How a High-Gradient Magnetic Field Could Affect Cell Life

Abstract

The biological effects of high-gradient magnetic fields (HGMFs) have steadily gained the increased attention of researchers from different disciplines, such as cell biology, cell therapy, targeted stem cell delivery and nanomedicine. We present a theoretical framework towards a fundamental understanding of the effects of HGMFs on intracellular processes, highlighting new directions for the study of living cell machinery: changing the probability of ion-channel on/off switching events by membrane magneto-mechanical stress, suppression of cell growth by magnetic pressure, magnetically induced cell division and cell reprograming, and forced migration of membrane receptor proteins. By deriving a generalized form for the Nernst equation, we find that a relatively small magnetic field (approximately 1 T) with a large gradient (up to 1 GT/m) can significantly change the membrane potential of the cell and thus have a significant impact on not only the properties and biological functionality of cells but also cell fate.

Figure 1. Spatial distribution of the scaled modulus of the magnetic field (B/μ₀M_r) calculated in the plane 5 μm above four micromagnets (M_r is remanent magnetization).

Several cells are schematically drawn to demonstrate that the magnetic field varies in the same length scale as the cell mean size. The micromagnet sizes are 100 × 100 μm, and the spacing is 100 μm.

Figure 2

Spatial distribution of the scaled planar component of the magnetic gradient (a) 5 μm above the micromagnets shown in Fig. 1. (a) Vector field {∇_x(B/μ₀M_r)²,∇_y(B/μ₀M_r)² } multiplied by the micro-magnet size. Arrows indicate the directions of the magnetic gradient forces. (b) Scaled modulus of the planar magnetic gradient (∇_x,y(B/μ₀M_r)²) multiplied by the micro-magnet size as a function of the x-coordinate. The gradient values were calculated along the OX-axis at distances from the magnet tops: 5 μm, 7 and 10 μm.

Figure 3

Vector fields of the magnetic induction (a and c) and magnetic gradient (b and d) in the vicinity of four magnetic nanoparticles magnetized parallel and perpendicular to the membrane surface. In (b and d) arrows indicate the directions of the magnetic gradient forces.

Figure 4

Vector fields of the magnetic induction (a) and magnetic gradient forces (b) between the two, pole-to-pole magnetic slabs and cell division. (c) Magnetic gradient forces (Equation 2) normalized to Δχa⁻¹μ₀M_r² as a function of the x-coordinate. A hypothetical division of a cell in the highly non-uniform magnetic field (the central area) is illustrated.

Figure 5

Distributions of the scaled moduli of the magnetic induction (a) and magnetic gradient force (b) in the plane above a cylindrical magnet with an axial hole. (c) 2D-plot of the magnetic gradient force as a function of the radial coordinate. The magnetic induction modulus is normalized to (μ₀M_r/4π), whereas the modulus of magnetic gradient force is normalized to R⁻(μ₀M_r/4π)². The calculations were performed for a magnet length 1 cm, magnet radius 0.5 cm, hole radius 0.1 cm, and distance between the magnet top and the plane of calculations of 0.1 cm.

Figure 6. Schematic illustration of the possible applications of HGMFs and intracellular effectors.