Systems analysis of thrombus formation

Abstract

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. Additionally, an integrated systems biology approach can rank safety and efficacy metrics of various pharmacological interventions or clinical trial designs.

INTRODUCTION

Despite gains in detection, stenting, and pharmacology, coronary vascular disease (CVD) caused >900,000 acute myocardial infarctions and ~1 in 6 deaths in the US in 2010.¹ Stroke and CVD result in >$315 billion each year in lost productivity and medical costs. Cofactors such as smoking, high cholesterol, obesity, hypertension, diabetes, and inactivity set the stage for complex thrombotic pathologies. Deep vein thrombosis/pulmonary embolism (DVT/PE) result in an additional >60,000 deaths per year in the US.²

Prevailing flow conditions, vessel wall biology, and blood biology all combine to influence the progression of arterial or venous thrombosis (Table 1). In CVD, stenotic plaque rupture exposes tissue factor (TF) and collagen to blood triggering the extrinsic pathway of coagulation (Fig. 1). Platelets respond to collagen and thrombin to release ADP from dense granules and synthesize thromboxane via cyclooxygenase-1 (COX1), both of which intensify platelet calcium mobilization. Relatively low sub-nM levels of thrombin can activate platelets. Relatively high levels of >10 nM thrombin are required to cleave fibrinogen to fibrin under flow, although only a small fraction of prothrombin (1.4 mM) is actually converted to thrombin during clotting. While unnecessary for hemostasis, the contact pathway may enhance thrombosis, possibly through platelet release of polyphosphate. Extreme shear forces exist in stenosed arteries which can cause unfolding of von Willebrand factor (VWF) and shear induced platelet activation (SIPA). In contrast, venous thrombosis occurs under low or no flow conditions as a result of inflammatory pathways in the blood and the vessel wall.

Table 1.

Venous vs. arterial thrombosis.

Attribute	Venous Thrombosis	Arterial Thrombosis
Wall shear rate, γw	100–200 s−1 (~ 0–50 s−1 if DVT)	1000–5000 s−1 (stenosis: 104–105 s−1)
Wall shear stress, τw	1–2 dyne/cm2	20–30 dyne/cm2 (stenosis: >100 dyne/cm2)
VWF	Yes, if elevated VWF/FVIII	platelet adhesion is VWF-dependent
VWF fiber aggregation	none	Yes, if > 10,000 s−1
SIPA	no role	relevant at >3000 s−1
Rouleaux formation	Yes	No
Platelet margination	Yes (unless stasis)	Yes
Neutrophils	Yes (NETosis)	Few initially
Wall trigger	inflamed endothelium	plaque rupture
Tissue factor source	endothelium/monocytes	plaque rupture
Contact pathway	DNA/NETs	thrombin feedback on FXIa; polyphosphate
O2/pH	hypoxic/acidosis	arterial oxygen
Key Receptors	P-selectin/PSGL1	GPIbα-VWF, α2β1-collagen
Key Receptors	Mac1/LFA-1, RBC-ICAM4	αIIbβ3-fibrinogen
FXIIIa	RBC retention	fibrin strength/α2-antiplasmin linking
Key enzymes	HNE/CatG/thrombin	thrombin-PAR1/4, thrombin
Fibrin Rich?	Less fibrin	More fibrin (White Clots)
Clot Hematocrit	50 %	<5 %
Platelet density	25 x PRP concentration	50–200 x PRP concentration
Porosity, ε	0.5	0.3 (core), 0.7 (shell)
V Leiden risk	yes	Not a strong risk factor
Time to form	hours/days	minutes

DVT, deep vein thrombosis; SIPA, shear induced platelet aggregation; NETs, neutrophil extracellular traps; HNE, human neutrophil elastase; CatG, cathepsin G; PRP, platelet rich plasma.

Fig. 1. Physical and biological processes during thrombosis.

Blood flow results in a cell free layer near the wall that is enriched in platelets due to margination. Exposure of matrix proteins like collagen and bound von Willebrand Factor (VWF) results in transient capture of platelets via GPIb_α, strong activation via GPVI, and firm arrest via integrin activation. Calcium mobilization is central to platelet activation and drives shape change, integrin activation, dense granule release of ADP and serotonin (5HT), and cyclooxygenase-1 dependent thromboxane (TXA₂) synthesis. Platelet deposition and autocrine-driven aggregation typically proceeds thrombin generation which is driven by plaque-derived tissue factor (TF) and potentially by contact pathway engagement of FXIIa and FXIa via wall derived activators or platelet polyphosphate. Thrombin is a potent platelet activator and at higher concentrations drives fibrin formation. In extreme flow typical of stenosis, shear forces can elongate VWF (particularly the large VWF) and drive shear induced platelet aggregation (SIPA). Soluble mediators such as ADP, thromboxane, thrombin, and fibrin mononmer are all diffusive and elute from the clot into the flow field as they are convected downstream. Shear forces can cause platelet erosion from the clot or larger scale embolism. (2°, secondary)

During thrombosis, many hundreds of unique reactions proceed in space and time at the dysfunctional vessel wall, within activating platelets, on the platelet surface, and in the coagulating plasma. A blood systems biology approach seeks to account for the biology of the vessel wall, platelets, and plasma in a given patient and local hemodynamic context (Fig. 2).^3,4 Computer simulation of blood function can impact drug target selection, preclinical drug testing, patient-specific drug dosing, clinical trial design, biomedical device design, and stratifying patient-specific disease risk. A multiscale approach quantifies the rates and connections of reactive events at various length scales to inform a coherent view of the overall pathological process (Table 2). In Sections 1–7, the kinetic processes at the individual levels of platelets, plasma coagulation, adhesion/VWF biophysics, and hemodynamics can be integrated together into a systems analysis of thrombus formation.

Fig. 2. The Systems Biology of thrombosis.

