© 1999 Robert A. Freitas Jr. All Rights Reserved.

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

4.7.2 Magnetic Fields

The most significant source of biomagnetic fields, generated by electric charges moving as currents through the body, is neural impulses. The magnetic field generated by these currents is given by Ampere's law as

{Eqn. 4.44}

where B is magnetic flux density (teslas), m₀ is the permeability constant (~4p x 10^-7 henry/m), relative permeability k_m = 1 for most biological materials and in vacuo, i is electric current (~0.2 microamperes for human nerve impulses), and r = distance from the current-carrying conductor. Hence B ~ 0.04 microtesla for r = 1 micron, adjacent to an axonal conductor. For comparison, magnetic fields directly beneath high-tension power lines are 10-40 microtesla, or 2-8 microtesla at a lateral displacement of 25 meters along the ground.⁴⁷⁷ Household appliances produce 1-1000 microtesla at a distance of 3 cm and 0.01-2 microtesla at a 1-meter range⁴⁷⁷ (electric shavers produce 0.4-60 microtesla at a range of 15 cm¹²⁹⁴). 20-amp Romex wiring in the walls of a house can produce 2 microtesla in mid-room, up to 80 microtesla at the wall, though in 1998 the average strength in 98% of U.S. homes from artificial sources was 0.05-0.09 microtesla, typical exposures throughout the day were 0.1-1 microtesla, and the federal workplace standard was a maximum of 100 microtesla.¹⁰⁹⁹ Magnetotactic marsh bacteria,⁵⁰¹ birds and insects^502,503,1089 can detect the geomagnetic field vector (identifying Earth's magnetic poles), which is 30-70 microtesla, depending on geographic position. Behavioral thresholds have been measured as 0.005-0.02 microtesla for pigeons and 0.001-0.01 microtesla for honeybees,^815,816 and no more than 1000-2000 microteslas for human subjects.¹¹³⁰ Some biochemical changes have been observed in human cells exposed to ~10-100 microtesla 60 Hz fields,^477,1099 although the data are controversial; it appears the fields pump iron atoms through cell membranes, potentially causing peroxidation or other damage to occur. In 1998, transcranial magnetic stimulation was used to expedite recovery of motor skills for stroke patients, and was being explored as a treatment for depression and a means of altering patient mood. Lightning bolts (i ~ 10,000 amp/discharge) produce 200 microtesla spikes at a distance of 10 meters from the strike, 2 microtesla at a range of 1 kilometer.

Computer simulations of a fully heterogeneous human body divided into 37,000 (1.31 cm)³ voxels produced a maximum induced current of 8.84 amp/m² (average ~1 amp/m²) when the body was exposed to a uniform 60 Hz 1-tesla magnetic field.⁹³⁰ Patients undergoing Echo-Planar MRI scanning report "tickling" and "pain" when exposed to field changes exceeding 60 tesla/sec; ventricular fibrillation may result from myocardial current densities of 4 amp/m², which is induced at 250 tesla/sec.⁴⁹⁰

The simplest magnetosensor is a freely pivoting permanent magnet that experiences a restoring force when the magnet's axis is not aligned with the external field. This "compass effect" is also employed by magnetotactic bacteria, which have ~0.1 micron ferromagnets in magnetosomes in their cells that allow them to detect and track the geomagnetic field vector.^501,2330 Permanent magnets of cross-sectional area A_magnet and length l_magnet made of Alnico or Alcomax (r ~ 8000 kg/m³) can provide B_magnet ~ 1.4 tesla. (In 1998, the record flux density was 13.5 tesla for dipole magnets,⁶⁹⁷ ~27 tesla for resistive magnets.¹⁰²⁶) The force on such a magnet immersed in an external field of flux B is F = B B_magnet A_magnet / m₀, so the minimum detectable flux B_min is

{Eqn. 4.45}

If the minimum detectable force is F_min = 10 pN (Section 4.4.1), B_min = 50 microtesla for A_magnet = 0.4 micron², about right for magnetotactic bacteria, and B_min = 2 microtesla for A_magnet = 2 micron².

The limitations of force sensing may be avoided by suspending the bar magnet from its center of mass and allowing it to oscillate in vacuo about its stable equilibrium position in the external field B, making a simple harmonic oscillator with period

{Eqn. 4.46}

where the moment of inertia I_mag = m_magnet ((A_magnet/4) + (l_magnet²/12)). Oscillator energy E_m ~ B B_magnet A_magnet l_magnet / m₀ k_m, so the minimum detectable external field is

{Eqn. 4.47}

For B_magnet = 1.4 tesla, A_magnet = (660 nm)², l_magnet = 660 nm, T = 310 K and SNR = 2, then B_min = 0.1 microtesla and t_magnet = 6 x 10^-4 sec (~t_meas), allowing a ~KHz sampling frequency. Magnet mass m_magnet ~ 2 x 10^-15 kg. Several classes of molecular magnets have been described in the literature.^2598-2600

Another class of magnetosensor detects the change in dimensions when a magnetic body is magnetized, which is called magnetostriction. For instance, iron-cobalt ferrite expands by DL / L ~ 7.5 x 10^-4 at saturation magnetostriction in a ~1 tesla field, permitting detection of ~10 millitesla field changes using a 1 micron sensor and Dx_min ~ 10 pm. Small magnetostrictive volume changes make possible a sensor of even greater sensitivity. A field of ~0.2 tesla causes a fractional volume increase of ~10^-6 in iron and up to 40 x 10^-6 in some iron-nickel (~30% Ni) alloys. A (370 nm)³ magnetostriction sensor monitored by stretch sensors with displacement sensitivity Dx_min = 0.1 nm (~1 atomic radius) can in theory detect B_min ~ 0.1 microtesla. Magnetostriction is nonlinear with applied field, and there are significant hysteresis effects which may confuse data interpretation. However, multisensor arrays combining positive- and negative-magnetostriction materials should enhance signal extraction. Since the change in volume is small, temperature compensation may be required.

Hall effect probe microscopes have demonstrated 10 microtesla sensitivity with 350 nm spatial resolution,⁴⁷⁸ and alternative nanoscale magnetic detectors such as direct-current SQUID (superconducting quantum interference device) magnetometers, stray field devices, and magnetic spin sensors are being developed.⁴⁵⁰ In 1999, microSQUID could measure magnetic moments as small as ~10⁴ Bohr magnetons³²⁷⁴ or ~10^-19 J/tesla, roughly 7 x 10⁶ protons or a 14-nm iron cube. Magnetoencephalographs using SQUID magnetometers to measure external electromagnetic fields produced by neural traffic in the brain can register 10^-6 - 10^-3 microtesla signals.⁸¹⁰ Other biomagnetic measurement techniques have helped to investigate electrophysiological disturbances in heart muscle and in the brain.⁴⁷⁹ By 1998, microcoils as small as 100 microns in diameter had been constructed using microcontact printing of 25 micron wide silver wires, producing magnetic flux densities >0.4 tesla with a 10 milliamp current, switchable in <10^-3 sec.¹¹⁹⁶

Last updated on 17 February 2003