Skip to main content
SpringerLink
Log in

Mathematical Modeling of Micro-/Nanoparticles Transport in Blood Vessels: A Review

  • Review Article
  • Published:
Korean Journal of Chemical Engineering Aims and scope Submit manuscript

Abstract

Targeted drug delivery using drug-carrying nanoparticles has emerged as a promising approach for the treatment of diseases such as cancer. This review paper provides an overview of the current state of the art in modeling the transport and margination of micro-/nanoparticles in blood vessels. The review examines single-particle models, which consider a single micro-/nanoparticle, and multi-particle models, which consider a large number of particles in the bloodstream. The models are assessed based on factors such as the geometry of the blood vessel, the type, shape, size, and concentration of micro-/nanoparticles, the type of blood flow, the mathematical modeling approach, investigated parameters, and observed results. By analyzing the literature, this review aims to identify the desired properties of micro-/nanopharmaceuticals and to highlight the limiting factors of particle transport in the vascular system. The findings of this review can provide useful insights for researchers working on the development of more effective drug delivery strategies.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /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.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Notes

  1. Movement of particles in blood flow toward the vessel wall.

  2. Volume percentage of red blood cells in the blood.

  3. Stenosis is the narrowing of the arteries as the result of the accumulation of fatty substances or plaque formation inside the lumen which can lead to cardiac-related problems.

References

  1. P.S. Stephanou, Rheol. Acta 60, 603 (2021)

    CAS  PubMed  PubMed Central  Google Scholar 

  2. M. Sheikhpour, M. Arabi, A. Kasaeian, A. Rokn Rabei, Z. Taherian, Nanotechnol. Sci. Appl. 13, 47 (2020)

    CAS  PubMed  PubMed Central  Google Scholar 

  3. E. Mostaghasi, A. Zarepour, A. Zarrabi, J. Taiwan Inst. Chem. Eng. 82, 33 (2018)

    CAS  Google Scholar 

  4. E.J. Lee, Korean J. Chem. Eng. 35, 1765 (2018)

    CAS  Google Scholar 

  5. E.K. Chow, X.Q. Zhang, M. Chen, R. Lam, E. Robinson, H. Huang, D. Schaffer, E. Osawa, A. Goga, D. Ho, Sci. Transl. Med. 3, 73ra21 (2011)

    PubMed  Google Scholar 

  6. P. Dogra, J.D. Butner, Y.-L. Chuang, S. Caserta, S. Goel, C.J. Brinker, V. Cristini, Z. Wang, Biomed. Microdevices 21, 40 (2019)

    PubMed  PubMed Central  Google Scholar 

  7. Y. Gao, Y. Shi, L. Wang, S. Kong, J. Du, G. Lin, Y. Feng, Comput. Methods Prog. Biomed. 184, 105106 (2020)

    Google Scholar 

  8. S. Jafarzadeh, A.N. Sadr, E. Kaffash, S. Goudarzi, E. Golab, A. Karimipour, Comput. Methods Prog. Biomed. 195, 105545 (2020)

    Google Scholar 

  9. G. Fullstone, J. Wood, M. Holcombe, G. Battaglia, Sci. Rep. 5, 10649 (2015)

    PubMed  PubMed Central  Google Scholar 

  10. U. Bulbake, S. Doppalapudi, N. Kommineni, W. Khan, Pharmaceutics 9, 12 (2017)

    PubMed  PubMed Central  Google Scholar 

  11. K. Venkatakrishnan, Y. Liu, D. Noe, J. Mertz, M. Bargfrede, T. Marbury, K. Farbakhsh, C. Oliva, A. Milton, Br. J. Clin. Pharmacol. 77, 986 (2014)

    CAS  PubMed  Google Scholar 

  12. R. Bawa, G. Audette, I. Rubinstein, Handbook of clinical nanomedicine: Nanoparticles, imaging, therapy and clinical applications (Pan Stanford Publishing, Singapore, 2020)