The computer simulation of clotting requires a multiscale and integrated description of platelet signaling and adhesion, coagulation kinetics, and hemodyamics. Platelet signaling is driven by soluble activators (ADP, TXA₂, thrombin), soluble inhibitors (NO, prostacyclin (PGI₂) and insoluble activators (collagen) to drive intracellular calcium mobilization. Calcium mobilization occurs rapidly through IP₃-mediated release and store operated calcium entry (STIM1-Orai1). Dense platelet deposits in clots result in significant ADP and thromboxane and thrombin driven signaling, often targeted by inhibition of P2Y₁₂, COX-1, and PAR1 respectively (red brakes). During coagulation, the generation of thrombin (FIIa) is primarily driven by TF/FVIIa (extrinsic tenase) via subsequent engagement of the FIXa/VIIIa (intrinsic tenase) and FXaVa (prothrombinase). Thrombin has significant regulatory control on its own production through activation of FVIIIa, FVa, FXIa, as well as regulation of fibrin through activation of FXIIIa which crosslinks fibrin. Local hemodynamics (insert, with permission⁶⁶) can be determined by computational fluid dynamics to define locations with at-risk plaque burden, stenosis, and high wall shear stress. Full Systems Biology models of platelet activation and coagulation in a patient-specific flow field are directed at simulation of acute coronary syndromes (bottom).

Table 2.

Computational models for the simulation of thrombotic and blood kinetic processes.

Biology	Model Type	Predictive Goal [Ref.]
Platelet Signaling
P2Y1/phosphoinositides(PIs)	ODE-multicompartment	PIs(t) and Ca2+(t) = F(ADP) 14,15
IP3/SOCE (Stim1-Orai1)	ODE-multicompartment	Ca2+(t) = F(IP3, SOCE) 16
Combinatorial stimuli	Neural Network	GPVI,IP,TP, GC, ADP, PAR1/4 19,21
cAMP/cGMP dynamics	ODE	pVASP(t)=F(iloprost, PDE inhibition)114
PAR1/Inside-out	ODE	Ca2+(t), Rap1GTP(t) = F(PAR1-AP)17
Receptor/2nd messenger/kinase	Boolean Network Model	Ca2+(t), cAMP(t), pVASP(t)115
Thrombin Generation
Extrinsic Pathway	ODE - pseudohomogenenous	thrombin(t)=F(TF) for synthetic plasma101
Extrinsic/Contact-Platelet	ODE - pseudohomogenenous	thrombin(t) for 50 initial conditions36
Extrinsic/lipid binding	ODE- heterogeneous	clotting within 100 sec at 5 pM TF116
Stochastic triggers	Monte Carlo	clotting in 1 nL volume28
Contact Pathway (FXIIa/FXIa)	ODE	biomaterial trigger36,39,117
Fibrin formation
Polymerization (no flow)	ODE, ODE-population balance	fibrin(t) & fiber diameter43/branching44
Polymerization on wall with flow	PDE-population balance	quenching at > 200 s−1 (45)
Fibrinolysis
1D and 2D dissolution fronts	PDE - heterogeneous	lytic rates=F(tPA or uPA)47–49
3D stochastic	Monte Carlo	lytic rates and front dynamics50
von Willebrand Factor Mechanics
elongational and shear rate (ε, γ)	Brownian dynamics	VWF stretching at ε>500s−1 or γ >104 s−1 (63)
GPIbα-VWF A1 bond mechanics	Molecular dynamics	maximum bond strength of 62 pN118
Platelet rolling on vWF	Adhesive dynamics	rolling velocity, thresholding56,57
Platelet Margination/RBC Dynamics/stenotic flows
Platelet drift velocity	Immersed boundary method	drift via RBC density fluctuation73
Platelet/RBC motions	2D-Lattice Boltzmann	cell free layer dynamics75
Stenotic hemodynamics	CFD	carotid119, coronary120, aortic coarctation65
Platelet deposition or thrombosis with flow
Kuharsky-Fogelson Model	ODE (well mixed wall layer)	threshold TF concentration80
Leiderman-Fogelson Model	PDE	spatial gradients, XI-feedback81,82,121
Flamm-Diamond Model	NN-LKMC-PDE-LB	Patient-specific platelet/drug response20
Xu-Albers Model	Cellular Potts	venous clot formation (implicit ADP)94
Tosenberger-Volpert Model	Dissipative Particle Dynamics/PDE	clot growth and fibrin propagation in clot95
Pharmacological or Device Response
Direct Xa inhibitor therapy	ODE: thrombin generation assay	apixaban/rivaroxaban comparison100
reFVIIa therapy	ODE: thrombin generation assay	clotting time =F(reFVIIa)102,122
target selection	ODE: MC sensitivity analysis	confirms utility of direct Xa/IIa inhibitors98
Stent Thrombosis	Discrete element method	distal strut eddies and strut deposits113

1. Platelet Signaling and Function

Omics approaches

The human platelet transcriptome contains over 9000 mRNA species⁵ comparable to that of megakaryocytes. The human platelet proteome presents ~4000 unique proteins, most of which have been assigned a copy number per platelet.⁶ While lacking a nucleus, the platelet is rich in mitochondria and has mRNA splicing, microRNA, protein synthesis, an immunoproteosome, and caspase-dependent apoptosis. A protein interaction network (PlateletWeb)⁷ curated 3628 platelet proteins with 13,652 interactions and 1704 phosphorylations. The platelet kinome contains 229 kinases and 73 phosphatases. Similarly, a platelet metabolic network⁸ has been constructed for platelets. Although platelets are unsuited for direct genetic manipulation, numerous genetically-modified mouse models have been developed to explore platelet phenotypes in vivo. Cosemans et al. review over 40 mouse models, the majority of which displayed increased embolic potential, while a few resulted in larger thrombi with less embolism.⁹ Overall, defects in various platelet receptors and membrane proteins (Gas6 receptor, α2A, CD40L, GPIbα, GPVI, LAT, P2Y₁₂, etc.) slow and reduce clot growth and enhance embolization, as do defects in signaling proteins (Akt2, phospholipase C_γ2, PI 3-kinase, Rac1, RhoA, STIM1) and defects in certain plasma proteins (complement factor 3, Factors XI, XII, fibrinogen, VWF, Gas6). Fortunately, ample correspondence exists between mouse genotype/phenotype linkages and the human biology of clot formation.

