Magnetophoresis is an important physical process with application to drug delivery, biomedical imaging, separation, and mixing. Other than empirically, little is known about how the magnetic field and magnetic properties of a solution affect the flux of magnetic particles. A comprehensive explanation of these effects on the transport of magnetic particles has not been developed yet. Here we formulate a consistent, constitutive equation for the magnetophoretic flux of magnetic nanoparticles suspended in a medium exposed to a stationary magnetic field. The constitutive relationship accounts for contributions from magnetic diffusion, magnetic convection, residual magnetization, and electromagnetic drift. We discovered that the key physical properties governing the magnetophoresis are magnetic diffusion coefficient, magnetic velocity, and activity coefficient, which depend on relative magnetic energy and the molar magnetic susceptibility of particles. The constitutive equation also reveals previously unknown ballistic and diffusive limits for magnetophoresis wherein the paramagnetic particles either aggregate near the magnet or diffusive away from the magnet, respectively. In the diffusive limit, the particle concentration is linearly proportional to the relative magnetic energy of the suspension of paramagnetic particles. The region of the localization of paramagnetic particles near the magnet decreases with increasing the strength of the magnet. The dynamic accumulation of nanoparticles, measured as the thickness of the nanoparticle aggregate, near the magnet compares well with the theoretical prediction. The effect of convective mixing on the rate of magnetophoresis is also discussed for the magnetic targeting applications.

Background Traditionally, there is a widely held belief that drug dispersion after intrathecal (IT) delivery is confined to a small location near the injection site. We posit that high volume infusions can overcome this perceived limitation of IT administration. Methods To test our hypothesis, subject-specific deformable phantom models of the human central nervous system were manufactured so that tracer infusion could be realistically replicated in vitro over the entire physiological range of pulsating cerebrospinal fluid (CSF) amplitudes and frequencies. Dispersion of IT injected tracers was studied systematically with high-speed optical methods to determine the relative impact of injection parameters including infusion volume, flow rate and catheter configurations and natural CSF oscillations. Results Optical imaging analysis of high-volume infusion experiments showed that tracer disperses quickly throughout the spinal subarachnoid space (SAS) reaching the cervical region in less than ten minutes; this is much faster than suggested by prior theories (Taylor-Aris-Watson dispersion). Our experiments indicate that micro-mixing patterns induced by oscillatory CSF flow around microanatomical features such as nerve roots significantly accelerate solute dispersion. Strong micro mixing effects caused by anatomical features in the spinal subarachnoid space are present in intrathecal drug administration, but absent in the prior dispersion experiments, which explains why prior dispersion theories developed in the engineering community are poor predictors for IT delivery. Conclusion Our experiments support the feasibility of targeting large sections of the neuroaxis or to the brain by means of high-volume injection protocols. The experimental tracer dispersion profiles acquired with an in vitro human CNS model informed a new predictive model of tracer dispersion as a function of physiological CSF pulsations and adjustable infusion parameters. The ability to predict spatiotemporal dispersion patterns is an essential prerequisite for exploring new indications of IT drug delivery which target specific regions in the central nervous system (CNS) or the brain.