Skip to main content
Log in

Computational investigation of blood flow and flow-mediated transport in arterial thrombus neighborhood

  • Original Paper
  • Published:
Biomechanics and Modeling in Mechanobiology Aims and scope Submit manuscript

Abstract

A pathologically formed blood clot or thrombus is central to major cardiovascular diseases like heart attack and stroke. Detailed quantitative evaluation of flow and flow-mediated transport processes in the thrombus neighborhood within large artery hemodynamics is crucial for understanding disease progression and assessing treatment efficacy. This, however, remains a challenging task owing to the complexity of pulsatile viscous flow interactions with arbitrary shape and heterogeneous microstructure of realistic thrombi. Here, we address this challenge by conducting a systematic parametric simulation-based study on characterizing unsteady hemodynamics and flow-mediated transport in the neighborhood of an arterial thrombus. We use a hybrid particle—continuum-based finite element approach to handle arbitrary thrombus shape and microstructural variations. Results from a cohort of 50 different unsteady flow scenarios are presented, including unsteady vortical structures, pressure gradient across the thrombus boundary, finite time Lyapunov exponents, and dynamic coherent structures that organize advective transport. We clearly illustrate the combined influence of three key parameters—thrombus shape, microstructure, and extent of wall disease—in terms of: (a) determining hemodynamic features in the thrombus neighborhood and (b) governing the balance between advection, permeation, and diffusion to regulate transport processes in the thrombus neighborhood.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Alnæs M, Blechta J, Hake J, Johansson A, Kehlet B, Logg A, Richardson C, Ring J, Rognes M, Wells G (2015) The fenics project version 1.5. Archiv Numer Softw 3(100):9–23

    Google Scholar 

  • Bajd F, Serša I (2013) Mathematical modeling of blood clot fragmentation during flow-mediated thrombolysis. Biophys J 104(5):1181–1190

    Article  Google Scholar 

  • Bark D, Para A, Ku D (2012) Correlation of thrombosis growth rate to pathological wall shear rate during platelet accumulation. Biotechnol Bioeng 109(10):2642–2650

    Article  Google Scholar 

  • Berndt M, Friedrich B, Maegerlein C, Moench S, Hedderich D, Lehm M, Zimmer C, Straeter A, Poppert H, Wunderlich S et al (2018) Thrombus permeability in admission computed tomographic imaging indicates stroke pathogenesis based on thrombus histology. Stroke 49(11):2674–2682

    Article  Google Scholar 

  • Brass LF, Diamond SL (2016) Transport physics and biorheology in the setting of hemostasis and thrombosis. J Thromb Haemost 14(5):906–917

    Article  Google Scholar 

  • Breugem W, Boersma B, Uittenbogaard R (2005) The laminar boundary layer over a permeable wall. Transp Porous Media 59(3):267–300

    Article  MathSciNet  Google Scholar 

  • Brooks A, Hughes T (1982) Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput Methods Applied Mech Eng 32(1–3):199–259

    Article  MathSciNet  MATH  Google Scholar 

  • Cabral B and Leedom L (1993). Imaging vector fields using line integral convolution. In: Proceedings of the 20th annual conference on Computer graphics and interactive techniques pp 263–270. ACM, 1993

  • Calaminus S, Auger J, McCarty O, Wakelam M, Machesky L, Watson S (2007) Myosiniia contractility is required for maintenance of platelet structure during spreading on collagen and contributes to thrombus stability. J Thromb Haemost 5(10):2136–2145

    Article  Google Scholar 

  • Chen J,Kim OV, Litvinov RI, Weisel JW, Alber MS and Chen DZ (2014) An automated approach for fibrin network segmentation and structure identification in 3d confocal microscopy images. In: 2014 IEEE 27th International Symposium on Computer-Based Medical Systems, pp 173–178. IEEE

  • Cines D, Lebedeva T, Nagaswami C, Hayes V, Massefski W, Litvinov R, Rauova L, Lowery T, Weisel J (2014) Clot contraction: compression of erythrocytes into tightly packed polyhedra and redistribution of platelets and fibrin. Blood 123(10):1596–1603

    Article  Google Scholar 

  • Colace T, Muthard R, Diamond S (2012) Thrombus growth and embolism on tissue factor-bearing collagen surfaces under flow. Arterioscler Thromb Vasc Biol 32(6):1466–1476

    Article  Google Scholar 

  • Diamond SL (1999) Engineering design of optimal strategies for blood clot dissolution. Ann Rev Biomed Eng 1(1):427–461

