Stochastic Modeling of Blood Coagulation Initiation

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.

Development of a paper-based lateral flow prothrombin assay

Disorders of haemostasis result in both excessive bleeding and clotting and are a major global cause of morbidity and mortality, particularly in the developing world. A small number of simple tests can be used to screen and monitor for such dysfunctions, one of which is the prothrombin time (PT) test and associated International Normalisation Ratio (INR). PT/INR is routine in hospital laboratories in developed countries, and can also be performed using point-of-care instruments. However, neither of these approaches is appropriate in low-resource settings. Significant interest has grown in paper-based devices to form the basis of simple and low-cost assays that may have the potential for application in such environments. This study describes the development of a simple, low-cost, paper-based lateral flow prothrombin assay. The assay employed wax printing on chromatography paper to define test channels, with deposition of thromboplastin reagent and calcium chloride onto the resulting strips. These were placed in a test housing and measurement of the flow rates of deposited plasma samples were performed in triplicate. The flow dynamics of the assay was optimised according to the type of paper substrate used, the nature and quantity of the thromboplastin reagent, the amount of calcium chloride required, and the volume of sample employed. An optimised assay configuration demonstrated a dynamic range of 6 mm between normal and factor-deficient plasmas. The assay showed good correlation with laboratory-based PT assay (Yumizen G200) in artificial plasmas in the 9.8 to 36 s range (r² = 0.8112). The assay also demonstrated good dynamic range and correlation in patient plasma samples in comparison with hospital PT, with a range of 9.8 to 45 s (r² = 0.7209).

Particle hydrodynamic simulation of thrombus formation using velocity decay factor

BACKGROUND AND OBJECTIVE

Thrombus simulation plays an important role in many specialist areas in the field of medicine such as surgical education and training, clinical diagnosis and prediction, treatment planning, etc. Although a considerable number of methods have been developed to simulate various kinds of fluid flows, it remains a non-trivial task to effectively simulate thrombus because of its unique physiological properties in contrast to other types of fluids. To tackle this issue, this study introduces a novel method to model the formation mechanism of thrombus and its interaction with blood flow.

METHODS

The proposed method for thrombus formation simulation mainly consists of three steps. First, we formulate the formation of thrombus as a particle-based model and obtain the fibrin concentration of the particles with a discretized form of the convection-diffusion-reaction equation; then, we calculate the velocity decay factor using the obtained fibrin concentration. Finally, the formation of thrombus can be simulated by applying the velocity decay factor on particles.

RESULTS

We carried out extensive experiments under different settings to verify the efficacy of the proposed method. The experimental results demonstrate that our method can yield more realistic simulation of thrombus and is superior to peer method in terms of computational efficiency, maintaining the stability of the dynamic particle motion, and preventing particle penetration at the boundary.

CONCLUSION

The proposed method can simulate the formation mechanism of thrombus and the interaction between blood flow and thrombus both efficiently and effectively.

In Silico Hemostasis Modeling and Prediction

Computational physiology, i.e., reproduction of physiological (and, by extension, pathophysiological) processes in silico, could be considered one of the major goals in computational biology. One might use computers to simulate molecular interactions, enzyme kinetics, gene expression, or whole networks of biochemical reactions, but it is (patho)physiological meaning that is usually the meaningful goal of the research even when a single enzyme is its subject. Although exponential rise in the use of computational and mathematical models in the field of hemostasis and thrombosis began in the 1980s (first for blood coagulation, then for platelet adhesion, and finally for platelet signal transduction), the majority of their successful applications are still focused on simulating the elements of the hemostatic system rather than the total (patho)physiological response in situ. Here we discuss the state of the art, the state of the progress toward the efficient "virtual thrombus formation," and what one can already get from the existing models.

Accelerating availability of clinically-relevant parameter estimates from thromboelastogram point-of-care device

BACKGROUND

Modeling approaches offer a novel way to detect and predict coagulopathy in trauma patients. A dynamic model, built and tested on thromboelastogram (TEG) data, was used to generate a virtual library of over 160,000 simulated RapidTEGs. The patient-specific parameters are the initial platelet count, platelet activation rate, thrombus growth rate, and lysis rate (P(0), k1, k2, and k3, respectively).

METHODS

Patient data from both STAAMP (n = 182 patients) and PAMPer (n = 111 patients) clinical trials were collected. A total of 873 RapidTEGs were analyzed. One hundred sixteen TEGs indicated maximum amplitude (MA) below normal and 466 TEGs indicated lysis percent above normal. Each patient's TEG response was compared against the virtual library of TEGs to determine library trajectories having the least sum-of-squared error versus the patient TEG up to each specified evaluation time ∈ (3, 4, 5, 7.5, 10, 15, 20 minutes). Using 10 nearest-neighbor trajectories, a logistic regression was performed to predict if the patient TEG indicated MA below normal (<50 mm), lysis percent 30 minutes after MA (LY30) greater than 3%, and/or blood transfusion need using the parameters from the dynamic model.

RESULTS

The algorithm predicts abnormal MA values using the initial 3 minutes of RapidTEG data with a median area under the curve of 0.95, and improves with more data to 0.98 by 10 minutes. Prediction of future platelet and packed red blood cell transfusion based on parameters at 4 and 5 minutes, respectively, provides equivalent predictions to the traditional TEG parameters in significantly less time. Dynamic model parameters could not predict abnormal LY30 or future fresh-frozen plasma transfusion.

CONCLUSION

This analysis could be incorporated into TEG software and workflow to quickly estimate if the MA would be below or above threshold value within the initial minutes following a TEG, along with an estimate of what blood products to have on hand.

LEVEL OF EVIDENCE

Therapeutic/Care Management: Level IV.

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.

Graph-facilitated resonant mode counting in stochastic interaction networks

Oscillations in dynamical systems are widely reported in multiple branches of applied mathematics. Critically, even a non-oscillatory deterministic system can produce cyclic trajectories when it is in a low copy number, stochastic regime. Common methods of finding parameter ranges for stochastically driven resonances, such as direct calculation, are cumbersome for any but the smallest networks. In this paper, we provide a systematic framework to efficiently determine the number of resonant modes and parameter ranges for stochastic oscillations relying on real root counting algorithms and graph theoretic methods. We argue that stochastic resonance is a network property by showing that resonant modes only depend on the squared Jacobian matrix J2, unlike deterministic oscillations which are determined by J By using graph theoretic tools, analysis of stochastic behaviour for larger interaction networks is simplified and stochastic dynamical systems with multiple resonant modes can be identified easily.

The Role of Biomarkers in Research on Caregivers for Cancer Patients: A Scoping Review

BACKGROUND

Biomarkers can be used as prognostic, predictive, or monitoring indicators of an associated outcome. The purpose of this review was to provide a comprehensive summary of the research examining the use of biomarkers as surrogate end points for clinical outcomes in family caregivers for cancer patients, identify gaps, and make recommendations for future research.

METHODS

A scoping review, a process of mapping the existing literature, was conducted. Studies comparing biomarkers across caregivers and controls and/or examining relationships between biomarkers and psychological health were reviewed.

RESULTS

The studies ( N = 18) of caregivers for cancer patients who were identified used biomarkers to predict outcomes ( n = 13) and to monitor the efficacy of interventions ( n = 6). Biomarkers were divided into two categories based on physiological systems involved: (1) neuroendocrine function (sympathetic-adrenal-medullary axis activity, hypothalamic-pituitary-adrenal axis activity) and (2) immune function. Predictive biomarkers were sensitive to differences between caregivers and controls. The biomarkers were used to evaluate outcomes frequently associated with stress, depression, and anxiety. Cortisol was the biomarker most commonly measured to monitor the efficacy of interventions.

DISCUSSION

Biomarkers are most commonly incorporated into caregiver studies to predict group membership and psychological health. Neuroendocrine biomarkers, specifically cortisol, are most frequently assessed. Future research should include biomarkers of other physiologic functions (e.g., cardiovascular function, cognitive dysfunction, and cell aging) and those that serve as multisystem indicators. Expanding the scientific study of biomarkers will contribute to our understanding of the mechanisms through which stress may influence caregiver health.

Modelling of thrombin generation under flow in realistic left anterior descending geometries

Currently there are no available methods for prediction of thrombotic complications in Coronary Artery disease. Additionally, blood coagulation tests are mainly performed in a steady system while coagulation in vivo occurs under flow conditions. In this work, a phenomenological model for coagulation up-to thrombin generation is proposed; the model is mainly based on the results of thrombin generation assays and therefore it can account for the variation of the coagulability that is observed in different individuals. The model is applied on 3 cases of left anterior descending arteries (LAD) with 50% maximum stenosis placed at a different location and have been statistically assessed as of different complication risk. The simulations showed that parameters of thrombin generation assays obtain different values when they refer to thrombin generation under realistic coronary flow conditions. The flow conditions prevailing locally because of the geometric differences among the arterial trees can lead to different initiation times and thrombin production rates and it also alters the spatial distribution of the coagulation products. Similarly, small changes of the coagulation characteristics of blood under identical flow conditions can allow or prevent the initiation of coagulation. The results indicate that combined consideration of geometry and coagulation characteristics of blood can lead to entirely different conclusions compared to independent assessment of each factor.

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.

Systems biology of the microvasculature

The vascular network carries blood throughout the body, delivering oxygen to tissues and providing a pathway for communication between distant organs. The network is hierarchical and structured, but also dynamic, especially at the smaller scales. Remodeling of the microvasculature occurs in response to local changes in oxygen, gene expression, cell-cell communication, and chemical and mechanical stimuli from the microenvironment. These local changes occur as a result of physiological processes such as growth and exercise, as well as acute and chronic diseases including stroke, cancer, and diabetes, and pharmacological intervention. While the vasculature is an important therapeutic target in many diseases, drugs designed to inhibit vascular growth have achieved only limited success, and no drug has yet been approved to promote therapeutic vascular remodeling. This highlights the challenges involved in identifying appropriate therapeutic targets in a system as complex as the vasculature. Systems biology approaches provide a means to bridge current understanding of the vascular system, from detailed signaling dynamics measured in vitro and pre-clinical animal models of vascular disease, to a more complete picture of vascular regulation in vivo. This will translate to an improved ability to identify multi-component biomarkers for diagnosis, prognosis, and monitoring of therapy that are easy to measure in vivo, as well as better drug targets for specific disease states. In this review, we summarize systems biology approaches that have advanced our understanding of vascular function and dysfunction in vivo, with a focus on computational modeling.

The balance of pro- and anticoagulant processes underlying thrombin generation

BACKGROUND

The generation of thrombin in time is the combined effect of the processes of prothrombin conversion and thrombin inactivation. Measurement of prothrombin consumption used to provide valuable information on hemostatic disorders, but is no longer used, due to its elaborate nature.

OBJECTIVES

Because thrombin generation (TG) curves are easily obtained with modern techniques, we developed a method to extract the prothrombin conversion curve from the TG curve, using a computational model for thrombin inactivation.

METHODS

Thrombin inactivation was modelled computationally by a reaction scheme with antithrombin, α(2) Macroglobulin and fibrinogen, taking into account the presence of the thrombin substrate ZGGR-AMC used to obtain the experimental data. The model was validated by comparison with data obtained from plasma as well as from a reaction mixture containing the same reactants as plasma.

RESULTS

The computational model fitted experimental data within the limits of experimental error. Thrombin inactivation curves were predicted within 2 SD in 96% of healthy subjects. Prothrombin conversion was calculated in 24 healthy subjects and validated by comparison with the experimental consumption of prothrombin during TG. The endogenous thrombin potential (ETP) mainly depends on the total amount of prothrombin converted and the thrombin decay capacity, and the peak height is determined by the maximum prothrombin conversion rate and the thrombin decay capacity.

CONCLUSIONS

Thrombin inactivation can be accurately predicted by the proposed computational model and prothrombin conversion can be extracted from a TG curve using this computational prediction. This additional computational analysis of TG facilitates the analysis of the process of disturbed TG.

Global assays of hemostasis

PURPOSE OF REVIEW

There exists an imbalance between our understanding of the physiology of the blood coagulation process and the translation of this understanding into useful assays for clinical application. As technology advances, the capabilities for merging the two areas have become more attainable. Global assays have advanced our understanding of the dynamics of the blood coagulation process beyond end point assays and are at the forefront of implementation in the clinic.

RECENT FINDINGS

We will review recent advances in the main global assays with a focus on thrombin generation that have potential for clinical utility. These assays include direct (thrombogram, whole blood, purified systems) and indirect empirical measures of thrombin generation (thromboelastography) and mechanism-based computational models that use plasma composition data from individuals to generate thrombin generation profiles.

SUMMARY

Empirical thrombin generation assays (direct and indirect) and computational modeling of thrombin generation have greatly advanced our understanding of the hemostatic balance. Implementation of these types of assays and visualization approaches in the clinic will potentially provide a basis for the development of individualized patient care. Advances in both empirical and computational global assays have made the goal of predicting precrisis changes in an individual's hemostatic state one step closer.

