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Strain Tensor Imaging (STI): Voxelwise assessment of cardiac-induced brain tissue strain at 7T MRI.

Jacob-Jan Sloots¹, Alberto De Luca¹, Geert Jan Biessels², and Jaco Zwanenburg¹
¹Radiology, University Medical Center Utrecht, Utrecht, Netherlands, ²Neurology, University Medical Center Utrecht, Utrecht, Netherlands

Synopsis

The heartbeat induces microvascular blood volume pulsations and subsequent tissue deformations in the brain. Although subtle (typically <1%), these deformations are highly relevant as they accelerate clearance of brain waste products. Moreover, they enable non-invasive assessment of mechanical tissue properties. We developed a sensitive MRI technique with full brain coverage for voxelwise quantification of the cardiac-induced brain tissue strain tensor with 3mm isotropic resolution, based on displacement encoding with stimulated echoes (DENSE). We visualize the strain tensor similar to diffusion tensor imaging. Strain tensor imaging opens a window on brain tissue mechanics and physiological blood volume dynamics in the brain.

Introduction

Brain tissue deformation is mainly induced by the cardiac cycle and is potentially a valuable source of information on the brain tissue’s mechanical properties^1,2. Moreover, this deformation contributes to driving the waste clearance system^3,4. The overall phenomenon of brain tissue motion is subtle, involving submillimeter displacements. Displacement encoding with stimulated echoes (DENSE)⁵ allows for acquisition of the motion field maps^6,7, from which the tissue strain can be computed. However, even at 7T MRI, the current 3D strain measurements lack a factor 10 of SNR to perform a voxelwise analysis of the tissue strain⁷. In this work, we present a sensitive single-shot multi-slice acquisition approach of the DENSE sequence, that provides sufficient SNR to perform a voxelwise analysis of the tissue strain tensor with whole brain coverage.

Methods

To obtain SNR-efficient whole brain DENSE acquisitions, we modified our previous developed cardiac triggered, single-shot sequence⁸ to be compatible with a multi-slice (MS) multi-band (MB)⁹ acquisition approach. Odd and even numbered slices were acquired in two separate packages, one package at each cardiac interval (Figure 1). The slice acquisition order was permuted for every successive repeated scan and a time-shift was implemented so that each slice was acquired at 18 post-trigger delays covering the cardiac cycle.

Written informed consent was obtained from all volunteers in accordance with the Ethical Review Board of our institution. Four healthy subjects (2 females, age 28±3 years) were included and scanned at 7T (Philips Healthcare) using an 8-channel transmit and 32-channel receive head coil (Nova Medical). DENSE measurements (60 slices, resolution: 3x3x3mm³, SENSE: 2.5 AP, multi-band factor: 3) were repeated 80 times: 10 slice order permutations $$$\times$$$ 2 motion encoding strengths (75 μm/π, 100μm/π) $$$\times$$$ 2 time shifts after triggering (one time shift of 0ms; one time shift of 8 times slice-time-interval) $$$\times$$$ 2 opposite encoding directions (to distinguish between motion induced phase and phase confounders). Acquisition of one DENSE series took 80$$$\cdot$$$2 (2 is the number of slice packages) heartbeats (2:40min for 60bpm heartrate). Physiological data was simultaneously recorded, using a vector cardiogram (VCG) for triggering and a respiration belt to trace abdominal breathing. For structural reference, DTI maps were acquired as well (1.5mm isotropic resolution, b_max=800s/mm², 16 directions).

Motion encoding was performed in three orthogonal directions with different acquisition orientations. For each acquisition orientation, in-plane motion encoded datasets were obtained, resulting in 6 datasets per subject. Tissue deformation was obtained by computing the in-plane spatial derivatives. The data was fitted voxelwise to the physiological data in a linear model¹⁰, thereby isolating the confounders, respiration and interpolating to 8 heart phases distributed over the cardiac cycle (see Figure 2).