    Google Scholar 

  13. L. Crocco, I. Karanasiou, M. James, R.C. Conceicao, Emerging electromagnetic technologies for brain diseases diagnostics, monitoring and therapy (Springer, Switzerland, 2018)

    Google Scholar 

  14. F.S. Praça, H.S. Marinho, M.B. Martins, R. Gaspar, M.L. Corvo, W.S. Medina, Current aspects of breast cancer therapy and diagnosis based on a nanocarrier approach, in Nanostructures for cancer therapy. ed. by A. Ficai, A.M. Grumezescu (Elsevier, The Netherlands, 2017), pp.749–774

    Google Scholar 

  15. J. Shi, P.W. Kantoff, R. Wooster, O.C. Farokhzad, Nat. Rev. Cancer 17, 20 (2017)

    CAS  PubMed  Google Scholar 

  16. Y. Liu, S. Shah, J. Tan, Rev. Nanosci. Nanotechnol. 1, 66 (2012)

    CAS  Google Scholar 

  17. M. Ramezanpour, S.S.W. Leung, K.H. Delgado-Magnero, B.Y.M. Bashe, J. Thewalt, D.P. Tieleman, Biochim. Biophys. Acta Biomembr. BBA-Biomembranes 1858, 1688 (2016)

    CAS  Google Scholar 

  18. S. Afkhami, Y. Renardy, J. Eng. Math. 107, 231 (2017)

    CAS  Google Scholar 

  19. H. Ye, Z. Shen, L. Yu, M. Wei, Y. Li, Proc. Math. Phys. Eng. Sci. 474, 20170845 (2018)

    PubMed  PubMed Central  Google Scholar 

  20. A. Karolak, D.A. Markov, L.J. McCawley, K.A. Rejniak, J. R. Soc. Interface. 15, 20170703 (2018)

    PubMed  PubMed Central  Google Scholar 

  21. H. Lopez, V. Lobaskin, J. Chem. Phys. 143, 243138 (2015)

    PubMed  Google Scholar 

  22. V. Tozzini, Curr. Opin. Struct. Biol. 15, 144 (2005)

    CAS  PubMed  Google Scholar 

  23. D.M. Eckmann, R.P. Bradley, S.K. Kandy, K. Patil, P.A. Janmey, R. Radhakrishnan, Curr. Opin. Struct. Biol. 64, 104 (2020)

    CAS  PubMed  PubMed Central  Google Scholar 

  24. M. Hadjicharalambous, P.A. Wijeratne, V. Vavourakis, Methods 185, 82 (2021)

    CAS  PubMed  Google Scholar 

  25. N. Sahai, M. Gogoi, N. Ahmad, Curr Pathobiol Rep 9, 1 (2021)

    Google Scholar 

  26. S. Sindhwani, A.M. Syed, J. Ngai, B.R. Kingston, L. Maiorino, J. Rothschild, P. MacMillan, Y. Zhang, N.U. Rajesh, T. Hoang, J.L.Y. Wu, S. Wilhelm, A. Zilman, S. Gadde, A. Sulaiman, B. Ouyang, Z. Lin, L. Wang, M. Egeblad, W.C.W. Chan, Nat. Mater. 19, 566 (2020)

    CAS  PubMed  Google Scholar 

  27. D.M. Moss, M. Siccardi, Br. J. Pharmacol. 171, 3963 (2014)

    CAS  PubMed  PubMed Central  Google Scholar 

  28. P. Charoenphol, S. Mocherla, D. Bouis, K. Namdee, D.J. Pinsky, O. Eniola-Adefeso, Atherosclerosis 217, 364 (2011)

    CAS  PubMed  Google Scholar 

  29. P. Charoenphol, P.J. Onyskiw, M. Carrasco-Teja, O. Eniola-Adefeso, J. Biomech. 45, 2822 (2012)

    PubMed  Google Scholar 

  30. J. Tan, A. Thomas, Y. Liu, Soft Matter 8, 1934 (2012)

    CAS  Google Scholar 

  31. K. Namdee, A.J. Thompson, P. Charoenphol, O. Eniola-Adefeso, Langmuir 29, 2530 (2013)

    CAS  PubMed  Google Scholar 

  32. A.J. Thompson, E.M. Mastria, O. Eniola-Adefeso, Biomaterials 34, 5863 (2013)

    CAS  PubMed  Google Scholar 

  33. M. Mehrabadi, D.N. Ku, C.K. Aidun, Ann. Biomed. Eng. 43, 1410 (2015)

    PubMed  Google Scholar 

  34. M. Mehrabadi, D.N. Ku, C.K. Aidun, Phys. Rev. E 93, 023109 (2016)

    PubMed  Google Scholar 

  35. H.W. Hou, A.A. Bhagat, A.G. Chong, P. Mao, K.S. Tan, J. Han, C.T. Lim, Lab Chip 10, 2605 (2010)

    CAS  PubMed  Google Scholar 

  36. S.S. Shevkoplyas, T. Yoshida, L.L. Munn, M.W. Bitensky, Anal. Chem. 77, 933 (2005)

    CAS  PubMed  PubMed Central  Google Scholar 

  37. T. Tanaka, T. Ishikawa, K. Numayama-Tsuruta, Y. Imai, H. Ueno, T. Yoshimoto, N. Matsuki, T. Yamaguchi, Biomed. Microdevices 14, 25 (2012)

    PubMed  Google Scholar 

  38. T. Suzuki, H. Takao, T. Suzuki, S. Hataoka, T. Kodama, K. Aoki, K. Otani, T. Ishibashi, H. Yamamoto, Y. Murayama, M. Yamamoto, J. Non-Newton, Fluid Mech 290, 104511 (2021)

    CAS  Google Scholar 

  39. J.-B. Choi, Y.-R. Park, S.-J. Kim, H.-S. Kang, B.-Y. Park, I.-S. Kim, Y.-S. Yang, G.-B. Kim, Korean J. Chem. Eng. 31, 402 (2014)