Massive exploration of perturbed conditions of the blood coagulation cascade through GPU parallelization

The introduction of general-purpose Graphics Processing Units (GPUs) is boosting scientific applications in Bioinformatics, Systems Biology, and Computational Biology. In these fields, the use of high-performance computing solutions is motivated by the need of performing large numbers of in silico analysis to study the behavior of biological systems in different conditions, which necessitate a computing power that usually overtakes the capability of standard desktop computers. In this work we present coagSODA, a CUDA-powered computational tool that was purposely developed for the analysis of a large mechanistic model of the blood coagulation cascade (BCC), defined according to both mass-action kinetics and Hill functions. coagSODA allows the execution of parallel simulations of the dynamics of the BCC by automatically deriving the system of ordinary differential equations and then exploiting the numerical integration algorithm LSODA. We present the biological results achieved with a massive exploration of perturbed conditions of the BCC, carried out with one-dimensional and bi-dimensional parameter sweep analysis, and show that GPU-accelerated parallel simulations of this model can increase the computational performances up to a 181× speedup compared to the corresponding sequential simulations.

A simplified mathematical model for thrombin generation

A new phenomenological mathematical model based directly on laboratory data for thrombin generation and having a patient-specific character is described. A set of the solved equations for cell-based models of blood coagulation that can reproduce the temporal evolution of thrombin generation is proposed; such equations are appropriate for use in computational fluid dynamic (CFD) simulations. The initial values for the reaction rates are either taken from already existing model or experimental data, or they can obtained from simple reasoning under certain assumptions; it is shown that coefficients can be adjusted in order to fit a range of different thrombin generation curves as derived from thrombin generation assays. The behaviour of the model for different platelet concentration seems to be in good agreement with reported experimental data. It is shown that the reduced set of equations used represents to a good approximation a low-order model of the detailed mechanism and thus it can represent a cost-effective and-case specific mathematical model of coagulation reactions up to thrombin generation.

Systems biology of coagulation

Accurate computer simulation of blood function can inform drug target selection, patient-specific dosing, clinical trial design, biomedical device design, as well as the scoring of patient-specific disease risk and severity. These large-scale simulations rely on hundreds of independently measured physical parameters and kinetic rate constants. However, the models can be validated against large-scale, patient-specific laboratory measurements. By validation with high-dimensional data, modeling becomes a powerful tool to predict clinically complex scenarios. Currently, it is possible to accurately predict the clotting rate of plasma or blood in a tube as it is activated with a dose of tissue factor, even as numerous coagulation factors are altered by exogenous attenuation or potentiation. Similarly, the dynamics of platelet activation, as indicated by calcium mobilization or inside-out signaling, can now be numerically simulated with accuracy in cases where platelets are exposed to combinations of agonists. Multiscale models have emerged to combine platelet function and coagulation kinetics into complete physics-based descriptions of thrombosis under flow. Blood flow controls platelet fluxes, delivery and removal of coagulation factors, adhesive bonding, and von Willebrand factor conformation. The field of blood systems biology has now reached a stage that anticipates the inclusion of contact, complement, and fibrinolytic pathways along with models of neutrophil and endothelial activation. Along with '-omics' data sets, such advanced models seek to predict the multifactorial range of healthy responses and diverse bleeding and clotting scenarios, ultimately to understand and improve patient outcomes.

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.

Multiscale systems biology and physics of thrombosis under flow

Blood clotting under hemodynamic conditions involves numerous multiscale interactions from the molecular scale to macroscopic vessel and systemic circulation scales. Transmission of shear forces to platelet receptors such as GPIbα, P-selectin, α(2)β(1), and α(2b)β(3) controls adhesion dynamics. These forces also drive membrane tether formation, cellular deformation, and mechanosignaling in blood cells. Blood flow results in red blood cell (RBC) drift towards the center of the vessel along with a near-wall plasma layer enriched with platelets. RBC motions also dramatically enhance platelet dispersion. Trajectories of individual platelets near a thrombotic deposit dictate capture-activation-arrest dynamics as these newly arriving platelets are exposed to chemical gradients of ADP, thromboxane, and thrombin within a micron-scale boundary layer formed around the deposit. If shear forces are sufficiently elevated (>50 dyne/cm(2)), the largest polymers of von Willebrand Factor may elongate with concomitant shear-induced platelet activation. Finally, thrombin generation enhances platelet recruitment and clot strength via fibrin polymerization. By combination of coarse-graining, continuum, and stochastic algorithms, the numerical simulation of the growth rate, composition, and occlusive/embolic potential of a thrombus now spans multiscale phenomena. These simulations accommodate particular flow geometries, blood phenotype, pharmacological regimen, and reactive surfaces to help predict disease risk or response to therapy.