The Bloodomics Consortium used platelet RNA expression profiling to explore individual heterogeneity in platelet response to ADP and collagen-related peptide and implicated 63 different genes that influenced platelet responsiveness.¹⁰ Several genome-wide association studies (GWAS) have focused on coronary artery disease (CAD) risk, typically identifying only small percentages of heritable risk such as polymorphisms in platelet derived growth factor (PDGF) pathways.¹¹ A population study (Plateletomics.com)¹² of platelet hyper-responsiveness to arachidonic acid, ADP, PAR1/4 activating petpides revealed: (1) 129 mRNAs and 15 miRNAs that were differentially expressed by age, (2) 54 mRNAs and 9 miRNA differentially expressed by gender, and (3) miR-376c differentially expressed by race (reduced in black subjects) and linked to increased platelet PAR4 signaling.¹³

Systems Biology models of platelet metabolism

Platelets have numerous receptors that mediate activation and inhibition (Table 3). Direct computer simulation of platelet metabolism is possible when sufficient information is available to define the reaction network and kinetic rate equations (ie. model topology) along with initial conditions and kinetic coefficents (ie. model parameterization). To model these reaction networks, ordinary differential equations (ODEs) are written for the concentration of the i-th species C_i in the reaction network containing n-species, basically answering the question how does the concentration of each species change with time [dC_i(t)/dt=F_i(C₁,…,C_n) for some initial state C_i(t=0) for i = 1 to n-species]. Several models have focused on outside-in signaling through G-protein coupled receptors. A model of P2Y₁ activation by ADP through G_q-mediated signaling and coupled phosphoinositide metabolism required 77 reactions, 132 rate constants, and 70 species in order to simulate IP₃-mediated calcium release and reuptake.^14,15 An important modeling constraint is that the resting platelet remains resting until exposed to sufficiently strong stimuli. This homeostasis constraint requires that the initial condition of the ODE system is also a steady state condition.¹⁵ Such an approach can predict resting levels of 50 – 100 nM intracellular calcium that can rise rapidly to ~300 – 500 nM intracellular calcium within 10 sec followed by rapid decay to resting levels within 250 sec. At the single platelet level, signaling may be highly noisy due to stochastic effects expected for low copy number systems (1 nM = 3 molecules/platelet). For a given initial condition, a set of kinetic reaction kinetics can be numerically integrated to obtain average dynamics (as displayed by a population of platelets) or can be solved by Monte Carlo simulation to predict single platelet dynamics. For example, the noisy calcium dynamics observed in single activated platelets has a stochastic origin that has been well simulated by Monte Carlo.¹⁴ Similarly, a model that simulates both IP₃-mediated calcium release and store operated calcium entry (SOCE) via STIM1-Orai1 required a 34 species model to predict calcium mobilization in the presence of external calcium.¹⁶

Table 3.

Platelet receptors mediating activation and inhibition.

Ligand	Receptors
Activators
collagen	GPVI, α2bβ1
thrombin	PAR1, PAR4
elastase/cathepsin G	PAR1
ADP	P2Y1, P2Y12
ATP	P2X1
thromboxane (TXA2)	TPα
histamine	H2
dopamine	D2
serotonin	5HT2A
histone/DNA	TLR4
endotoxin	TLR4
HMGB1	TLR4
epinephrine	α2A
oxLDL	CD36
vWF	GPIbα
vasopressin	V1
succinate	SUCNR1
Inhibitors
PGI2	IP
PGD2	DP
PGE2	IP, EP1-4
NO	guanylate cyclase
Estrogen	ERβ (ERα)
adenosine	A2A
acidosis	SOCE (orai1/TRPC6?)
(Pharmacological)
clopidogrel	P2Y12 inhibitor
aspirin	COX1 inhibitor
ethanol	nonspecific
dipyridamole	PDE
cilostazol	PDE3

Computer models of PAR1 and PAR4 signaling can simulate thrombin-induced calcium mobilization, Rap1GTP generation, and associated inside-out signaling to result in granule release and integrin activation.¹⁷ Collagen activation of GPVI results in receptor multimerization and intense and sustained mobilization of intracellular calcium. Recent simulations of GPVI signaling required over 20 parameters to predict Syk phosphorylation dynamics.¹⁸ From these studies, it becomes apparent that a fully mechanistic kinetic model of platelet responses to multiple agonists would require on the order 20 to 100 parameters for each signaling input (ADP, TXA₂, thrombin, etc.). Whereas a complete thrombin generation models typically require <100 kinetic constants and initial concentrations that are fairly well measured and understood, a full platelet model could require 200 to 1000 parameters, most of which are not yet quantified precisely. In fact, the NN model trained to multicomponent activation data required 180 weight factors. Few models in Systems Biology are this massive, which presents a number of challenges in model validation, parameterization, and training to the patient’s own platelets.

Large models with many unknown parameters (initial concentrations or kinetic constants) present a different challenge compared to ambiguity of model uncertainty (ambiguous or unknown reaction mechanisms). The “parameterization challenge” has several layers. Different sets of parameters may equally fit the data. This situation is interesting and has been explored in Purvis et al.¹⁵ using principal component analysis for efficient search directions dictated by the steady states of smaller modules in the system. In fortunate cases, the available data is highly constraining and forces attention on those unknown parameters that must take on values in a narrow range, indicative of their regulatory importance. In unfortunate cases, a unique set of parameters cannot be found to match the constraining data, thus highlighting (i) potential weaknesses in the model that require additional mechanisms (a symptom of model uncertainty) or (ii) the computational challenge of high dimensional searching. Regardless, high dimensional data sets obtained under many conditions and constraints which measure important species at several times are outstanding for model testing.

