model enabled us to study structural details and quantify mechanical effects of the fiber-fiber cohesive crisscrossing during stretching of fibrin gels at various spatial scales. The contribution of the fiber-fiber cohesive contacts to the elasticity of stretched fibrin networks was characterized by changes in individual fiber stiffness, the length, width, and alignment of fibers, as well as connectivity and density of the entire network. The results show that the nascent cohesive crisscrossing of fibers in stretched fibrin networks comprise an underappreciated important structural mechanism underlying the mechanical response of fibrin to (patho)physiological stresses that determine the course and outcomes of thrombotic and hemostatic disorders, such as heart attack and ischemic stroke. STATEMENT OF SIGNIFICANCE: Fibrin is a viscoelastic proteinaceous polymer that determines the deformability and integrity of blood clots and fibrin-based biomaterials in response to biomechanical forces. In this paper, a novel structural mechanism of fibrin clots' mechanical response to external tensile loads is tested using high-resolution confocal microscopy and newly developed computational model. This mechanism, underlying local strain-stiffening of individual fibers as well as global stiffening of the entire network, is based on previously neglected nascent cohesive pairwise interactions between individual fibers (crisscrossing) in fibrin networks formed under tensile load. Cohesive crisscrossing is an important structural mechanism that influences the mechanical response of blood clots and which can determine the outcomes of blood coagulation disorders, such as heart attacks and strokes.

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.

Simple Synthetic Molecular Hydrogels from Self-Assembling Alkylgalactonamides as Scaffold for 3D Neuronal Cell Growth

In this work, we demonstrated that the hydrogel obtained from a very simple and single synthetic molecule, N-heptyl-galactonamide was a suitable scaffold for the growth of neuronal cells in 3D. We evidenced by confocal microscopy the presence of the cells into the gel up to a depth of around 200 μm, demonstrating that the latter was permissive to cell growth and enabled a true 3D colonization and organization. It also supported successfully the differentiation of adult human neuronal stem cells (hNSCs) into both glial and neuronal cells and the development of a really dense neurofilament network. So the gel appears to be a good candidate for neural tissue regeneration. In contrast with other molecular gels described for cell culture, the molecule can be obtained at the gram scale by a one-step reaction. The resulting gel is very soft, a quality in accordance with the aim of growing neuronal cells, that requires low modulus substrates similar to the brain. But because of its fragility, specific procedures had to be implemented for its preparation and for cell labeling and confocal microscopy observations. Notably, the implementation of a controlled slow cooling of the gel solution was needed to get a very soft but nevertheless cohesive gel. In these conditions, very wide straight and long micrometric fibers were formed, held together by a second network of flexible narrower nanometric fibers. The two kinds of fibers guided the neurite and glial cell growth in a different way. We also underlined the importance of a tiny difference in the molecular structure on the gel performances: parent molecules, differing by a one-carbon increment in the alkyl chain length, N-hexyl-galactonamide and N-octyl-galactonamide, were not as good as N-heptyl-galactonamide. Their differences were analyzed in terms of gel fibers morphology, mechanical properties, solubility, chain parity, and cell growth.

Displacement Propagation in Fibrous Networks Due to Local Contraction

The extracellular matrix provides macroscale structure to tissues and microscale guidance for cell contraction, adhesion, and migration. The matrix is composed of a network of fibers, which each deform by stretching, bending, and buckling. Whereas the mechanics has been well characterized in uniform shear and extension, the response to more general loading conditions remains less clear, because the associated displacement fields cannot be predicted a priori. Studies simulating contraction, such as due to a cell, have observed displacements that propagate over a long range, suggesting mechanisms such as reorientation of fibers toward directions of tensile force and nonlinearity due to buckling of fibers under compression. It remains unclear which of these two mechanisms produces the long-range displacements and how properties like fiber bending stiffness and fiber length affect the displacement field. Here, we simulate contraction of an inclusion within a fibrous network and fit the resulting radial displacements to ur ∼ r−n where the power n quantifies the decay of displacements over distance, and a value of n less than that predicted by classical linear elasticity indicates displacements that propagate over a long range. We observed displacements to propagate over a longer range for greater contraction of the inclusion, for networks having longer fibers, and for networks with lower fiber bending stiffness. Contraction of the inclusion also caused fibers to reorient into the radial direction, but, surprisingly, the reorientation was minimally affected by bending stiffness. We conclude that both reorientation and nonlinearity are responsible for the long-range displacements.

A review of fibrin and fibrin composites for bone tissue engineering

Tissue engineering has emerged as a new treatment approach for bone repair and regeneration seeking to address limitations associated with current therapies, such as autologous bone grafting. While many bone tissue engineering approaches have traditionally focused on synthetic materials (such as polymers or hydrogels), there has been a lot of excitement surrounding the use of natural materials due to their biologically inspired properties. Fibrin is a natural scaffold formed following tissue injury that initiates hemostasis and provides the initial matrix useful for cell adhesion, migration, proliferation, and differentiation. Fibrin has captured the interest of bone tissue engineers due to its excellent biocompatibility, controllable biodegradability, and ability to deliver cells and biomolecules. Fibrin is particularly appealing because its precursors, fibrinogen, and thrombin, which can be derived from the patient's own blood, enable the fabrication of completely autologous scaffolds. In this article, we highlight the unique properties of fibrin as a scaffolding material to treat bone defects. Moreover, we emphasize its role in bone tissue engineering nanocomposites where approaches further emulate the natural nanostructured features of bone when using fibrin and other nanomaterials. We also review the preparation methods of fibrin glue and then discuss a wide range of fibrin applications in bone tissue engineering. These include the delivery of cells and/or biomolecules to a defect site, distributing cells, and/or growth factors throughout other pre-formed scaffolds and enhancing the physical as well as biological properties of other biomaterials. Thoughts on the future direction of fibrin research for bone tissue engineering are also presented. In the future, the development of fibrin precursors as recombinant proteins will solve problems associated with using multiple or single-donor fibrin glue, and the combination of nanomaterials that allow for the incorporation of biomolecules with fibrin will significantly improve the efficacy of fibrin for numerous bone tissue engineering applications.

