Relevance to functional magnetic resonance: Magnetic resonance techniques for quantification of magnetic fields linked to electric currents applied to the brain

Last update: 2023-12-27

Magnetic resonance current density imaging (MRCDI) and magnetic resonance electrical impedance tomography (MREIT) 

Relevance to magnetoencephalography based on magnetic resonance

When we perform electric stimulation therapy for the brain, in which case we apply a certain current on the head, we would like to know how the current accesses the different areas of the head. Specifically, we would like to know the current distribution or the current density. Alternatively, we would like to determine the opposition that the current encounters, which is termed electrical impedance, and this in a 3D-manner like in tomography.

The electric current that will flow in different parts of the head will create a magnetic field, which the magnetic resonance technique can quantify through imaging. Therefore, indirectly, the density of the electric current can be determined. This is performed using the technique termed "magnetic resonance current density imaging" (MRCDI). Similarly, the electrical impedance can be found. This is possible using the technique named "magnetic resonance electrical impedance tomography" (MREIT). It could be argued that these techniques resemble magnetic resonance-based magnetoencephalography.

In magnetic resonance imaging (MRI), the subject is placed in a strong static magnetic field termed Bz (considered to be conventionally on the z axis) which aligns the spins, resulting in a net longitudinal magnetization, represented by vector Mz.

In magnetic resonance current density imaging (MRCDI), a current applied to the head induces a magnetic field which is added (vectorially) to that of the scanner and which is considered to constitute a perturbation (Göksu et al 2018). The total magnetic field B(total) can be written as a vector sum of Bz and the perturbation. 

Such a perturbation can be analyzed in two components, one perpendicular to Bz (Bz(I)) and one parallel to it (Bz(II)) (Jog MV et al 2016 - Supplement). Given that the perturbation is expected to be in the order of parts per million (ppm), both components are considered to be very small. However, in the z axis, adding a small magnetic field (Bz(II)) to the large magnetic field of the MRI scanner (Bz) gives a measurable sum. On the contrary, in the y axis, where there was no magnetic field, the small magnetic field Bz (Bz(I)), which now occurs, is below the measurable threshold and can thus be neglected. Therefore, the B(total) would be considered to be along the static magnetic field of the scanner Bz and to be equal to Bz+Bz(II)

The above resultant magnetic field, referred to as ΔBz, will slightly change the precession frequency of the magnetization vector Mz, given that this frequency depends on the magnetic field strength. Specifically, it will change the phase i.e. it will introduce a phase shift. The change of the phase will modulate the measured MRI signal proportionally to ΔBz. By measuring the phase change, we can determine the induced ΔBz and quantify the magnetic field of the brain and specifically, the magnetic field induced by the current injection. This enables the reconstruction of the inner current flow and the conductivity distribution.

The technical protocol of the study by Göksu et al (2018) uses specific MRI sequences i.e. sets of pulses and gradients such as "multi-echo spin echo" (MESE) and "steady-state free precession free induction decay" (SSFP-FID), with the purpose of generating an optimal signal. Representative images of SSFP-FID measurements with multi-gradient-echo readouts performed in five subjects using three different repetition times TR are shown in Figure 1 below (Figure 10 of Göksu et al 2018) where (a) shows ΔBz(c) without current injection and (b) demonstrates ΔBz(c) with current injection.

The follow-up MRCDI publication by Göksu et al (2021) reports sensitivity and resolution improvement. 

Figure 1: Experiment 4 (Göksu et al 2018) represents a comparison of SSFP-FID measurements with multi-gradient-echo readouts performed in five subjects using three different repetition times TR. (a) ΔΒz(c) without current injection. (b) ΔΒz(c) with current injection

The technique has been used for quantification of magnetic field changes induced in the human brain by tDCS (Jog MV et al 2016). A similar technique, magnetic resonance electrical impedance tomography (MREIT), has been used in a tACS study (Kasinadhuni AK et al 2017).

Technical details

Below are excerpts from (Jog MV et al 2016 - Supplement).

As mentioned by Jog MV et al (2016), section Methods/Theory/“MRI detects induced magnetic fields”, using MRI field mapping, field variations along Bz can be measured as phase angles according to:

Φm = (γ *ΔBz * TE) mod(2π)

where Φm is the measured phase angle between 0 and 2π radians, γ is the gyromagnetic ratio, ΔBz is the field deviation along Bz and TE is the echo time. The results show that it is possible to detect magnetic field changes as small as a nanotesla (nT) with a spatial resolution of a few millimeters.

The above equation can be written as ΔBz = ΔΦm / γ * ΔTE as mentioned by Jog MV et al (2016 - Supplement).

The above source also mentions that the modulo-2π operation has been removed indicating that the phase angles have been unwrapped. Δ represents the phase difference between two TE’s. In an ideal scenario without noise, the minimum (unbiased) detectable field corresponds to the smallest possible non-zero phase change generated by the smallest applied current (0.5mA). Because the full phase range of 0 to 2π radians is divided into 4096 discrete levels in MRI, the smallest non-zero phase change evaluates to 2π/4096 radians. For a given ΔTE of 9.84 msec, the minimum (unbiased) detectable field equates to 0.58nT at 0.5mA, or ~ 1.2nT/mA. It is possible to increase the ΔTE by minimizing TE1, or, increasing TE2 permitted by SNR.

It is noted that in General Linear Model Analysis the measured phase was modeled as:

Φm = ΦCurrent (TE, i(s)) + Φ0(s) + ΦNon-Current (TE) + Φdrift(TE, s) + Φnoise



1. Göksu C, Hanson LG, Siebner HR, Ehses P, Scheffler K, Thielscher A. Human in-vivo brain magnetic resonance current density imaging (MRCDI). Neuroimage. 2018;171:26-39.

2. Jog MV, Smith RX, Jann K, et al. In-vivo Imaging of Magnetic Fields Induced by Transcranial Direct Current Stimulation (tDCS) in Human Brain using MRI. Sci Rep. 2016;6:34385.

3. Göksu C., Scheffler K, Gregersen F, et al. Sensitivity and resolution improvement for in vivo magnetic resonance current‐density imaging of the human brain. Magnetic Resonance in Medicine. 2021;86(6):3131-3146. doi:

4. Kasinadhuni AK, Aprinda Indahlastari, Chauhan M, Schär M, Mareci TH, Sadleir R. Imaging of current flow in the human head during transcranial electrical therapy. Brain Stimulation. 2017;10(4):764-772. doi: