Abstract
Magnetic driven targeted drug delivery (TDD) involves the manipulation of magnetic drug carriers, such as nano/micro particles or bubbles, within the body using external magnetic fields to precisely reach the intended target location. This method is utilized in treating severe illnesses like cancerous tumors and nervous disorders, offering higher efficacy with reduced drug dosages and side effects. While numerous studies have simulated magnetic driven TDD, comprehensive reviews remain scarce. This article presents an extensive review of computational/numerical work done on magnetic driven TDD utilizing both microbubbles and non-bubbles (nano/micro particles) within human vasculature and lung airways. The study aims to analyze the drug delivery problem from physical and numerical perspectives. Key highlights include artery wall models (rigid, flexible, or porous), models of force acting on particles, relevant governing equations, discussions on parameters of interest and their effects on drug delivery efficacy. Finally, the article briefly outlines common trends observed in magnetic driven TDD problems and their underlying physical principles.
Similar content being viewed by others
Data availability
The authors confirm that the data supporting the findings of this study are available within the article itself and its supplementary materials.
Notes
Magnetic number: A non-dimensional number that is proportional to magnetic field strength.
CE is the fraction of the number of particles that get captured in the region of interest with respect to the total number of injected particles.
Targeting efficiency is defined as the fraction of the inlet particles that got captured in the target region with respect to the number of particles released at the inlet.
A drug elimination parameter represents an irrevocable body mechanism that removes administered drugs from it.
The MFF comprised a combination of positive and negative pulsed magnetic fields generated by electromagnetic coils. The purpose of the MFF was to prevent nanoparticles from adhering to the vessel walls during magnetic guidance.
References
Elghobashi S (1994) On predicting particle-laden turbulent flows. Appl Sci Res 52:309–329
Sommerfeld M (2000) Theoretical and experimental modeling of particulate flow. VKI lecture series 2000-06
Elghobashi S, Truesdell G (1992) Direct simulation of particle dispersion in a decaying isotropic turbulence. J Fluid Mech 242:655–700
Turton R, Levenspiel O (1986) A short note on the drag correlation for spheres. Powder Technol 47(1):83–86
Haik Y, Pai CJC V (1999) Biomagnetic fluid dynamics, fluid dynamics at interfaces, pp 439–452
Bernad SI, Bernad E (2022) Magnetic forces by permanent magnets to manipulate magnetoresponsive particles in drug-targeting applications. Micromachines 13(11):1818
Lunnoo T, Puangmali T (2015) Capture efficiency of biocompatible magnetic nanoparticles in arterial flow: a computer simulation for magnetic drug targeting. Nanoscale Res Lett 10:1–11
Ounis H, Ahmadi G, McLaughlin JB (1991) Brownian diffusion of submicrometer particles in the viscous sublayer. J Colloid Interface Sci 143(1):266–277
Crowe CT, Schwarzkopf JD, Sommerfeld M, Tsuji Y (2011) Multiphase Flows with Droplets and Particles. CRC Press, Boca Raton
Saffman PG (1965) The lift on a small sphere in a slow shear flow. J Fluid Mech 22(2):385–400
Shamloo A, Amani A, Forouzandehmehr M, Ghoytasi I (2019) In silico study of patient-specific magnetic drug targeting for a coronary lad atherosclerotic plaque. Int J Pharm 559:113–129
Karimi A, Navidbakhsh M, Shojaei A, Hassani K, Faghihi S (2014) Study of plaque vulnerability in coronary artery using Mooney–Rivlin model: a combination of finite element and experimental method. Biomed Eng Appl Basis Commun 26(01):1450013
Morega A, Dobre A, Morega M (2011) Magnetic field-flow interactions in drug delivery through an arterial system. Rev Roumaine des Sci Tech Electrotech Energetique 56:199–208
