Microfluidics and Nanofluidics

, Volume 14, Issue 1–2, pp 77–87 | Cite as

The influence of size, shape and vessel geometry on nanoparticle distribution

  • Jifu Tan
  • Samar Shah
  • Antony Thomas
  • H. Daniel Ou-Yang
  • Yaling Liu
Research Paper


Nanoparticles (NPs) are emerging as promising carrier platforms for targeted drug delivery and imaging probes. To evaluate the delivery efficiency, it is important to predict the distribution of NPs within blood vessels. NP size, shape and vessel geometry are believed to influence its biodistribution in circulation. Whereas, the effect of size on nanoparticle distribution has been extensively studied, little is known about the shape and vessel geometry effect. This paper describes a computational model for NP transport and distribution in a mimetic branched blood vessel using combined NP Brownian dynamics and continuum fluid mechanics approaches. The simulation results indicate that NPs with smaller size and rod shape have higher binding capabilities as a result of smaller drag force and larger contact area. The binding dynamics of rod-shaped NPs is found to be dependent on their initial contact points and orientations to the wall. Higher concentration of NPs is observed in the bifurcation area compared to the straight section of the branched vessel. Moreover, it is found that Péclet number plays an important role in determining the fraction of NPs deposited in the branched region and the straight section. Simulation results also indicate that NP binding decreases with increased shear rate. Dynamic NP re-distribution from low to high shear rates is observed due to the non-uniform shear stress distribution over the branched channel. This study would provide valuable information for NP distribution in a complex vascular network.


