Structural basis for the nonlinear mechanics of fibrin networks under compression

Novel method for emboli analog formation towards improved stroke retrieval devices

BACKGROUND

Unsuccessful recanalization attempts in stroke patients have been associated with fibrin-rich thromboemboli linking retrieval mechanism performance and clot composition. To continue development of stroke retrieval mechanisms, the material properties of cerebral thromboemboli must be replicated; however, current methods for emboli analog formation lack quantitative measurements for both material stiffness and composition of cerebral thromboemboli. This study investigates emboli analog (EA) formation to mimic the material stiffness and composition of cerebral thromboemboli to develop new retrieval mechanisms.

METHODS

To induce static and dynamic environments for clot replication, a 9:1 ratio of porcine whole blood and 2.45% calcium chloride remained stationary or rotated at 34, 50 and 80 RPM. Histology and a custom MATLAB code provided composition analysis results. Likewise, quantitative results from biomechanical testing were obtained for direct comparison of the material stiffness of cerebral thromboemboli.

RESULTS

Fibrin/platelet content as well as material stiffness increased due to increasing rotational speed. Approximately 11% of the biomechanical testing results exhibited nonlinearity after an initial yield point, of which 60% were from statically formed EAs. Those formed at 50 RPM were most similar in material stiffness to thromboemboli extracted from carotid endarterectomy (CEA) procedures (p = 0.97).

CONCLUSIONS

The dynamically formed EAs may be altered to obtain a range of fibrin/platelet to erythrocyte ratios. The proposed methodology for EA formation offers a platform for continued development of retrieval mechanism prototypes.

Observation of Ultrafast Vibrational Energy Transfer in Fibrinogen and Fibrin Fibers

We study the secondary structure of the blood protein fibrinogen using two-dimensional infrared spectroscopy. With this technique, we identify the amide I′ vibrational modes of the antiparallel β-sheets and turns of fibrinogen. We observe ultrafast energy flow among these amide I′ vibrational modes with a time constant of ∼7 ps. This energy transfer time constant does not change significantly upon fibrin fiber formation, indicating that the secondary structure of the fibrinogen monomers remains largely unchanged in the polymerization process.

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.

ELECTROMAGNETICALLY INDUCED DISTORTION OF A FIBRIN MATRIX WITH EMBEDDED MICROPARTICLES

Blood clots occur in the human body when they are required to prevent bleeding. In pathological states such as diabetes and sickle cell disease, blood clots can also form undesirably due to hypercoagulable plasma conditions. With the continued effort in developing fibrin therapies for potential life-saving solutions, more mechanical modeling is needed to understand the properties of fibrin structures with inclusions. In this study, a fibrin matrix embedded with magnetic micro particles (MMPs) was subjected to a magnetic field to determine the magnitude of the required force to create plastic deformation within the fibrin clot. Using finite element (FE) analysis, we estimated the magnetic force from an electromagnet at a sample space located approximately 3 cm away from the coil center. This electromagnetic force coupled with gravity was applied on a fibrin mechanical system with MMPs to calculate the stresses and displacements. Using appropriate coil parameters, it was determined that application of a magnetic field of 730 A/m on the fibrin surface was necessary to achieve an electromagnetic force of 36 nN (to engender plastic deformation).

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.

Network Topology in Soft Gels: Hardening and Softening Materials

The structural complexity of soft gels is at the origin of a versatile mechanical response that allows for large deformation, controlled elastic recovery, and toughness in the same material. A limit to exploiting the potential of such materials is the insufficient fundamental understanding of the microstructural origin of the bulk mechanical properties. Here we investigate the role of the network topology in a model gel through 3D numerical simulations. Our study links the topology of the network organization in space to its nonlinear rheological response preceding yielding and damage: our analysis elucidates how the network connectivity alone could be used to modify the gel mechanics at large strains, from strain-softening to hardening and even to a brittle response. These findings provide new insight for smart material design and for understanding the nontrivial mechanical response of a potentially wide range of technologically relevant materials.