High dimensional platelet phenotyping methods

Given the responsiveness of platelets to diverse signals present during clotting (Table 3), various high throughput methods have been developed to functionally phenotype platelets. The pairwise agonist scanning (PAS) approach¹⁹ is a 384-well plate assay that measures platelet intracellular calcium mobilization in response to all single and pairwise stimulations with agonists used at 0.1, 1, and 10 x EC₅₀ of each agonist. A total of 154 responses using 6 agonists (convulxin, U46619, PAR1-activating peptide, PAR4-activating peptide, ADP, and PGE₂) to stimulate GPVI, TP, PAR1, PAR4, P2Y₁/P2Y₁₂, and IP/EP_1-4 were then used to train neural network (NN) models. NN models are an example of machine learning where measured outputs are predicted from a set of input conditions and trained signal processing nodes linked together, akin to neuron signaling. The NN model is patient-specific and was able to predict responses beyond the training set such as: response to trinary stimulation, response to 4–6 agonists, and responses to sequential stimulation. NN models are ideal for incorporation into multiscale models of thrombosis²⁰ as will be discussed in Section 6. Similarly, an “average” platelet NN was generated for an ensemble of 10 healthy donors (50% male) to predict calcium mobilization dynamics in response to combinations of collagen mimetic (convulxin), thrombin, ADP, thromboxane mimetic, NO donor, and prostacyclin mimetic.²¹ The pairwise agonist scanning method has also been extended to monitor single platelet α_2bβ₃ activation, P-selectin display, and phosphatidylserine exposure by flow cytometry.²² Microspot printing of collagen matrix-tissue factor features on glass allows high throughput testing of blood response to a surface, such as for the determination of TF concentration threshold for robust fibrin production by whole blood under flow.^23,24 Similarly, to conduct high dimensional phenotyping of platelet adhesion and aggregation under flow, de Witt et al.²⁵ printed 52 different combinations of proteins (VWF, fibrinogen, laminin, fibronectin, fibrinogen, vitronectin, CRP, thrombospondin-1, etc.) in microspots exposed to flowing whole blood (with no thrombin generation). The relative contributions of adhesion receptors from most to least important for platelet accumulation at high shear rate were: [GPVI, CLEC-2] > GPIbα > [α₆β₁, α_IIbβ₃] > α₂β₁ > [CD36, α₅β₁, α_vβ₃]. While platelets respond to the CLEC-2 activator rhodocytin or lymphatic podoplanin, the intravascular role of CLEC-2 during thrombosis is still emerging. For example, Hitchcock et al.²⁶ recently found a thrombotic role for platelet CLEC-2 during salmonella infection via interferon-g induction of podoplanin expression by monocytes and Kupffer cells in the liver. The microspot patterning method provide clear and expected signals for patients with genetic defects affecting platelet function. One additional high throughput phenotyping assay (Optimul assay)²⁷ involves the aliquoting of stimulants to 96-well plates (which can be stored frozen) followed by testing platelet aggregation in the thawed plates subjected to mixing in a plate reader. This type of assay is particularly sensitive for identifying platelet hypoactivity and associated bleeding risk, but in theory could also reveal hyperactivity and thrombotic risk.

High dimensional and miniaturized phenotyping tools help quantify platelet signaling, granule release, integrin activation, and retraction. For patient-specific predictions, a quantitative mathematical model needs to meet two criteria: (1) match or predict the available training data for a specific patient, and (2) predict phenomenon beyond the training data such as clotting rates at venous and arterial flow as measured using microfluidics. Meeting these two criteria would represent a first step towards validation of patient-specific models for stratification of disease risk or drug responsiveness.

2. Thrombin/Coagulation models

Evolution requires that blood remain a flowing liquid for oxygen delivery over large length scales, while simultaneously providing intense yet highly regulated and localized responsiveness to vessel disruption by engaging platelet activation and coagulation. As a dynamical system in balance, healthy blood is robustly homeostatic (i.e. flowing) and robustly hemostatic. This tense balance is maintained by numerous activators, inhibitors, amplifiers, and feedback mechanisms: the source of consternation for the pharmacologist, clinician, and patient alike seeking to manage thrombotic risk without increasing bleeding risk.

The most proximal triggers of clotting

The central objective of the coagulation system is to convert prothrombin to thrombin. Platelets are intensely responsive to sub-nM levels of thrombin whereas >10 nM thrombin is required to polymerize fibrin robustly under flow conditions. The extrinsic pathway relies on exposure of tissue factor (TF) within lipid membranes to bind factor VIIa. Factor VII is the one clotting factor that is cleaved to a significant extent (~1% of Factor VII) in healthy blood, although FVIIa remains in a zymogen-like conformation until binding to TF, resulting in enhanced FVIIa activity against FX and FIX. The cellular pathway involves FVIIa binding to activated platelet membrane facilitating FVIIa activity toward FX in the absence of TF, a reaction only relevant during high dose recombinant FVIIa therapy. While not required for hemostasis, the contact pathway involves anionic materials (such as DNA, RNA, collagen, polyphosphate or artificial surfaces) that bind Factor XII, leading to a FXII conformation that can then enzymatically generate FXIIa and FXIa. The contact pathway begins with the activation of FXII to FXIIa on a “contact” surface. Other factors distal of FXIIa such as FXIa, FIXa, and FVIIIa can be thought as part of the contact pathway. However, it is important to recognize that FXIa and FIXa can be generated by routes independent of FXIIa (and thus the older “intrinsic pathway” nomenclature has fallen out of use to some degree). In addition to zymogens in the blood, extremely low levels of active clotting factors likely exist in healthy blood as the blood remains in an idling state (“engine running model”) as evidenced by detectable level of activation peptides in healthy plasma. Intravascular thrombosis, typically in the absence of bleeding, progresses when attributes of the vessel wall, the blood, and the hemodynamics are pathological (ie. Virchow’s Triad).

From TF to thrombin

The kinetic analysis of thrombin generation in purified protein systems, plasma, platelet rich plasma (PRP), or whole blood usually begins by considering the entire reaction network in an isotropic context that lacks spatial gradients and fluid shearing (i.e. a test tube). With 100s of published studies of enzyme kinetics, bottom-up models can accommodate complete definition of reaction pathways and their parameterization (initial concentrations and rate constants). These ODE mathematical simulations encapsulate a modeling philosophy such as: ignore platelets, include platelets, complexify, simplify, emphasize regulatory dynamics, validate against real data, or tune the model against real data. For small sub-nanoliter volumes and low copy number of important proteins (like TF), the clotting reactions can display stochasticity due to random variations. For stochastic simulation, the kinetic rates of clotting must be solved by Monte Carlo simulation.²⁸ Table 2 summarizes several computational models of coagulation, many of which are downloadable. For a given set of clotting factor concentrations, some key features of these various models are: damping if triggering stimuli are sub-threshold, nonlinear sensitivity to initial condition, and nonlinear amplification:

1. Great sensitivity to exogeneously added [TF(t=0)] or [FXIa(t=0)] at 1 to 10 pM.

2. Accurate prediction of an initiation time, amplification phase, and inhibition phase.

3. Generation of Factor Xa being rate-limiting with most FXa made via FIXa/FVIIIa.

4. Prediction of poor thrombin production for hemophilia A and B.

5. TF and consequently Factor Xa operate with steep, switch-like dose-response curves.

Certain regulatory dynamics of coagulation require continual refinement from a modeling perspective such as: (1) the precise rates and mechanisms of prothrombinase (FXaVa) inhibition on a platelet surface; (2) the role of FXIa autoactivation; (3) endogenous levels of contact activation within blood (eg. platelet polyphosphate); (4) the role of disulfide isomerases in protein regulation and de-encryption; and (5) the state of blood obtained by phlebotomy vs. the in vivo state. Importantly, if a particular molecule such as TF or FXIa is potent at 10–100 fM levels, antigenic determinations will lack sufficient sensitivity and specificity; thus, kinetic measurements and kinetic arguments must carry the day. While adding features and complexity to models is always possible, systems biology approaches should also prioritize key regulatory features that are most important in controlling clotting. Such insights, often from sensitivity analysis²⁹ can allow the creation of reduced models^30,31 that capture the major features of clotting dynamics with considerably fewer parameters.

