Journal of Medical and Biological Engineering

, Volume 39, Issue 4, pp 605–621 | Cite as

A Predictive Model of Thrombus Growth in Stenosed Vessels with Dynamic Geometries

  • Hamid Hosseinzadegan
  • Danesh K. TaftiEmail author
Original Article


This paper introduces a dynamic model of platelet-rich thrombus growth in stenosed vessels using computational fluid dynamics methods. Platelet adhesion, aggregation and activation kinetics are modeled by solving mass transport equations for blood components involved in thrombosis. Arbitrary Lagrangian–Eulerian formulation is used to model the growing thrombi with variable geometry. The wall boundaries are discretely moved based on the amount of platelet deposition that occurs on vessel wall. To emulate the dynamic behavior of platelet adhesion kinetics during thrombus growth, a validated model for platelet adhesion, which calculates platelet-surface adhesion rates as a function of stenosis severity and Reynolds number, is applied to the model. Results of the present model for vessel occlusion times and platelet deposition in stenosed region are compared to ex vivo and in vitro experimental data. The model successfully predicts the nonlinear growth of thrombi in the stenosed area. These simulations provide a useful guideline to understand the effect of growing thrombus on thrombus growth rate, platelet activation kinetics and recurrence of embolism in highly stenosed arteries.


Numerical modeling Platelet adhesion Platelet activation Shear stress Embolism 

List of Symbols


Region of interest area (mm2)


Concentration of species \(i\) (PLT ml−1, μΜ, U ml−1)


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


Brownian diffusivity of species \(i\) (m2 s−1)


Enhanced diffusivity of species \(i\) (m2 s−1)


Heparin concentration (U ml−1)

\(k_{{1,TxA_{2} }}\)

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


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


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


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


Characteristic length (m)

\(M_{\infty }\)

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


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


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


Deposition due to activated platelets (PLT cm−1)


Radius of red blood cell (m)


Reynolds number at inlet


Reynolds number at the apex

\(s_{{p,TxA_{2} }}\)

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


Available free surface


Platelet activation time (s)


Simulation time corresponding to quasi-steady state (s)



Conversion factor to convert thrombin concentration from \({\text{U}}\;{\text{ml}}^{ - 1}\) to μM (nmol U−1)

\(\dot{\gamma }\)

Local fluid shear rate (s−1)

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

Wall shear rate (s−1)


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


Fraction of resting platelets that activate upon surface contact


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


Plasma viscosity (Pa s)


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


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


Plasma density (kg m−3)



This study was funded by the National Science Foundation (Grant CBET-1235790). The authors acknowledge the computational support and resources provided by Advanced Research Computing (ARC) at Virginia Tech. Authors declare that they have no conflict of interest. This article does not contain any studies with animals or human participants performed by any of the authors.


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Copyright information

© Taiwanese Society of Biomedical Engineering 2018

Authors and Affiliations

  1. 1.Mechanical Engineering DepartmentVirginia Polytechnic Institute and State UniversityBlacksburgUSA

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