Skip to main content

Advertisement

Springer Nature Link
Log in

Multi-scale study of nanoparticle transport and deposition in tissues during an injection process

  • Original Article
  • Published:
Medical & Biological Engineering & Computing Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

In magnetic nanoparticle hyperthermia for cancer treatment, controlling the nanoparticle distribution delivered in tumors is vital for achieving an optimum distribution of temperature elevations that enables a maximum damage of the tumorous cells while minimizing the heating in the surrounding healthy tissues. A multi-scale model is developed in this study to investigate the spatial distribution of nanoparticles in tissues after nanofluid injection into the extracellular space of tissues. The theoretical study consists of a particle trajectory tracking model that considers particle–surface interactions and a macroscale model for the transport of nanoparticles in the carrier solution in a porous structure. Simulations are performed to examine the effects of a variety of injection parameters and particle properties on the particle distribution in tissues. The results show that particle deposition on the cellular structure is the dominant mechanism that leads to a non-uniform particle distribution. The particle penetration depth is sensitive to the injection rate and surface properties of the particles, but relatively insensitive to the injected volume and concentration of the nanofluid.

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
$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.

Institutional subscriptions

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

Similar content being viewed by others

References

  1. Adomeit P, Renz U (2000) Correlation for the particle deposition rate accounting for lift forces and hydrodynamic mobility reduction. Can J Chem Eng 78:32–39

    Article  CAS  Google Scholar 

  2. Bobo RH, Laske DW, Akbasak A, Morrison PF, Dedrick RL, Oldfield EH (1994) Convection-enhanced delivery of macromolecules in the brain. Proc Natl Acad Sci USA 91(6):2076–2080

    Article  CAS  PubMed  Google Scholar 

  3. Chen ZJ, Broaddus WC, Viswanathan RR, Raghavan R, Gillies GT (2002) Intraparenchymal drug delivery via positive-pressure infusion: experimental and modeling studies of poroelasticity in brain phantom gels. IEEE Trans Biomed Eng 49(2):85–96

    Article  PubMed  Google Scholar 

  4. Cox RG, Hsu SK (1977) The lateral migration of solid particles in a laminar flow near a plane. Int J Multiph Flow 3(3):201–222

    Article  CAS  Google Scholar 

  5. D’Ambrosio V, Dughiero F (2007) Numerical model for RF capacitive regional deep hyperthermia in pelvic tumors. Med Biol Eng Comput 45(5):459–466

    Article  PubMed  Google Scholar 

  6. Dillehay LE (1997) Decreasing resistance during fast infusion of a subcutaneous tumor. Anticancer Res 17(1A):461–466

    CAS  PubMed  Google Scholar 

  7. Dughiero F, Corazza S (2005) Numerical simulation of thermal disposition with induction heating used for oncological hyperthermic treatment. Med Biol Eng Comput 43(1):40–46

    Article  CAS  PubMed  Google Scholar 

  8. Gilchrist RK, Medal R, Shorey WD, Hanselman RC, Parrott JC, Taylor CB (1957) Selective inductive heating of lymph nodes. Ann Surg 146(4):596–606

    Article  CAS  PubMed  Google Scholar 

  9. Goodman TT, Chen J, Matveev K, Pun SH (2008) Spatio-temporal modeling of nanoparticle delivery to multicellular tumor spheroids. Biotechnol Bioeng 101(2):388–399

    Article  CAS  PubMed  Google Scholar 

  10. Guy Y, Sandberg M, Weber SG (2008) Determination of ζ-potential in rat organotypic hippocampal cultures. Biophys J 94(11):4561–4569

    Article  CAS  PubMed  Google Scholar 

  11. Happel J (1958) Viscous flow in multiparticle systems: slow motion of fluids relative to beds of spherical particles. AIChE J 4:197–201

    Article  CAS  Google Scholar 

  12. Hilger I, Andra W, Hergt R, Hiergeist R, Schubert H, Kaiser WA (2001) Electromagnetic heating of breast tumors in interventional radiology: in vitro and in vivo studies in human cadavers and mice. Radiology 218(2):570–575

    CAS  PubMed  Google Scholar 

  13. Hilger I, Hergt R, Kaiser WA (2005) Towards breast cancer treatment by magnetic heating. J Magn Magn Mater 293(1):314–319

    Article  CAS  Google Scholar 

  14. Israelachvili JN (1991) Intermolecular and surface forces. Academic Press, London

    Google Scholar 

  15. Jackson GW, James DF (1986) The permeability of fibrous porous media. Can J Chem Eng 64:364–374

    Article  CAS  Google Scholar 

  16. Jain RK (1997) Delivery of molecular and cellular medicine to solid tumors. Adv Drug Deliv Rev 26(2–3):71–90

    Article  CAS  PubMed  Google Scholar 

  17. Johnson R (1998) The handbook of fluid dynamics. CRC Press, Boca Raton, pp 18-29–18-32

  18. Jordan A, Scholz R, Maier-Hauff K, van Landeghem FKH, Waldoefner N, Teichgraeber U, Pinkernelle J, Bruhn H, Neumann F, Thiesen B, von Deimling A, Felix R (2006) The effect of thermotherapy using magnetic nanoparticles on rat malignant glioma. J Neuro-Oncol 78(1):7–14

    Article  CAS  Google Scholar 

  19. Khaled A-RA, Vafai K (2003) The role of porous media in modeling flow and heat transfer in biological tissues. Int J Heat Mass Transf 46(26):4989–5003

    Article  Google Scholar 

  20. Kloeden PE, Platen E (1992) Numerical solution of stochastic differential equations. Springer, Berlin, pp 110–154

    Google Scholar 

  21. Lazaro FJ, Abadia AR, Romero MS, Gutierrez L, Lazaro J, Morales MP (2005) Magnetic characterisation of rat muscle tissues after subcutaneous iron dextran injection. Biochim Biophys Acta Mol Basis Dis 1740(3):434–445

    CAS  Google Scholar 

  22. Maniero R, Canu P (2006) A model of fine particles deposition on smooth surfaces: I—theoretical basis and model development. Chem Eng Sci 61(23):7626–7635

    Article  CAS  Google Scholar 

  23. Matas JP, Morris JF, Guazzelli E (2004) Lateral forces on a sphere. Oil Gas Sci Technol – Rev Inst Fr Pet 59(1):59–70

    Article  Google Scholar 

  24. Matsuki H, Yanada T, Sato T, Murakami K, Minakawa S (1994) Temperature-sensitive amorphous magnetic flakes for intratissue hyperthermia. Mater Sci Eng A181(182):1366–1368

    Google Scholar 

  25. McGuire S, Yuan F (2001) Quantitative analysis of intratumoral infusion of color molecules. Am J Physiol Heart Circ Physiol 281(2):H715–H721

    CAS  PubMed  Google Scholar 

  26. McGuire S, Zaharoff D, Yuan F (2006) Nonlinear dependence of hydraulic conductivity on tissue deformation during intratumoral infusion. Ann Biomed Eng 34(7):1173–1181

    Article  PubMed  Google Scholar 

  27. Moroz P, Jones SK, Gray BN (2002) Magnetically mediated hyperthermia: current status and future directions. Int J Hyperth 18(4):267–284

    Article  CAS  Google Scholar 

  28. Morrison PF, Laske DW, Bobo H, Oldfield EH, Dedrick RL (1994) High-flow microinfusion: tissue penetration and pharmacodynamics. Am J Physiol Regul Integr Comp Physiol 266:R292–R305

    CAS  Google Scholar 

  29. Morrison PF, Chen MY, Chadwick RS, Lonser RR, Oldfield EH (1999) Focal delivery during direct infusion to brain: role of flow rate, catheter diameter, and tissue mechanics. Am J Physiol Regul Integr Comp Physiol 277(4):R1218–R1229

    CAS  Google Scholar 

  30. Nelson KE, Ginn TR (2005) Colloid filtration theory and the Happel sphere-in-cell model revisited with direct numerical simulation of colloids. Langmuir 21(6):2173–2184

    Article  CAS  PubMed  Google Scholar 

  31. Netti PA, Berk DA, Swartz MA, Grodzinsky AJ, Jain RK (2000) Role of extracellular matrix assembly in interstitial transport in solid tumors. Cancer Res 60(9):2497–2503

    CAS  PubMed  Google Scholar 

  32. Rajagopalan R, Tien C (1976) Trajectory analysis of deep-bed filtration with sphere-in-cell porous media model. AIChE J 22(3):523–533

    Article  CAS  Google Scholar 

  33. Ramanujan S, Pluen A, McKee TD, Brown EB, Boucher Y, Jain RK (2002) Diffusion and convection in collagen gels: implications for transport in the tumor interstitium. Biophys J 83(3):1650–1660