Calibrated automated thrombinogram (CAT) uses a fluorogenic thrombin substrate in plasma (or platelet rich plasma) that is activated with 1 to 10 pM of TF.^32,33 For healthy plasma, a lag phase exists for several minutes prior to a burst of 200 to 400 nM thrombin over a period of 2 to 5 minutes and a decay over the next 10 or 20 minutes. The thrombin signal is ideal for testing computational models of plasma function,^34–36 especially for bleeding phenotypes. Brummel-Ziedins et al. found the CAT assay a reliable metric of hypofunctional thrombin generation due to pharmacological inhibitors (rivaroxaban, warfarin) and, importantly, hyperfunctional thrombin generation in advanced pregnancy. However, the CAT assay does not recreate the accumulating platelet density and spatial gradients that are unique to thrombosis. A plasma-based assay that recreates spatial gradients involves the incubation of plasma against a TF-rich surface. In this assay, an easily-visualized fibrin front propagates away from the triggering surface, controlled by diffusion of proteins such as thrombin and fibrin monomer, all amenable to computational analysis of reaction-diffusion.³⁷ Such thrombin activity and fibrin polymerization fronts typically travel slowly at a rate of ~ 3 mm in 60 min, consistent with simulation. This slow traveling wave propagation is akin to the physics in stagnant blood clotting in a wound site triggered by TF in the wound boundary.

Role of FXIIa and FXIa in thrombin generation

The contact pathway has received renewed interest as a therapeutic target to reduce thrombosis. FXIIa deficiency is not associated with a bleeding risk, while FXI deficiency results in a bleeding risk (hemophilia C) in some individuals. Mice deficient in FXII display reduced thrombosis in a vessel injury model.³⁸ To date, most modeling of the contact pathway usually focuses on biomaterial thrombosis³⁹ or in the diagnostic setting where containers and corn trypsin inhibitor are employed.³⁶ The natural activators of FXII in human pathology during plaque rupture could include DNA, RNA, collagen, and platelet polyphosphate. The kinetics of FXII activation by ruptured plaque are not well established although contact activation can occur in this context.⁴⁰ Kuijpers et al. ⁴⁰ showed in a rupture plaque model in Apoe(−/−) mice that FXII also functions at later stages of clotting. In venous thrombosis, neutrophil release of NETs (neutrophil extracellular traps) that are chromosomal contents with the potential for contact activating activity.⁴¹

Fibrin generation and fibrinolysis

With the ability to simulate and predict thrombin generation, the kinetics of fibrin polymerization under stagnant and flow conditions becomes tractable. The generation of reactive monomers that polymerize under isotropic conditions (no gradients) can be solved by Monte Carlo simulation⁴² or by numerical integration of ODEs for the formation and consumption of dimers, trimers, and higher ordered species.⁴³ The rates of protofibril extension, protofibril lateral aggregation, and branchpoint all control final fiber diameter and network branching.⁴⁴ Computer simulations predict that flow suppresses fibrin formation above ~ 200 sec⁻¹ wall shear rate since washout of monomers can occur faster than their incorporation into fibrin.⁴⁵ The structural mechanics of fibrin and fibrin-rich clots and consequent effects on clot retraction and embolism rates are experimentally accessible⁴⁶, but represent a large computational challenge to predict clot strength based on fibrin-platelet ensembles. The kinetics of fibrinolysis are essential to wound healing, impaired hemostasis, as well as thrombolytic therapy of arterial and venous blockages. Kinetic simulations of thrombolytic therapy and of fibrinolysis allow prediction of lysis front propagation under conditions of diffusive or pressure-driven permeation.^47–50 Interestingly, concepts of clot porosity, permeability, and intrathrombus protein diffusivity which are critical to thrombolytic therapy⁵¹ are also essential for understanding the progression of hemostatic and thrombotic events.

3. Adhesion models and Von Willebrand Factor (VWF)

With systems models of platelet activation and thrombin production, accounting for cell adhesion is required to predict clot growth. Numerous adhesion receptors are operative during thrombosis including: GPIbα/VWF, GPVI/collagen, α₂β₁/collagen, α_IIbβ₃/fibrinogen, and α_IIbβ₃/VWF (Fig. 1). The proximity of two adhering membranes defines the ability of receptors to bind their counter-ligands. In general, binding events must be sufficiently rapid if they are to capture a platelet from the flow field. As bonds are loaded with hemodynamic forces, the expectation is usually that the bonds break more rapidly, referred to as a slip bond. Bonding that becomes stronger when loaded with force is described as a catch bond, and may result by formation of extra points of protein-protein contact as atomic-level conformations at the molecular interface are presumably altered by force.^52,53 The force to rupture a typical bond depends on loading conditions from the prevailing hemodynamic environment as transmitted through the cell body, typically requiring ~ 10 to 100 pN to rupture a single bond between P-selectin-PSGL1, GPIbα/VWF,⁵⁴ α_IIbβ₃/fibrinogen or α₂β₁/collagen⁵⁵ for loading rates in the range of 10² to 10⁴ pN/s. Adhesive dynamic simulations for single platelet capture⁵⁶, single platelet translocation on VWF,^56,57 or neutrophil rolling have single molecule resolution on molecular length scales and are quite time consuming computations that are not feasible for whole clot growth simulations involving 100s to millions of platelets in a clot. Also, cells are deformable and platelet membrane tether pulling may significantly affect loading mechanics at pathologically high shear rates. Therefore, simpler adhesion models based upon apparent rates²⁰ of attachment and detachment and the cellular activation state are typically used for clotting simulations under flow.