    CAS  Google Scholar 

  40. Z. Liu, Y. Zhu, R.R. Rao, J.R. Clausen, C.K. Aidun, Comput. Fluids 172, 609 (2018)

    Google Scholar 

  41. S.S. Ashrafmansouri, M.N. Esfahany, Int. J. Therm. Sci. 82, 84 (2014)

    CAS  Google Scholar 

  42. S.S. Ashrafmansouri, M.N. Esfahany, G. Azimi, N. Etesami, Int. J. Therm. Sci. 86, 166 (2014)

    CAS  Google Scholar 

  43. S.S. Ashrafmansouri, M.N. Esfahany, Sep. Purif. Technol. 151, 74 (2015)

    CAS  Google Scholar 

  44. S.S. Ashrafmansouri, M.N. Esfahany, AIChE J. 62, 852 (2016)

    CAS  Google Scholar 

  45. S.-S. Ashrafmansouri, S. Willersinn, M.N. Esfahany, H.-J. Bart, RSC Adv. 6, 19089 (2016)

    CAS  Google Scholar 

  46. S.S. Ashrafmansouri, S. Willersinn, M.N. Esfahany, H.J. Bart, Chem. Ing. Tech. 87, 1054 (2015)

    Google Scholar 

  47. S.Z. Heris, M.N. Esfahany, S.G. Etemad, Int. J. Heat Fluid Flow 28, 203 (2007)

    Google Scholar 

  48. S.M. Fotukian, M.N. Esfahany, Int. Commun Heat Mass Transf. 37, 214 (2010)

    CAS  Google Scholar 

  49. S.H. Esmaeili-Faraj, M. Nasr Esfahany, Ind. Eng. Chem. Res. 55, 4682 (2016)

    CAS  Google Scholar 

  50. M.H.K. Darvanjooghi, M.N. Esfahany, S.H. Esmaeili-Faraj, Sep. Purif. Technol. 195, 208 (2018)

    CAS  Google Scholar 

  51. H.H. Goodarzi, M.N. Esfahany, Sep. Purif. Technol. 170, 130 (2016)

    Google Scholar 

  52. P. Decuzzi, S. Lee, B. Bhushan, M. Ferrari, Ann. Biomed. Eng. 33, 179 (2005)

    CAS  PubMed  Google Scholar 

  53. J.N. Israelachvili, Intermolecular and surface forces (Academic Press, London, 1991)

    Google Scholar 

  54. S.Y. Lee, M. Ferrari, P. Decuzzi, J. Biomech. 42, 1885 (2009)

    PubMed  Google Scholar 

  55. E. Gavze, M. Shapiro, Int. J. Multiph. Flow 23, 155 (1997)

    CAS  Google Scholar 

  56. E. Gavze, M. Shapiro, J. Fluid Mech. 371, 59 (1998)

    CAS  Google Scholar 

  57. S.Y. Lee, M. Ferrari, P. Decuzzi, Nanotechnology 20, 495101 (2009)

    PubMed  Google Scholar 

  58. S. Shah, Y. Liu, W. Hu, J. Gao, J. Nanosci. Nanotechnol. 11, 919 (2011)

    CAS  PubMed  PubMed Central  Google Scholar 

  59. M. Dembo, D.C. Torney, K. Saxman, D. Hammer, Proceedings of the royal society of London. Ser. B Biol. Sci. 234, 55 (1988)

    CAS  Google Scholar 

  60. L. Zhang, A. Gerstenberger, X. Wang, W.K. Liu, Comput. Methods Appl. Mech. Eng. 193, 2051 (2004)

    Google Scholar 

  61. W.K. Liu, Y. Liu, D. Farrell, L. Zhang, X.S. Wang, Y. Fukui, N. Patankar, Y. Zhang, C. Bajaj, J. Lee, J. Hong, X. Chen, H. Hsu, Comput. Methods Appl. Mech. Eng. 195, 1722 (2006)

    PubMed  PubMed Central  Google Scholar 

  62. W.K. Liu, D.W. Kim, S. Tang, Comput. Mech. 39, 211 (2007)

    Google Scholar 

  63. N. Mori, M. Kumagae, K. Nakamura, Rheol. Acta 37, 151 (1998)

    CAS  Google Scholar 

  64. A.D. Grief, G. Richardson, J. Magn. Magn. Mater. 293, 455 (2005)

    CAS  Google Scholar 

  65. L.I. Kolitsi, S.G. Yiantsios, Microvasc. Res. 130, 104007 (2020)

    CAS  PubMed  Google Scholar 

  66. E.P. Furlani, K.C. Ng, Phys. Rev. E 73, 061919 (2006)

    CAS  Google Scholar 

  67. P. Decuzzi, F. Causa, M. Ferrari, P.A. Netti, Ann. Biomed. Eng. 34, 633 (2006)

    CAS  PubMed  Google Scholar 

  68. F. Gentile, M. Ferrari, P. Decuzzi, Ann. Biomed. Eng. 36, 254 (2008)

    PubMed  Google Scholar 

  69. G.I. Taylor, Proc Math Phys Eng Sci 219, 186 (1953)

    CAS  Google Scholar 

  70. R. Aris, G.I. Taylor, Proc Math Phys Eng Sci 235, 67 (1956)

    Google Scholar 

  71. X.L. Li, K.L. Yao, Z.L. Liu, J. Magn. Magn. Mater. 320, 1753 (2008)

    CAS  Google Scholar 

  72. M. Mahmoudi, M.A. Shokrgozar, A. Simchi, M. Imani, A.S. Milani, P. Stroeve, H. Vali, U.O. Häfeli, S. Bonakdar, J. Phys. Chem. C 113, 2322 (2009)

    CAS  Google Scholar 

  73. M. Lohakan, P. Junchaichanakun, S. Boonsang and C. Pintavirooj, A computational model of magnetic drug targeting in blood vessel using finite flement method. In: 2nd IEEE conference on industrial electronics and applications (ICIEA 2007), Harbin, China, pp 231–234 (2007)

