Skip to main content
SpringerLink
Log in

Numerical Investigation of Magnetic Nanoparticles Distribution Inside a Cylindrical Porous Tumor Considering the Influences of Interstitial Fluid Flow

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

A numerical simulation of interstitial fluid flow and blood flow and diffusion of magnetic nanoparticles (MNPs) are developed, based on the governing equations for the fluid flow, i.e., the continuity and momentum and mass diffusion equations, to a tissue containing two-dimensional cylindrical tumor. The tumor is assumed to be rigid porous media with a necrotic core, interstitial fluid and two capillaries with arterial pressure input and venous pressure output. Blood flow through the capillaries and interstitial fluid flow in tumor tissues are carried by extended Poiseuille’s law and Darcy’s law, respectively. Transvascular flows are also described using Starling’s law. MNPs diffuse by interstitial fluid flow in tumor. The finite difference method has been used to simulate interstitial fluid pressure and velocity, blood pressure and velocity and diffusion of MNPs injected inside a biological tissue during magnetic fluid hyperthermia (MFH). Results show that the interstitial pressure has a maximum value at the center of the tumor and decreases toward the first capillary. The reduction continues between two capillaries, and interstitial pressure finally decreases in direction of the tumor perimeter. This study also shows that decreasing in intercapillary distance may cause a decrease in interstitial pressure. Furthermore, multi-site injection of nanoparticles has better effect on MFH.

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

Access this article

Log in via an institution

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
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31
Fig. 32
Fig. 33

Similar content being viewed by others

References

  • Attaluri, A., Ma, R., Qiu, Y., Li, W., Zhu, L.: Nanoparticle distribution and temperature elevations in prostatic tumours in mice during magnetic nanoparticle hyperthermia. Int. J. Hyperth. 27, 491–502 (2011)

    Article  Google Scholar 

  • Attar, M.M., Haghpanahi, M., Amanpour, S., Mohaqeq, M.: Analysis of bioheat transfer equation for hyperthermia cancer treatment. J. Mech. Sci. Technol. 28, 763–771 (2014)

    Article  Google Scholar 

  • Baish, J.W., Netti, P.A., Jain, R.K.: Transmural coupling of fluid flow in microcirculatory network and interstitium in tumors. Microvasc. Res. 53, 128–141 (1997)

    Article  Google Scholar 

  • Baxter, L.T., Jain, R.K.: Transport of fluid and macromolecules in tumors (II): role of heterogeneous perfusion and lymphatics. Microvasc. Res. 40, 246–263 (1990)

    Article  Google Scholar 

  • Baxter, L.T., Jain, R.K.: Transport of fluid and macromolecules in tumors (III): role of binding and metabolism. Microvasc. Res. 4, 15–23 (1991a)

    Google Scholar 

  • Baxter, L.T., Jain, R.K.: Transport of fluid and macromolecules in tumors IV: a microscopic model of the perivascular distribution. Microvasc. Res. 41, 252–272 (1991b)

    Article  Google Scholar 

  • Bear, J.: Dynamics of Fluids in Porous Media. Dover Publications, New York (1988)

    Google Scholar 

  • Charjouei Moghadam, M., Deyranlou, A., Sharifi, A., Niazmand, H.: Numerical simulation of the tumor interstitial fluid transport: consideration of drug delivery mechanism. Microvasc. Res. 101, 62–71 (2015)

    Article  Google Scholar 

  • Di Michele, F., Pizzichelli, G., Mazzolai, B., Sinibaldi, E.: On the preliminary design of hyperthermia treatments based on infusion and heating of magnetic nanofluids. Math. Biosci. 262, 105–116 (2015)

    Article  Google Scholar 

  • Goldacre, R.J., Sylven, B.: On the access of blood-borne dyes to various tumor regions. Br. J. Cancer 16, 306–322 (1962)

    Article  Google Scholar 

  • Golneshan, A.A., Lahonian, M.: Diffusion of magnetic nanoparticles in a multi-site injection process within a biological tissue during magnetic fluid hyperthermia using lattice Boltzmann method. Mech. Res. Commun. 38, 425–430 (2011)

    Article  Google Scholar 

  • Hassanpour, S., Saboonchi, A.: Interstitial hyperthermia treatment of countercurrent vascular tissue: a comparison of Pennes, WJ and porous media bioheat models. J. Therm. Biol. 46, 47–55 (2014)

    Article  Google Scholar 

  • Jain, R.K.: Determinants of tumor blood flow: a review. Cancer Res. 48, 2641–2658 (1988a)

    Google Scholar 

  • Jain, R.K., Baxter, L.T.: Mechanisms of heterogeneous distribution of monoclonal antibodies and other macromolecules in tumors: significance of elevated interstitial pressure. Cancer Res. 48, 7022–7032 (1988)

    Google Scholar 

  • Jain, R.K., Hartley, K.W.: Tumor blood flow-characterization, modifications, and role in hyperthermia. IEEE Trans. Sonics Ultrason. 31, 504–525 (1984)

    Article  Google Scholar 

  • Lin, ChT, Liu, KCh.: Estimation for the heating effect of magnetic nanoparticles in perfused tissues. Int. Commun. Heat Mass Transf. 36, 241–244 (2009)

    Article  Google Scholar 

  • Maenosono, S., Saita, S.: Theoretical assessment of FePt nanoparticles as heating elements for magnetic hyperthermia. IEEE Trans. Magn. 42, 1638–1642 (2006)