Von Willebrand Factor (VWF) released by endothelium is the largest soluble molecule in blood, reaching sizes of 100 nm to 1000 nm and molecular weights > 20 × 10⁶ MW. As a colloid in the plasma, VWF has a globular conformation and can undergo structural changes when subject to hemodynamic forces. VWF also binds and carries FVIII. VWF is required for platelet capture under arterial shear conditions (wall shear rates > 1000 s⁻¹). Molecular dynamics simulations of A1 and A2 domains of VWF suggest that the A2 domain obscures the A1 domain from GPIbα binding, unless stretching forces unshield the A1 domain.⁵⁸ The linker between the D3 and A1 domains may also interact with A1 domain to modulate GP1bα bonding dynamics.⁵⁹ Additionally, under the conditions of extreme flows found in stenotic arteries, VWF can undergo elongation and self-association into massive fiber aggregates^60,61 that have been detected at the end stages of a thrombotic event in vivo.⁶² Predictive models of VWF conformation in flow are not yet molecularly resolved, but can be based upon a coarse-grained approximation of VWF structure and subunits using concepts from polymer theory. Interaction energies between domains have been assumed (~0.5–2 K_bT) in order to estimate critical elongational rates (ε_crit ~ 500 s⁻¹) or critical shear rates γ_crit ~ 10⁴ s⁻¹ to drive globule-stretch transitions.⁶³ The development of quantitative descriptions of platelet GPIbα bonding and VWF conformation under the extreme hemodynamic conditions of arterial stenotic thrombosis remains an intensive research challenge.

4. Vascular Hemodynamic and Computational Fluid Dynamics (CFD)

Intravascular thrombosis propagates in the presence of local prevailing hemodynamics. Flow affects clotting and clotting affects flow. With flow, the wall shear rate (γ_w) dictates the collision rate of cells with the wall and the wall shear stress (τ_w) dictates the drag forces on adherent clot assemblies. By combination of direct imaging and computational fluid dynamics (CFD), the prevailing instantaneous or time-averaged velocity profile can be calculated. CFD involves numerical solution of the Navier-Stokes equation, which defines force = mass x acceleration for a liquid. With the velocity profile, numerous metrics of the instantaneous or time-averaged flow can be calculated including: γ_w, τ_w, oscillatory shear index, and fractional flow reserve (FFR). Arterial shear stresses in healthy vessels are pulsatile and typically in the range of 10 to 40 dyne/cm² (time-averaged) but can exceed 100s of dyne/cm² in a narrowed stenotic region. In coronary and carotid vessels, locations with low and oscillatory shear stress are considered atheroprone.⁶⁴ In contrast, venous flows are slow (~ 100–200 s⁻¹ wall shear rate and 1–8 dyne/cm² wall shear stress), have steady flow, and may approach stasis (velocity goes to zero) as a high risk setting for deep vein thrombosis.

Arterial stenotic flows are notable for their extremely high shear stresses, marked pressure drops when >75% stenosis causes angina, helical flows for asymmetric lesions, recirculation zones distal of the stenosis, and display of turbulence if the Reynolds number > 300–400 during certain moments of the pulse cycle. The Reynolds number is defined as Re = ρDV/μ for ρ = density, V = velocity, D = diameter, and μ = viscosity. Whole coronary hemodynamic simulations have emerged as a powerful tool to access vunerable heart muscle at risk.⁶⁵ These pulsatile flow calculations⁶⁶ require an estimation of the upstream pressure at the aorta inlet (lumped-parameter heart model) and the downstream pressure due to coronary microvascular resistance, typically employing 1-dimensional lumped models of the microvascular resistance. Often the fractional flow reserve (FFR) can be calculated if the vascular geometry has been measured and a resting flow or hyperemia flow has been estimated or induced. A stenosis or thrombosis of only 50% results in very high shear stresses and high velocities as blood jets through the narrowing, however such a narrowing offers little resistance to blood flow, with few symptoms of angina. Only as a stenosis or a clot grows in the coronary artery to severely reduce the available lumen (> 75 % stenosis by both plaque and thrombus) does a significant pressure drop exist across the narrowing to reduce flow rate. Velocities in the severe narrowing may remain pathological until complete occlusion occurs, the onset of acute myocardial infarction, and blood is diverted to other vessels. Severe arterial stenoses cause acceleration and deceleration of blood flow and are associated with pathological wall shear rates that can range from 5,000 to >100,000 s⁻¹ (wall shear stresses of 150 to >3000 dyne/cm²).^67–70 Spatial gradients of wall shear rate (grad γ_w) are tremendous in severe stenosis reaching values of 600,000 s⁻¹/cm for the inlet to a human coronary stenosis.⁶⁹ Values for the inlet and outlet of a stenosed carotid arteries are similar (grad γ_w = ± 570,000 s⁻¹/cm).

Patient-specific CFD has been demonstrated for vascular anatomies derived from computed tomography (CT) angiography. The FFR is the critical metric for determining if a stenosis causes ischemia. The FFR calculates the hyperemic flow through the vessel with stenosis to a hypothetical case in which the vessel lacks the stenosis. The FFR can be applied to decisions about risk and the need for coronary intervention (particularly when FFR < 0.8).⁷¹ However, the FFR makes no statement about the severity of a thrombotic event within the stenosis or the patient-specific response to anti-platelet agents or anticoagulants. The opportunity now exists to combine multiscale systems biology models of thrombosis with patient-specific CFD calculations of coronary artery hemodynamics, as discussed in the next section.

5. Multiscale thrombosis models

The physics and biochemistry of thrombosis exists over several length scales that are coupled. Enzyme kinetics, receptor activation, and signal transduction proceed at the molecular scale. Cell-cell interactions at the micron scale result in the buildup of a clot on the 0.1 to 1-millimeter scale while prevailing hemodynamics are driven by coronary and heart scale phenomenon over many centimeters. Similarly, dynamics in vein valve pockets can trigger thrombosis over the length of an entire femoral vein. Diffusion moves proteins and small solutes efficiently over cellular length scales (< 100 μm) but transport of species over many millimeters requires bulk flow or pressure-driven permeation across porous clots.

Computer simulations of individual deformable RBCs and platelets in flow can predict the bulk viscosity of blood, the thickness of the near-wall plasma layer, enhanced platelet diffusivity due to flow, and the drift and accumulation of platelets in the near-wall plasma layer.^4,72–75 Modeling blood as a continuum fluid is far more computationally efficient for calculation of complex velocity fields in vessels and does not require detailed descriptions of single cell dynamics. For simulations of thrombosis that involve single platelets depositing to a growing thrombus under flow conditions, the blood is still often treated as a continuum fluid, however the near wall excess concentration of platelets must be calculated or imposed as a way of accounting for the suspension nature of flowing blood.

