Prediction of motion induced magnetic fields for human brain MRI at 3 T

Abstract

Objective: Maps of B₀ field inhomogeneities are often used to improve MRI image quality, even in a retrospective fashion. These field inhomogeneities depend on the exact head position within the static field but acquiring field maps (FM) at every position is time consuming. Here we propose a forward simulation strategy to obtain B₀ predictions at different head-positions.

Methods: FM were predicted by combining (1) a multi-class tissue model for estimation of tissue-induced fields, (2) a linear k-space model for capturing gradient imperfections, (3) a dipole estimation for quantifying lower-body perturbing fields (4) and a position-dependent tissue mask to model FM alterations caused by large motion effects. The performance of the combined simulation strategy was compared with an approach based on a rigid body transformation of the FM measured in the reference position to the new position.

Results: The transformed FM provided inconsistent results for large head movements (> 5° rotation, approximately), while the simulation strategy had a superior prediction accuracy for all positions. The simulated FM was used to optimize B₀ shims with up to 22.2% improvement with respect to the transformed FM approach.

Conclusion: The proposed simulation strategy is able to predict movement-induced B₀ field inhomogeneities yielding more precise estimates of the ground truth field homogeneity than the transformed FM.

Keywords: B0 homogeneity; Head motion; Susceptibility model; UTE.

Fig. 1

The threshold-based air, bone, and soft tissue segmentation of inverting the logarithmically scaled UTE dataset. A Three orthogonal views of the inverted logarithmically scaled UTE image, with full range [− 7,0]. B The image histogram with two distinctive peaks as soft-tissue (left) and noise (right) signals. Gaussian-fitting results with center peak (dashed line) and full-width-half-maximum (FWHM) information (dashed lines) for soft-tissue (red) and noise (green). The 3-class segment model is based on the bone signal threshold [Center (soft) + 1.4*FWHM (soft), Center (noise)-1.4*FWHM (noise)], which is positioned in between the two peaks, leading more toward soft tissue. The multiple segment model is defined as a linear interval between [Center (soft)-1.4*FWHM (soft): 0.1: Center (noise)]. C Middle sagittal slices of 3-classes segment model and multiple segment model

Fig. 2

Schematic of simulated field map. The simulation field map is based on a 5 steps magnetic field estimation: A the system SH shim field is calculated from the SH shim coefficients; B the forward approximated sample induced B_χ field; C Linear phase errors by the imaging gradients; D Dipole approximation of the B_χ’ field from the lower body part; E Susceptibility model fitting to reduce the simulation residual error with the B_{χ_m} field

Fig. 3

A Schematic of the iterative fitting algorithm. B The simple model residual field map, SMR, when using a 3-class susceptibility map. C The multiple segment model with additional spatial anatomical constrains. D The multiple model residual field map, MMR, when using a fitted susceptibility map E The fitted susceptibility map for one volunteer

Fig. 4

A, B, C illustrates the calculation of transformed FM, simulated FM, and combined FM from a reference position (Position 1) to a new head position (Position 4). The transform FM utilizes the measured FM in reference position with a simple rigid-body transform operation. The absolute rotation and translation values have been marked in red squares. The simulated FM is calculated from the forward B₀ approximation, with a rigid-body transformed susceptibility map. The combined FM adds a rigid-body transform MMR field map from Position 1 into the simulated FM at a new head position. C and D, show the process of susceptibility map mask adjustment when the large head rotation on X-axis causes subject tissue boundary changes. The updated head-mask is calculated from the measured field map at Position 4 and applied to the rigid body transformed susceptibility map. For large head movement, the simulated FM and combined FM were recalculated using the head-mask updated susceptibility map (dash square). The red arrow indicates the mask displacement

Fig. 5

Four volunteers simulation results at the reference position. First row: Measured field maps, color range [− 100 Hz, 100 Hz]; Second row: Simulated field maps, color range [− 100 Hz, 100 Hz]; Third row: Residual field maps (Measured—Simulated), color range [− 50 Hz, 50 Hz]; Bottom row: Fitted susceptibility maps, color range [− 12 ppm, 0 ppm]

Fig. 6

Motion induced field map estimation comparison in three representative slices from two subjects. The Vol. σB₀ of the field map and RMSE of the estimated strategies were reported. The absolute rotation and translation values have been marked in red squares

Fig. 7

Mask updated susceptibility models used for Position 4 in two volunteers. A Mask of volunteer 1 tissue boundary update process. B Mask of volunteer 2 tissue boundary update process. C Compare the simulation improvement (RMSE) by introducing the new subject tissue boundary for volunteer 1 (the second row vs. the third row). D Compare the simulation improvement (RMSE) by introducing the new subject tissue boundary for volunteer 2 (the second row vs. the third row). The absolute rotation and translation values have been marked in red squares

Fig. 8

Comparison of prediction performance between the rigid-body transform, the simulation, and the combined strategies at multiple head angles. The yellow window indicates the simulation and combined strategies with subject head-mask update

Fig. 9

Global shimming simulation off-resonance magnetic field maps at three representative slices from two volunteers. For positions 2 and 3, the first column is the target measured FM for B₀ shimming. The second column to the fifth column compared the residual field map after B₀ shimming with proposed strategies, where the second column used the measured FM itself as the baseline. For position 4, additional B₀ shimming results using the mask update susceptibility model is compared with the B₀ shimming result using measured field FM