Nanoparticle distribution Shape effect Vascular network Péclet number 


  1. Almeida JPM, Chen AL, Foster A, Drezek R (2011) In vivo biodistribution of nanoparticles. Nanomedicine 6(5):815–835CrossRefGoogle Scholar
  2. Barber J, Alberding J, Restrepo J, Secomb T (2008) Simulated two-dimensional red blood cell motion, deformation, and partitioning in microvessel bifurcations. Ann Biomed Eng 36(10):1690–1698CrossRefGoogle Scholar
  3. Bell G (1978) Models for the specific adhesion of cells to cells. Science 200(4342):618–627CrossRefGoogle Scholar
  4. Bell GI, Dembo M, Bongrand P (1984) Cell adhesion. Competition between nonspecific repulsion and specific bonding. Biophys J 45(6):1051–1064CrossRefGoogle Scholar
  5. Chang K-C, Tees DFJ, Hammer DA (2000) The state diagram for cell adhesion under flow: leukocyte rolling and firm adhesion. Proc Nat Acad Sci 97(21):11262–11267CrossRefGoogle Scholar
  6. Chauvierre C, Labarre D, Couvreur P, Vauthier C (2003) Novel polysaccharide-decorated poly(isobutyl cyanoacrylate) nanoparticles. Pharm Res 20(11):1786–1793CrossRefGoogle Scholar
  7. Chen H, Ruckenstein E (2009) Nanoparticle aggregation in the presence of a block copolymer. J Chem Phys 131(24):244904–244907CrossRefGoogle Scholar
  8. Chen H, Ruckenstein E (2011) Aggregation of nanoparticles in a block copolymer bilayer. J Colloid Interface Sci 363(2):573–578CrossRefGoogle Scholar
  9. Cho K, Wang X, Nie S, Chen Z, Shin DM (2008) Therapeutic nanoparticles for drug delivery in cancer. Clin Cancer Res 14(5):1310–1316CrossRefGoogle Scholar
  10. Christian DA, Cai S, Garbuzenko OB, Harada T, Zajac AL, Minko T, Discher DE (2009) Flexible filaments for in vivo imaging and delivery: persistent circulation of filomicelles opens the dosage window for sustained tumor shrinkage. Mol Pharm 6(5):1343–1352CrossRefGoogle Scholar
  11. Cozens-Roberts C, Lauffenburger DA, Quinn JA (1990a) Receptor-mediated cell attachment and detachment kinetics. I. Probabilistic model and analysis. Biophys J 58(4):841–856CrossRefGoogle Scholar
  12. Cozens-Roberts C, Quinn JA, Lauffenberger DA (1990b) Receptor-mediated adhesion phenomena. Model studies with the radical-flow detachment assay. Biophys J 58(1):107–125CrossRefGoogle Scholar
  13. Decuzzi P, Ferrari M (2006) The adhesive strength of non-spherical particles mediated by specific interactions. Biomaterials 27(30):5307–5314CrossRefGoogle Scholar
  14. Decuzzi P, Godin B, Tanaka T, Lee SY, Chiappini C, Liu X, Ferrari M (2010) Size and shape effects in the biodistribution of intravascularly injected particles. J Control Release 141(3):320–327CrossRefGoogle Scholar
  15. Doshi N, Prabhakarpandian B, Rea-Ramsey A, Pant K, Sundaram S, Mitragotri S (2010) Flow and adhesion of drug carriers in blood vessels depend on their shape: a study using model synthetic microvascular networks. J Control Release 146(2):196–200CrossRefGoogle Scholar
  16. Einstein A (1956) In: Fürth R (ed) Investigations on the theory of Brownian Movement, translated by A. D. Cowper (1926, reprinted 1956), Dover Publ., New YorkGoogle Scholar
  17. Ermak DL, Mccammon JA (1978) Brownian dynamics with hydrodynamic interactions. J Chem Phys 69(4):1352–1360CrossRefGoogle Scholar
  18. Farokhzad OC, Langer R (2006) Nanomedicine: developing smarter therapeutic and diagnostic modalities. Adv Drug Deliv Rev 58(14):1456–1459CrossRefGoogle Scholar
  19. Freitas RA Jr (ed) (1999) Nanomedicine. Volume I: basic capabilities. Landes Bioscience, GeorgetownGoogle Scholar
  20. Geng Y, Dalhaimer P, Cai S, Tsai R, Tewari M, Minko T, Discher DE (2007) Shape effects of filaments versus spherical particles in flow and drug delivery. Nat Nanotechnol 2(4):249–255CrossRefGoogle Scholar
  21. Gentile F, Ferrari M, Decuzzi P (2008) The transport of nanoparticles in blood vessels: the effect of vessel permeability and blood rheology. Ann Biomed Eng 36(2):254–261CrossRefGoogle Scholar
  22. Haun JB, Hammer DA (2008) Quantifying nanoparticle adhesion mediated by specific molecular interactions. Langmuir 24(16):8821–8832CrossRefGoogle Scholar
  23. Hoganson DM, Howard PI II, Spool ID, Burns OH, Gilmore JR, Vacanti JP (2010) Principles of biomimetic vascular network design applied to a tissue-engineered liver scaffold. Tissue Eng Part A 16(5):1469–1477CrossRefGoogle Scholar
  24. Kona S, Dong J-F, Liu Y, Tan J, Nguyen KT (2012) Biodegradable nanoparticles mimicking platelet binding as a targeted and controlled drug delivery system. Int J Pharm 423(2):516–524CrossRefGoogle Scholar
  25. Lee TR, Chang YS, Choi JB, Liu WK, Kim YJ (2009) Numerical simulation of a nanoparticle focusing lens in a microfluidic channel by using immersed finite element method. J Nanosci Nanotechnol 9(12):7407–7411Google Scholar
  26. Li A, Ahmadi G (1992) Dispersion and deposition of spherical-particles from point sources in a turbulent channel flow. Aerosol Sci Tech 16(4):209–226CrossRefGoogle Scholar
  27. Li M, Panagi Z, Avgoustakis K, Reineke J (2012) Physiologically based pharmacokinetic modeling of PLGA nanoparticles with varied mPEG content. Int J Nanomed 7:1345–1356Google Scholar
  28. Liu Y, Liu WK, Belytschko T, Patankar N, To AC, Kopacz A, Chung JH (2007) Immersed electrokinetic finite element method. Int J Numer Meth Eng 71(4):379–405MathSciNetMATHCrossRefGoogle Scholar
  29. Liu J, Weller GER, Zern B, Ayyaswamy PS, Eckmann DM, Muzykantov VR, Radhakrishnan R (2010) Computational model for nanocarrier binding to endothelium validated using in vivo, in vitro, and atomic force microscopy experiments. Proc Nat Acad Sci 107(38):16530–16535CrossRefGoogle Scholar