In an early study, Hubbell and McIntire⁷⁶ calculated local concentrations of ADP, TXA₂ and thrombin in the boundary layer over a thin platelet patch on a surface subjected to flow. This approach was extended⁷⁷ to clots that protruded into the flow stream, resulting in solute accumulation in distal recirculation zones. However, these studies were not directed at predicting the flow-dependent clot growth dynamics. Using phenomenological equations relating agonists and platelet activation, Sorensen and Antaki^78,79 simulated combined platelet deposition and autocrinic activation by solving a pseudo-homogenous, single-phase continuum model of blood clotting over a reactive surface.

In these early computer models, the generation of thrombin was treated with extremely simplified descriptions of coagulation. The Kuharsky-Fogelson model was one of the first detailed continuum based descriptions of clotting under flow conditions. The model emphasizes platelet coverage of exposed TF as a means of limiting clot growth.⁸⁰ Assuming a thin, well-mixed and stagnant layer at the surface of the wound, this model predicted a narrowly-defined, threshold concentration range (10–15 fmol/cm²) over which TF has dramatic impact on thrombin production, as found experimentally²³ at 1–10 TF molecules/μm². The model also passed an important test of predicting poor thrombin generation under conditions of severe hemophilia A and B. The Leiderman-Fogelson model⁸¹ was a full PDE model of thrombosis under flow over a TF surface which calculated spatial gradients of numerous soluble species including platelet-released ADP as the clot grew into the flow field (~30 μm thick in 10 min at a shear rate of 1500 s⁻¹). These simulations have been extended⁸² to include thrombin-feedback activation of Factor XIa, which potentiates clot growth at later times, a phenomenon recently observed experimentally⁸³ with an inhibitor of platelet polyphosphate (which greatly potentiates thrombin-feedback activation of FXIa). Using various FXIa antibodies and polyphosphate inhibitor, Zhu et al.⁸³ also concluded that platelet polyphosphate function in clots was largely related to thrombin-feedback activation of FXIa and not FXIIa generation.

The importance of spatial gradients within clots as they grow is highlighted by the observation of a core-shell architecture in clots (Fig. 3A).^84–86 In both mouse laser injury models and in human clots formed ex vivo under flow, the core is a thin clot region that is immediately adjacent to the damaged vessel wall and contains P-selectin positive platelets, thrombin, and fibrin. Compared to the shell of P-selectin negative platelets lacking thrombin and fibrin, the core is highly retracted with a more restricted pore space for protein diffusion (Fig. 3B)⁸⁷. The mobility of solutes within porous clots can be simulated using 3D architectures derived from confocal images of in vivo clots (Fig. 3C)⁸⁸ indicating that clots have a tortuosity of 2 to 2.5, meaning protein diffusion is reduced by >50% in the core relative to pure Brownian motion in water. Additionally, platelet-fibrin clots formed under flow conditions have an extremely dense structure with a Darcy permeability of 2.7 × 10⁻¹⁴ cm², with most of the resistance to pressure-driven permeation due to platelet packing.⁸⁹

Fig. 3. Intraclot transport dynamics.

As a clot develops under flow in vivo, a dense platelet accumulation displays a core/shell architecture with a dense platelet-retracted, P-selectin positive and thrombin-rich core surrounded by less dense, less activated shell of platelets (A). Albumin transport is slower in the core than the shell region indicating a more tortuous path as it elutes from the clot (B). Full simulation of an in silico porous architecture derived from in vivo imaging demonstrates the complex interstitial paths of fluid permeation within the clot (C, scale bar has units of cm/sec). Used with permission^87,88.

Toward patient-specific simulation of clotting, Flamm and Diamond²⁰ incorporated data-driven models of platelet activation using neural networks trained by high dimensional pairwise agonist scanning (PAS)¹⁹. Individual platelet locations were simulated by lattice kinetic Monte Carlo (LKMC)^90,91 to account for convection, platelet diffusion, and platelet drift to the wall along with capture to collagen or other platelets. Flow over the rough platelet deposit was calculated by Lattice Boltzmann method and soluble species were determined by finite element method (FEM) solution of PDEs for ADP and TXA₂. In this approach, individual donor platelet deposition rates on collagen were accurately predicted as was the rank ordered sensitivity to COX1 inhibition, P2Y₁ inhibition, and IP activation. The approach revealed a single donor whose platelets were insensitive to COX1 inhibition with platelets resistant to TP activation by U46619, revealing a novel heterozygote V241G point mutation in the TP receptor. Platelet deposition rates were accurately predicted for both venous and arterial flows. This LKMC approach has been extended (Y. Lu, T. Sinno, and S.L. Diamond, unpublished results) to include thrombin activation of platelets²¹ and thrombin generation at the wall using a validated 76-species ODE model³⁶ (Fig. 4). The simulations made accurate prediction of occlusion time in a microfluidic test under constant pressure-drop conditions⁹² for whole blood flow over collagen/TF, a key metric for coronary risk assessment.

Fig. 4. Systems biology simulation of thrombosis.

A trained neural network model is based upon 154 measurements of platelet calcium mobilization using pairwise agonist scanning (PAS) in which all single and pairs of agonists are used at low, medium, and high concentration (A). This NN model can predict complex platelet responses such as calcium mobilization during sequential exposure to agonists (B) as intracellular calcium is mobilized from a resting level (blue, ~50–100 nM) to maximum levels (red, ~0.5–1 μM). A platelet-plasma kinetic model of thrombin production (FIIa) corresponds to a set of ordinary differential equations for 76 species that can be solved for any level of initial TF. When TF is absent the model allows for FXIIa generation as an alternative trigger of clotting (C). Combining the PAS-trained NN model and the platelet-plasma ODE model at the collagen/TF boundary (red) allows full simulation (D) of a thrombotic event under flow (velocity streamlines and shear rate from Lattice Boltzmann simulation) where all platelet positions are known (via Monte Carlo), along with prevailing concentrations of ADP, thromboxane, and thrombin in the clot and in the boundary layers just outside the clot (from finite element simulation of convection-diffusion PDE equations).