    Article  Google Scholar 

  • Matsuki, H., Yanada, T.: Temperature sensitive amorphous magnetic flakes for intra-tissue hyperthermia. Mater. Sci. Eng. A 181–182, 1366–1368 (1994)

    Article  Google Scholar 

  • McDougall, S.R., Anderson, A.R.A., Chaplain, M.A.J., Sherratt, J.A.: Mathematical modeling of flow through vascular network: implications for tumor-induced angiogenesis and chemotherapy strategies. Bull. Math. Biol. 64, 673–702 (2002)

    Article  Google Scholar 

  • Nabil, M., Decuzzi, P., Zuninol, P.: Modelling mass and heat transfer in nano-based cancer hyperthermia. R. Soc. Open Sci. 2, 150447 (2015)

    Article  Google Scholar 

  • Netti, P.A., Baxter, L.T., Boucher, Y., Skalak, R., Jain, R.K.: Time-dependent behavior of interstitial fluid pressure in solid tumors: implication for drug delivery. Cancer Res. 55, 5451–5458 (1995)

    Google Scholar 

  • Nicholson, C.: Diffusion and related transport mechanism in brain tissue. Rep. Prog. Phys. 64, 815–884 (2001)

    Article  Google Scholar 

  • Pozrikidis, C.: Numerical simulation of blood and interstitial flow through a solid tumor. J. Math. Biol. 60, 75–94 (2010)

    Article  Google Scholar 

  • Pozrikidis, C., Farrow, D.A.: A model of fluid flow in solid tumors. Ann. Biomed. Eng. 31, 181–194 (2003)

    Article  Google Scholar 

  • Robinson, J.E., Wizenberg, M.J., Mccready, W.A.: Combined hyperthermia and radiation, an alternative to heavy particle therapy for reduced oxygen enhancement ratios. Nature 251, 521–522 (1974)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Saltzman, W.M., Radomsky, M.L.: Drugs released from polymers: diffusion and elimination in brain tissue. Chem. Eng. Sci. 46, 2429–2444 (1991)

    Article  Google Scholar 

  • Sefidgar, M., Soltani, M., Raahemifar, K., Bazmara, H.: Effect of fluid friction on interstitial fluid flow coupled with blood flow through solid tumor microvascular network. Comput. Math. Methods Med. (2015). doi:10.1155/2015/673426

    Google Scholar 

  • Sefidgar, M., Soltani, M., Raahemifar, K., Sadeghi, M., Bazmara, H., Bazargan, M., Mousavi Naeenian, M.: Numerical modeling of drug delivery in a dynamic solid tumor microvasculature. Microvasc. Res. 99, 43–56 (2015b)

    Article  Google Scholar 

  • Sefidgar, M., Soltani, M., Raahemifar, K., Bazmara, H., Nayinian, S.M.M., Bazargan, M.: Effect of tumor shape, size, and tissue transport properties on drug delivery to solid tumors. J. Biol. Eng. 8, 1 (2014)

    Article  Google Scholar 

  • Soltani, M., Chen, P.: Effect of tumor shape and size on drug delivery to solid tumors. J. Biol. Eng. 6, 1 (2012)

    Article  Google Scholar 

  • Soltani, M., Chen, P.: Numerical modeling of fluid flow in solid tumors. PLoS One 6, e20344 (2011)

    Article  Google Scholar 

  • Steeves, R.A.: Hyperthermia in cancer therapy: where are we today and where are we going? Bull. N.Y. Acad. Med. 68, 342–350 (1992)

    Google Scholar 

  • Stohrer, M., Boucher, Y., Stangassinger, M., Jain, R.K.: Oncotic pressure in solid tumors is elevated. Cancer Res. 60, 4251–4255 (2000)

    Google Scholar 

  • Vallooran, J.J., Negrini, R., Mezzenga, R.: Controlling anisotropic drug diffusion in lipid-Fe\(_{3}\)O\(_{4}\) nanoparticle hybrid mesophases by magnetic alignment. Langmuir 29, 999–1004 (2013)

    Article  Google Scholar 

  • Wang, C.H., Li, J.: Three dimensional simulation of IgG delivery to tumors. Chem. Eng. Sci. 53, 3579–3600 (1998)

    Article  Google Scholar 

  • Wang, C.H., Li, J., Teo, C.S., Lee, T.: The delivery of BCNU to brain tumors. J. Control. Release 61, 21–41 (1999)

    Article  Google Scholar 

  • Welter, M., Rieger, H.: Interstitial fluid flow and drug delivery in vascularized tumors: a computational model. PLoS One 8, e70395 (2013)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, K.N.T. University of Technology, Pardis Street, Tehran, Iran

    Mostafa Zakariapour & Mohammad Hossein Hamedi

  2. Department of Biomedical Engineering, Amirkabir University of Technology, Hafez Street, Tehran, Iran

    Nasser Fatouraee

Authors
  1. Mostafa Zakariapour
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohammad Hossein Hamedi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nasser Fatouraee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mostafa Zakariapour.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zakariapour, M., Hamedi, M.H. & Fatouraee, N. Numerical Investigation of Magnetic Nanoparticles Distribution Inside a Cylindrical Porous Tumor Considering the Influences of Interstitial Fluid Flow. Transp Porous Med 116, 251–274 (2017). https://doi.org/10.1007/s11242-016-0772-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11242-016-0772-1

Keywords

Search

Navigation