    Article  CAS  PubMed  Google Scholar 

  34. Ramarao BV, Tien C, Mohan S (1994) Calculations of single fiber efficiencies for interception and impaction with superposed Brownian motion. J Aerosol Sci 25(2):295–313

    Article  CAS  Google Scholar 

  35. Russel W, Saville AD, Schowalter W (1989) Colloidal dispersions. Cambridge University Press, UK

    Google Scholar 

  36. Saffman PG (1965) The lift on a small sphere in a slow shear flow. J Fluid Mech Digit Arch 22:385–400

    Google Scholar 

  37. Salloum M, Ma RH, Weeks D, Zhu L (2008) Controlling nanoparticle delivery in magnetic nanoparticle hyperthermia for cancer treatment: experimental study in agarose gel. Int J Hyperth 24(4):337–345

    Article  CAS  Google Scholar 

  38. Salloum M, Ma RH, Zhu L (2008) An in vivo experimental study of temperature elevations in animal tissue during magnetic nanoparticle hyperthermia. Int J Hyperth 24(7):589–601

    Article  CAS  Google Scholar 

  39. Salloum M, Ma RH, Zhu L (2009) Enhancement in treatment planning for magnetic nanoparticle hyperthermia: optimization of the heat absorption pattern. Int J Hyperth 25(4):309–321

    Article  CAS  Google Scholar 

  40. Satterfield CN (1970) Mass transport in heterogeneous catalysis. MIT Press, Cambridge

    Google Scholar 

  41. Swartz MA, Fleury ME (2007) Interstitial flow and its effects in soft tissues. Annu Rev Biomed Eng 9:229–256

    Article  CAS  PubMed  Google Scholar 

  42. Teixeira CA, Ruano AE, Ruano MG, Pereira WC, Negreira C (2006) Non-invasive temperature prediction of in vitro therapeutic ultrasound signals using neural networks. Med Biol Eng Comput 44(1–2):111–116

    Article  CAS  PubMed  Google Scholar 

  43. Tien C, Ramarao BV (2007) Granular filtration of aerosols and hydrosols, 2nd edn. Elsevier, Oxford

    Google Scholar 

  44. Tong M (2006) Colloid transport in porous media and impinging jet systems: experiments versus theory. PhD thesis, University of Utah

  45. Tufenkji N, Elimelech M (2004) Correlation equation for predicting single-collector efficiency in physicochemical filtration in saturated porous media. Env Sci Technol 38(2):529–536

    Article  CAS  Google Scholar 

  46. Unni HN, Yang C (2005) Brownian dynamics simulation and experimental study of colloidal particle deposition in a microchannel flow. J Colloid Interface Sci 291(1):28–36

    Article  CAS  PubMed  Google Scholar 

  47. Wang Y, Wang H, Li CY, Yuan F (2006) Effects of rate, volume, and dose of intratumoral infusion on virus dissemination in local gene delivery. Mol Cancer Ther 5(2):362–366

    Article  CAS  PubMed  Google Scholar 

  48. Warszynski P (2000) Coupling of hydrodynamic and electric interactions in adsorption of colloidal particles. Adv Colloid Interface Sci 84(1–3):47–142

    Article  CAS  PubMed  Google Scholar 

  49. Zhang XY, Luck J, Dewhirst MW, Yuan F (2000) Interstitial hydraulic conductivity in a fibrosarcoma. Am J Physiol Heart Circul Physiol 279(6):H2726–H2734

    CAS  Google Scholar 

  50. Zhang A, Mi X, Yang G, Xu LX (2009) Numerical study of thermally targeted liposomal drug delivery in tumor. J Heat Transf 131(4): 043209-1-10

    Google Scholar 

Download references

Acknowledgments

This research was supported by an NSF grant CBET-0730732, CBET-0828728, and a UMBC DRIF grant.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Maryland, Baltimore County, Baltimore, MD, 21250, USA

    Di Su, Ronghui Ma & Liang Zhu

  2. Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD, 21218, USA

    Maher Salloum

Authors
  1. Di Su
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ronghui Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Maher Salloum
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Liang Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ronghui Ma.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (DOC 56 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Su, D., Ma, R., Salloum, M. et al. Multi-scale study of nanoparticle transport and deposition in tissues during an injection process. Med Biol Eng Comput 48, 853–863 (2010). https://doi.org/10.1007/s11517-010-0615-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11517-010-0615-0

Keywords