  74. W.F. Robert, T.M. Alan, J.P. Philip, Introduction to fluid mechanics (John Wiley & Sons, New York, 2004)

    Google Scholar 

  75. S. Kayal, D. Bandyopadhyay, T.K. Mandal, R.V. Ramanujan, RSC Adv. 1, 238 (2011)

    CAS  Google Scholar 

  76. A.E. David, A.J. Cole, B. Chertok, Y.S. Park, V.C. Yang, J. Control. Release 152, 67 (2011)

    CAS  PubMed  PubMed Central  Google Scholar 

  77. P. Yue, S. Lee, S. Afkhami, Y. Renardy, Acta Mech. 223, 505 (2012)

    Google Scholar 

  78. E.G.D. Cohen, R. van Zon, C. R. Phys. 8, 507 (2007)

    CAS  Google Scholar 

  79. S.S. Hossain, S.F.A. Hossainy, Y. Bazilevs, V.M. Calo, T.J.R. Hughes, Comput. Mech. 49, 213 (2012)

    Google Scholar 

  80. T.J.R. Hughes, J.A. Cottrell, Y. Bazilevs, Comput. Methods Appl. Mech. Eng. 194, 4135 (2005)

    Google Scholar 

  81. Y. Bazilevs, V.M. Calo, Y. Zhang, T.J.R. Hughes, Comput. Mech. 38, 310 (2006)

    Google Scholar 

  82. S.S. Hossain, Y. Zhang, X. Liang, F. Hussain, M. Ferrari, T.J. Hughes, P. Decuzzi, Nanomedicine (Lond.) 8, 343 (2013)

    CAS  PubMed  Google Scholar 

  83. J. Tan, S. Shah, A. Thomas, H.D. Ou-Yang, Y. Liu, Microfluid Nanofluidics 14, 77 (2013)

    CAS  PubMed  Google Scholar 

  84. Y. Saad, M.H. Schultz, SIAM J. Sci. Stat. Comput. 7, 856 (1986)

    Google Scholar 

  85. J. Tan, S. Wang, J. Yang, Y. Liu, Comput. Struct. 122, 128 (2013)

    PubMed  PubMed Central  Google Scholar 

  86. S. Sharma, V.K. Katiyar, U. Singh, J. Magn. Magn. Mater. 379, 102 (2015)

    CAS  Google Scholar 

  87. T. Elnaqeeb, K.S. Mekheimer, F. Alghamdi, Math. Biosci. 282, 135 (2016)

    CAS  PubMed  Google Scholar 

  88. S.C. Hossain, X. Zhang, Z. Liu, Z. Haider, K. Memon, F. Panhwar, M. karmah Mbogba, P. Hu, G. Zhao, Int. Commun. Heat Mass Transf. 98, 239 (2018)

    Google Scholar 

  89. A. Zaman, N. Ali, I. Ali, Therm. Sci. Eng. Prog. 5, 482 (2018)

    Google Scholar 

  90. M.K.D. Manshadi, M. Saadat, M. Mohammadi, M. Shamsi, M. Dejam, R. Kamali, A. Sanati-Nezhad, Drug Deliv. 25, 1963 (2018)

    CAS  PubMed  PubMed Central  Google Scholar 

  91. A. Ochsner, G. Murch, Cellular and porous materials: thermal properties simulation and prediction (Wiley, Weinheim, 2008)

