Multiscale model of fibrin accumulation on the blood clot surface and platelet dynamics

Advances in Fibrin-Based Materials in Wound Repair: A Review

The first bioprocess that occurs in response to wounding is the deterrence of local hemorrhage. This is accomplished by platelet aggregation and initiation of the hemostasis cascade. The resulting blood clot immediately enables the cessation of bleeding and then functions as a provisional matrix for wound healing, which begins a few days after injury. Here, fibrinogen and fibrin fibers are the key players, because they literally serve as scaffolds for tissue regeneration and promote the migration of cells, as well as the ingrowth of tissues. Fibrin is also an important modulator of healing and a host defense system against microbes that effectively maintains incoming leukocytes and acts as reservoir for growth factors. This review presents recent advances in the understanding and applications of fibrin and fibrin-fiber-incorporated biomedical materials applied to wound healing and subsequent tissue repair. It also discusses how fibrin-based materials function through several wound healing stages including physical barrier formation, the entrapment of bacteria, drug and cell delivery, and eventual degradation. Pure fibrin is not mechanically strong and stable enough to act as a singular wound repair material. To alleviate this problem, this paper will demonstrate recent advances in the modification of fibrin with next-generation materials exhibiting enhanced stability and medical efficacy, along with a detailed look at the mechanical properties of fibrin and fibrin-laden materials. Specifically, fibrin-based nanocomposites and their role in wound repair, sustained drug release, cell delivery to wound sites, skin reconstruction, and biomedical applications of drug-loaded fibrin-based materials will be demonstrated and discussed.

Recent advances in computational modeling of fibrin clot formation: A review

The field of thrombosis and hemostasis is crucial for understanding and developing new therapies for pathologies such as deep vein thrombosis, diabetes related strokes, pulmonary embolisms, and hemorrhaging related diseases. In the last two decades, an exponential growth in studies related to fibrin clot formation using computational tools has been observed. Despite this growth, the complete mechanism behind thrombus formation and hemostasis has been long and rife with obstacles; however, significant progress has been made in the present century. The computational models and methods used in this context are diversified into different spatiotemporal scales, yet there is no single model which can predict both physiological and mechanical properties of fibrin clots. In this review, we list the major strategies employed by researchers in modeling fibrin clot formation using recent and existing computational techniques. This review organizes the computational strategies into continuum level, system level, discrete particle (DPD), and multi-scale methods. We also discuss strengths and weaknesses of various methods and future directions in which computational modeling of fibrin clots can advance.

Utilizing Plasma Composition Data to Help Determine Procoagulant Dynamics in Patients with Thermal Injury: A Computational Assessment

INTRODUCTION

The development of methods that generate individualized assessments of the procoagulant potential of burn patients could improve their treatment. Beyond its role as an essential intermediate in the formation of thrombin, factor (F)Xa has systemic effects as an agonist to inflammatory processes. In this study, we use a computational model to study the FXa dynamics underlying tissue factor-initiated thrombin generation in a small cohort of burn patients.

MATERIALS AND METHODS

Plasma samples were collected upon admission (Hour 0) from nine subjects (five non-survivors) with major burn injuries and then at 48 hours. Coagulation factor concentrations (II, V, VII, VIII, IX, X, TFPI, antithrombin (AT), protein C (PC)) were measured and used in a computational model to generate time course profiles for thrombin (IIa), FXa, extrinsic tenase, intrinsic tenase and prothrombinase complexes upon a 5 pM tissue factor stimulus in the presence of 1 nM thrombomodulin. Parameters were extracted from the thrombin and FXa profiles (including max rate (MaxRIIa and MaxRFXa) and peak level (MaxLIIa and MaxLFXa)). Procoagulant potential was also evaluated by determining the concentration of the complexes at select times. Parameter values were compared between survivors and non-survivors in the burn cohort and between the burn cohort and a simulation based on the mean physiological (100%) concentration for all factor levels.