    Article  Google Scholar 

  • Flamm M, Diamond S (2012) Multiscale systems biology and physics of thrombosis under flow. Ann Biomed Eng 40(11):2355–2364

    Article  Google Scholar 

  • Fogelson AL, Neeves KB (2015) Fluid mechanics of blood clot formation. Ann Rev Fluid Mech 47:377–403

    Article  MathSciNet  Google Scholar 

  • Franca L, Frey S, Hughes T (1992) Stabilized finite element methods: I application to the advective-diffusive model. Comput Methods Appl Mech Eng 95(2):253–276

    Article  MathSciNet  MATH  Google Scholar 

  • Gogia S, Neelamegham S (2015) Role of fluid shear stress in regulating vwf structure, function and related blood disorders. Biorheology 52(5–6):319–335

    Google Scholar 

  • Gorog DA, Fayad ZA, Fuster V (2017) Arterial thrombus stability: does it matter and can we detect it? J Am Coll Cardiol 70(16):2036–2047

    Article  Google Scholar 

  • Haller G (2015) Lagrangian coherent structures. Ann Rev Fluid Mech 47:137–162

    Article  MathSciNet  Google Scholar 

  • Hathcock J (2006) Flow effects on coagulation and thrombosis. Arterioscler Thromb Vasc Biol 26(8):1729–1737

    Article  Google Scholar 

  • Jaffer I, Fredenburgh J, Hirsh J, Weitz J (2015) Medical device-induced thrombosis: what causes it and how can we prevent it? J Thromb Haemost 13(S1):S72–S81

    Article  Google Scholar 

  • Kenwright DN, Lane DA (1996) Interactive time-dependent particle tracing using tetrahedral decomposition. IEEE Trans Vis Comput Graph 2(2):120–129

    Article  Google Scholar 

  • Kim H, Vignon-Clementel I, Figueroa C, LaDisa J, Jansen K, Feinstein J, Taylor C (2009) On coupling a lumped parameter heart model and a three-dimensional finite element aorta model. Ann Biomed Eng 37(11):2153–2169

    Article  Google Scholar 

  • Kim OV, Xu Z, Rosen ED, Alber MS (2013) Fibrin networks regulate protein transport during thrombus development. PLoS Comput Biol 9(6):e1003095

    Article  Google Scholar 

  • Lam W, Chaudhuri O, Crow A, Webster K, Li T, Kita A, Huang J, Fletcher D et al (2011) Mechanics and contraction dynamics of single platelets and implications for clot stiffening. Nat Mater 10(1):61–66

    Article  Google Scholar 

  • Lee S, Antiga L, Spence J, Steinman D (2008) Geometry of the carotid bifurcation predicts its exposure to disturbed flow. Stroke 39(8):2341–2347

    Article  Google Scholar 

  • Leiderman K, Fogelson A (2011) Grow with the flow: a spatial-temporal model of platelet deposition and blood coagulation under flow. Math Med Biol 28(1):47–84

    Article  MathSciNet  MATH  Google Scholar 

  • Leiderman K, Fogelson A (2014) An overview of mathematical modeling of thrombus formation under flow. Thromb Res 133:S12–S14

    Article  Google Scholar 

  • Liu D and Yu J (2009) Otsu method and k-means. In: 2009 Ninth International Conference on Hybrid Intelligent Systems 1: 344–349. IEEE

  • Mirramezani M, Herbig B, Stalker T, Nettey L, Cooper M, Weisel J, Diamond S, Sinno T, Brass L, Shadden S et al (2018) Platelet packing density is an independent regulator of the hemostatic response to injury. J Thromb Haemost 16(5):973–983

    Article  Google Scholar 

  • Mukherjee D, Shadden SC (2018) Modeling blood flow around a thrombus using a hybrid particle-continuum approach. Biomech Modeling Mechanobiol 17(3):645–663

    Article  Google Scholar 

  • Muthard RW, Diamond SL (2012) Blood clots are rapidly assembled hemodynamic sensors: flow arrest triggers intraluminal thrombus contraction. Arterioscler Thromb Vasc Biol 32(12):2938–2945

    Article  Google Scholar 

  • Nesbitt W, Westein E, Tovar-Lopez F, Tolouei E, Mitchell A, Fu J, Carberry J, Fouras A, Jackson S (2009) A shear gradient-dependent platelet aggregation mechanism drives thrombus formation. Nat Med 15(6):665–673