Gels with sense: supramolecular materials that respond to heat, light and sound

Advances in the field of supramolecular chemistry have made it possible, in many situations, to reliably engineer soft materials to address a specific technological problem. Particularly exciting are "smart" gels that undergo reversible physical changes on exposure to remote, non-invasive environmental stimuli. This review explores the development of gels which are transformed by heat, light and ultrasound, as well as other mechanical inputs, applied voltages and magnetic fields. Focusing on small-molecule gelators, but with reference to organic polymers and metal-organic systems, we examine how the structures of gelator assemblies influence the physical and chemical mechanisms leading to thermo-, photo- and mechano-switchable behaviour. In addition, we evaluate how the unique and versatile properties of smart materials may be exploited in a wide range of applications, including catalysis, crystal growth, ion sensing, drug delivery, data storage and biomaterial replacement.

Programming the mechanics of cohesive fiber networks by compression

Fibrous networks are ideal functional materials since they provide mechanical rigidity at low weight. Here, we demonstrate that fibrous networks of the blood clotting protein fibrin undergo a strong and irreversible increase in their mechanical rigidity in response to uniaxial compression. This rigidification can be precisely controlled by the level of applied compressive strain, providing a means to program the network rigidity without having to change its composition. To identify the underlying mechanism we measure single fiber-fiber interactions using optical tweezers. We further develop a minimal computational model of cohesive fiber networks that shows that stiffening arises due to the formation of new bonds in the compressed state, which develop tensile stress when the network is re-expanded. The model predicts that the network stiffness after a compression cycle obeys a power-law dependence on tensile stress, which we confirm experimentally. This finding provides new insights into how biological tissues can adapt themselves independently of any cellular processes, offering new perspectives to inspire the design of reprogrammable materials.

Phase transitions during compression and decompression of clots from platelet-poor plasma, platelet-rich plasma and whole blood

Blood clots are required to stem bleeding and are subject to a variety of stresses, but they can also block blood vessels and cause heart attacks and ischemic strokes. We measured the compressive response of human platelet-poor plasma (PPP) clots, platelet-rich plasma (PRP) clots and whole blood clots and correlated these measurements with confocal and scanning electron microscopy to track changes in clot structure. Stress-strain curves revealed four characteristic regions, for compression-decompression: (1) linear elastic region; (2) upper plateau or softening region; (3) non-linear elastic region or re-stretching of the network; (4) lower plateau in which dissociation of some newly made connections occurs. Our experiments revealed that compression proceeds by the passage of a phase boundary through the clot separating rarefied and densified phases. This observation motivates a model of fibrin mechanics based on the continuum theory of phase transitions, which accounts for the pre-stress caused by platelets, the adhesion of fibrin fibers in the densified phase, the compression of red blood cells (RBCs), and the pumping of liquids through the clot during compression/decompression. Our experiments and theory provide insights into the mechanical behavior of blood clots that could have implications clinically and in the design of fibrin-based biomaterials.

STATEMENT OF SIGNIFICANCE

The objective of this paper is to measure and mathematically model the compression behavior of various human blood clots. We show by a combination of confocal and scanning electron microscopy that compression proceeds by the passage of a front through the sample that separates a densified region of the clot from a rarefied region, and that the compression/decompression response is reversible with hysteresis. These observations form the basis of a model for the compression response of clots based on the continuum theory of phase transitions. Our studies may reveal how clot rheology under large compression in vivo due to muscle contraction, platelet retraction and hydrodynamic flow varies under various pathophysiological conditions and could inform the design of fibrin based biomaterials.