Bangash MYH, Al-Obaid Y, Bangash F, Bangash T (2007) Trauma—an engineering analysis: with medical case studies investigation. Springer, Berlin
Zhang X, Luo M, Wang E, Zheng L, Shu C (2020) Numerical simulation of magnetic nano drug targeting to atherosclerosis: effect of plaque morphology (stenosis degree and shoulder length). Comput Methods Programs Biomed 195:105556
Alimohamadi H, Imani M (2014) Transient non-Newtonian blood flow under magnetic targeting drug delivery in an aneurysm blood vessel with porous walls. Int J Comput Methods Eng Sci Mech 15(6):522–533
Tiwari A, Chauhan SS (2019) Effect of varying viscosity on two-fluid model of pulsatile blood flow through porous blood vessels: a comparative study. Microvasc Res 123:99–110
Ochoa-Tapia JA, Whitaker S (1995) Momentum transfer at the boundary between a porous medium and a homogeneous fluid—I. Theoretical development. Int J Heat Mass Transf 38(14):2635–2646
Srivastava A, Srivastava N (2005) Flow past a porous sphere at small reynolds number. Zeitschrift für angewandte Mathematik und Physik ZAMP 56:821–835
Merrill E, Benis A, Gilliland E, Sherwood T, Salzman E (1965) Pressure-flow relations of human blood in hollow fibers at low flow rates. J Appl Physiol 20(5):954–967
Kim S (2002) A study of non-Newtonian viscosity and yield stress of blood in a scanning capillary-tube rheometer. Drexel University, Philadelphia, PA 19104, United States
Baskurt OK, Meiselman HJ (2003) Blood rheology and hemodynamics. In: Seminars in thrombosis and hemostasis, vol 29, pp. 435–450. Copyright 2003 by Thieme Medical Publishers, Inc., 333 Seventh Avenue, New
Johnston BM, Johnston PR, Corney S, Kilpatrick D (2004) Non-Newtonian blood flow in human right coronary arteries: steady state simulations. J Biomech 37(5):709–720
Ballyk P, Steinman D, Ethier C (1994) Simulation of non-Newtonian blood flow in an end-to-side anastomosis. Biorheology 31(5):565–586
Sodagar H, Sodagar-Abardeh J, Shakiba A, Niazmand H (2021) Numerical study of drug delivery through the 3D modeling of aortic arch in presence of a magnetic field. Biomech Model Mechanobiol 20:787–802
González HA, Moraga NO (2005) On predicting unsteady non-Newtonian blood flow. Appl Math Comput 170(2):909–923
Bose S, Banerjee M (2015) Effect of non-Newtonian characteristics of blood on magnetic particle capture in occluded blood vessel. J Magn Magn Mater 374:611–623
Tang HS, Kalyon DM (2004) Estimation of the parameters of Herschel–Bulkley fluid under wall slip using a combination of capillary and squeeze flow viscometers. Rheol Acta 43:80–88
Haghdel M, Kamali R, Haghdel A, Mansoori Z (2017) Effects of non-Newtonian properties of blood flow on magnetic nanoparticle targeted drug delivery. Nanomed J 4(2):1
Molla MM, Paul M (2012) Les of non-Newtonian physiological blood flow in a model of arterial stenosis. Med Eng Phys 34(8):1079–1087
Taylor M (1955) The flow of blood in narrow tubes. Aust J Exp Biol Med Sci 33(1):1
Phillips RJ, Armstrong RC, Brown RA, Graham AL, Abbott JR (1992) A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration. Phys Fluids A 4(1):30–40
Lin X, Zhang C, Li K (2015) Statistical mechanics transport model of magnetic drug targeting in permeable microvessel. J Nanotechnol Eng Med 6(1):011001
Badfar H, Yekani Motlagh S, Sharifi A (2020) Numerical simulation of magnetic drug targeting to the stenosis vessel using Fe\(_3\) O\(_4\) magnetic nanoparticles under the effect of magnetic field of wire. Cardiovasc Eng Technol 11:162–175
Ardalan A, Aminian S, Seyfaee A, Gharehkhani S (2021) Effects of geometrical parameters on the capture efficiency of nanoparticles under the influence of the magnetic field in a stenosed vessel. Powder Technol 380:39–46
Gul A, Tzirtzilakis EE, Makhanov SS (2022) Simulation of targeted magnetic drug delivery: Two-way coupled biomagnetic fluid dynamics approach. Phys Fluids 34(2):1
Kelly M, Yeoh GH, Timchenko V (2015) On computational fluid dynamics study of magnetic drug targeting. J Comput Multiphase Flows 7(1):43–56
Shaw S, Shit G, Tripathi D (2022) Impact of drug carrier shape, size, porosity and blood rheology on magnetic nanoparticle-based drug delivery in a microvessel. Colloids Surf A 639:128370
Salem S, Tuchin VV (2020) Trapping of magnetic nanoparticles in the blood stream under the influence of a magnetic field. News of Saratov University. New episode. Series: Physics 20(1):72–79
Mirzababaei S, Gorji TB, Baou M, Gorji-Bandpy M, Fatouraee N (2017) Investigation of magnetic nanoparticle targeting in a simplified model of small vessel aneurysm. J Magn Magn Mater 426:126–131
Pálovics P, Németh M, Rencz M (2020) Investigation and modeling of the magnetic nanoparticle aggregation with a two-phase CFD model. Energies 13(18):4871
Ndenda J, Shaw S, Njagarah J (2021) Solute dispersion of drug carrier during magnetic drug targeting for blood flow through a microvessel. J Appl Phys 130(2):1
Banerjee MK, Datta A, Ganguly R (2010) Magnetic drug targeting in partly occluded blood vessels using magnetic microspheres
Gómez-Pastora J, Karampelas IH, Xue X, Bringas E, Furlani EP, Ortiz I (2017) Magnetic bead separation from flowing blood in a two-phase continuous-flow magnetophoretic microdevice: theoretical analysis through computational fluid dynamics simulation. J Phys Chem C 121(13):7466–7477
Bernad SI, Susan-Resiga D, Vekas L, Bernad ES (2019) Drug targeting investigation in the critical region of the arterial bypass graft. J Magn Magn Mater 475:14–23
Ping G, Xin-Xia L, Ping X, Ji-Shan H (2009) Local magnetic nanoparticle delivery in microvasculature. Chin Phys Lett 26(1):018703
Kayal S, Bandyopadhyay D, Mandal TK, Ramanujan RV (2011) The flow of magnetic nanoparticles in magnetic drug targeting. RSC Adv 1(2):238–246
Shazri S, Idres M (2017) Numerical investigation of magnetic nanoparticles trajectories for magnetic drug targeting. In: IOP conference series: materials science and engineering, vol 184. IOP Publishing, p 012061
Babinec P, Krafčík A, Babincová M, Rosenecker J (2010) Dynamics of magnetic particles in cylindrical Halbach array: implications for magnetic cell separation and drug targeting. Med Biolog Eng Comput 48:745–753
Nacev A, Beni C, Bruno O, Shapiro B (2011) The behaviors of ferromagnetic nano-particles in and around blood vessels under applied magnetic fields. J Magn Magn Mater 323(6):651–668
Sulttan S, Rohani S (2023) Modeling and simulation of smart magnetic self-assembled nanomicelle trajectories in an internal thoracic artery flow for breast cancer therapy. Drug Del Transl Res 13(2):675–688
Sarraf SS, Saeidfar A, Navidbakhsh M, Islami SB (2021) Modeling and simulation of magnetic nanoparticles’ trajectories through a tumorous and healthy microvasculature. J Magn Magn Mater 537:168178
Mashiku LR, Shaw S (2023) Unsteady nano-magnetic drug dispersion for pulsatile Darcy flow through microvessel with drug elimination phenomena. Phys Fluids 35(10):1
Manshadi M, Mohammadi M, Sanati-Nezhad A (2018) Investigation of non-Newtonian blood effects on magnetic drug delivery for chemotherapy applications in an artery vessel. Anal Comput Theor Chem Lett 1:8–14
Varmazyar M, Habibi M, Amini M, Pordanjani AH, Afrand M, Vahedi SM (2020) Numerical simulation of magnetic nanoparticle-based drug delivery in presence of atherosclerotic plaques and under the effects of magnetic field. Powder Technol 366:164–174
Ndenda J, Shaw S, Njagarah J (2023) Shear induced fractionalized dispersion during magnetic drug targeting in a permeable microvessel. Colloids Surf B 221:113001
Gkountas AA, Polychronopoulos ND, Sofiadis GN, Karvelas EG, Spyrou LA, Sarris IE (2021) Simulation of magnetic nanoparticles crossing through a simplified blood–brain barrier model for glioblastoma multiforme treatment. Comput Methods Programs Biomed 212:106477
Gonella VC, Hanser F, Vorwerk J, Odenbach S, Baumgarten D (2021) Influence of local particle concentration gradient forces on the flow-mediated mass transport in a numerical model of magnetic drug targeting. J Magn Magn Mater 525:167490