Computational analysis of intersubject variability and thrombin generation in dilutional coagulopathy

BACKGROUND

Blood dilution is a frequent complication of massive transfusion during trauma and surgery. This article investigates the quantitative effects of blood plasma dilution on thrombin generation in the context of intersubject variability.

STUDY DESIGN AND METHODS

A thoroughly validated computational model was used to simulate thrombin generation curves for 472 healthy subjects in the Leiden Thrombophilia Study. Individual thrombin curves were calculated for undiluted blood and for different dilution scenarios. For every such curve, five standard quantitative parameters of thrombin generation were calculated and analyzed.

RESULTS

Thrombin generation parameters in diluted blood plasma displayed significant intersubject variability (with a coefficient of variation up to approx. 28%). Nevertheless, dilutional effects in the majority (or all) of the subjects in the study group were characterized by persistent patterns. In particular, the largest dilution-induced change typically occurred in the maximum slope (MS) of the thrombin curve, followed by a change in thrombin peak height (PH), whereas the smallest change often occurred in the area under the curve. The identified patterns demonstrated considerable robustness to variations in dilution scenario and tissue factor concentration.

CONCLUSION

Dilutional effects on thrombin generation in a human population can be predicted from trends identified for the "average" subject and then refined by performing an analysis of actual subjects in the study group. The MS and PH are dilution indicators that are both sensitive and reliable across a large subject group and could potentially be used as disease markers in the diagnosis of coagulopathic conditions.

Multiscale models of thrombogenesis

To restrict the loss of blood follow from the rupture of blood vessels, the human body rapidly forms a clot consisting of platelets and fibrin. However, to prevent pathological clotting within vessels as a result of vessel damage, the response must be regulated. Clots forming within vessels (thrombi) can restrict the flow of blood causing damage to tissues in the flow field. Additionally, fragments dissociating from the primary thrombus (emboli) may lodge and clog vessels in the brain (causing ischemic stroke) or lungs (resulting in pulmonary embolism). Pathologies related to the obstruction of blood flow through the vasculature are the major cause of mortality in the United States. Venous thromboembolic disease alone accounts for 900,000 hospitalizations and 300,000 deaths per year and the incidence will increase as the population ages (Wakefield et al. J Vasc Surg 2009, 49:1620-1623). Thus, understanding the interplay between the many processes involved in thrombus development is of significant biomedical value. In this article, we first review computational models of important subprocesses of hemostasis/thrombosis including coagulation reactions, platelet activation, and fibrin assembly, respectively. We then describe several multiscale models integrating these subprocesses to simulate temporal and spatial development of thrombi. The development of validated computational models and predictive simulations will enable one to explore how the variation of multiple hemostatic factors affects thrombotic risk providing an important new tool for thrombosis research.

Computational approaches to studying thrombus development

In addition to descriptive biological models, many computational models have been developed for hemostasis/thrombosis that provide quantitative characterization of thrombus development. Simulations using computational models that have been developed for coagulation reactions, platelet activation, and fibrinogen assembly have been shown to be in close agreement with experimental data. Models of processes involved in hemostasis/thrombosis are being integrated to simulate the development of the thrombus simultaneously in time and space. Further development of computational approaches can provide quantitative insights leading to predictions that are not obvious from qualitative biological models.

Stochastic exit from mitosis in budding yeast: model predictions and experimental observations

Unlike many mutants that are completely viable or inviable, the CLB2-dbΔ clb5Δ mutant of Saccharomyces cerevisiae is inviable in glucose but partially viable on slower growth media such as raffinose. On raffinose, the mutant cells can bud and divide but in each cycle there is a chance that a cell will fail to divide (telophase arrest), causing it to exit the cell cycle. This effect gives rise to a stochastic phenotype that cannot be explained by a deterministic model. We measure the inter-bud times of wild type and mutant cells growing on raffinose and compute statistics and distributions to characterize the mutant's behavior. We convert a detailed deterministic model of the budding yeast cell cycle to a stochastic model and determine the extent to which it captures the stochastic phenotype of the mutant strain. Predictions of the mathematical model are in reasonable agreement with our experimental data and suggest directions for improving the model. Ultimately, the ability to accurately model stochastic phenotypes may prove critical to understanding disease and therapeutic interventions in higher eukaryotes.