Compression-induced structural and mechanical changes of fibrin-collagen composites

Fibrin and collagen as well as their combinations play an important biological role in tissue regeneration and are widely employed in surgery as fleeces or sealants and in bioengineering as tissue scaffolds. Earlier studies demonstrated that fibrin-collagen composite networks displayed improved tensile mechanical properties compared to the isolated protein matrices. Unlike previous studies, here unconfined compression was applied to a fibrin-collagen filamentous polymer composite matrix to study its structural and mechanical responses to compressive deformation. Combining collagen with fibrin resulted in formation of a composite hydrogel exhibiting synergistic mechanical properties compared to the isolated fibrin and collagen matrices. Specifically, the composite matrix revealed a one order of magnitude increase in the shear storage modulus at compressive strains>0.8 in response to compression compared to the mechanical features of individual components. These material enhancements were attributed to the observed structural alterations, such as network density changes, an increase in connectivity along with criss-crossing, and bundling of fibers. In addition, the compressed composite collagen/fibrin networks revealed a non-linear transformation of their viscoelastic properties with softening and stiffening regimes. These transitions were shown to depend on protein concentrations. Namely, a decrease in protein content drastically affected the mechanical response of the networks to compression by shifting the onset of stiffening to higher degrees of compression. Since both natural and artificially composed extracellular matrices experience compression in various (patho)physiological conditions, our results provide new insights into the structural biomechanics of the polymeric composite matrix that can help to create fibrin-collagen sealants, sponges, and tissue scaffolds with tunable and predictable mechanical properties.

Compressive elasticity of polydisperse biopolymer gels

We theoretically predict the nonlinear elastic responses of polydisperse biopolymer gels to uniaxial compression. We analyze the competition between compressive stiffening due to polymer densification by out-going solvent flow and compressive softening due to continuous polymer buckling. We point out that the polydispersity in polymer lengths can result in an intrinsic, equilibrium mode of nonaffine compression: nonuniform strain but with uniform force distribution, which is found to be more energetically preferable than affine deformation. In this case, the gel softens significantly after the onset of polymer buckling at small compression, but as compression increases, densification-induced stiffening becomes important and a modulus plateau should be observed for a large range of strain. We also relate our results to recent compression experiments on collagen gels and fibrin gels.

Multi-component model of intramural hematoma

A novel multi-component model is introduced for studying interaction between blood flow and deforming aortic wall with intramural hematoma (IMH). The aortic wall is simulated by a composite structure submodel representing material properties of the three main wall layers. The IMH is described by a poroelasticity submodel which takes into account both the pressure inside hematoma and its deformation. The submodel of the hematoma is fully coupled with the aortic submodel as well as with the submodel of the pulsatile blood flow. Model simulations are used to investigate the relation between the peak wall stress, hematoma thickness and permeability in patients of different age. The results indicate that an increase in hematoma thickness leads to larger wall stress, which is in agreement with clinical data. Further simulations demonstrate that a hematoma with smaller permeability results in larger wall stress, suggesting that blood coagulation in hematoma might increase its mechanical stability. This is in agreement with previous experimental observations of coagulation having a beneficial effect on the condition of a patient with the IMH.

Fibrin mechanical properties and their structural origins

Fibrin is a protein polymer that is essential for hemostasis and thrombosis, wound healing, and several other biological functions and pathological conditions that involve extracellular matrix. In addition to molecular and cellular interactions, fibrin mechanics has been recently shown to underlie clot behavior in the highly dynamic intra- and extravascular environments. Fibrin has both elastic and viscous properties. Perhaps the most remarkable rheological feature of the fibrin network is an extremely high elasticity and stability despite very low protein content. Another important mechanical property that is common to many filamentous protein polymers but not other polymers is stiffening occurring in response to shear, tension, or compression. New data has begun to provide a structural basis for the unique mechanical behavior of fibrin that originates from its complex multi-scale hierarchical structure. The mechanical behavior of the whole fibrin gel is governed largely by the properties of single fibers and their ensembles, including changes in fiber orientation, stretching, bending, and buckling. The properties of individual fibrin fibers are determined by the number and packing arrangements of double-stranded half-staggered protofibrils, which still remain poorly understood. It has also been proposed that forced unfolding of sub-molecular structures, including elongation of flexible and relatively unstructured portions of fibrin molecules, can contribute to fibrin deformations. In spite of a great increase in our knowledge of the structural mechanics of fibrin, much about the mechanisms of fibrin's biological functions remains unknown. Fibrin deformability is not only an essential part of the biomechanics of hemostasis and thrombosis, but also a rapidly developing field of bioengineering that uses fibrin as a versatile biomaterial with exceptional and tunable biochemical and mechanical properties.

Nonlinearities of biopolymer gels increase the range of force transmission

We present a model of biopolymer gels that includes two types of elastic nonlinearities, stiffening under extension and softening (due to buckling) under compression, to predict the elastic anisotropy induced by both external as well as internal (e.g., due to cell contractility) stresses in biopolymer gels. We show how the stretch-induced anisotropy and the strain-stiffening nonlinearity increase both the amplitude and power-law range of transmission of internal, contractile, cellular forces, and relate this to recent experiments.