    Article  Google Scholar 

  • Ono A, Westein E, Hsiao S, Nesbitt W, Hamilton J, Schoenwaelder S, Jackson S (2008) Identification of a fibrin-independent platelet contractile mechanism regulating primary hemostasis and thrombus growth. Blood 112(1):90–99

    Article  Google Scholar 

  • Otsu N (1979) A threshold selection method from gray-level histograms. IEEE Trans Syst Man Cybern 9(1):62–66

    Article  Google Scholar 

  • Piebalgs A, Gu B, Roi D, Lobotesis K, Thom S, Xu XY (2018) Computational simulations of thrombolytic therapy in acute ischaemic stroke. Sci Rep 8(1):1–13

    Article  Google Scholar 

  • Pivkin I, Richardson P, Karniadakis G (2006) Blood flow velocity effects and role of activation delay time on growth and form of platelet thrombi. Proc Nat Acad Sci 103(46):17164–17169

    Article  Google Scholar 

  • Rha J-H, Saver JL (2007) The impact of recanalization on ischemic stroke outcome: a meta-analysis. Stroke 38(3):967–973

    Article  Google Scholar 

  • Schlichting H, Gersten K (2016) Boundary-layer theory. Springer, Berlin

    MATH  Google Scholar 

  • Shadden S (2011) Lagrangian coherent structures. In: Grigoriev R (ed) Transport and mixing in laminar flows: from microfluidics to oceanic currents, chapter 3. Wiley, Hoboken, pp 59–89

    Chapter  Google Scholar 

  • Shadden SC, Hendabadi S (2013) Potential fluid mechanic pathways of platelet activation. Biomech Modeling Mechanobiol 12(3):467–474

    Article  Google Scholar 

  • Shadden SC, Taylor CA (2008) Characterization of coherent structures in the cardiovascular system. Ann Biomed Eng 36(7):1152–1162

    Article  Google Scholar 

  • Shadden SC, Lekien F, Marsden JE (2005) Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. Phys D Nonlinear Phenom 212(3–4):271–304

    Article  MathSciNet  MATH  Google Scholar 

  • Stalker TJ, Welsh JD, Tomaiuolo M, Wu J, Colace TV, Diamond SL, Brass LF (2014) A systems approach to hemostasis: 3 thrombus consolidation regulates intrathrombus solute transport and local thrombin activity. Blood J Am Soc Hematol 124(11):1824–1831

    Google Scholar 

  • Sweet CR, Chatterjee S, Xu Z, Bisordi K, Rosen ED, Alber M (2011) Modelling platelet-blood flow interaction using the subcellular element Langevin method. J R Soc Interface 8(65):1760–1771

    Article  Google Scholar 

  • Tilton N, Cortelezzi L (2015) Stability of boundary layers over porous walls with suction. AIAA J 53(10):2856–2868

    Article  Google Scholar 

  • Tomaiuolo M, Stalker T, Welsh J, Diamond S, Sinno T, Brass L (2014) A systems approach to hemostasis: 2. computational analysis of molecular transport in the thrombus microenvironment. Blood 124(11):1816–1823

    Article  Google Scholar 

  • Tomaiuolo M, Brass LF, Stalker TJ (2017) Regulation of platelet activation and coagulation and its role in vascular injury and arterial thrombosis. Interv Cardiol Clin 6(1):1

    Google Scholar 

  • Van der Walt S, Schönberger JL, Nunez-Iglesias J, Boulogne F, Warner JD, Yager N, Gouillart E, Yu T (2014) Scikit-image: image processing in python. Peer J 2:e453

    Article  Google Scholar 

  • Vignon-Clementel I, Figueroa C, Jansen K, Taylor C (2006) Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries. Comput Methods Appl Mech Eng 195(29):3776–3796

    Article  MathSciNet  MATH  Google Scholar 

  • Virani SS, Alonso A, Benjamin EJ, Bittencourt MS, Callaway CW, Carson AP, Chamberlain AM, Chang AR, Cheng S, Delling FN, Djousse L, Elkind MSV, Ferguson JF, Fornage M, Khan SS, Kissela BM, Knutson KL, Kwan TW, Lackland DT, Lewis TT, Lichtman JH, Longenecker CT, Loop MS, Lutsey PL, Martin SS, Matsushita K, Moran AE, Mussolino ME, Perak AM, Rosamond WD, Roth GA, Sampson UKA, Satou GM, Schroeder EB, Shah SH, Shay CM, Spartano NL, Stokes A, Tirschwell DL, VanWagner LB, Tsao CW (2020) Heart disease and stroke statistics—2020 update: a report from the american heart association. Circulation 141(9):e139–e596