Evaluation of activated partial thromboplastin time (aPTT) reagents for application in biomedical diagnostic device development

INTRODUCTION

The most commonly used test for monitoring heparin therapy is the activated partial thromboplastin time (aPTT). The response of available aPTT reagents to heparin varies significantly. The aim of this study was to highlight the differences between aPTT reagents stored in a dried format to select the most suitable formulations to be used for the development of point-of-care diagnostic devices used for monitoring of unfractionated heparin dose response.

METHODS

Ten reagents were analysed in terms of their performance in liquid and in dried form after storage for 24 h and 14 days. Performance was assessed by measurement of the clotting time (CT) as evidenced by the onset of thrombin formation using a chromogenic thrombin substrate in plasma samples activated with these formulations.

RESULTS

Reagents in all of the three forms tested (liquid, 24 h and 14 days) resulted in significant shortening of CTs in comparison with the nonactivated plasma CT. Liquids returned more rapid CTs in comparison with dried reagents. Most of the reagents were more sensitive to heparin in dried, rather than in liquid form. Dried reagents based on kaolin as a surface activator were notably more effective in achieving short CT than others, while dried reagents composed of silica and synthetic phospholipids were the most sensitive to heparin.

CONCLUSION

Two reagents, namely aPTT-SP and SynthASIL both of which are based on synthetic phospholipids and silica, were identified as promising candidates for incorporation into point-of-care diagnostic device platforms as dried reagents.

Fluorescence-based blood coagulation assay device for measuring activated partial thromboplastin time

The measurement of blood clotting time is important in a range of clinical applications such as assessing coagulation disorders and controlling the effect of various anticoagulant drug therapies. Clotting time tests essentially measure the onset of clot formation which results from the formation of fibrin fibers in the blood sample. However, such assays are inherently imprecise due to the highly variable nature of the clot formation process and the sample matrix. This work describes a clotting time measurement assay which uses a fluorescent probe to very precisely detect the onset of fibrin clot formation. It uses a microstructured surface which enhances the formation of multiple localized clot loci and which results in the abrupt redistribution of the fluorescent label at the onset of clot formation in both whole blood and plasma. This methodology was applied to the development of an activated partial thromboplastin time (aPTT) test in a lateral flow microfluidic platform and used to monitor the effect of heparin dosage where it showed linearity from 0 to 2 U/mL in spiked plasma samples (R(2)=0.996, n = 3), correlation against gold standard coagulometry of 0.9986, and correlation against standard hospital aPTT in 32 patient samples of 0.78.

Systems biology of coagulation initiation: kinetics of thrombin generation in resting and activated human blood

Blood function defines bleeding and clotting risks and dictates approaches for clinical intervention. Independent of adding exogenous tissue factor (TF), human blood treated in vitro with corn trypsin inhibitor (CTI, to block Factor XIIa) will generate thrombin after an initiation time (T_i) of 1 to 2 hours (depending on donor), while activation of platelets with the GPVI-activator convulxin reduces T_i to ∼20 minutes. Since current kinetic models fail to generate thrombin in the absence of added TF, we implemented a Platelet-Plasma ODE model accounting for: the Hockin-Mann protease reaction network, thrombin-dependent display of platelet phosphatidylserine, VIIa function on activated platelets, XIIa and XIa generation and function, competitive thrombin substrates (fluorogenic detector and fibrinogen), and thrombin consumption during fibrin polymerization. The kinetic model consisting of 76 ordinary differential equations (76 species, 57 reactions, 105 kinetic parameters) predicted the clotting of resting and convulxin-activated human blood as well as predicted T_i of human blood under 50 different initial conditions that titrated increasing levels of TF, Xa, Va, XIa, IXa, and VIIa. Experiments with combined anti-XI and anti-XII antibodies prevented thrombin production, demonstrating that a leak of XIIa past saturating amounts of CTI (and not “blood-borne TF” alone) was responsible for in vitro initiation without added TF. Clotting was not blocked by antibodies used individually against TF, VII/VIIa, P-selectin, GPIb, protein disulfide isomerase, cathepsin G, nor blocked by the ribosome inhibitor puromycin, the Clk1 kinase inhibitor Tg003, or inhibited VIIa (VIIai). This is the first model to predict the observed behavior of CTI-treated human blood, either resting or stimulated with platelet activators. CTI-treated human blood will clot in vitro due to the combined activity of XIIa and XIa, a process enhanced by platelet activators and which proceeds in the absence of any evidence for kinetically significant blood borne tissue factor.

