Kinetics of the coagulation cascade including the contact activation system: sensitivity analysis and model reduction

Mathematical models of coagulation-are we there yet?

BACKGROUND

Mathematical models of coagulation have been developed to mirror thrombin generation in plasma, with the aim of investigating how variation in coagulation factor levels regulates hemostasis. However, current models vary in the reactions they capture and the reaction rates used, and their validation is restricted by a lack of large coherent datasets, resulting in questioning of their utility.

OBJECTIVES

To address this debate, we systematically assessed current models against a large dataset, using plasma coagulation factor levels from 348 individuals with normal hemostasis to identify the causes of these variations.

METHODS

We compared model predictions with measured thrombin generation, quantifying and comparing the ability of each model to predict thrombin generation, the contributions of the individual reactions, and their dependence on reaction rates.

RESULTS

We found that no current model predicted the hemostatic response across the whole cohort and all produced thrombin generation curves that did not resemble those obtained experimentally. Our analysis has identified the key reactions that lead to differential model predictions, where experimental uncertainty leads to variability in predictions, and we determined reactions that have a high influence on measured thrombin generation, such as the contribution of factor XI.

CONCLUSION

This systematic assessment of models of coagulation, using large dataset inputs, points to ways in which these models can be improved. A model that accurately reflects the effects of the multiple subtle variations in an individual's hemostatic profile could be used for assessing antithrombotics or as a tool for precision medicine.

Enhancing diabetic wound healing: advances in electrospun scaffolds from pathogenesis to therapeutic applications

Diabetic wounds are a significant subset of chronic wounds characterized by elevated levels of inflammatory cytokines, matrix metalloproteinases (MMPs), and reactive oxygen species (ROS). They are also associated with impaired angiogenesis, persistent infection, and a high likelihood of hospitalization, leading to a substantial economic burden for patients. In severe cases, amputation or even mortality may occur. Diabetic foot ulcers (DFUs) are a common complication of diabetes, with up to 25% of diabetic patients being at risk of developing foot ulcers over their lifetime, and more than 70% ultimately requiring amputation. Electrospun scaffolds exhibit a structural similarity to the extracellular matrix (ECM), promoting the adhesion, growth, and migration of fibroblasts, thereby facilitating the formation of new skin tissue at the wound site. The composition and size of electrospun scaffolds can be easily adjusted, enabling controlled drug release through fiber structure modifications. The porous nature of these scaffolds facilitates gas exchange and the absorption of wound exudate. Furthermore, the fiber surface can be readily modified to impart specific functionalities, making electrospinning nanofiber scaffolds highly promising for the treatment of diabetic wounds. This article provides a concise overview of the healing process in normal wounds and the pathological mechanisms underlying diabetic wounds, including complications such as diabetic foot ulcers. It also explores the advantages of electrospinning nanofiber scaffolds in diabetic wound treatment. Additionally, it summarizes findings from various studies on the use of different types of nanofiber scaffolds for diabetic wounds and reviews methods of drug loading onto nanofiber scaffolds. These advancements broaden the horizon for effectively treating diabetic wounds.

Epidemiological study of hereditary hemorrhagic disorders in Najaf province, Iraq

Hemophilia and Von Willbrand disease (VWD) are the most well known types of hereditary hemorrhagic disorders (HHD). Hemophilia affects about 200 000 people worldwide, while VWD affects about 80 000. Because there is a scarcity of epidemiologic studies on hemophilia in Iraq, this study was carried out to evaluate the prevalence and incidence trends, as well as to identify some clinical and epidemiological features of hemophilia patients in Najaf province, Iraq. This study was carried out in the Najaf's hemophilia center. The data were obtained by reviewing all patients' documents, as well as the center registration book from 2011 to 2021. In addition, the Ministry of Health provided relevant population data for Najaf. Notably, there are currently 214 patients registered in Najaf province. The results revealed that the severe form of hemophilia A was the permanent type of HHDs in the patients compared with the rest of the types that include HHD with no significant difference Pat least 0.05. The frequency of this group of disorders appeared to increase in the period between 2011 and 2013, especially in 2012 followed by a decline in the incidence until 2021, which recorded a sudden increase in these disorders. These findings highlight that hemophilia types A and B were the most prevalent disorders of HHD in Najaf province, and the increase in number of newly recorded cases because of consanguineous marriage increased recently in this area.

