Research Papers

The Relationship of Three-Dimensional Human Skull Motion to Brain Tissue Deformation in Magnetic Resonance Elastography Studies

[+] Author and Article Information
Andrew A. Badachhape

Biomedical Engineering,
Washington University in St. Louis,
St. Louis, MO 63105
e-mail: abadachhape@wustl.edu

Ruth J. Okamoto, Brent D. Efron, Sam J. Nadell

Mechanical Engineering and Materials Science,
Washington University in St. Louis,
St. Louis, MO 63105

Ramona S. Durham

Biomedical Engineering,
Washington University in St. Louis,
St. Louis, MO 63105

Curtis L. Johnson

Biomedical Engineering,
University of Delaware,
Newark, DE 19716

Philip V. Bayly

Biomedical Engineering,
Washington University in St. Louis,
St. Louis, MO 63105;
Mechanical Engineering and Materials Science,
Washington University in St. Louis,
St. Louis, MO 63105

1Corresponding author.

Manuscript received September 1, 2016; final manuscript received February 15, 2017; published online March 21, 2017. Assoc. Editor: Barclay Morrison.

J Biomech Eng 139(5), 051002 (Mar 21, 2017) (12 pages) Paper No: BIO-16-1363; doi: 10.1115/1.4036146 History: Received September 01, 2016; Revised February 15, 2017

In traumatic brain injury (TBI), membranes such as the dura mater, arachnoid mater, and pia mater play a vital role in transmitting motion from the skull to brain tissue. Magnetic resonance elastography (MRE) is an imaging technique developed for noninvasive estimation of soft tissue material parameters. In MRE, dynamic deformation of brain tissue is induced by skull vibrations during magnetic resonance imaging (MRI); however, skull motion and its mode of transmission to the brain remain largely uncharacterized. In this study, displacements of points in the skull, reconstructed using data from an array of MRI-safe accelerometers, were compared to displacements of neighboring material points in brain tissue, estimated from MRE measurements. Comparison of the relative amplitudes, directions, and temporal phases of harmonic motion in the skulls and brains of six human subjects shows that the skull–brain interface significantly attenuates and delays transmission of motion from skull to brain. In contrast, in a cylindrical gelatin “phantom,” displacements of the rigid case (reconstructed from accelerometer data) were transmitted to the gelatin inside (estimated from MRE data) with little attenuation or phase lag. This quantitative characterization of the skull–brain interface will be valuable in the parameterization and validation of computer models of TBI.

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Grahic Jump Location
Fig. 1

Schematic illustration of the accelerometer mouth guard array (MGA) and its positioning for a human subject. (a) Spacing of the three accelerometers within the MGA. (b) The subject bites down firmly on the mouth guard while lying supine on the pillow actuator. (c) Three-dimensional rendering of the relative placement of the subject, pillow actuator, and MGA inside the head coil.

Grahic Jump Location
Fig. 2

Three-dimensional kinematics are estimated at four points around the skull. (a) Schematic diagram of the accelerometer positions relative to the origin. (b) Sagittal MR image showing the relative distance, rA1/O, between the skull origin, approximated as the posterior clinoid process (circle), and accelerometer 1 (A1) within the MGA. The relative location of the pillow actuator is outlined as the rectangle. The MRE acquisition planes, encompassing twenty slices at 2 mm voxel resolution, are shown. (c) Anatomical (T1-weighted) images are used to determine the position of the four reconstruction points anterior (A), right (R), left (L), and posterior (P) relative to the origin. (d) Regional analysis of MRE measurements is performed by segmenting the MRE images into three rings and four quadrants. A mask based on image amplitude was applied to isolate brain tissue from the skull (dotted oval).

Grahic Jump Location
Fig. 3

Validation of accelerometer motion reconstruction using constrained angular and linear motion. (a-i) The accelerometer MGA was placed on the bottom disk of a torsional vibration demonstration system (ECP 205 Torsional Plant, ECP©, Bell Canyon, CA) and used to reconstruct in-plane motion at the location of a fourth reference accelerometer placed at the top of the platform. Oscillation frequency: 10 Hz. (a-ii) Normalized reconstruction RMS error in the AP direction, NRMSE = 0.04; (a-iii) normalized RMS error in the SI direction, NRMSE = 0.02. (b-i) A horizontal shaker (APS Electro-seis 113 Long Stroke Shaker, APS Dynamics ©, San Juan Capistrano, CA) was used to validate translational motion reconstruction. The MGA was placed on the posterior of the platform while the reference accelerometer was placed on the side. Oscillation frequency: 50 Hz. (b-ii) AP direction NRMSE = 0.04, (b-iii) SI direction NRMSE = 0.08.