Clotting of blood involves a series of reactions wherein at each step an inactive zymogen is converted to an active enzyme by the product of the previous step, sometimes in plasma and usually on efficient catalytic surfaces provided by the activating platelet. The protein Tissue Factor (TF) initiates this cascade when blood vessels are disrupted, but how this cascade is triggered in the absence of exogenous TF remains the subject of much debate. First, we validated a high throughput experimental system that allowed the noninvasive quantification of thrombin generation dynamics. Next, we showed that “contact activation,” despite use of the best available inhibitor (CTI) to prevent it, builds up enough autocatalytic strength to trigger coagulation without exogenous TF, particularly upon activated platelets. Further, we build an ODE based model to predict the stability of blood resulting from multiple perturbations with active enzymes at various physiologically realizable concentrations. Unlike existing models, we consider the dynamics of platelet activation on reaction rates due to phosphatiylserine exposure. The “Platelet-Plasma” model lays the groundwork for integration of coagulation reaction kinetics and donor specific descriptions of platelet function.

Problem behavior of dementia patients predicts low-grade hypercoagulability in spousal caregivers

BACKGROUND

Low-grade hypercoagulability might be one pathway to explain how the chronic stress of dementia caregiving increases cardiovascular disease risk, but the specific aspects of caregiver stress that elicit hypercoagulability are elusive. We hypothesized that dementia patients' problem behaviors and negative reactions of caregivers to these behaviors would relate to hypercoagulability in caregivers.

METHODS

One hundred and eight participants (mean age 74 +/- 8 years, 70% women) providing in-home care for their spouse with Alzheimer's disease were examined. Caregivers were interviewed about the number of 24 predefined patient problem behaviors in the previous week (range 0-24) and how upset or bothered they felt in response to these behaviors (total score 0-96). Von Willebrand factor, plasminogen activator inhibitor-1, and D-dimer were determined in plasma and standardized z-scores of their concentrations summed into a procoagulant index.

RESULTS

Greater number of problem behaviors (Delta R(2) = 0.046, p = .014) and negative reactions of caregivers to these behaviors (Delta R(2) = 0.044, p = .017) were associated with greater procoagulant index after controlling for sociodemographic factors, major cardiovascular risk factors, health habits, and health problems. However, the number of and reaction to problem behaviors did not significantly predict procoagulant activity independent from each other. Post hoc analysis revealed a positive association between the number of problem behaviors and D-dimer (p = .010, Delta R(2) = 0.053), even when controlling for negative reactions (p = .033, Delta R(2) = 0.036). Caregiver reaction to problem behaviors was not significantly associated with any procoagulant factor individually.

CONCLUSION

Alzheimer patients' problem behavior and their negative appraisal by the caregiver may contribute to the chronic low-grade hypercoagulable state in dementia caregivers.

Systems biology to predict blood function

Systems biology seeks to provide a quantitative framework to understand blood as a reactive biological fluid whose function is dictated by prevailing haemodynamics, vessel wall characteristics, platelet metabolism, numerous coagulation factors in plasma, and small molecules released during thrombosis. The hierarchical nature of thrombosis requires analysis of adhesive bond dynamics of activated platelets captured from a flow field to a growing thrombus boundary along with the simultaneous assembly of the coagulation pathway. Several kinetic models of protease cascades have been developed. A full bottom-up model of platelet intracellular metabolism is now available to simulate the metabolism of resting platelets and platelets exposed to activators. Monte Carlo algorithms can finally accommodate platelet reaction, dispersion, and convection for full simulation of platelet deposition and clotting under flow. For clinical applications, the systems biology prediction of patient-specific pharmacological response requires the final assembly of platelet intracellular metabolism models with coagulation protease network models.

