Magnetic resonance techniques for quantification of magnetic fields and determination of current density of the brain



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


Relevance to magnetoencephalography based on magnetic resonance



When we wish to perform brain electric stimulation therapy, 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. In other words, we wish to know the current distribution or the current density. Alternatively, we would like to know the opposition that the current encounters, which is termed electrical impedance, and this in a 3D-manner like in tomography.
The electric current creates a magnetic field which the magnetic resonance technique can quantify, can image. Therefore the current density or the electrical impedance can be determined. These are performed with the following emerging techniques: magnetic resonance current density imaging (MRCDI) and 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 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 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. The perturbation could be considered to be at an angle θ with Bz. 


Such a perturbation can be analyzed in two components, one perpendicular to Bz (Bz(I)) and one parallel to it (Bz(II)). Since the perturbation is expected to be in the order of ppm, while the MRI scanner magnetic field is approximately 1.5 T, the angle θ would be approximately 0 and B(total) would be considered to be along Bz (Jog MV et al 2016 - Supplement). Similarly, the contribution of the parallel component Bz(I) is expected to be of an order than can be neglected. Therefore, the resultant magnetic field following the perturbation is considered to be along the static magnetic field of the scanner. 


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 and will therefore 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.


This technical protocol of the study of Göksu et al 2018 uses 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 10 (Göksu et al 2018) where (a) shows ΔΒz(c) without current injection and (b) demonstrates ΔΒz(c) with current injection.


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


(Record accessible by title on the Max Planck repository.)




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


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 x ΔTE as mentioned by (Jog MV et al 2016Supplement).


The above source also mentions that the modulo-2π operation has been removed indicating that the phase angles have been unwrapped. Δ represents the fact that we are referring to 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:

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




MRCDI for objects



MRI detection of an electric signal based on the phase change of the proton magnetic resonance signal.

In a neural context, detection of neural activity would be instantaneous in contrast to the BOLD signal (fMRI-BOLD) which has a latency of 2 to 5 seconds.


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.


"We hypothesize that electric current-induced phase alternations could be imaged by fast magnetic resonance imaging (MRI) technology."


In this study, an electric signal of square waveform (figure) is applied on a copper wire (implementation with 2 seconds current ON and 2 seconds current OFF). The detection of the electric signal with MRI is shown below.


"The amount of phase change (Δφ)" of the proton magnetic resonance signal "was obtained from phase images and its magnetic flux density change (ΔΒ) was calculated based on the echo time used and amount of phase change: ΔΒ=(Δφ)/(γTE)."


"Because the magnetic flux density induced by the electric currents (Bc) used in this study is much smaller than the external magnetic flux density (B0), the most pronounced phase changes should be expected only in the direction parallel (ΔΒ = B0 + Bc) or antiparallel (ΔΒ = B0 - Bc) to B0."



Additional information: