Estimation of conductivities in a personalized volume conductor model of the human head using MRCDI

Introduction: In MR current density imaging (MRCDI) and MR electrical impedance tomography (MREIT) the current
density or conductivity is reconstructed from internal current-induced magnetic flux densities measured with MRI.
However, the current density and conductivity reconstruction is challenging due to low SNR, limited volume coverage,
and most importantly that only the component of the magnetic flux density parallel to the main field of the MR scanner
is measurable (Bz). The “projected current density” method [1] has been used in recent human in-vivo brain MRCDI
studies [2–5]. Comparing the results to simulated data we observed that the method only gives very coarse estimates of
the “true” current density.
Here we first analyze the accuracy of the projected current density algorithm when used to reconstruct currents in the
human head. Secondly, we propose to use an anatomically detailed head model and optimize the conductivities based on
the difference between simulated and measured magnetic fields. Parts of the work presented in this abstract have
previously been published in a journal article [6].
Methods: The projected current density algorithm attempts to reconstruct the current density from measured magnetic
flux density images Bz, and from a simulated current density J
0
and a magnetic flux density Bz
0 obtained from a model
with homogeneous conductivity. The equation derived from Ampère’s law is expressed as
𝑱
𝒓𝒆𝒄 = 𝑱𝟎 +
ଵ
ఓబ
ቂ
ఋ(஻೥ି஻೥
బ
)
ఋ௬
,
ିఋ(஻೥ି஻೥
బ
)
ఋ௫
, 0ቃ, [1]
where the directional derivatives of Bx and By are neglected since only Bz is measured in MRCDI. μ0 is the magnetic
permeability of free space. We analyzed the accuracy of the projected current density algorithm with simulated data using
the finite element method (FEM) implemented in SimNIBS
3.1.0 [7]. With a forward simulation using an anatomically
detailed head model, the current density was calculated and
used as the ground truth to evaluate the current density
reconstructed with the projected current density algorithm.
A simplified head model with no variation in the z-direction
(Fig. 1c) was also used to test the accuracy of the projected
current density algorithm for a simpler structure. For the
simplified head model, Jz as well as δBy/δz and δBx/δz
from the injected currents, are minimal, rendering all the
neglected terms in the projected current density method
insignificant.
Instead of reconstructing the current density from Bz, we
propose to compare the measured Bz with simulated Bz
obtained from a personalized head model with multiple
tissue types. The tissue conductivities are then estimated by
minimizing the difference between measured and simulated
Bz (fig 2). We scanned 5 subjects with two electrode
montages (right-left (RL) and anterior-posterior (AP))
using an acquisition-weighted multi-echo GRE acquisition
strategy [5]. The five variable tissue types used in the
optimization were white matter, gray matter, cortical CSF,
skull, and scalp. Ventricular CSF was kept constant to act
as an anchor point for the other conductivities since all
conductivities can be scaled with a common factor resulting
in the same current density and magnetic flux density. To
avoid overfitting of the conductivities to individual
subjects, we used leave-one-out cross-validation (LOOCV)
Figure 1: Evaluation of the accuracy of the projection current density
algorithm when used on simulated magnetic flux measurements from a
human head. a) Simulations based on the ernie head model (available as
example dataset in SimNIBS) showing the head model, tissue
conductivities, true current density, J
0 used in the algorithm and the
reconstructed current density. There is a remarkably clear difference
between true and reconstructed current density (R2=0.22). b) The true Bz
(simulated measurement), the neglected and used directional derivatives,
and the reconstructed current density, respectively. c) same figure as in a,
but with a simplified head model with no variation in the z-direction. The
similarity between true and reconstructed current density has greatly
improved (R2=0.63). d) The Bz and directional derivatives for the
simplified head model.
where four subjects were used for optimization and the error was evaluated
on the remaining subject with the obtained conductivities. Optimization was
performed both for RL and AP separately and combined. The error metric
was the relative root mean square difference between measurements and
simulations.
Results and Discussions: The results from the simulation of the projected
current density algorithm using a realistic head model and a simplified head
model with no variation in the z-direction are shown in fig. 1a,b and c,d,
respectively. The reconstructed current density for the simplified head model
(R2
= 0.63) outperforms the reconstruction for a realistic head model (R2
=
0.22). The reason for the poor performance with the realistic head model is
clear when visualizing the neglected terms as shown in fig. 1b and d. The
neglected terms are much stronger for the realistic head model than for the
simplified. Jz is additionally fully ignored by the projected current density
algorithm.
In fig. 2 a diagram of the proposed conductivity optimization is shown where
the difference between measured and simulated Bz is minimized. An example
optimization shows the improved similarity of measured and simulated Bz for
the RL montage. Less change is observed for the AP montage. This is also
apparent in fig. 3 where the RL errors are larger for all subjects while also
displaying a greater reduction of the error after optimization. The
improvements for the RL montage for all subjects when using LOOCV
indicates a systematic difference between head models and reality that needs
to be accounted for in simulations. We have here proposed to use conductivity
optimization to increase the robustness of the simulations. However, the
obtained conductivities are not necessarily accurate for the given tissue types
but do improve the current density simulations for a given electrode montage
that gives rise to the simulated Bz. This is further emphasized by the
difference in the tissue conductivities for the two electrode positions.
Conclusions: We have here shown that the projection current density
algorithm performs poorly for anatomically complex structures such as the
human head due to the neglected terms needed for an accurate current density
reconstruction. However, for simple structures with little variations in the zdirection, the algorithm provides reasonable results.
We have instead suggested using conductivity optimization of a personalized
head model to improve current density simulations for a given electrode
montage. Our results indicate a systematic difference between simulation and
reality for the RL electrode montage in all five subjects. This can be improved
using our proposed method