The impact of uncertainty in a blood coagulation model

Deterministic mathematical models of biochemical processes operate as if the empirically derived rate constants governing the dynamics are known with certainty. Our objective in this study was to explore the sensitivity of a deterministic model of blood coagulation to variations in the values of its 44 rate constants. This was accomplished for each rate constant at a given time by defining a normalized ensemble standard deviation (w(k(i))(f)(t)) that accounted for the sensitivity of the predicted concentration of each protein species to variation in that rate constant (from 10 to 1000% of the accepted value). A mean coefficient of variation derived from (w(k(i))(f)(t)) values for all protein species was defined to quantify the overall variation introduced into the model's predictive capacity at that time by the assumed uncertainty in that rate constant. A time-average value of the coefficient of variation over the 20-min simulation for each rate constant was then used to rank rate constants. The model's predictive capacity is particularly sensitive (50% of the aggregate variation) to uncertainty in five rate constants involved in the regulation of the formation and function of the factor VIIa-tissue factor complex. Therefore, our analysis has identified specific rate constants to which the predictive capability of this model is most sensitive and thus where improvements in measurement accuracy will yield the greatest increase in predictive capability.

Rate of mixing controls rate and outcome of autocatalytic processes: theory and microfluidic experiments with chemical reactions and blood coagulation

This article demonstrates that the rate of mixing can regulate the rate and outcome of both biological and nonbiological autocatalytic reaction systems that display a threshold response to the concentration of an activator. Plug-based microfluidics was used to control the timing of reactions, the rate of mixing, and surface chemistry in blood clotting and its chemical model. Initiation of clotting of human blood plasma required addition of a critical concentration of thrombin. Clotting could be prevented by rapid mixing when thrombin was added near the critical concentration, and mixing also affected the rate of clotting when thrombin was added at concentrations far above the critical concentration in two clinical clotting assays for human plasma. This phenomenon was modeled by a simple mechanism--local and global competition between the clotting reaction, which autocatalytically produces an activator, and mixing, which removes the activator. Numerical simulations showed that the Damköhler number, which describes this competition, predicts the effects of mixing. Many biological systems are controlled by thresholds, and these results shed light on the dynamics of these systems in the presence of spatial heterogeneities and provide simple guidelines for designing and interpreting experiments with such systems.

Computationally derived points of fragility of a human cascade are consistent with current therapeutic strategies

The role that mechanistic mathematical modeling and systems biology will play in molecular medicine and clinical development remains uncertain. In this study, mathematical modeling and sensitivity analysis were used to explore the working hypothesis that mechanistic models of human cascades, despite model uncertainty, can be computationally screened for points of fragility, and that these sensitive mechanisms could serve as therapeutic targets. We tested our working hypothesis by screening a model of the well-studied coagulation cascade, developed and validated from literature. The predicted sensitive mechanisms were then compared with the treatment literature. The model, composed of 92 proteins and 148 protein-protein interactions, was validated using 21 published datasets generated from two different quiescent in vitro coagulation models. Simulated platelet activation and thrombin generation profiles in the presence and absence of natural anticoagulants were consistent with measured values, with a mean correlation of 0.87 across all trials. Overall state sensitivity coefficients, which measure the robustness or fragility of a given mechanism, were calculated using a Monte Carlo strategy. In the absence of anticoagulants, fluid and surface phase factor X/activated factor X (fX/FXa) activity and thrombin-mediated platelet activation were found to be fragile, while fIX/FIXa and fVIII/FVIIIa activation and activity were robust. Both anti-fX/FXa and direct thrombin inhibitors are important classes of anticoagulants; for example, anti-fX/FXa inhibitors have FDA approval for the prevention of venous thromboembolism following surgical intervention and as an initial treatment for deep venous thrombosis and pulmonary embolism. Both in vitro and in vivo experimental evidence is reviewed supporting the prediction that fIX/FIXa activity is robust. When taken together, these results support our working hypothesis that computationally derived points of fragility of human relevant cascades could be used as a rational basis for target selection despite model uncertainty.

Mathematical Modeling and Computer Simulation in Blood Coagulation

Over the last two decades, mathematical modeling has become a popular tool in study of blood coagulation. The in silico methods were able to yield interesting and significant results in the understanding of both individual reaction mechanisms and regulation of large sections of the coagulation cascade. The objective of this paper is to review the development of theoretical research in hemostasis and thrombosis, to summarize the main findings, and outline problems and possible prospects in the use of mathematical modeling and computer simulation approaches. This review is primarily focused on the studies dealing with: (1) the membrane-dependent reactions of coagulation; (2) regulation of the coagulation cascade, including effects of positive and negative feedback loops, diffusion of coagulation factors, and blood flow.