    Article  Google Scholar 

  • Wardlaw JM, Murray V, Berge E, Del Zoppo G, Sandercock P, Lindley RL, Cohen G (2012) Recombinant tissue plasminogen activator for acute ischaemic stroke: an updated systematic review and meta-analysis. Lancet 379(9834):2364–2372

    Article  Google Scholar 

  • Weisel JW and Litvinov RI (2017) Fibrin formation, structure and properties. Fibrous proteins: structures and mechanisms, pp 405–456. Springer

  • Welsh JD, Stalker TJ, Voronov R, Muthard RW, Tomaiuolo M, Diamond SL, Brass LF (2014) A systems approach to hemostasis: 1. the interdependence of thrombus architecture and agonist movements in the gaps between platelets. Blood J Am Soc Hematol 124(11):1808–1815

    Google Scholar 

  • Wendelboe AM, Raskob GE (2016) Global burden of thrombosis: epidemiologic aspects. Circ Res 118(9):1340–1347

    Article  Google Scholar 

  • Wolberg AS (2007) Thrombin generation and fibrin clot structure. Blood Rev 21(3):131–142

    Article  Google Scholar 

  • Wootton DM, Ku DN (1999) Fluid mechanics of vascular systems, diseases, and thrombosis. Ann Rev Biomed Eng 1(1):299–329

    Article  Google Scholar 

  • Wufsus A, Macera N, Neeves K (2013) The hydraulic permeability of blood clots as a function of fibrin and platelet density. Biophys J 104(8):1812–1823

    Article  Google Scholar 

  • Xu Z, Chen N, Kamocka M, Rosen E, Alber M (2008) A multiscale model of thrombus development. J R Soc Interface 5(24):705–722

    Article  Google Scholar 

  • Xu Z, Chen N, Shadden SC, Marsden JE, Kamocka MM, Rosen ED, Alber M (2009) Study of blood flow impact on growth of thrombi using a multiscale model. Soft Matter 5(4):769–779

    Article  Google Scholar 

  • Yazdani A, Li H, Humphrey JD, Karniadakis GE (2017) A general shear-dependent model for thrombus formation. PLoS Comput Biol 13(1):e1005291

    Article  Google Scholar 

  • Zhang C, Neelamegham S (2017) Application of microfluidic devices in studies of thrombosis and hemostasis. Platelets 28(5):434–440

    Article  Google Scholar 

  • Zheng X, Yazdani A, Li H, Humphrey JD, Karniadakis GE (2020) A three-dimensional phase-field model for multiscale modeling of thrombus biomechanics in blood vessels. PLoS Comput Biol 16(4):e1007709

    Article  Google Scholar 

  • Zubairova LD, Nabiullina RM, Nagaswami C, Zuev YF, Mustafin IG, Litvinov RI, Weisel JW (2015) Circulating microparticles alter formation, structure and properties of fibrin clots. Sci Rep 5(1):1–13

    Article  Google Scholar 

Download references

Acknowledgements

This work was partly supported by the American Heart Association (Award: 16POST27500023) and the Burroughs Wellcome Fund (Award: 1016360). This work utilized resources from the University of Colorado Boulder Research Computing Group, which is supported by the National Science Foundation (Awards ACI-1532235 and ACI-1532236), the University of Colorado Boulder, and Colorado State University. The Authors also gratefully acknowledge guidance, support, and the many valuable discussions with Prof. Scott L. Diamond, Department of Chemical and Biomolecular Engineering, University of Pennsylvania. These fruitful discussions strongly benefited the study design and interpretation of results. CT performed the flow simulations, data analysis, and contributed toward manuscript content. ZI performed Lagrangian computations and data analysis. DM developed the numerical methods and computer libraries, designed the study, and wrote the manuscript. SCS contributed key inputs to finalize study design, and simulation data analysis and interpretation. All authors reviewed the manuscript and agreed to the final version.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Debanjan Mukherjee.

Ethics declarations

Conflict of interest

The authors declare no conflicts of interest pertaining to the research presented here.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary material 1 (mp4 4524 KB)

Supplementary material 2 (mp4 10375 KB)

Supplementary material 3 (pdf 41532 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Teeraratkul, C., Irwin, Z., Shadden, S.C. et al. Computational investigation of blood flow and flow-mediated transport in arterial thrombus neighborhood. Biomech Model Mechanobiol 20, 701–715 (2021). https://doi.org/10.1007/s10237-020-01411-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10237-020-01411-7

Keywords

Navigation