    Google Scholar 

  92. A. Sharifi, S.Y. Motlagh, H. Badfar, J. Magn. Magn. Mater. 474, 236 (2019)

    CAS  Google Scholar 

  93. I. Shahzadi, N. Kousar, Comput. Methods Programs Biomed. 179, 104980 (2019)

    PubMed  Google Scholar 

  94. I. Shahzadi, S. Bilal, Comput. Methods Programs Biomed. 187, 105248 (2020)

    PubMed  Google Scholar 

  95. S. Majee, G.C. Shit, Eur. J. Mech. B. Fluids 83, 42 (2020)

    Google Scholar 

  96. A. Ali, M. Hussain, Z. Ali, J.U. Rahman, M. Hussan, IEEE Access 8, 195021 (2020)

    Google Scholar 

  97. S. F. Salem, V. V. Tuchin, Numerical simulation of magnetic nanoparticles in the blood stream, Saratov Fall Meeting 2019: optical and nano-technologies for biology and medicine, SPIE—International society for optics and photonics, saratov, russian federation, p 114571N (2020)

  98. W. Alghamdi, A. Alsubie, P. Kumam, A. Saeed, T. Gul, Sci. Rep. 11, 11621 (2021)

    CAS  PubMed  PubMed Central  Google Scholar 

  99. S. Liao, Appl. Math. Comput. 147, 499 (2004)

    Google Scholar 

  100. S.S. Meschi, A. Farghadan, A. Arzani, J. Biomech. 119, 110307 (2021)

    PubMed  Google Scholar 

  101. M. Mortensen, K. Valen-Sendstad, Comput. Phys. Commun. 188, 177 (2015)

    CAS  Google Scholar 

  102. M. Khazayinejad, M. Hafezi, B. Dabir, Powder Technol. 384, 452 (2021)

    CAS  Google Scholar 

  103. M.A. Nuwairan, B. Souayeh, Micromachines (Basel) 13, 374 (2022)

    PubMed  Google Scholar 

  104. Y. Li, W. Stroberg, T.-R. Lee, H.S. Kim, H. Man, D. Ho, P. Decuzzi, W.K. Liu, Comput. Mech. 53, 511 (2014)

    Google Scholar 

  105. S.E.A. Gratton, P.D. Pohlhaus, J. Lee, J. Guo, M.J. Cho, J.M. Desimone, J. Control. Release 121, 10 (2007)

    CAS  PubMed  PubMed Central  Google Scholar 

  106. J.W. Haverkort, S. Kenjeres, C.R. Kleijn, Ann. Biomed. Eng. 37, 2436 (2009)

    CAS  PubMed  PubMed Central  Google Scholar 

  107. E.M. Cherry, J.K. Eaton, Int. J. Multiph. Flow 59, 173 (2014)

    CAS  Google Scholar 

  108. M.R. Habibi, M. Ghasemi, J. Magn. Magn. Mater. 323, 32 (2011)

    Google Scholar 

  109. S. Kenjereš, B.W. Righolt, Int. J. Heat Fluid Flow 35, 68 (2012)

    Google Scholar 

  110. G. Doig, G.H. Yeoh, V. Timchenko, G. Rosengarten, T.J. Barber, S.C.P. Cheung, J Comput Multiph Flows 4, 85 (2012)

    CAS  Google Scholar 

  111. A. Li, G. Ahmadi, Aerosol Sci. Technol. 16, 209 (1992)

    CAS  Google Scholar 

  112. G.F. Carrier, J. Fluid Mech. 4, 376 (1958)

    Google Scholar 

  113. M. Varmazyar, M. Habibi, M. Amini, A.H. Pordanjani, M. Afrand, S.M. Vahedi, Powder Technol. 366, 164 (2020)

    CAS  Google Scholar 

  114. N.H. Abu-Hamdeh, R.A.R. Bantan, F. Aalizadeh, A. Alimoradi, Alex. Eng. J. 59, 4049 (2020)

