A mathematical model to quantify the effects of platelet count, shear rate, and injury size on the initiation of blood coagulation under venous flow conditions

Multistep model reduction of coagulation schemes

This study introduces a comprehensive multistep reduction technique for coagulation models, specifically targeting the dynamics of thrombin generation. By employing a synergistic approach that combines direct relation graph with error propagation, chemical lumping, quasi-steady-state assumption, and conservation analysis, the method efficiently reduces the complexity of original coagulation models without compromising accuracy. Applied to both extrinsic and intrinsic coagulation pathway schemes, this approach significantly diminishes the number of species and reactions, and the resulting reduced schemes appear to be robust to changes in initial conditions relevant to hemophilia A. The findings underscore the potential of this reduction method to facilitate more efficient computational simulations that retain the essential characteristics of different coagulation models.

Integrating biomarkers for hemostatic disorders into computational models of blood clot formation: A systematic review

In the pursuit of personalized medicine, there is a growing demand for computational models with parameters that are easily obtainable to accelerate the development of potential solutions. Blood tests, owing to their affordability, accessibility, and routine use in healthcare, offer valuable biomarkers for assessing hemostatic balance in thrombotic and bleeding disorders. Incorporating these biomarkers into computational models of blood coagulation is crucial for creating patient-specific models, which allow for the analysis of the influence of these biomarkers on clot formation. This systematic review aims to examine how clinically relevant biomarkers are integrated into computational models of blood clot formation, thereby advancing discussions on integration methodologies, identifying current gaps, and recommending future research directions. A systematic review was conducted following the PRISMA protocol, focusing on ten clinically significant biomarkers associated with hemostatic disorders: D-dimer, fibrinogen, Von Willebrand factor, factor Ⅷ, P-selectin, prothrombin time (PT), activated partial thromboplastin time (APTT), antithrombin Ⅲ, protein C, and protein S. By utilizing this set of biomarkers, this review underscores their integration into computational models and emphasizes their integration in the context of venous thromboembolism and hemophilia. Eligibility criteria included mathematical models of thrombin generation, blood clotting, or fibrin formation under flow, incorporating at least one of these biomarkers. A total of 53 articles were included in this review. Results indicate that commonly used biomarkers such as D-dimer, PT, and APTT are rarely and superficially integrated into computational blood coagulation models. Additionally, the kinetic parameters governing the dynamics of blood clot formation demonstrated significant variability across studies, with discrepancies of up to 1, 000-fold. This review highlights a critical gap in the availability of computational models based on phenomenological or first-principles approaches that effectively incorporate affordable and routinely used clinical test results for predicting blood coagulation. This hinders the development of practical tools for clinical application, as current mathematical models often fail to consider precise, patient-specific values. This limitation is especially pronounced in patients with conditions such as hemophilia, protein C and S deficiencies, or antithrombin deficiency. Addressing these challenges by developing patient-specific models that account for kinetic variability is crucial for advancing personalized medicine in the field of hemostasis.

Coagulo-Net: Enhancing the mathematical modeling of blood coagulation using physics-informed neural networks

Blood coagulation, which involves a group of complex biochemical reactions, is a crucial step in hemostasis to stop bleeding at the injury site of a blood vessel. Coagulation abnormalities, such as hypercoagulation and hypocoagulation, could either cause thrombosis or hemorrhage, resulting in severe clinical consequences. Mathematical models of blood coagulation have been widely used to improve the understanding of the pathophysiology of coagulation disorders, guide the design and testing of new anticoagulants or other therapeutic agents, and promote precision medicine. However, estimating the parameters in these coagulation models has been challenging as not all reaction rate constants and new parameters derived from model assumptions are measurable. Although various conventional methods have been employed for parameter estimation for coagulation models, the existing approaches have several shortcomings. Inspired by the physics-informed neural networks, we propose Coagulo-Net, which synergizes the strengths of deep neural networks with the mechanistic understanding of the blood coagulation processes to enhance the mathematical models of the blood coagulation cascade. We assess the performance of the Coagulo-Net using two existing coagulation models with different extents of complexity. Our simulation results illustrate that Coagulo-Net can efficiently infer the unknown model parameters and dynamics of species based on sparse measurement data and data contaminated with noise. In addition, we show that Coagulo-Net can process a mixture of synthetic and experimental data and refine the predictions of existing mathematical models of coagulation. These results demonstrate the promise of Coagulo-Net in enhancing current coagulation models and aiding the creation of novel models for physiological and pathological research. These results showcase the potential of Coagulo-Net to advance computational modeling in the study of blood coagulation, improving both research methodologies and the development of new therapies for treating patients with coagulation disorders.