  30. Liu Y, Tan J, Thomas A, Ou-Yang D, Muzykantov VR (2012) The shape of things to come: importance of design in nanotechnology for drug delivery. Ther Deliv 3(2):181–194CrossRefGoogle Scholar
  31. Longest PW, Kleinstreuer C (2003) Comparison of blood particle deposition models for non-parallel flow domains. J Biomech 36(3):421–430CrossRefGoogle Scholar
  32. Mathiowitz E, Jacob JS, Jong YS, Carino GP, Chickering DE, Chaturvedi P, Santos CA, Vijayaraghavan K, Montgomery S, Bassett M, Morrell C (1997) Biologically erodable microsphere as potential oral drug delivery system. Nature 386(6623):410–414CrossRefGoogle Scholar
  33. Mitragotri S, Lahann J (2009) Physical approaches to biomaterial design. Nat Mater 8(1):15–23CrossRefGoogle Scholar
  34. Mody NA, King MR (2007) Influence of Brownian motion on blood platelet flow behavior and adhesive dynamics near a planar wall. Langmuir 23(11):6321–6328CrossRefGoogle Scholar
  35. Mori N, Kumagae M, Nakamura K (1998) Brownian dynamics simulation for suspensions of oblong-particles under shear flow. Rheol Acta 37(2):151–157CrossRefGoogle Scholar
  36. Muro S, Garnacho C, Champion JA, Leferovich J, Gajewski C, Schuchman EH, Mitragotri S, Muzykantov VR (2008) Control of endothelial targeting and intracellular delivery of therapeutic enzymes by modulating the size and shape of ICAM-1-targeted carriers. Mol Ther 16(8):1450–1458CrossRefGoogle Scholar
  37. Muzykantov VR, Radhakrishnan R, Eckmann DM (2012) Dynamic factors controlling targeting nanocarriers to vascular endothelium. Curr Drug Metab 13(1):70–81CrossRefGoogle Scholar
  38. Nasongkla N, Bey E, Ren JM, Ai H, Khemtong C, Guthi JS, Chin SF, Sherry AD, Boothman DA, Gao JM (2006) Multifunctional polymeric micelles as cancer-targeted, MRI-ultrasensitive drug delivery systems. Nano Lett 6(11):2427–2430CrossRefGoogle Scholar
  39. Peppas NA (2006) Intelligent biomaterials as pharmaceutical carriers in microfabricated and nanoscale devices. MRS Bull 31(11):888–893CrossRefGoogle Scholar
  40. Prabhakarpandian B, Pant K, Scott R, Patillo C, Irimia D, Kiani M, Sundaram S (2008) Synthetic microvascular networks for quantitative analysis of particle adhesion. Biomed Microdevices 10(4):585–595CrossRefGoogle Scholar
  41. Roney C, Kulkarni P, Arora V, Antich P, Bonte F, Wu AM, Mallikarjuana NN, Manohar S, Liang HF, Kulkarni AR, Sung HW, Sairam M, Aminabhavi TM (2005) Targeted nanoparticles for drug delivery through the blood–brain barrier for Alzheimer’s disease. J Control Release 108(2–3):193–214CrossRefGoogle Scholar
  42. Saad Y, Schultz MH (1986) Gmres—a generalized minimal residual algorithm for solving nonsymmetric linear-systems. Siam J Sci Stat Comp 7(3):856–869MathSciNetMATHCrossRefGoogle Scholar
  43. Sanhai WR, Sakamoto JH, Canady R, Ferrari M (2008) Seven challenges for nanomedicine. Nat Nano 3(5):242–244CrossRefGoogle Scholar
  44. Shah P (2006) Use of nanotechnologies for drug delivery. MRS Bull 31(11):894–899CrossRefGoogle Scholar
  45. Shah S, Liu Y (2011) Modeling particle shape-dependent dynamics in nanomedicine. J Nanosci Nanotechnol 11(2):919–928CrossRefGoogle Scholar
  46. Sharma N, Patankar NA (2004) Direct numerical simulation of the Brownian motion of particles by using fluctuating hydrodynamic equations. J Comput Phys 201(2):466–486MATHCrossRefGoogle Scholar
  47. Shuvaev VV, Ilies MA, Simone E, Zaitsev S, Kim Y, Cai S, Mahmud A, Dziubla T, Muro S, Discher DE, Muzykantov VR (2011) Endothelial targeting of antibody-decorated polymeric filomicelles. ACS Nano 5(9):6991–6999CrossRefGoogle Scholar
  48. Stolnik S, Illum L, Davis SS (1995) Long circulating microparticulate drug carriers. Adv Drug Deliv Rev 16(2–3):195–214CrossRefGoogle Scholar
  49. Sukhorukov GB, Mohwald H (2007) Multifunctional cargo systems for biotechnology. Trend Biotechnol 25(3):93–98CrossRefGoogle Scholar
  50. Tan J, Thomas A, Liu Y (2012) Influence of red blood cells on nanoparticle targeted delivery in microcirculation. Soft Matter 8(6):1934–1946CrossRefGoogle Scholar
  51. Tousi N, Wang B, Pant K, Kiani MF, Prabhakarpandian B (2010) Preferential adhesion of leukocytes near bifurcations is endothelium independent. Microvasc Res 80(3):384–388CrossRefGoogle Scholar
  52. Ward MD, Hammer DA (1993) A theoretical analysis for the effect of focal contact formation on cell-substrate attachment strength. Biophys J 64(3):936–959CrossRefGoogle Scholar
  53. Wischgoll T, Choy JS, Kassab GS (2009) Extraction of morphometry and branching angles of porcine coronary arterial tree from CT images. Am J Physiol Heart Circu Physiol 297(5):H1949–H1955CrossRefGoogle Scholar
  54. Xiong W, Zhang J (2012) Two-dimensional lattice Boltzmann study of red blood cell motion through microvascular bifurcation: cell deformability and suspending viscosity effects. Biomech Model Mechanobiol 11(3):575–583CrossRefGoogle Scholar
  55. Yang K, Ma Y-Q (2010) Computer simulation of the translocation of nanoparticles with different shapes across a lipid bilayer. Nat Nano 5(8):579–583CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Jifu Tan
    • 1
  • Samar Shah
    • 1
  • Antony Thomas
    • 2
  • H. Daniel Ou-Yang
    • 2
    • 3
  • Yaling Liu
    • 1
    • 2
  1. 1.Department of Mechanical Engineering and MechanicsLehigh UniversityBethlehemUSA
  2. 2.Bioengineering ProgramLehigh UniversityBethlehemUSA
  3. 3.Department of PhysicsLehigh UniversityBethlehemUSA

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