Introduction

The study of brain injury mechanics is currently limited by the inability to observe relative motion between the skull and brain in vivo. Imaging the displacement of bone and soft tissue simultaneously would improve the modeling of brain-skull coupling and its contribution to traumatic brain injury (TBI).¹ Magnetic resonance elastography (MRE) is a noninvasive imaging technique for estimating mechanical properties in vivo, but also captures small-scale brain tissue displacement from harmonic vibration and, as such, can be used to safely examine how the brain deforms². Simultaneously imaging skull motion with MRE is challenging due to the ultrashort T2 of cortical bone³. A potential solution to this is imaging the fatty marrow within the medullary cavity of the bone⁴, which in turn requires acquisition and reconstruction considerations to avoid distortion and signal loss due to the difference in resonance frequency. In this work we develop a fat-water MRE sequence with a spiral-in/out trajectory to measure relative skull-brain displacement with the goal of quantifying transmission of motion from the skull to the brain during TBI.

Methods

To obtain high-resolution displacement data of the brain and skull simultaneously, we combined fat-water imaging with a novel 2D multishot spiral in/out MRE sequence. Spiral-in/out is unique in its ability to employ multiple trajectories in a single excitation⁵, and thus achieve multiple echo times. Here, an echo time shift of 0.5 ms was built into the spiral-in/out trajectory to sample data when fat and water were both in-phase and relatively out-of-phase with each other (Figure 1).
Imaging: MRE protocol parameters included 240 x 240 mm² field-of-view, 2 mm isotropic resolution, 20 slices, TR/TE = 2400/52 ms, 4 phase offsets, and 6 spiral shots (R=2). All scanning was conducted using a Siemens 3T Prisma MRI scanner and a 20-channel head coil. Vibrations were generated at 50 Hz using a Resoundant pneumatic actuation system (Rochester, MN) and a passive pillow driver. Data was collected at both low (5 mT/m) and high (70 mT/m) motion encoding gradient amplitudes to capture rigid body motion (RBM) while avoiding temporal phase wrapping² and to calculate mechanical properties, respectively. We also collected Dixon fat-water images with an in-plane resolution of 0.6 mm to create masks of brain, skull, and scalp to obtain displacement maps for each region of interest.
Reconstruction: A joint fat-water iterative reconstruction was used to obtain separate images for fat and water from the data with two echo times, similar to Wang, et al⁷. A standard system matrix for iterative MR reconstruction was divided into fat and water components, $$$A_{f}$$$ and $$$A_{w}$$$, where $$$\overrightarrow{k}_m$$$ and $$$\overrightarrow{r}_n$$$ are k-space and image-space coordinates respectively, is the phase accumulation due to field inhomogeneity, $$$t$$$ is the time at which data is sampled, and $$$\Delta\omega_{f}$$$ is the chemical shift between fat and water:
$$A_{w,mn} = e^{j2\pi(\overrightarrow{k}_m\cdot\overrightarrow{r}_n)}e^{j\omega_{n}t_{m}}$$
$$A_{f,mn} = e^{j2\pi(\overrightarrow{k}_m\cdot\overrightarrow{r}_n)}e^{j\omega_{n}t_{j}}e^{j\Delta\omega_{f}t_{m}}$$
This matrix was implemented with time segmentation and a nonuniform fast Fourier transform⁸. The resulting equation for separate fat and water images (below) was then solved using Fessler’s penalized least squares solver via conjugate gradient descent,⁹ where $$$y$$$ is the data from multiple echo times, $$$R$$$ is roughness regularization penalty, and $$$\beta$$$ is the regularization constant:
$$\hat{x}_{w},\hat{x}_f =\begin{matrix}argmin \\x_{w},x_{f} \end{matrix}{\begin{Vmatrix}\begin{bmatrix}y_{TE_{1}} \\ y_{TE_{2}} \end{bmatrix} - \begin{bmatrix}A_{w} \\A_{f} \end{bmatrix} \begin{bmatrix}x_{w} \\x_{f} \end{bmatrix} \end{Vmatrix}}^{2}_{2} + \beta(R(x_{w}) + R(x_{f}))$$
Analysis: Reconstructed phase images were processed to obtain maps of complex motion with sensitization in the x (left-right), y (anterior-posterior), and z (superior-inferior) directions. Displacement amplitude and relative phase of the harmonic motion was quantified for each point in both skull and brain. Low sensitivity data was used to estimate translational and rotational RBM of the skull and brain. High sensitivity brain displacement data was input into a nonlinear inversion algorithm (NLI)¹⁰ to calculate maps of mechanical properties, stiffness and damping ratio.

Results

The in vivo analysis of brain and skull motion showed an overall lower displacement amplitude of the brain relative to the skull, indicating reduced transmission of motion to the brain in all three directions. Figure 2 shows the skull and brain moving roughly in phase with each other but independently of the scalp. Rigid body motion fitting showed that 98.7% of skull motion was RBM in contrast to only 42.9% of scalp motion, as expected, confirming that our acquisition was successful in isolating the skull without contamination (Figure 3). Further quantification of brain and skull rigid body displacement show the highest translational motion in y and rotational motion about the x-axis which corresponds with the direction of actuation (Figure 4). Mechanical properties calculated from NLI show high-quality property maps in a representative slice in Figure 5.

Discussion & Conclusions

The fat-water spiral-in/out MRE sequence and reconstruction developed in this study was successful in measuring skull and brain displacement simultaneously. This approach allows us to improve resolution through interleaved spiral readouts¹¹ in half the acquisition time and without the need for repeated acquisitions with separate echo times, as in previous work¹². This shortened scan time will enable us to look at multiple frequencies and actuation directions to further quantify the transmission of motion from skull to brain. Future work will also incorporate dual-sensitivity motion encoding⁴ to obtain rigid-body measurements and mechanical property estimates simultaneously.

Acknowledgements

This project was supported by NIH grant U01-NS112120, the NIH Bench-to-Bedside program, and Office of Naval Research grant N00014-22-1-2198.