Grahic Jump Location
Fig. 4

Reconstructed acceleration profile (RL, AP, and SI components of motion) at skull anterior (A), right (R), and posterior (P) points during MRE of a typical human subject (actuator frequency: 50 Hz, actuator amplitude = 18%)

Grahic Jump Location
Fig. 5

(a) and (d) Representative total MRE displacement fields in (a) the gelatin phantom and (d) a human subject at the first of eight time points; (b) and (e) corresponding wave displacement fields; (c) and (f) corresponding curl fields. Wave displacement is obtained by subtracting rigid-body motion from the total displacement field. Note the different displacement amplitudes in panels (d) and (e). The bar at the bottom of each image indicates the approximate location of the pillow actuator.

Grahic Jump Location
Fig. 6

Rigid-body motion of the gelatin phantom (estimated from MRE measurements) compared with motion of the case (reconstructed from accelerometer data). (a) Motion reconstructed at individual points on the case anterior (A), right (R), left (L), and posterior (P) are compared with corresponding material points within the outermost shell of corresponding gelatin regions. Filled circles on the elliptical trajectory indicate the reference time, t = 0. b) Rigid-body motion coefficients for translation and rotation about the gelatin phantom origin are compared between the phantom case and gelatin. (c) The component of displacement in the AP direction for the case and gelatin posterior reconstruction points is shown as a function of time.

Grahic Jump Location
Fig. 7

Magnitudes (RMS) of (b) wave displacement; (c) curl; and (d) octahedral shear strain in the gelatin phantom. Values are shown for each quadrant-shell ROI (a). For comparison to curl and strain (dimensionless measures of displacement/length), the case displacement magnitude is normalized by the radius of the case (striped). Error bars in all three plots represent the standard deviation of each quantity within the shell ROI.

Grahic Jump Location
Fig. 8

Rigid-body motion of human brain tissue estimated from MRE measurements, compared with skull motion reconstructed from accelerometer data. (a) Trajectories at individual reconstruction points on the skull anterior (A), right (R), left (L), and posterior (P) are compared with analogous trajectories of neighboring brain tissue material points selected from the outer shell ROI. Filled circles on the elliptical trajectories indicate the reference time, t = 0. (b) The amplitude of the rigid-body motion coefficients for translation and rotation about the skull origin are compared between the skull and brain (n = 6). Error bars indicate standard deviation between subjects. (c) The component of displacement in the AP direction is plotted for the skull and brain posterior reconstruction points.

Grahic Jump Location
Fig. 9

Magnitudes (RMS) of (a) wave displacement; (b) curl; and (c) octahedral shear strain, in the human brain. Values are shown for each quadrant-shell ROI. For comparison with curl and strain (dimensionless measures of displacement/length), skull displacement magnitude is normalized by the major semi-axis of the skull (striped). Error bars in all three plots show the standard deviation among subjects (n = 6).

Grahic Jump Location
Fig. 10

Comparison of MRE phase contrast (Φ)  captured by different motion-encoding gradient strengths (MEGS). (a) Visualization of the wrapped and unwrapped phase contrast encoded by the maximum MEGS of 25.9 mT/m at time point 2. (b) Comparison of wrapped and unwrapped MRE phase contrast at a single voxel (circle) between EPI-MRE trials at 4, 7, 10, and 25.9 mT/m. (c) Line plot of MRE phase contrast, normalized to the unwrapped phase contrast at 25.9 mT/m. Unwrapped data points were fitted to a linear model (R2 = 0.99).

Grahic Jump Location
Fig. 11

Artifact in the accelerometer trace can be used to locate landmarks in the MR pulse sequence, such as the RF pulse, refocusing gradient, and spiral gradients. A two-dimensional spiral MRE pulse sequence diagram is shown in Ref. [20]. Bipolar motion-encoding gradients (dashed boxes) are applied sequentially.

Grahic Jump Location
Fig. 12

During 3D harmonic motion, the trajectory of each point depends on the amplitude and phase of each component. (a) The trajectory is a straight line when all three components have the same temporal phase, ψ, even if the component magnitudes, rn, are different. (b) The trajectory becomes an ellipse when the three components have different temporal phase. (c) The spatial angle, β, between the vectors normal to the plane of each ellipse (arrows) was used to describe the difference in spatial orientation of motion (β  = 0.9 rad in this example).




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