An adjoint-based method for the computation of gradients in coagulation schemes

An adjoint-based methodology is proposed to compute the gradient of the outcomes of mathematical models for the coagulation cascade. The method is first exposed and validated by considering a simple, analytically tractable case involving only 3 species. Its potential is further illustrated by considering a detailed model for the extrinsic pathway involving 34 chemical species interacting through 45 chemical reactions and for which the gradient of Endogeneous Thrombin Potential, clotting time, maximum rate and peak value of thrombin with respect to the initial concentrations and reactions rates are computed. It is shown that the method produces gradients estimates that are fully consistent with the finite differences approximation used so far in the literature, but at a much lower computational cost.

A Review of Quantitative Systems Pharmacology Models of the Coagulation Cascade: Opportunities for Improved Usability

Despite the numerous therapeutic options to treat bleeding or thrombosis, a comprehensive quantitative mechanistic understanding of the effects of these and potential novel therapies is lacking. Recently, the quality of quantitative systems pharmacology (QSP) models of the coagulation cascade has improved, simulating the interactions between proteases, cofactors, regulators, fibrin, and therapeutic responses under different clinical scenarios. We aim to review the literature on QSP models to assess the unique capabilities and reusability of these models. We systematically searched the literature and BioModels database reviewing systems biology (SB) and QSP models. The purpose and scope of most of these models are redundant with only two SB models serving as the basis for QSP models. Primarily three QSP models have a comprehensive scope and are systematically linked between SB and more recent QSP models. The biological scope of recent QSP models has expanded to enable simulations of previously unexplainable clotting events and the drug effects for treating bleeding or thrombosis. Overall, the field of coagulation appears to suffer from unclear connections between models and irreproducible code as previously reported. The reusability of future QSP models can improve by adopting model equations from validated QSP models, clearly documenting the purpose and modifications, and sharing reproducible code. The capabilities of future QSP models can improve from more rigorous validation by capturing a broader range of responses to therapies from individual patient measurements and integrating blood flow and platelet dynamics to closely represent in vivo bleeding or thrombosis risk.

Model reduction of coagulation cascade based on genetic algorithm

Fibrin is an important product of the coagulation cascade, and plays an eminent role in platelet stabilization. Since coagulation cascade models typically involve the reaction kinetics of dozens of proteins, which will incur burdensome computational costs when coupled to blood flow in complex geometries, researchers often ignore this process when constructing thrombosis models. However, previous studies have shown that fundamental aspects of coagulation can be reproduced with simpler models, which motivated us to obtain a reduced-order model of fibrin generation through a systematic approach. Therefore, we introduced a semi-automatic framework to perform model-reduction of cascade reactions in this study, which consisted of two processes. Specifically, the retained protein species and cascade reactions were determined based on published studies and simulation results from the full cascade model, while the optimal reaction rates for the new cascade network were determined using a genetic algorithm. The framework has been applied to a 19-species coagulation model that triggers fibrin generation in internal fields via reactive boundaries, and a 10-species reduced-order model was obtained to reproduce the kinetics of fibrinogenesis in the full cascade model at different boundary tissue factor concentrations. This reduced-order model of fibrinogenesis would be valuable for thrombosis modeling that considers both the coagulation cascade and platelet activity. Furthermore, the framework proposed herein can also be applied to the reductions of other cascade reaction models.

Toward modeling thrombosis and thromboembolism in laminar and turbulent flow regimes

Thrombosis and thromboembolism are deadly risk factors in blood-contacting biomedical devices, and in-silico models of thrombosis are attractive tools to understand the mechanics of these processes, though the simulation of thromboembolism remains underdeveloped. The purpose of this study is to modify an existing computational thrombosis model to allow for thromboembolism and to investigate the behavior of the modified model at a range of flow rates. The new and existing models are observed to lead to similar predictions of thrombosis in a canonical backward-facing step geometry across flow rates, and neither model predicts thrombosis in a turbulent flow. Simulations are performed by increasing flow rates in the case of a clot formed at lower flow to induce embolization. While embolization is observed, most of the clot breakdown is by shear rather than by breakup and subsequent transport of clotted material, and further work is required in the formulation and validation of embolization. This model provides a framework to further investigate thromboembolization.