    Google Scholar 

  115. M. Ameenuddin, M. Anand, M. Massoudi, Appl. Math. Comput. 356, 299 (2019)

    Google Scholar 

  116. H. Sodagar, J. Sodagar-Abardeh, A. Shakiba, H. Niazmand, Biomech. Model. Mechanobiol. 20, 787 (2021)

    PubMed  Google Scholar 

  117. J.B. Freund, B. Shapiro, Phys. Fluids 24, 051904 (2012)

    Google Scholar 

  118. D. Saintillan, E. Darve, E.S.G. Shaqfeh, Phys. Fluids 17, 033301 (2005)

    Google Scholar 

  119. Y. Saad, M.H. Schultz, SIAM J. Sci. Comput. 7, 856 (1986)

    Google Scholar 

  120. J.F. Brady, G. Bossis, Annu. Rev. Fluid Mech. 20, 111 (1988)

    Google Scholar 

  121. W.B. Russel, D.A. Saville, W.R. Schowalter, Colloidal dispersions (Cambridge University Press, Cambridge, 1989)

    Google Scholar 

  122. T.-R. Lee, M. Choi, A.M. Kopacz, S.-H. Yun, W.K. Liu, P. Decuzzi, Sci. Rep. 3, 2079 (2013)

    PubMed  PubMed Central  Google Scholar 

  123. X. Yu, I. Trase, M. Ren, K. Duval, X. Guo, Z. Chen, J. Nanomater. 2016, 1087250 (2016)

    PubMed  PubMed Central  Google Scholar 

  124. J. Tan, W. Keller, S. Sohrabi, J. Yang, Y. Liu, Nanomaterials (Basel) 6, 30 (2016)

    PubMed  Google Scholar 

  125. Y. Liu, W.K. Liu, T. Belytschko, N. Patankar, A.C. To, A. Kopacz, J.-H. Chung, Int J Numer Methods Eng 71, 379 (2007)

    Google Scholar 

  126. K. Müller, D.A. Fedosov, G. Gompper, Sci. Rep. 4, 4871 (2014)

    PubMed  PubMed Central  Google Scholar 

  127. P.J. Hoogerbrugge, J.M.V.A. Koelman, EPL 19, 155 (1992)

    Google Scholar 

  128. P. Español, P. Warren, EPL 30, 191 (1995)

    Google Scholar 

  129. P. Español, M. Revenga, Phys. Rev. E 67, 026705 (2003)

    Google Scholar 

  130. K. Müller, D.A. Fedosov, G. Gompper, Med. Eng. Phys. 38, 2 (2016)

    PubMed  Google Scholar 

  131. C.K. Aidun, J.R. Clausen, Annu. Rev. Fluid Mech. 42, 439 (2009)

    Google Scholar 

  132. C.K. Aidun, Y. Lu, J. Stat. Phys. 81, 49 (1995)

    Google Scholar 

  133. C.K. Aidun, Y. Lu, E.J. Ding, J. Fluid Mech. 373, 287 (1998)

    CAS  Google Scholar 

  134. D.A. Fedosov, B. Caswell, G.E. Karniadakis, Biophys. J. 98, 2215 (2010)

    CAS  PubMed  PubMed Central  Google Scholar 

  135. I.V. Pivkin, G.E. Karniadakis, Phys. Rev. Lett. 101, 118105 (2008)

    PubMed  Google Scholar 

  136. Z. Liu, J.R. Clausen, R.R. Rao, C.K. Aidun, J. Fluid Mech. 871, 636 (2019)

    CAS  Google Scholar 

  137. H. Ye, Z. Shen, Y. Li, Comput. Mech. 62, 457 (2018)

    Google Scholar 

  138. S. Plimpton, J. Comput. Phys. 117, 1 (1995)

    CAS  Google Scholar 

  139. H. Cabral, Y. Matsumoto, K. Mizuno, Q. Chen, M. Murakami, M. Kimura, Y. Terada, M.R. Kano, K. Miyazono, M. Uesaka, N. Nishiyama, K. Kataoka, Nat. Nanotechnol. 6, 815 (2011)