Analysis

Each of the 6 motion-encoded datasets for each subject provided 2 components to fill the displacement gradient tensor for each voxel (see Figure 3).$$\mathbf{F}=\begin{bmatrix}\frac{{\partial}u_{RL}}{{\partial}RL}&\frac{{\partial}u_{RL}}{{\partial}AP}&\frac{{\partial}u_{RL}}{{\partial}FH}\\\frac{{\partial}u_{AP}}{{\partial}RL}&\frac{{\partial}u_{AP}}{{\partial}AP}&\frac{{\partial}u_{AP}}{{\partial}FH}\\\frac{{\partial}u_{FH}}{{\partial}RL}&\frac{{\partial}u_{FH}}{{\partial}AP}&\frac{{\partial}u_{FH}}{{\partial}FH}\end{bmatrix}-\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}$$where $$$u_{RL,AP,FH}$$$ are the measured displacements in Right-to-Left, Anterior-to-Posterior and Feet-to-Head, respectively. $$$\mathbf{F}$$$ is the gradient deformation tensor from which the Lagrangian strain tensor $$$\mathbf{E}$$$ can be computed as¹¹$$\mathbf{E}=\frac{1}{2}\left(\mathbf{F^TF}-\mathbf{I}\right)$$with $$$\mathbf{I}$$$ the identity matrix. $$$\mathbf{E}$$$ is independent of rigid body motion or orientation. Similar to DTI analysis and visualization¹², an eigenvalue decomposition was performed on $$$\mathbf{E}$$$ which resulted in three eigenvectors with associated eigenvalues. The eigenvector with the largest positive value is associated with the direction of largest expansion of the tissue (first principal strain), whereas the eigenvector with the largest negative value is associated with the direction of largest compression (third principal strain) (see Figure 4).

Results and Discussion

Fitting the data to the physiological information resulted in smooth displacement gradient maps over the complete brain. Combining the 3D volumes with different components of the displacement gradient tensor was done without registration and resulted in smooth Strain Tensor Imaging (STI) maps (see Figure 5). Although the mathematics of STI and DTI are very similar, their physical interpretation differs substantially. DTI represents microstructural tissue organization, whereas STI describes mechanical strain induced in the tissue by heartbeat-related blood volume pulsations. STI yields both positive and negative eigenvalues, whereas DTI only has positive eigenvalues. We therefore showed both the positive principal strains (maximum expansion) and negative principal strains (maximum compression reflecting the Poisson effect), respectively. The STI maps showed similar trends for all subjects. The positive principal strain direction not only follows the known brain motion pattern (funnel shaped, pointing towards the foramen magnum¹³), but also largely follows the direction of the fiber bundles represented in the DTI maps. The corpus callosum fiber bundles (running from left to right, see middle slice), however, do not expand along their orientation but perpendicular to it. Future work needs to incorporate registration and EPI distortion correction, together with a more rigorous comparison between the diffusion and strain tensors throughout the brain.

Discussion

Strain tensor imaging can be performed by using a single-shot multi-slice DENSE sequence. Together with high-sensitive motion encoding, this yields sufficient SNR in the displacement maps to compose the gradient displacement tensor from which the 3D strain tensor can be computed. First results in four subjects show similar maps of the strain tensor. This novel approach may serve as a physiological marker to study the brain tissue mechanics and physiological blood volume dynamics in the brain.

Acknowledgements

The research leading to these results was supported by Vici Grant 918.16.616 from the Netherlands Organization for Scientific Research (NWO); the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement n°337333 and the European Union’s Horizon 2020 research an innovation programme under grant agreement no. 666881.

References

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Figures

Data acquisition scheme. The top row represents snapshot acquisition with motion encoding directly after the ECG trigger. The second shows motion encoding after the trigger with an additional time delay. For both acquisition schemes, the slices within each package are permuted in each subsequent repeated scan such that in the end each slice is acquired at 18 different post-trigger delays, covering the complete cardiac interval.

Time-series of displacement-encoded phase images were used to derive the components of the displacement gradient tensor by computing both in-plane spatial derivative along and perpendicular to the encoding direction, respectively. The figure shows an example for the spatial derivative along the FH encoded dataset. Together with the associated physiological data, these gradient maps were used in a linear model to isolate the components of cardiac and respiration displacement gradients.

Overview of the displacement gradient tensor components obtained from the different datasets to fill the full displacement gradient tensor from which the gradient deformation tensor $$$\mathbf{F}$$$ is obtained (see Equation 1). The components on the diagonal are obtained twice in this scheme, at different acquisition orientations. These double components were averaged before further analysis.

Strain tensor representation. The eigenvector of each voxel is represented using the RGB color scheme (red: RL direction, green: AP direction, blue: FH direction). The gray-scale maps on the bottom row show the sum of all positive (left) and negative (right) eigenvalues (principal strains), respectively. For the negative eigenvalues, the absolute value was taken, resulting in a map with only positive values. Eigenvectors are combined with the eigenvalues by using intensity mapping.

Transverse slices of 4 subjects visualizing the strain tensor at peak systole as explained in Figure 3. A DTI and T1 map are shown for reference. Three slices were selected manually located at the top, middle and inferior-brain. Although mathematically similar, STI and DTI substantially differ in physical interpretation. DTI represents the microstructural tissue organization, whereas STI describes the heartbeat-induced mechanical deformation of the tissue.

Proc. Intl. Soc. Mag. Reson. Med. 28 (2020)

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