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Prediction of Thrombus Growth: Effect of Stenosis and Reynolds Number

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Abstract

Shear stresses play a major role in platelet-substrate interactions and thrombus formation and growth in blood flow, where under both pathological and physiological conditions platelet adhesion and accumulation occur. In this study, a shear-dependent continuum model for platelet activation, adhesion and aggregation is presented. The model was first verified under three different shear conditions and at two heparin levels. Three-dimensional simulations were then carried out to evaluate the performance of the model for severely damaged (stripped) aortas with mild and severe stenosis degrees in laminar flow regime. For these cases, linear shear-dependent functions were developed for platelet-surface and platelet–platelet adhesion rates. It was confirmed that the platelet adhesion rate is not only a function of Reynolds number (or wall shear rate) but also the stenosis severity of the vessel. General correlations for adhesion rates of platelets as functions of stenosis and Reynolds number were obtained based on these cases. Finally using the new platelet adhesion rates, the model was applied to different experimental systems and shown to agree well with measured platelet deposition.

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Abbreviations

A ROI :

Region of interest area (mm2)

C i :

Concentration of species i (PLT−1 mL, μM, U mL−1)

D i :

Total mass diffusivity of species i (m2 s−1)

D b,i :

Brownian diffusivity of species i (m2 s−1)

D s,i :

Enhanced diffusivity of species i (m2 s−1)

[H]:

Heparin concentration (U mL−1)

\(k_{{1,{\text{TxA}}_{2} }}\) :

Reaction rate constant for inhibition of TxA2 (s−1)

k rs :

Resting platelet-surface adhesion rate (cm s−1)

k as :

Activated platelet-surface adhesion rate (cm s−1)

k aa :

Activated platelet–platelet adhesion rate (cm s−1)

L :

Half width of the channel, tube radius (cm)

L mar :

Platelet margination length scale (m)

\(M_{\infty }\) :

Capacity of surface for first platelet layer (PLT cm−2)

M as :

Surface coverage due to resting platelets (PLT cm−2)

M as :

Surface coverage due to activated platelets (PLT cm−1)

M at :

Deposition due to activated platelets (PLT cm−1)

N :

Average near-wall platelet count (PLT cm−3)

\(Q_{\text{intial}}\) :

Initial flow rate applied at the stenosed channel inlet (mL s−1)

\(Q_{\text{mean}}\) :

Mean flow rate averaged over total perfusion time (mL s−1)

\(R_{\text{acc}}\) :

Number of accumulated platelets per unit time (PLT s−1)

\(R_{RBC}\) :

Radius of red blood cell (m)

\(Re\) :

Reynolds number at inlet

\(Re_{\text{apex}}\) :

Reynolds number at the apex

\(s_{{p,{\text{TxA}}_{2} }}\) :

Rate of synthesis of TxA2 by platelet (nmol PLT s−1)

S :

Available free surface

\(t_{\text{qss}}\) :

Simulation time corresponding to quasi-steady state (s)

\(V_{\text{acc}}\) :

Platelet accumulation rate in region of interest (mm s−1)

\(\beta\) :

Conversion factor to convert thrombin concentration from U mL−1 to μM (nmol U−1)

\(\dot{\gamma }\) :

Local fluid shear rate (s−1)

\(\dot{\gamma }_{\text{w}}\) :

Wall shear rate (s−1)

\({{\varGamma }}\) :

Griffith’s template model for the kinetics of the heparin-catalyzed inactivation of thrombin by antithrombin

\(\theta\) :

Fraction of resting platelets that activate upon surface contact

\(\lambda_{\text{ADP}}\) :

Amount of ADP per activated platelet (nmol PLT−1)

\(\mu\) :

Plasma viscosity (Pa s)

\(\phi_{\text{rt}}\) :

Rate of thrombin generation from prothrombin at the surface of resting platelets

\(\phi_{\text{at}}\) :

Rate of thrombin generation from prothrombin at the surface of activated platelets

\(\rho\) :

Plasma density (kg m−3)

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Acknowledgments

The authors acknowledge the computational support and resources provided by Advanced Research Computing (ARC) at Virginia Tech. This study was funded by the National Science Foundation (Grant CBET-1235790).

Conflict of interest

Hamid Hosseinzadegan declares that he has no conflict of interest. Danesh K. Tafti declares that he has no conflict of interest.

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This article does not contain any studies with animals or human participants performed by any of the authors.

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    Hamid Hosseinzadegan & Danesh K. Tafti

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Hosseinzadegan, H., Tafti, D.K. Prediction of Thrombus Growth: Effect of Stenosis and Reynolds Number. Cardiovasc Eng Tech 8, 164–181 (2017). https://doi.org/10.1007/s13239-017-0304-3

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