Detection of electric/magnetic activity with magnetic resonance
Last update: 2024-02-07
Use of magnetic resonance for electric/magnetic field detection
A less known application of magnetic resonance is the possibility to detect electric and magnetic fields. We may consider that the spin, which resembles a bar magnet, performs a 360° rotation around the magnetic field lines (Figure 1, where B is symbolizing the magnetic field). This is actually a special rotation, called precession, as the spin is tilted and draws a cone, similarly to a top toy. We may also compare a spin to a clock with one hand running 360 degrees.
In general, in science, if an object performs a circle motion and we want to describe the position of the object on the circle, we may use an angle measure called "phase" (reference "unit circle"). We may say for instance that the object is found at 30° or has a phase of 30°.
Let us consider the example of an electric current running on a wire as in the study by Bodurka J. et al. entitled “Current-Induced Magnetic Resonance Phase Imaging.” [Journal of Magnetic Resonance, vol. 137, no. 1, 1 Mar. 1999, pp. 265–271, https://doi.org/10.1006/jmre.1998.1680 (PDF)]. We use an electric current which has a specific waveform, known as a "square waveform", shown in Figure 2 on the top. This signal is generated by having the current ON for two seconds and OFF for two seconds.
While a spin rotates, the magnetic field at a given time point may exert a magnetic force on the spin and change its phase i.e. its position on the circle. For example, from a 20° phase, the spin may acquire a 90° phase (Figure 1). The phase change in this case is 70°. It is possible to measure the phase change (or phase shift) and determine the strength of the magnetic field which caused it at a certain time point. By measuring the phase shift at different time points, we can determine the magnetic field at these time points and thereby obtain the changing magnetic field for a certain interval. It can be said that the magnetic field modulates the phase change of the spins.
Figure 1: Principle of measuring the magnetic activity based on spin phase change. The magnetic field exerts a magnetic force on the spin and changes its phase i.e. its position on the circle: from a 20° phase, the spin acquires a 90° phase. The phase change in this case is 70°. It is possible to measure the phase change (or phase shift) and determine the strength of the magnetic field which caused it.
In Figure 2, at the bottom, we can appreciate how the phase of the spins changes by following the strength of the electric field. When the electric field increases, the phase increases and vice versa. The changing electric field creates a magnetic field which exerts a force on the spins, changing their phase φ.
The amount of phase change (Δφ) is obtained from magnetic resonance phase images. The magnetic flux density change (ΔΒ) which induced the phase change is calculated by multiplying the latter with a time quantity, the time of echo (TE):
ΔΒ=(Δφ)/(γTE)
Figure 2: Excerpt from Figure 2 of the publication by Bodurka J., et al. “Current-Induced Magnetic Resonance Phase Imaging.” Journal of Magnetic Resonance, vol. 137, no. 1, 1 Mar. 1999, pp. 265–271, https://doi.org/10.1006/jmre.1998.1680 (https://bit.ly/2JhxtXj). On the top, an electric current waveform (square waveform implemented with a boxcar function) . On the bottom, the phase measured with MRI.
Theoretically, if we applied this technique to the brain, we could obtain the magnetic field of the brain over a time interval. That would correspond to an magnetoencephalogram.
In accordance with what is mentioned in the above publication, neuronal activity consists of "the flow of ionic current across the neuron cell membrane, along the interior of the axon, and in the surrounding medium. This ionic current will produce" a magnetic flux density (Bc), that, superimposed with the B0 field, will alter the phase of the magnetic resonance signal (cf. precession) of surrounding water protons.
(Please note that this is applicable to environmental water protons as well.)
It must be noted that the most pronounced phase changes are expected only parallelly/antiparallely to the static magnetic field Bo, which in this case is the Earth's magnetic field. Practically, if we analyze the induced magnetic flux in two components, one parallel and one perpendicular to the static (external) magnetic flux, the perpendicular component would be below the threshold of measurement; conversely, the parallel could be measured by adding it or subtracting it from the Bo, which itself is measurable.