RESULTS

Burn patients differed at Hour 0 (p < 0.05) from 100% mean physiological levels for all coagulation factor levels except FV and FVII. The concentration of FX, FII, TFPI, AT and PC was lower; FIX and FVIII were increased. The composition differences resulted in all nine burn patients at Hour 0 displaying a procoagulant phenotype relative to 100% mean physiological simulation (MaxLIIa (306 ± 90 nM vs. 52 nM), MaxRIIa (2.9 ± 1.1 nM/s vs. 0.3 nM/s), respectively p < 0.001); MaxRFXa and MaxLFXa were also an order of magnitude greater than 100% mean physiological simulation (p < 0.001). When grouped by survival status and compared at the time of admission, non-survivors had lower PC levels (56 ± 18% vs. 82 ± 9%, p < 0.05), and faster MaxRFXa (29 ± 6 pM/s vs. 18 ± 6 pM/s, p < 0.05) than those that survived; similar trends were observed for all other procoagulant parameters. At 48 hours when comparing non-survivors to survivors, TFPI levels were higher (108 ± 18% vs. 59 ± 18%, p < 0.05), and MaxRIIa (1.5 ± 1.4 nM/s vs. 3.6 ± 0.7 nM/s, p < 0.05) and MaxRFXa (13 ± 12 pM/s vs. 35 ± 4 pM/s, p < 0.05) were lower; similar trends were observed with all other procoagulant parameters. Overall, between admission and 48 hours, procoagulant potential, as represented by MaxR and MaxL parameters for thrombin and FXa, in non-survivors decreased while in survivors they increased (p < 0.05). In patients that survived, there was a positive correlation between FX levels and MaxLFXa (r = 0.96) and reversed in mortality (r= -0.91).

CONCLUSIONS

Thrombin and FXa generation are increased in burn patients at admission compared to mean physiological simulations. Over the first 48 hours, burn survivors became more procoagulant while non-survivors became less procoagulant. Differences between survivors and non-survivors appear to be present in the underlying dynamics that contribute to FXa dynamics. Understanding how the individual specific balance of procoagulant and anticoagulant proteins contributes to thrombin and FXa generation could ultimately guide therapy and potentially reduce burn injury-related morbidity and mortality.

Modeling of the effects of IL-17 and TNF-α on endothelial cells and thrombus growth

Rheumatoid and psoriatic arthritis are chronic inflammatory diseases, with massive increase of cardiovascular events (CVE), and contribution of the cytokines TNF-α and IL-17. Chronic inflammation inside the joint membrane or synovium results from the activation of fibroblasts/synoviocytes, and leads to the release of cytokines from monocytes (Tumor Necrosis Factor or TNF) and from T lymphocytes (Interleukin-17 or IL-17). At the systemic level, the very same cytokines affect endothelial cells and vessel wall. We have previously shown [1,2] that IL-17 and TNF-α, specifically when combined, increase procoagulation, decrease anticoagulation and increase platelet aggregation, leading to thrombosis. These results are the basis for the models of interactions between IL-17 and TNF, and genes expressed by activated endothelial cells. This work is devoted to mathematical modeling and numerical simulations of blood coagulation and clot growth under the influence of IL-17 and TNF-α. We show that they can provoke thrombosis, leading to the complete or partial occlusion of blood vessels. The regimes of blood coagulation and conditions of occlusion are investigated in numerical simulations and in approximate analytical models. The results of mathematical modeling allow us to predict thrombosis development for an individual patient.

Conditions of microvessel occlusion for blood coagulation in flow

Vessel occlusion is a perturbation of blood flow inside a blood vessel because of the fibrin clot formation. As a result, blood circulation in the vessel can be slowed down or even stopped. This can provoke the risk of cardiovascular events. In order to explore this phenomenon, we used a previously developed mathematical model of blood clotting to describe the concentrations of blood factors with a reaction-diffusion system of equations. The Navier-Stokes equations were used to model blood flow, and we treated the clot as a porous medium. We identify the conditions of partial or complete occlusion in a small vessel depending on various physical and physiological parameters. In particular, we were interested in the conditions on blood flow and diameter of the wounded area. The existence of a critical flow velocity separating the regimes of partial and complete occlusion was demonstrated through the mathematical investigation of a simplified model of thrombin wave propagation in Poiseuille flow. We observed different regimes of vessel occlusion depending on the model parameters both for the numerical simulations and in the theoretical study. Then, we compared the rate of clot growth in flow obtained in the simulations with experimental data. Both of them showed the existence of different regimes of clot growth depending on the velocity of blood flow.

Computational Study of Thrombus Formation and Clotting Factor Effects under Venous Flow Conditions

A comprehensive understanding of thrombus formation as a physicochemical process that has evolved to protect the integrity of the human vasculature is critical to our ability to predict and control pathological states caused by a malfunctioning blood coagulation system. Despite numerous investigations, the spatial and temporal details of thrombus growth as a multicomponent process are not fully understood. Here, we used computational modeling to investigate the temporal changes in the spatial distributions of the key enzymatic (i.e., thrombin) and structural (i.e., platelets and fibrin) components within a growing thrombus. Moreover, we investigated the interplay between clot structure and its mechanical properties, such as hydraulic resistance to flow. Our model relied on the coupling of computational fluid dynamics and biochemical kinetics, and was validated using flow-chamber data from a previous experimental study. The model allowed us to identify the distinct patterns characterizing the spatial distributions of thrombin, platelets, and fibrin accumulating within a thrombus. Our modeling results suggested that under the simulated conditions, thrombin kinetics was determined predominantly by prothrombinase. Furthermore, our simulations showed that thrombus resistance imparted by fibrin was ∼30-fold higher than that imparted by platelets. Yet, thrombus-mediated bloodflow occlusion was driven primarily by the platelet deposition process, because the height of the platelet accumulation domain was approximately twice that of the fibrin accumulation domain. Fibrinogen supplementation in normal blood resulted in a nonlinear increase in thrombus resistance, and for a supplemented fibrinogen level of 48%, the thrombus resistance increased by ∼2.7-fold. Finally, our model predicted that restoring the normal levels of clotting factors II, IX, and X while simultaneously restoring fibrinogen (to 88% of its normal level) in diluted blood can restore fibrin generation to ∼78% of its normal level and hence improve clot formation under dilution.

Multiscale modeling methods in biomechanics

More and more frequently, computational biomechanics deals with problems where the portion of physical reality to be modeled spans over such a large range of spatial and temporal dimensions, that it is impossible to represent it as a single space-time continuum. We are forced to consider multiple space-time continua, each representing the phenomenon of interest at a characteristic space-time scale. Multiscale models describe a complex process across multiple scales, and account for how quantities transform as we move from one scale to another. This review offers a set of definitions for this emerging field, and provides a brief summary of the most recent developments on multiscale modeling in biomechanics. Of all possible perspectives, we chose that of the modeling intent, which vastly affect the nature and the structure of each research activity. To the purpose we organized all papers reviewed in three categories: 'causal confirmation,' where multiscale models are used as materializations of the causation theories; 'predictive accuracy,' where multiscale modeling is aimed to improve the predictive accuracy; and 'determination of effect,' where multiscale modeling is used to model how a change at one scale manifests in an effect at another radically different space-time scale. Consistent with how the volume of computational biomechanics research is distributed across application targets, we extensively reviewed papers targeting the musculoskeletal and the cardiovascular systems, and covered only a few exemplary papers targeting other organ systems. The review shows a research subdomain still in its infancy, where causal confirmation papers remain the most common. WIREs Syst Biol Med 2017, 9:e1375. doi: 10.1002/wsbm.1375 For further resources related to this article, please visit the WIREs website.

Systems Analysis of Thrombus Formation

The systems analysis of thrombosis seeks to quantitatively predict blood function in a given vascular wall and hemodynamic context. Relevant to both venous and arterial thrombosis, a Blood Systems Biology approach should provide metrics for rate and molecular mechanisms of clot growth, thrombotic risk, pharmacological response, and utility of new therapeutic targets. As a rapidly created multicellular aggregate with a polymerized fibrin matrix, blood clots result from hundreds of unique reactions within and around platelets propagating in space and time under hemodynamic conditions. Coronary artery thrombosis is dominated by atherosclerotic plaque rupture, complex pulsatile flows through stenotic regions producing high wall shear stresses, and plaque-derived tissue factor driving thrombin production. In contrast, venous thrombosis is dominated by stasis or depressed flows, endothelial inflammation, white blood cell-derived tissue factor, and ample red blood cell incorporation. By imaging vessels, patient-specific assessment using computational fluid dynamics provides an estimate of local hemodynamics and fractional flow reserve. High-dimensional ex vivo phenotyping of platelet and coagulation can now power multiscale computer simulations at the subcellular to cellular to whole vessel scale of heart attacks or strokes. In addition, an integrated systems biology approach can rank safety and efficacy metrics of various pharmacological interventions or clinical trial designs.