Mechanical response of collagen networks to nonuniform microscale loads

As force is applied to fibrous proteins such as collagen or fibrin, the fibers respond by bending, stretching, or buckling, which together bring about a nonlinear relationship between force and displacement. The nonlinearity is typically understood in terms of strain stiffening in uniform extension or shear, but there remains a critical lack of data on how fibrous materials respond to other more complicated loadings. Here we study the mechanics of collagen networks in response to nonuniform loads applied on the local scale of the fibers. For this, we use particles made of an active hydrogel that undergoes a temperature-induced phase transition causing a large decrease in volume. We embed these particles in networks of fibrous collagen and use them as microactuators to apply controlled microscale loading. The resulting fiber displacements propagate over a long range with radial displacements u scaling as r^-n with n ≈ 1. By contrast, we find linear homogeneous materials have n ≈ 2, in agreement with classical linear elastic theory. Our experimental data supports the notion that the long range displacements result from buckling of fibers in compression and local straightening of fibers in tension, in agreement with previous studies. Surprisingly, global network anisotropy appears to have only a modest effect on the displacement propagation. These insights into the microscale mechanics demonstrate that the decay power n provides a useful metric to quantify the mechanics of fibrous materials. We therefore suggest it is a means to compare new theories with experimental data.

Whole blood clot optical clearing for nondestructive 3D imaging and quantitative analysis

A technological revolution in both light and electron microscopy imaging now allows unprecedented views of clotting, especially in animal models of hemostasis and thrombosis. However, our understanding of three-dimensional high-resolution clot structure remains incomplete since most of our recent knowledge has come from studies of relatively small clots or thrombi, due to the optical impenetrability of clots beyond a few cell layers in depth. Here, we developed an optimized optical clearing method termed cCLOT that renders large whole blood clots transparent and allows confocal imaging as deep as one millimeter inside the clot. We have tested this method by investigating the 3D structure of clots made from reconstituted pre-labeled blood components yielding new information about the effects of clot contraction on erythrocytes. Although it has been shown recently that erythrocytes are compressed to form polyhedrocytes during clot contraction, observations of this phenomenon have been impeded by the inability to easily image inside clots. As an efficient and non-destructive method, cCLOT represents a powerful research tool in studying blood clot structure and mechanisms controlling clot morphology. Additionally, cCLOT optical clearing has the potential to facilitate imaging of ex vivo clots and thrombi derived from healthy or pathological conditions.

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.

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.

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.

Fibrin Formation, Structure and Properties

Fibrinogen and fibrin are essential for hemostasis and are major factors in thrombosis, wound healing, and several other biological functions and pathological conditions. The X-ray crystallographic structure of major parts of fibrin(ogen), together with computational reconstructions of missing portions and numerous biochemical and biophysical studies, have provided a wealth of data to interpret molecular mechanisms of fibrin formation, its organization, and properties. On cleavage of fibrinopeptides by thrombin, fibrinogen is converted to fibrin monomers, which interact via knobs exposed by fibrinopeptide removal in the central region, with holes always exposed at the ends of the molecules. The resulting half-staggered, double-stranded oligomers lengthen into protofibrils, which aggregate laterally to make fibers, which then branch to yield a three-dimensional network. Much is now known about the structural origins of clot mechanical properties, including changes in fiber orientation, stretching and buckling, and forced unfolding of molecular domains. Studies of congenital fibrinogen variants and post-translational modifications have increased our understanding of the structure and functions of fibrin(ogen). The fibrinolytic system, with the zymogen plasminogen binding to fibrin together with tissue-type plasminogen activator to promote activation to the active proteolytic enzyme, plasmin, results in digestion of fibrin at specific lysine residues. In spite of a great increase in our knowledge of all these interconnected processes, much about the molecular mechanisms of the biological functions of fibrin(ogen) remains unknown, including some basic aspects of clotting, fibrinolysis, and molecular origins of fibrin mechanical properties. Even less is known concerning more complex (patho)physiological implications of fibrinogen and fibrin.

Contraction of Blood Clots Is Impaired in Acute Ischemic Stroke

OBJECTIVE

Obstructive thrombi or thrombotic emboli are the pathogenic basis of ischemic stroke. In vitro blood clots and in vivo thrombi can undergo platelet-driven contraction (retraction), resulting in volume shrinkage. Clot contraction can potentially reduce vessel occlusion and improve blood flow past emboli or thrombi. The aim of this work was to examine a potential pathogenic role of clot contraction in ischemic stroke.

APPROACH AND RESULTS

We used a novel automated method that enabled us to quantify time of initiation and extent and rate of clot contraction in vitro. The main finding is that clot contraction from the blood of stroke patients was reduced compared with healthy subjects. Reduced clot contraction correlated with a lower platelet count and their dysfunction, higher levels of fibrinogen and hematocrit, leukocytosis, and other changes in blood composition that may affect platelet function and properties of blood clots. Platelets from stroke patents were spontaneously activated and displayed reduced responsiveness to additional stimulation. Clinical correlations with respect to severity and stroke pathogenesis suggest that the impaired clot contraction has the potential to be a pathogenic factor in ischemic stroke.

CONCLUSIONS

The changeable ability of clots and thrombi to shrink in volume may be a novel unappreciated mechanism that aggravates or alleviates the course and outcomes of ischemic stroke. The clinical importance of clot or thrombus transformations in vivo and the diagnostic and prognostic value of this blood test for clot contraction need further exploration.

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.

Relevance of interfacial viscoelasticity in stability and conformation of biomolecular organizates at air/fluid interface

Soft materials are complex macromolecular systems often exhibiting perplexing non-Newtonian viscoelastic properties, especially when the macromolecules are entangled, crowded or cross-linked. These materials are ubiquitous in the biology, food and pharma industry and have several applications in biotechnology and in the field of biosensors. Based on the length scales, topologies, flexibility and concentration, the systems behave both as liquids (viscous) and solids (elastic). Particularly, for proteins and protein-lipid systems, viscoelasticity is an important parameter because it often relates directly to stability and thermodynamic interactions of the pure biological components as well as their mixtures. Despite the large body of work that is available in solution macro-rheometry, there are still a number of issues that need to be addressed in dealing with proteins at air/fluid interfaces and with protein-polymer or protein-lipid interfaces that often exhibit very low interfacial viscosity values. Considering the important applications that they have in biopharmaceutical, biotechnological and nutraceutical industries, there is a need for developing methods that meet the following three specific issues: small volume, large dynamic range of shear rates and interfacial properties of different biomolecules. Further, the techniques that are developed should include Newtonian, shear thinning and yielding properties, which are representative of the different solution behaviors typically encountered. The review presented here is a comprehensive account of the rheological properties of different biomolecules at air/fluid and solid/fluid interfaces. It addresses the usefulness of 'viscoelasticity' of the systems at the interfaces analyzed at the molecular level that can be correlated with the microscopic material properties and touches upon some recent techniques in microrheology that are being used to measure the unusually low viscosity values sensitively.

Structure-induced nonlinear viscoelasticity of non-woven fibrous matrices

Fibrous materials are widely utilized as tissue engineering scaffolds for tissue regeneration and other bioengineering applications. The structural as well as mechanical characteristics of the fibrous matrices under static and dynamic mechanical loading conditions influence the response of the cells. In this paper, we study the mechanical response of the non-woven fibrous matrices under oscillatory loading conditions and its dependence on the structural properties of fibrous matrix. We demonstrate that under oscillatory shear and elongation, the fibrous matrices demonstrate nonlinear viscoelasticity at all strain amplitudes. This is contrary to the behavior of other soft polymeric materials for which nonlinearity in the viscoelastic response vanishes for small strains. These observations suggest that despite their prevalence, the measures of linear viscoelasticity (e.g., storage and loss moduli) are inadequate for the general description of the viscoelastic nature of the fibrous materials. It was, however, found that linear viscoelastic nature of fibrous matrices for small amplitudes is restored when a pre-stretch is applied to the fibrous matrix along with oscillatory strains. Further, we also explored the influence of the structural properties of the fibrous matrices (fiber orientation, alignment and curvature) on their viscoelastic nature.