Computational Analysis of Flow Structures in Turbulent Ventricular Blood Flow Associated With Mitral Valve Intervention

Cardiac disease and clinical intervention may both lead to an increased risk for thrombosis events due to a modified blood flow in the heart, and thereby a change in the mechanical stimuli of blood cells passing through the chambers of the heart. Specifically, the degree of platelet activation is influenced by the level and type of mechanical stresses in the blood flow. In this article we analyze the blood flow in the left ventricle of the heart through a computational model constructed from patient-specific data. The blood flow in the ventricle is modelled by the Navier-Stokes equations, and the flow through the mitral valve by a parameterized model which represents the projected opening of the valve. A finite element method is used to solve the equations, from which a simulation of the velocity and pressure of the blood flow is constructed. The intraventricular blood flow is complex, in particular in diastole when the inflow jet from the atrium breaks down into turbulent flow on a range of scales. A triple decomposition of the velocity gradient tensor is then used to distinguish between rigid body rotational flow, irrotational straining flow, and shear flow. The triple decomposition enables the separation of three fundamentally different flow structures, that each generates a distinct type of mechanical stimulus on the blood cells in the flow. We compare the results in a simulation where a mitral valve clip intervention is modelled, which leads to a significant modification of the intraventricular flow. Further, we perform a sensitivity study of the results with respect to the positioning of the clip. It was found that the shear in the simulation cases treated with clips increased more compared to the untreated case than the rotation and strain did. A decrease in valve opening area of 64% in one of the cases led to a 90% increase in rotation and strain, but a 150% increase in shear. The computational analysis opens up for improvements in models of shear-induced platelet activation, by offering an algorithm to distinguish shear from other modalities in intraventricular blood flow.

Uncertainty quantification of a thrombosis model considering the clotting assay PFA-100®

Mathematical models of thrombosis are currently used to study clinical scenarios of pathological thrombus formation. As these models become more complex to predict thrombus formation dynamics high computational cost must be alleviated and inherent uncertainties must be assessed. Evaluating model uncertainties allows to increase the confidence in model predictions and identify avenues of improvement for both thrombosis modeling and anti-platelet therapies. In this work, an uncertainty quantification analysis of a multi-constituent thrombosis model is performed considering a common assay for platelet function (PFA-100®). The analysis is facilitated thanks to time-evolving polynomial chaos expansions used as a parametric surrogate for the full thrombosis model considering two quantities of interest; namely, thrombus volume and occlusion percentage. The surrogate is thoroughly validated and provides a straightforward access to a global sensitivity analysis via computation of Sobol' coefficients. Six out of 15 parameters linked to thrombus consitution, vWF activity, and platelet adhesion dynamics were found to be most influential in the simulation variability considering only individual effects; while parameter interactions are highlighted when considering the total Sobol' indices. The influential parameters are related to thrombus constitution, vWF activity, and platelet to platelet adhesion dynamics. The surrogate model allowed to predict realistic PFA-100® closure times of 300,000 virtual cases that followed the trends observed in clinical data. The current methodology could be used including common anti-platelet therapies to identify scenarios that preserve the hematological balance.

An Accelerated Thrombosis Model for Computational Fluid Dynamics Simulations in Rotary Blood Pumps

Purpose

Thrombosis ranks among the major complications in blood-carrying medical devices and a better understanding to influence the design related contribution to thrombosis is desirable. Over the past years many computational models of thrombosis have been developed. However, numerically cheap models able to predict localized thrombus risk in complex geometries are still lacking. The aim of the study was to develop and test a computationally efficient model for thrombus risk prediction in rotary blood pumps.

Methods

We used a two-stage approach to calculate thrombus risk. The first stage involves the computation of velocity and pressure fields by computational fluid dynamic simulations. At the second stage, platelet activation by mechanical and chemical stimuli was determined through species transport with an Eulerian approach. The model was compared with existing clinical data on thrombus deposition within the HeartMate II. Furthermore, an operating point and model parameter sensitivity analysis was performed.

Results

Our model shows good correlation (R² > 0.93) with clinical data and identifies the bearing and outlet stator region of the HeartMate II as the location most prone to thrombus formation. The calculation of thrombus risk requires an additional 10–20 core hours of computation time.

Conclusion

The concentration of activated platelets can be used as a surrogate and computationally low-cost marker to determine potential risk regions of thrombus deposition in a blood pump. Relative comparisons of thrombus risk are possible even considering the intrinsic uncertainty in model parameters and operating conditions.

Supplementary Information

The online version contains supplementary material available at 10.1007/s13239-021-00606-y.

Application of Electrospun Nanofiber Membrane in the Treatment of Diabetic Wounds

Diabetic wounds are complications of diabetes which are caused by skin dystrophy because of local ischemia and hypoxia. Diabetes causes wounds in a pathological state of inflammation, resulting in delayed wound healing. The structure of electrospun nanofibers is similar to that of the extracellular matrix (ECM), which is conducive to the attachment, growth, and migration of fibroblasts, thus favoring the formation of new skin tissue at the wound. The composition and size of electrospun nanofiber membranes can be easily adjusted, and the controlled release of loaded drugs can be realized by regulating the fiber structure. The porous structure of the fiber membrane is beneficial to gas exchange and exudate absorption at the wound, and the fiber surface can be easily modified to give it function. Electrospun fibers can be used as wound dressing and have great application potential in the treatment of diabetic wounds. In this study, the applications of polymer electrospun fibers, nanoparticle-loaded electrospun fibers, drug-loaded electrospun fibers, and cell-loaded electrospun fibers, in the treatment of diabetic wounds were reviewed, and provide new ideas for the effective treatment of diabetic wounds.

Multi-constituent simulation of thrombus formation at LVAD inlet cannula connection: Importance of Virchow's triad

As pump thrombosis is reduced in current-generation ventricular assist devices (VAD), adverse events such as bleeding or stroke remain at unacceptable rates. Thrombosis around the VAD inlet cannula (IC) has been highlighted as a possible source of stroke events. Recent computational fluid dynamics (CFD) studies have attempted to characterize the thrombosis risk of different IC-ventricle configurations. However, purely CFD simulations relate thrombosis risk to ad hoc criteria based on flow characteristics, with little consideration of biochemical factors. This study investigates the genesis of IC thrombosis including two elements of the Virchow's triad: endothelial injury and hypercoagulability. To this end a multi-scale thrombosis simulation that includes platelet activity and coagulation reactions was performed. Our results show significant thrombin formation in stagnation regions (|u| < 0.005 m/s) close to the IC wall. In addition, high shear-mediated platelet activation was observed over the leading-edge tip of the cannula. The current study reveals the importance of biochemical factors to the genesis of thrombosis at the ventricular-cannula junction in a perioperative state. This study is a first step toward the long-term objective of including clinically relevant pharmacological kinetics such as heparin or aspirin in simulations of inflow cannula thrombosis.

Computationally Driven Discovery in Coagulation

Bleeding frequency and severity within clinical categories of hemophilia A are highly variable and the origin of this variation is unknown. Solving this mystery in coagulation requires the generation and analysis of large data sets comprised of experimental outputs or patient samples, both of which are subject to limited availability. In this review, we describe how a computationally driven approach bypasses such limitations by generating large synthetic patient data sets. These data sets were created with a mechanistic mathematical model, by varying the model inputs, clotting factor, and inhibitor concentrations, within normal physiological ranges. Specific mathematical metrics were chosen from the model output, used as a surrogate measure for bleeding severity, and statistically analyzed for further exploration and hypothesis generation. We highlight results from our recent study that employed this computationally driven approach to identify FV (factor V) as a key modifier of thrombin generation in mild to moderate hemophilia A, which was confirmed with complementary experimental assays. The mathematical model was used further to propose a potential mechanism for these observations whereby thrombin generation is rescued in FVIII-deficient plasma due to reduced substrate competition between FV and FVIII for FXa (activated factor X).