Modelling of platelet-fibrin clot formation in flow with a DPD-PDE method

The paper is devoted to mathematical modelling of clot growth in blood flow. Great complexity of the hemostatic system dictates the need of usage of the mathematical models to understand its functioning in the normal and especially in pathological situations. In this work we investigate the interaction of blood flow, platelet aggregation and plasma coagulation. We develop a hybrid DPD-PDE model where dissipative particle dynamics (DPD) is used to model plasma flow and platelets, while the regulatory network of plasma coagulation is described by a system of partial differential equations. Modelling results confirm the potency of the scenario of clot growth where at the first stage of clot formation platelets form an aggregate due to weak inter-platelet connections and then due to their activation. This enables the formation of the fibrin net in the centre of the platelet aggregate where the flow velocity is significantly reduced. The fibrin net reinforces the clot and allows its further growth. When the clot becomes sufficiently large, it stops growing due to the narrowed vessel and the increase of flow shear rate at the surface of the clot. Its outer part is detached by the flow revealing the inner part covered by fibrin. This fibrin cap does not allow new platelets to attach at the high shear rate, and the clot stops growing. Dependence of the final clot size on wall shear rate and on other parameters is studied.

Modeling thrombin generation: plasma composition based approach

Thrombin has multiple functions in blood coagulation and its regulation is central to maintaining the balance between hemorrhage and thrombosis. Empirical and computational methods that capture thrombin generation can provide advancements to current clinical screening of the hemostatic balance at the level of the individual. In any individual, procoagulant and anticoagulant factor levels together act to generate a unique coagulation phenotype (net balance) that is reflective of the sum of its developmental, environmental, genetic, nutritional and pharmacological influences. Defining such thrombin phenotypes may provide a means to track disease progression pre-crisis. In this review we briefly describe thrombin function, methods for assessing thrombin dynamics as a phenotypic marker, computationally derived thrombin phenotypes versus determined clinical phenotypes, the boundaries of normal range thrombin generation using plasma composition based approaches and the feasibility of these approaches for predicting risk.

Three-dimensional multi-scale model of deformable platelets adhesion to vessel wall in blood flow

When a blood vessel ruptures or gets inflamed, the human body responds by rapidly forming a clot to restrict the loss of blood. Platelets aggregation at the injury site of the blood vessel occurring via platelet-platelet adhesion, tethering and rolling on the injured endothelium is a critical initial step in blood clot formation. A novel three-dimensional multi-scale model is introduced and used in this paper to simulate receptor-mediated adhesion of deformable platelets at the site of vascular injury under different shear rates of blood flow. The novelty of the model is based on a new approach of coupling submodels at three biological scales crucial for the early clot formation: novel hybrid cell membrane submodel to represent physiological elastic properties of a platelet, stochastic receptor-ligand binding submodel to describe cell adhesion kinetics and lattice Boltzmann submodel for simulating blood flow. The model implementation on the GPU cluster significantly improved simulation performance. Predictive model simulations revealed that platelet deformation, interactions between platelets in the vicinity of the vessel wall as well as the number of functional GPIbα platelet receptors played significant roles in platelet adhesion to the injury site. Variation of the number of functional GPIbα platelet receptors as well as changes of platelet stiffness can represent effects of specific drugs reducing or enhancing platelet activity. Therefore, predictive simulations can improve the search for new drug targets and help to make treatment of thrombosis patient-specific.

Systems biology of platelet-vessel wall interactions

Platelets are small, anucleated cells that participate in primary hemostasis by forming a hemostatic plug at the site of a blood vessel's breach, preventing blood loss. However, hemostatic events can lead to excessive thrombosis, resulting in life-threatening strokes, emboli, or infarction. Development of multi-scale models coupling processes at several scales and running predictive model simulations on powerful computer clusters can help interdisciplinary groups of researchers to suggest and test new patient-specific treatment strategies.

Fibrin networks regulate protein transport during thrombus development

Thromboembolic disease is a leading cause of morbidity and mortality worldwide. In the last several years there have been a number of studies attempting to identify mechanisms that stop thrombus growth. This paper identifies a novel mechanism related to formation of a fibrin cap. In particular, protein transport through a fibrin network, an important component of a thrombus, was studied by integrating experiments with model simulations. The network permeability and the protein diffusivity were shown to be important factors determining the transport of proteins through the fibrin network. Our previous in vivo studies in mice have shown that stabilized non-occluding thrombi are covered by a fibrin network (‘fibrin cap’). Model simulations, calibrated using experiments in microfluidic devices and accounting for the permeable structure of the fibrin cap, demonstrated that thrombin generated inside the thrombus was washed downstream through the fibrin network, thus limiting exposure of platelets on the thrombus surface to thrombin. Moreover, by restricting the approach of resting platelets in the flowing blood to the thrombus core, the fibrin cap impaired platelets from reaching regions of high thrombin concentration necessary for platelet activation and limited thrombus growth. The formation of a fibrin cap prevents small thrombi that frequently develop in the absence of major injury in the 60000 km of vessels in the body from developing into life threatening events.