What Is the Biological and Clinical Relevance of Fibrin?

As our knowledge of the structure and functions of fibrinogen and fibrin has increased tremendously, several key findings have given some people a superficial impression that the biological and clinical significance of these clotting proteins may be less than earlier thought. Most strikingly, studies of fibrinogen knockout mice demonstrated that many of these mice survive to weaning and beyond, suggesting that fibrin(ogen) may not be entirely necessary. Humans with afibrinogenemia also survive. Furthermore, in recent years, the major emphasis in the treatment of arterial thrombosis has been on inhibition of platelets, rather than fibrin. In contrast to the initially apparent conclusions from these results, it has become increasingly clear that fibrin is essential for hemostasis; is a key factor in thrombosis; and plays an important biological role in infection, inflammation, immunology, and wound healing. In addition, fibrinogen replacement therapy has become a preferred, major treatment for severe bleeding in trauma and surgery. Finally, fibrin is a unique biomaterial and is used as a sealant or glue, a matrix for cells, a scaffold for tissue engineering, and a carrier and/or a vector for targeted drug delivery.

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.

Microbuckling of fibrin provides a mechanism for cell mechanosensing

Biological cells sense and respond to mechanical forces, but how such a mechanosensing process takes place in a nonlinear inhomogeneous fibrous matrix remains unknown. We show that cells in a fibrous matrix induce deformation fields that propagate over a longer range than predicted by linear elasticity. Synthetic, linear elastic hydrogels used in many mechanotransduction studies fail to capture this effect. We develop a nonlinear microstructural finite-element model for a fibre network to simulate localized deformations induced by cells. The model captures measured cell-induced matrix displacements from experiments and identifies an important mechanism for long-range cell mechanosensing: loss of compression stiffness owing to microbuckling of individual fibres. We show evidence that cells sense each other through the formation of localized intercellular bands of tensile deformations caused by this mechanism.

Foam-like compression behavior of fibrin networks

The rheological properties of fibrin networks have been of long-standing interest. As such there is a wealth of studies of their shear and tensile responses, but their compressive behavior remains unexplored. Here, by characterization of the network structure with synchronous measurement of the fibrin storage and loss moduli at increasing degrees of compression, we show that the compressive behavior of fibrin networks is similar to that of cellular solids. A nonlinear stress-strain response of fibrin consists of three regimes: (1) an initial linear regime, in which most fibers are straight, (2) a plateau regime, in which more and more fibers buckle and collapse, and (3) a markedly nonlinear regime, in which network densification occurs by bending of buckled fibers and inter-fiber contacts. Importantly, the spatially non-uniform network deformation included formation of a moving "compression front" along the axis of strain, which segregated the fibrin network into compartments with different fiber densities and structure. The Young's modulus of the linear phase depends quadratically on the fibrin volume fraction while that in the densified phase depends cubically on it. The viscoelastic plateau regime corresponds to a mixture of these two phases in which the fractions of the two phases change during compression. We model this regime using a continuum theory of phase transitions and analytically predict the storage and loss moduli which are in good agreement with the experimental data. Our work shows that fibrin networks are a member of a broad class of natural cellular materials which includes cancellous bone, wood and cork.

Uncoupling shear and uniaxial elastic moduli of semiflexible biopolymer networks: compression-softening and stretch-stiffening

Gels formed by semiflexible filaments such as most biopolymers exhibit non-linear behavior in their response to shear deformation, e.g., with a pronounced strain stiffening and negative normal stress. These negative normal stresses suggest that networks would collapse axially when subject to shear stress. This coupling of axial and shear deformations can have particularly important consequences for extracellular matrices and collagenous tissues. Although measurements of uniaxial moduli have been made on biopolymer gels, these have not directly been related to the shear response. Here, we report measurements and simulations of axial and shear stresses exerted by a range of hydrogels subjected to simultaneous uniaxial and shear strains. These studies show that, in contrast to volume-conserving linearly elastic hydrogels, the Young’s moduli of networks formed by the biopolymers are not proportional to their shear moduli and both shear and uniaxial moduli are strongly affected by even modest degrees of uniaxial strain.

