Numerical modeling of the effect of field configurations on the magnetic nanoparticle delivery

M.K. Ghantasala, P. Ikonomov, T. Rajh, A. David
Western Michigan University,
United States

Keywords: nanoparticle drug delivery, FEA modelling, COMSOL, blood velocity

Summary:

Numerical modeling of the effect of field configurations on the magnetic nanoparticle delivery Muralidhar K. Ghantasala1, Pavel Ikonomov2, Tijana Rajh#, and Allen David* 1Department of Mechanical and Aerospace Engineering,2 Department of Engineering Design, Manufacturing, and Management Systems, Western Michigan University, 1903, West Michigan Avenue, Kalamazoo, MI-49024, USA *Department of Chemical Engineering, Auburn University, Auburn, AL 36849 # Center for Nanoscale Materials, Argonne National Laboratory, 9700, S. Cass Ave, Argonne, IL – 60439 Abstract This paper presents the details of our studies on the numerical modeling of magnetic nanoparticle drug delivery using Ferrohydrodynamics based numerical models. The magnetic field and fluid flow were governed by Maxwell and the Navier-Stokes equations. At first, Maxwell’s equations were solved in the full modeling domain formed by permanent-magnet, blood-vessel, tissue, and air domains. Numerical analysis mainly utilized two sets of equations for magnetic field and fluid flow within COMSOL software. A magnetic volume force couples the resulting magnetic field to a fluid-flow problem in the blood-vessel domain described by the Navier-Stokes equations. The magnetic field generates magnetic volume forces that affect the flow field in the blood vessel. The fluid has the properties of blood (e.g. viscosity, flow rate and others) and magnetic characteristics of nanoparticles and hence becomes a ferrofluid. Further, fluid-dynamics analysis was performed by calculating the velocity field and pressure distribution of the blood (variable in time and in space). This helped in understanding the effect of variation of magnetic field distribution on the fluid velocity profiles. In specific, the magnetic field and the volume force will be more dominating in the region underneath the field, which affected fluid velocity. Interestingly, the velcoity will be high (0.4 to 0.45 m/sec depending on the applied field) in the middle of blood vessel whereas the blood velocity near the walls will be relatively low (0.1 m/sec). This has been correlated to the variation of magnetic flux density across the blood vessel diameter. Further analysis clearly showed that as magnetic field strength increased, the velocity decreased, which is in agreement with the analytical model. It also correlates well with the pressure variation along the length of the vessel especially underneath the magnetic field compared to outside. The pressure is found to be high (greater than 2000 Pa), right below the magnet, where a high velocity gradient is observed. Two different field configurations, with symmetric and asymmetric pole fields, were considered and the fluid velocities in different gradient fields were compared. It was observed that the fluid velocity in the electromagnet with symmetric pole faces (0.16 m/sec) is less than that seen in asymmetric configuration (0.2 m/sec). This shows the gradient field is better suitable than the symmetric field configuration, to generate higher particle velocities. The details of the simulation and the analysis of all the results are presented.