Modeling Fibrin Accumulation on Flow-Diverting Devices for Intracranial Aneurysms

The mechanisms leading to aneurysm occlusion after treatment with flow-diverting devices are not fully understood. Flow modification induces thrombus formation within the aneurysm cavity, but fibrin can simultaneously accumulate and cover the device scaffold, leading to further flow modification. However, the interplay and relative importance of these processes are not clearly understood. A computational model of fibrin accumulation and flow modification after flow diversion treatment of cerebral aneurysms has been developed under the guidance of in vitro experiments and observations. The model is based on the loose coupling of flow and transport-reaction equations that are solved separately by independent codes. Interaction or reactive terms account for thrombin production from prothrombin stimulated by thrombogenic metallic wires and inhibition by antithrombin as well as fibrin production from fibrinogen stimulated by thrombin and flow shear stress, and fibrin adhesion to device wires and already attached fibrin. The computational model was demonstrated and tested on idealized vessel and aneurysm geometries. The model was able to reproduce the salient features of fibrin accumulation after the deployment of flow-diverting devices in idealized in vitro models of cerebral aneurysms. Namely, fibrin production in regions of high shear stress, initial accumulation at the inflow zone, and progressive occlusion of the device and corresponding flow attenuation. The computational model linking flow dynamics to fibrin production, transport, and adhesion can be used to investigate and better understand the effects that lead to fibrin accumulation and the resulting aneurysm inflow reduction and intra-aneurysmal flow modulation.

A Role of Effector CD 8 + T Cells Against Circulating Tumor Cells Cloaked with Platelets: Insights from a Mathematical Model

Cancer metastasis accounts for a majority of cancer-related deaths worldwide. Metastasis occurs when the primary tumor sheds cells into the blood and lymphatic circulation, thereby becoming circulating tumor cells (CTCs) that transverse through the circulatory system, extravasate the circulation and establish a secondary distant tumor. Accumulating evidence suggests that circulating effector CD 8 + T cells are able to recognize and attack arrested or extravasating CTCs, but this important antitumoral effect remains largely undefined. Recent studies highlighted the supporting role of activated platelets in CTCs's extravasation from the bloodstream, contributing to metastatic progression. In this work, a simple mathematical model describes how the primary tumor, CTCs, activated platelets and effector CD 8 + T cells participate in metastasis. The stability analysis reveals that for early dissemination of CTCs, effector CD 8 + T cells can present or keep secondary metastatic tumor burden at low equilibrium state. In contrast, for late dissemination of CTCs, effector CD 8 + T cells are unlikely to inhibit secondary tumor growth. Moreover, global sensitivity analysis demonstrates that the rate of the primary tumor growth, intravascular CTC proliferation, as well as the CD 8 + T cell proliferation, strongly affects the number of the secondary tumor cells. Additionally, model simulations indicate that an increase in CTC proliferation greatly contributes to tumor metastasis. Our simulations further illustrate that the higher the number of activated platelets on CTCs, the higher the probability of secondary tumor establishment. Intriguingly, from a mathematical immunology perspective, our simulations indicate that if the rate of effector CD 8 + T cell proliferation is high, then the secondary tumor formation can be considerably delayed, providing a window for adjuvant tumor control strategies. Collectively, our results suggest that the earlier the effector CD 8 + T cell response is enhanced the higher is the probability of preventing or delaying secondary tumor metastases.

Venous Thromboembolism: Review of Clinical Challenges, Biology, Assessment, Treatment, and Modeling

Venous thromboembolism (VTE) is a massive clinical challenge, annually affecting millions of patients globally. VTE is a particularly consequential pathology, as incidence is correlated with extremely common risk factors, and a large cohort of patients experience recurrent VTE after initial intervention. Altered hemodynamics, hypercoagulability, and damaged vascular tissue cause deep-vein thrombosis and pulmonary embolism, the two permutations of VTE. Venous valves have been identified as likely locations for initial blood clot formation, but the exact pathway by which thrombosis occurs in this environment is not entirely clear. Several risk factors are known to increase the likelihood of VTE, particularly those that increase inflammation and coagulability, increase venous resistance, and damage the endothelial lining. While these risk factors are useful as predictive tools, VTE diagnosis prior to presentation of outward symptoms is difficult, chiefly due to challenges in successfully imaging deep-vein thrombi. Clinically, VTE can be managed by anticoagulants or mechanical intervention. Recently, direct oral anticoagulants and catheter-directed thrombolysis have emerged as leading tools in resolution of venous thrombosis. While a satisfactory VTE model has yet to be developed, recent strides have been made in advancing in silico models of venous hemodynamics, hemorheology, fluid-structure interaction, and clot growth. These models are often guided by imaging-informed boundary conditions or inspired by benchtop animal models. These gaps in knowledge are critical targets to address necessary improvements in prediction and diagnosis, clinical management, and VTE experimental and computational models.

Dynamic adaptive moving mesh finite-volume method for the blood flow and coagulation modeling

In this work, we develop numerical methods for the solution of blood flow and coagulation on dynamic adaptive moving meshes. We consider the blood flow as a flow of incompressible Newtonian fluid governed by the Navier-Stokes equations. The blood coagulation is introduced through the additional Darcy term, with a permeability coefficient dependent on reactions. To this end, we introduce moving mesh collocated finite-volume methods for the Navier-Stokes equations, advection-diffusion equations, and a method for the stiff cascade of reactions. A monolithic nonlinear system is solved to advance the solution in time. The finite volume method for the Navier-Stokes equations features collocated arrangement of pressure and velocity unknowns and a coupled momentum and mass flux. The method is conservative and inf-sup stable despite the saddle point nature of the system. It is verified on a series of analytical problems and applied to the blood flow problem in the deforming domain of the right ventricle, reconstructed from a time series of computed tomography scans. At last, we demonstrate the ability to model the coagulation process in deforming microfluidic capillaries.

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.

In-stent restenosis and stent compression following stenting for chronic iliofemoral venous obstruction

OBJECTIVE

In-stent restenosis (ISR) and stent compression (SC) are problems encountered after stenting for chronic iliofemoral venous obstruction that are responsible for a majority of reinterventions. However, characteristics of ISR and SC, in addition to outcomes after reintervention, have not been explored in detail and represent the focus of this study.

METHODS

A retrospective analysis of contemporaneously entered electronic medical record data on 578 limbs/patients with initial unilateral iliofemoral venous stents placed from 2014 to 2018 was performed. ISR was estimated from stent and flow channel diameters measured using duplex ultrasound. SC was estimated from rated stent diameter and actual stent diameter on duplex ultrasound. Characteristics evaluated included onset of ISR/SC after stent placement and progression over time. Analysis was performed to evaluate risk factors for the development of ISR and SC. Outcomes after reintervention for ISR/SC were also appraised.

RESULTS

A total of 578 limbs underwent stenting for stenotic lesions (nonthrombotic iliac vein lesion/post-thrombotic syndrome). ISR was noted in 27% of limbs on post-intervention day 1. The prevalence of ISR increased to 74% by 3 months and stabilized thereafter. SC was noted in 80% of limbs on day 1 and plateaued. Of the variables evaluated as potential risk factors for ISR, intravascular ultrasound determined that stent inflow luminal area and shear rate were found to be significant. For SC, asymmetric stent sizing was a significant risk factor. Over a median follow-up of 24 months, 95 of 578 (16.4%) limbs underwent reintervention for ISR, SC, or a combination. The median time to reintervention was 11 months. There was no statistically significant difference in the degree of ISR/SC among patients who underwent reintervention vs those who did not (P > .05). However, there was a statistically significant difference in the grade of swelling (P = .006) and visual analog scale pain scores (P < .0001) between those who underwent reintervention and those who did not. Primary, primary assisted, and secondary patencies at 60 months were 70%, 98%, and 84% after reintervention for ISR and 70%, 99%, and 84% for SC, respectively.

CONCLUSIONS

Although ISR and SC are both common after stenting for chronic iliofemoral venous obstruction, neither are relentlessly progressive. Indication for reintervention must be a recurrence of symptoms with impairment of quality of life and not the percentage of ISR or degree of SC. After reintervention good outcomes can be expected both in terms of clinical improvement and stent patency. Further study of the impact of shear rate on stent flow is required to help reduce the incidence of ISR.

Patient-Specific Modelling of Blood Coagulation

Blood coagulation represents one of the most studied processes in biomedical modelling. However, clinical applications of this modelling remain limited because of the complexity of this process and because of large inter-patient variation of the concentrations of blood factors, kinetic constants and physiological conditions. Determination of some of these patients-specific parameters is experimentally possible, but it would be related to excessive time and material costs impossible in clinical practice. We propose in this work a methodological approach to patient-specific modelling of blood coagulation. It begins with conventional thrombin generation tests allowing the determination of parameters of a reduced kinetic model. Next, this model is used to study spatial distributions of blood factors and blood coagulation in flow, and to evaluate the results of medical treatment of blood coagulation disorders.