The Xu-Albers model^93,94 deployed a new platelet-explicit simulation in a cellular Potts model. In this approach, each position of discretized space can be occupied by platelet mass, fluid, or other cell types. Thrombin production utilized the Kuharsky-Fogelson model in this approach and a novel prediction was maximal clot growth at an intermediate flow rate. One limitation of the cellular Potts model is that energy parameters used to make Metropolis Monte Carlo moves do not necessarily correspond to actual physical and measurable quantities. One of the newest computational approaches to be added to the tool set of thrombosis simulation is dissipative particle dynamics (DPD).^95–97 In DPD, fluid flow is modeled as the motion of mesoscale DPD “particles”. Similarly, platelets are comprised of DPD “particles” in the simulation. Each DPD particle is subject to various forces such as repulsive, dissipative, and random (Brownian) forces. Also, the wall can exert an “attractive” force. Tosenberger et al.⁹⁵ used DPD-PDE to model platelet deposition and embolization from a surface in the presence of fibrin polymerization. Various force coefficients, reaction coefficients, and time step coefficients must be picked carefully to span the range of observed phenomenon.

Most simulations of thrombosis that incorporate detailed coagulation kinetics and platelet signaling are solved for 2D reaction domains. However, flow over growing clots is three dimensional. Diffusion occurs in three dimensions. Also, clots formed under flow display an elongated, 3D structure under flow. Full 3D simulation is certainly possible with increasingly faster computers and algorithms. Approaches for faster computation include: remeshing, coarse-graining, graphical processing unit (GPU) based computation, and reduced models of coagulation.

6. Pharmacological models

With the ability of predicting thrombin production, platelet activation, and clot growth for human blood triggered to clot, a linkage between drug pharmacokinetics and clot pharmacodynamics is possible. Since the balance between minimizing both thrombotic risk and adverse bleeding events creates a narrow therapeutic window, computational models have been applied to predict optimal dosing for single or combination therapy, target selection for drug discovery, and elucidation of mechanism in complex biochemical networks. With a massive 92-protein (148 interaction) model of coagulation and platelet activation, Luan et al.⁹⁸ searched for reactions in the network that displayed the largest degree of druggability with respect to the control of clotting. They ranked the 25 most “fragile” reactions that present themselves as most druggable. Both Factor Xa and thrombin were identified as the most fragile points for targeting, exactly consistent with the development of the new class of direct Xa inhibitors and direct thrombin inhibitors. In contrast, FVIIIa and FIXa were more “robust” in the sensitivity analysis and thus less optimal for targeting with inhibitors, consistent with the bleeding risk of hemophilia A and B. In comparing two different direct FXa inhibitors, the dose-response curve of prothrombin time (PT) with drug concentration is sensitive to rivaroxaban, but not apixaban. Using the Jones-Mann model⁹⁹ expanded to include reactions for the direct FXa inhibitor drugs, Jourdi et al.¹⁰⁰ found that the on-rate for drug association with FXa was the likely underlying cause of this variance between the two drugs. In a similar approach to understand reFVIIa hemostatic therapy in different hemophilias, the Hockin-Mann¹⁰¹ model was used¹⁰² to predict clotting times and thrombin production as a function of FVIIa concentration in normal blood and blood deficient in FVIII, FIX, FVII, or TFPI. FVIIa was shown to accelerate the onset of clotting with less effect on the maximal amount of thrombin generated.

7. Microfluidic models of clot growth

The rate of clot growth for a given blood sample can be followed ex vivo using microfluidic devices that allow a defined flow field and defined surface for triggering the clotting event.⁴⁶ For in vitro research, drawn blood is often treated with corn trypsin inhibitor, either at low doses to allow some contact activation or higher doses to more fully prevent the function of FXIIa.⁸³ Microfluidic devices use small blood samples that are perfused through a defined geometry. These devices have been used to test blood from hemophiliacs,^103,104 trauma patients,¹⁰⁵ and individuals taking combinations of anti-platelet agents such as NSAIDs with aspirin.¹⁰⁶ Microfluidic experiments can be run under conditions of strong contact activation using kaolin/collagen surfaces,¹⁰⁷ strong extrinsic activation using TF-coated collagen,⁹² or full anticoagulation of thrombin production to study only platelet function.²⁰ Numerous pharmacological agents^108–110 that target P2Y₁, P2Y₁₂, COX1, reVIIa can be tested using microfluidics to allow a functional determination of drug potency under defined flow conditions. Typically for TF-triggered clotting of flowing whole blood on a collagen surface, platelet accumulation will lead to dense deposits that grow over 60 microns thick within 300 sec with fibrin forming subsequently after ~1–2 minutes in a location very close to the surface where the TF and thrombin resides in the experiment.^83,85,86,92 More pathological flow regimes with extreme shear stresses^111,112 can be created with microfluidic devices, especially for studies focused on VWF structure/function.^60,61 Microfluidic studies with human blood provide data sets that allow the testing of multiscale computer simulations (Table 2) of platelet function, thrombin and fibrin generation, and alterations of the local flow field during the clotting event. Such computer simulations, once validated, can then be useful to predict phenomenon within the human body that are difficult to observe quantitatively in real time.

SUMMARY

Using individual models of platelet activation, coagulation cascades, cell adhesion, VWF structure/function, and regional hemodynamics as discussed in the prior sections, multiscale models of thrombosis can predict clot morphology and growth rate.^3,4 In addition to helping to evaluate pharmacological options, modeling of thrombosis may be helpful in predicting cardiovascular device performance such as stents¹¹³ where in vivo observation of slowly evolving thrombotic processes may be difficult. Multiscale calculations rely on kinetic information at the molecular, cellular, and tissue (whole vessel) length scale and the millisecond to many minutes time scale. These calculations challenge the fastest computers available and continually push the boundaries of algorithm development. Common numerical tools are finite element method, immersed boundary elements, lattice Boltzmann, Monte Carlo, and dissipative particle dyamics (Table 2). Simulations of multicomponent spatial gradients from the damaged wall, across the clot, and into the flow are computationally intensive. Simulations of high velocity, pulsatile reactive blood flows and three dimensional phenomena over tissue scales of the coronary vasculature are also computationally expensive. With nearly 50 years of accumulating computing power and blood research (>10⁵ publications in Pubmed for “blood coagulation”), a number of labs have begun to attack the challenge of systems analysis of thrombosis (>350 publications in Pubmed for “blood coagulation simulation”). In combination with genomics, high dimensional phenotyping, biomarker surveillance, and imaging, systems biology seeks to provide an integrative framework for the clinician treating patients with thrombotic disorders.

Non-standard Abbreviations and Acronyms

CAT

calibrated automated thrombinogram/thrombinography

CFD

computational fluid dynamics

DPD

dissipative particle dynamics

FFR

fractional flow reserve

LKMC

lattice kinetic Monte Carlo

ODE

ordinary differential equation

PDE

partial differential equation

SIPA

shear induced platelet aggregation/activation