Mahmoodpour M, Goharkhah M, Ashjaee M, Najafi M (2021) A three dimensional numerical investigation on trajectories and capture of magnetic drug carrier nanoparticles in a y-shaped vessel. J Drug Del Sci Technol 61:102207
Patronis A, Richardson RA, Schmieschek S, Wylie BJ, Nash RW, Coveney PV (2018) Modeling patient-specific magnetic drug targeting within the intracranial vasculature. Front Physiol 9:331
Liu C, Deng S, Zou S, Chen P, Liu Y (2022) Analysis and design of a new hybrid array for magnetic drug targeting. IEEE Trans Magn 58(3):1–11
Bernad SI, Totorean AF, Vekas L (2016) Particles deposition induced by the magnetic field in the coronary bypass graft model. J Magn Magn Mater 401:269–286
Cherry EM, Eaton JK (2014) A comprehensive model of magnetic particle motion during magnetic drug targeting. Int J Multiph Flow 59:173–185
Aryan H, Beigzadeh B, Siavashi M (2022) Euler–Lagrange numerical simulation of improved magnetic drug delivery in a three-dimensional CT-based carotid artery bifurcation. Comput Methods Programs Biomed 219:106778
Bose S, Datta A, Ganguly R, Banerjee M (2013) Lagrangian magnetic particle tracking through stenosed artery under pulsatile flow condition. J Nanotechnol Eng Med 4(3):031006
Karvelas E, Lampropoulos N, Karakasidis T, Sarris I (2022) Blood flow and diameter effect in the navigation process of magnetic nanocarriers inside the carotid artery. Comput Methods Programs Biomed 221:106916
Abu-Hamdeh NH, Bantan RA, Aalizadeh F, Alimoradi A (2020) Controlled drug delivery using the magnetic nanoparticles in non-Newtonian blood vessels. Alex Eng J 59(6):4049–4062
Hoshiar AK, Le T-A, Amin FU, Kim MO, Yoon J (2017) Studies of aggregated nanoparticles steering during magnetic-guided drug delivery in the blood vessels. J Magn Magn Mater 427:181–187
Gleich B, Hellwig N, Bridell H, Jurgons R, Seliger C, Alexiou C, Wolf B, Weyh T (2007) Design and evaluation of magnetic fields for nanoparticle drug targeting in cancer. IEEE Trans Nanotechnol 6(2):164–170
Bhatti M, Abdelsalam SI (2021) Bio-inspired peristaltic propulsion of hybrid nanofluid flow with tantalum (Ta) and gold (Au) nanoparticles under magnetic effects. Waves Random Complex Med 2021:1–26
Boutopoulos ID, Lampropoulos DS, Bourantas GC, Miller K, Loukopoulos VC (2020) Two-phase biofluid flow model for magnetic drug targeting. Symmetry 12(7):1083
Agiotis L, Theodorakos I, Samothrakitis S, Papazoglou S, Zergioti I, Raptis Y (2016) Magnetic manipulation of superparamagnetic nanoparticles in a microfluidic system for drug delivery applications. J Magn Magn Mater 401:956–964
Lampropoulos N, Karvelas E, Sarris IE (2015) Computational modeling of an MRI guided drug delivery system based on magnetic nanoparticle aggregations for the navigation of paramagnetic nanocapsules. Preprint arXiv:1504.03490
Reinelt M, Ahlfs J, Stein R, Alexiou C, Bänsch E, Friedrich RP, Lyer S, Neuss-Radu M, Neuß N (2023) Simulation and experimental validation of magnetic nanoparticle accumulation in a bloodstream mimicking flow system. J Magn Magn Mater 582:170984
Manshadi MK, Saadat M, Mohammadi M, Shamsi M, Dejam M, Kamali R, Sanati-Nezhad A (2018) Delivery of magnetic micro/nanoparticles and magnetic-based drug/cargo into arterial flow for targeted therapy. Drug Del 25(1):1963–1973
Majee S, Shit G (2020) Modeling and simulation of blood flow with magnetic nanoparticles as carrier for targeted drug delivery in the stenosed artery. Eur J Mech B/Fluids 83:42–57
Shojaee P, Niroomand-Oscuii H, Sefidgar M, Alinezhad L (2020) Effect of nanoparticle size, magnetic intensity, and tumor distance on the distribution of the magnetic nanoparticles in a heterogeneous tumor microenvironment. J Magn Magn Mater 498:166089
Tripathi J, Vasu B, Bég OA, Gorla RSR (2021) Unsteady hybrid nanoparticle-mediated magneto-hemodynamics and heat transfer through an overlapped stenotic artery: Biomedical drug delivery simulation. Proc Inst Mech Eng [H] 235(10):1175–1196
Hedayati N, Ramiar A, Larimi M (2018) Investigating the effect of external uniform magnetic field and temperature gradient on the uniformity of nanoparticles in drug delivery applications. J Mol Liq 272:301–312