    CAS  PubMed  Google Scholar 

  140. S.D. Perrault, C. Walkey, T. Jennings, H.C. Fischer, W.C.W. Chan, Nano Lett. 9, 1909 (2009)

    CAS  PubMed  Google Scholar 

  141. M. Ferrari, Nat. Rev. Cancer 5, 161 (2005)

    CAS  PubMed  Google Scholar 

  142. E. Blanco, A. Hsiao, A.P. Mann, M.G. Landry, F. Meric-Bernstam, M. Ferrari, Cancer Sci. 102, 1247 (2011)

    CAS  PubMed  Google Scholar 

  143. J.L. McWhirter, H. Noguchi, G. Gompper, Proc. Natl. Acad. Sci. U.S.A. 106, 6039 (2009)

    CAS  PubMed  PubMed Central  Google Scholar 

  144. R. Skalak, P.I. Branemark, Science 164, 717 (1969)

    CAS  PubMed  Google Scholar 

  145. N.R. Stillman, M. Kovacevic, I. Balaz, S. Hauert, Npj Comput Mater 6, 92 (2020)

    CAS  Google Scholar 

  146. J.A. Weis, M.I. Miga, L.R. Arlinghaus, X. Li, V. Abramson, A.B. Chakravarthy, P. Pendyala, T.E. Yankeelov, Cancer Res. 75, 4697 (2015)

    CAS  PubMed  PubMed Central  Google Scholar 

  147. P. Macklin, M.E. Edgerton, A.M. Thompson, V. Cristini, J. Theor. Biol. 301, 122 (2012)

    PubMed  PubMed Central  Google Scholar 

  148. J. Borgdorff, M. Mamonski, B. Bosak, K. Kurowski, M.B. Belgacem, B. Chopard, D. Groen, P.V. Coveney, A.G. Hoekstra, J. Comput. Sci. 5, 719 (2014)

    Google Scholar 

  149. D. Tartarini, K. Duan, N. Gruel, D. Testi, D. Walker and M. Viceconti, The vph hypermodelling framework for cancer multiscale models in the clinical practice. In: Proceedings of the 2014 6th international advanced research workshop on in silico oncology and cancer investigation—The CHIC project workshop (IARWISOCI), IEEE Xplore, Athens, Greece, pp 1–4 (2014)

  150. K. Wolstencroft, R. Haines, D. Fellows, A. Williams, D. Withers, S. Owen, S. Soiland-Reyes, I. Dunlop, A. Nenadic, P. Fisher, J. Bhagat, Nucleic Acids Res. 41, 557 (2013)

    Google Scholar 

  151. C. Chen, Z. Yaari, E. Apfelbaum, P. Grodzinski, Y. Shamay, D.A. Heller, Adv. Drug Deliv. Rev. 183, 114172 (2022)

    CAS  PubMed  PubMed Central  Google Scholar 

  152. Y.K. Wan, C. Hendra, P.N. Pratanwanich, J. Göke, Trends Genet. 38, 246 (2022)

    CAS  PubMed  Google Scholar 

Download references

Acknowledgements

Seyedeh-Saba Ashrafmansouri thanks the University of Larestan for their support. Mohsen Nasr Esfahany acknowledges the Isfahan University of Technology, and Seyedeh-Samira Ashrafmansouri thanks Shiraz University.

Author information

Authors and Affiliations

  1. Department of Chemical Engineering, University of Larestan, Lar, 7431813115, Iran

    Seyedeh-Saba Ashrafmansouri

  2. Department of Chemical Engineering, Isfahan University of Technology, Isfahan, 8415683111, Iran

    Mohsen Nasr Esfahany

  3. Department of Biology, School of Science, Shiraz University, Shiraz, 7146713565, Iran

    Seyedeh-Samira Ashrafmansouri

Authors
  1. Seyedeh-Saba Ashrafmansouri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohsen Nasr Esfahany
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Seyedeh-Samira Ashrafmansouri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Seyedeh-Saba Ashrafmansouri.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ashrafmansouri, SS., Nasr Esfahany, M. & Ashrafmansouri, SS. Mathematical Modeling of Micro-/Nanoparticles Transport in Blood Vessels: A Review. Korean J. Chem. Eng. 41, 1273–1305 (2024). https://doi.org/10.1007/s11814-024-00071-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11814-024-00071-y

Keywords

Search

Navigation