Kinetics and mechanics of clot contraction are governed by the molecular and cellular composition of the blood

Platelet-driven blood clot contraction (retraction) is thought to promote wound closure and secure hemostasis while preventing vascular occlusion. Notwithstanding its importance, clot contraction remains a poorly understood process, partially because of the lack of methodology to quantify its dynamics and requirements. We used a novel automated optical analyzer to continuously track in vitro changes in the size of contracting clots in whole blood and in variously reconstituted samples. Kinetics of contraction was complemented with dynamic rheometry to characterize the viscoelasticity of contracting clots. This combined approach enabled investigation of the coordinated mechanistic impact of platelets, including nonmuscle myosin II, red blood cells (RBCs), fibrin(ogen), factor XIIIa (FXIIIa), and thrombin on the kinetics and mechanics of the contraction process. Clot contraction is composed of 3 sequential phases, each characterized by a distinct rate constant. Thrombin, Ca(2+), the integrin αIIbβ3, myosin IIa, FXIIIa cross-linking, and platelet count all promote 1 or more phases of the clot contraction process. In contrast, RBCs impair contraction and reduce elasticity, while increasing the overall contractile stress generated by the platelet-fibrin meshwork. A better understanding of the mechanisms by which blood cells, fibrin(ogen), and platelet-fibrin interactions modulate clot contraction may generate novel approaches to reveal and to manage thrombosis and hemostatic disorders.

The simultaneous occurrence of both hypercoagulability and hypofibrinolysis in blood and serum during systemic inflammation, and the roles of iron and fibrin(ogen)

Although the two phenomena are usually studied separately, we summarise a considerable body of literature to the effect that a great many diseases involve (or are accompanied by) both an increased tendency for blood to clot (hypercoagulability) and the resistance of the clots so formed (hypofibrinolysis) to the typical, 'healthy' or physiological lysis. We concentrate here on the terminal stages of fibrin formation from fibrinogen, as catalysed by thrombin. Hypercoagulability goes hand in hand with inflammation, and is strongly influenced by the fibrinogen concentration (and vice versa); this can be mediated via interleukin-6. Poorly liganded iron is a significant feature of inflammatory diseases, and hypofibrinolysis may change as a result of changes in the structure and morphology of the clot, which may be mimicked in vitro, and may be caused in vivo, by the presence of unliganded iron interacting with fibrin(ogen) during clot formation. Many of these phenomena are probably caused by electrostatic changes in the iron-fibrinogen system, though hydroxyl radical (OH˙) formation can also contribute under both acute and (more especially) chronic conditions. Many substances are known to affect the nature of fibrin polymerised from fibrinogen, such that this might be seen as a kind of bellwether for human or plasma health. Overall, our analysis demonstrates the commonalities underpinning a variety of pathologies as seen in both hypercoagulability and hypofibrinolysis, and offers opportunities for both diagnostics and therapies.

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.

Multiscale mechanobiology: computational models for integrating molecules to multicellular systems

Mechanical signals exist throughout the biological landscape. Across all scales, these signals, in the form of force, stiffness, and deformations, are generated and processed, resulting in an active mechanobiological circuit that controls many fundamental aspects of life, from protein unfolding and cytoskeletal remodeling to collective cell motions. The multiple scales and complex feedback involved present a challenge for fully understanding the nature of this circuit, particularly in development and disease in which it has been implicated. Computational models that accurately predict and are based on experimental data enable a means to integrate basic principles and explore fine details of mechanosensing and mechanotransduction in and across all levels of biological systems. Here we review recent advances in these models along with supporting and emerging experimental findings.

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.