Calandrini S, Capodaglio G, Aulisa E (2018) Magnetic drug targeting simulations in blood flows with fluid–structure interaction. Int J Numer Methods Biomed Eng 34(4):2954
Shamloo A, Ebrahimi S, Ghorbani G, Alishiri M (2022) Targeted drug delivery of magnetic microbubble for abdominal aortic aneurysm: an in silico study. Biomech Model Mech 21(2):735–753
Ostrovski Y, Hofemeier P, Sznitman J (2016) Augmenting regional and targeted delivery in the pulmonary acinus using magnetic particles. Int J Nanomed 2016:3385–3395
Nikookar H, Abouali O, Eghtesad M, Sadrizadeh S, Ahmadi G (2019) Enhancing drug delivery to human trachea through oral airway using magnetophoretic steering of microsphere carriers composed of aggregated superparamagnetic nanoparticles and nanomedicine: a numerical study. J Aerosol Sci 127:63–92
Manshadi MK, Saadat M, Mohammadi M, Kamali R, Shamsi M, Naseh M, Sanati-Nezhad A (2019) Magnetic aerosol drug targeting in lung cancer therapy using permanent magnet. Drug Del 26(1):120–128
Xie Y, Zeng P, Siegel RA, Wiedmann TS, Hammer BE, Longest PW (2010) Magnetic deposition of aerosols composed of aggregated superparamagnetic nanoparticles. Pharm Res 27:855–865
Li B, Feng Y (2022) In silico study to enhance delivery efficiency of charged nanoscale nasal spray aerosols to the olfactory region using external magnetic fields. Bioengineering 9(1):40
Pourmehran O, Rahimi-Gorji M, Gorji-Bandpy M, Gorji T (2015) Simulation of magnetic drug targeting through tracheobronchial airways in the presence of an external non-uniform magnetic field using Lagrangian magnetic particle tracking. J Magn Magn Mater 393:380–393
Mohammadian M, Pourmehran O (2019) CFPD simulation of magnetic drug delivery to a human lung using an saw nebulizer. Biomech Model Mechanobiol 18:547–562
Kenjereš S, Tjin JL (2017) Numerical simulations of targeted delivery of magnetic drug aerosols in the human upper and central respiratory system: A validation study. R Soc Open Sci 4(12):170873
Wu C, Yan W, Chen R, Liu Y, Li G (2022) Numerical study on targeted delivery of magnetic drug particles in realistic human lung. Powder Technol 397:116984
Cregg P, Murphy K, Mardinoglu A, Prina-Mello A (2010) Many particle magnetic dipole–dipole and hydrodynamic interactions in magnetizable stent assisted magnetic drug targeting. J Magn Magn Mater 322(15):2087–2094
Bose S, Datta A, Ganguly R, Banerjee M (2023) Implant assisted magnetic drug targetting for non-Newtonian blood flow
Vyas S, Genis V, Friedman G (2015) Computational study of kinematics of capture of magnetic particles by stent: 2-D model. IEEE Trans Magn 52(7):1–4
Cregg P, Murphy K, Mardinoglu A (2012) Inclusion of interactions in mathematical modelling of implant assisted magnetic drug targeting. Appl Math Model 36(1):1–34
Zhang C, Xia K, Xu K, Lin X, Jiang S, Wang C (2019) Two-phase fluid modeling of magnetic drug targeting in a permeable microvessel implanted with a toroidal permanent magnetic stent. J Fluids Eng 141(8):081301
Choomphon-anomakhun N, Natenapit M (2018) 3-D MDT with spherical targets by bilinear interpolation for determining blood velocity profiles including the vessel wall effect. J Magn Magn Mater 447:101–109
Hewlin RL Jr, Smith M, Kizito JP (2023) Computational assessment of unsteady flow effects on magnetic nanoparticle targeting efficiency in a magnetic stented carotid bifurcation artery. Cardiovasc Eng Technol 14(5):694–712
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
On behalf of all authors, the corresponding author states that there is no Conflict of interest.
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.
About this article
Cite this article
Tamboli, N.K., Murallidharan, J.S. Numerical Studies on Magnetic Driven Targeted Drug Delivery in Human Vasculature. J Indian Inst Sci (2024). https://doi.org/10.1007/s41745-024-00428-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s41745-024-00428-6