To restrict the loss of blood following rupture of blood vessels, the human body rapidly forms a clot consisting mainly of platelets and fibrin. However, to prevent formation of a pathological clot within vessels (thrombus) as a result of vessel damage or dysfunction, the response must be regulated, and clot formation must be limited. Our previous studies demonstrated that as a laser-induced thrombus stabilized in mice, the ratio of fibrin to platelets at the thrombus surface increased significantly. Stabilized non-occluding thrombi were observed to be covered by a fibrin network (‘fibrin cap’). In the present work the role of the fibrin network in protein transport is examined by integrating experiments in microfluidic devices with the hemodynamic thrombus model. The study reveals permeability of the fibrin network and protein diffusivity to be important factors determining the transport of blood proteins inside the thrombus. It is shown that the fibrin network does not dramatically limit the diffusion of thrombin but impairs flowing platelets in blood from reaching regions of high thrombin concentration thus, reducing the probability they are activated and stably integrated into the thrombus. This novel, counter-intuitive mechanism suggests that a fibrin network formed at early stages of thrombus initiation can prevent normally asymptomatic thrombi from developing into pathological clots.

Models for thrombin generation and risk of disease

Computational models can offer an integrated view of blood clotting dynamics and may ultimately be instructive regarding an individual's risk of bleeding or clotting. Appropriately, developed and validated models could allow clinicians to simulate the outcomes of therapeutics and estimate risk of disease. Computational models that describe the dynamics of thrombin generation have been developed and have been used in combination with empirical studies to understand thrombin dynamics on a mechanistic basis. The translation of an individual's specific coagulation factor composition data using these models into an integrated assessment of hemostatic status may provide a route for advancing the long-term goal of individualized medicine. This review details the integrated approaches to understanding: (i) What is normal thrombin generation in individuals? (ii) What is the effect of normal range plasma composition variation on thrombin generation in pathologic states? (iii) Can disease progression or anticoagulation be followed by understanding the boundaries of normal thrombin generation defined by plasma composition? (iv) What are the controversies and limitations of current computational approaches? Progress in these areas can bring us closer to developing models that can be used to aid in identifying hemostatic risk.

Bayesian inference of the lung alveolar spatial model for the identification of alveolar mechanics associated with acute respiratory distress syndrome

Acute respiratory distress syndrome (ARDS) is acute lung failure secondary to severe systemic inflammation, resulting in a derangement of alveolar mechanics (i.e. the dynamic change in alveolar size and shape during tidal ventilation), leading to alveolar instability that can cause further damage to the pulmonary parenchyma. Mechanical ventilation is a mainstay in the treatment of ARDS, but may induce mechano-physical stresses on unstable alveoli, which can paradoxically propagate the cellular and molecular processes exacerbating ARDS pathology. This phenomenon is called ventilator induced lung injury (VILI), and plays a significant role in morbidity and mortality associated with ARDS. In order to identify optimal ventilation strategies to limit VILI and treat ARDS, it is necessary to understand the complex interplay between biological and physical mechanisms of VILI, first at the alveolar level, and then in aggregate at the whole-lung level. Since there is no current consensus about the underlying dynamics of alveolar mechanics, as an initial step we investigate the ventilatory dynamics of an alveolar sac (AS) with the lung alveolar spatial model (LASM), a 3D spatial biomechanical representation of the AS and its interaction with airflow pressure and the surface tension effects of pulmonary surfactant. We use the LASM to identify the mechanical ramifications of alveolar dynamics associated with ARDS. Using graphical processing unit parallel algorithms, we perform Bayesian inference on the model parameters using experimental data from rat lung under control and Tween-induced ARDS conditions. Our results provide two plausible models that recapitulate two fundamental hypotheses about volume change at the alveolar level: (1) increase in alveolar size through isotropic volume change, or (2) minimal change in AS radius with primary expansion of the mouth of the AS, with the implication that the majority of change in lung volume during the respiratory cycle occurs in the alveolar ducts. These two model solutions correspond to significantly different mechanical properties of the tissue, and we discuss the implications of these different properties and the requirements for new experimental data to discriminate between the hypotheses.