Relationships between Scalp, Brain, and Skull Motion Estimated using Magnetic Resonance Elastography

Abstract

The objective of this study was to characterize the relationships between motion in the scalp, skull, and brain. In vivo estimates of motion transmission from the skull to the brain may illuminate the mechanics of traumatic brain injury. Because of challenges in directly sensing skull motion, it is useful to know how well motion of soft tissue of the head, i.e., the scalp, can approximate skull motion or predict brain tissue deformation. In this study, motion of the scalp and brain were measured using magnetic resonance elastography (MRE) and separated into components due to rigid-body displacement and dynamic deformation. Displacement estimates in the scalp were calculated using low motion-encoding gradient strength in order to reduce “phase wrapping” (an ambiguity in displacement estimates caused by the 2π-periodicity of MRE phase contrast). MRE estimates of scalp and brain motion were compared to skull motion estimated from three tri-axial accelerometers. Comparison of the relative amplitudes and phases of harmonic motion in the scalp, skull, and brain of six human subjects indicate that data from scalp-based sensors should be used with caution to estimate skull kinematics, but that fairly consistent relationships exist between scalp, skull, and brain motion. In addition, the measured amplitude and phase relationships of scalp, skull, and brain can be used to evaluate and improve mathematical models of head biomechanics.

1. Introduction

Traumatic brain injury (TBI) is a prevalent neurological disorder with few available treatments (Faul and Coronado, 2015). Computational models of TBI hold promise for injury prediction and prevention; however, these models require experimental data for validation and parameterization (Coats et al., 2012; Miller et al., 2017). A limitation of many models is that the mechanical coupling between the skull and brain remains largely uncharacterized. Measurements of skull and brain motion in vivo would help improve models of head dynamics for use in modeling TBI. Furthermore, using scalp motion, which is easier to measure than either skull or brain motion, to characterize brain-skull dynamics, estimate brain deformation, and assess injury risk would be valuable.

Magnetic resonance imaging (MRI) can provide noninvasive, in vivo assessments of soft tissue displacement during head motion. MRI studies of head and brain motion in vivo have used image registration (Monea et al., 2012) or tagged MRI (Feng et al., 2010; Sabet et al., 2008). Another potential modality for characterizing head dynamics is magnetic resonance elastography (MRE). In MRE, an MRI sequence is modified by the addition of motion-encoding gradients (MEGs) to produce phase-contrast images of harmonic displacements (Scott A. Kruse et al., 2008; Muthupillai et al., 1995). In most MRE studies of the brain, authors have removed the rigid-body component of harmonic displacements and analyzed the resulting wave displacement field, which describes the dynamic deformation of tissue, in order to estimate viscoelastic properties in vivo (Green et al., 2008; Hiscox et al., 2016; Johnson et al., 2016; Scott A Kruse et al., 2008; Murphy et al., 2011; Sack et al., 2008).

In a prior study (Badachhape et al., 2017), we acquired estimates of brain tissue displacement from MRE to characterize rigid-body motion and dynamic deformation of the brain during skull vibration. Estimates of rigid-body motion of the brain were then compared with estimates of rigid-body motion of the skull acquired from three MRI-safe tri-axial accelerometers. We found that (1) rigid-body displacement of the skull was larger than rigid-body displacement of the brain and (2) rigid-body displacement of the brain was larger than its displacements from dynamic deformation.

Though accelerometers can provide estimates of 3D skull kinematics (Badachhape et al., 2017), data acquisition from accelerometers during MRE is cumbersome and susceptible to variability in accelerometer mounting. Using scalp motion from MRE as a surrogate measure of skull motion would enable simpler and more robust comparison of head motion to brain tissue deformation. Importantly, both signals would be measured by the same instrument (MRE). Furthermore, in studies of head impacts in athletes, sensors have been mounted to head scalp tissue to estimate head motion (Wu et al., 2016a). Relating scalp motion to skull and brain motion would be of great value in interpreting data from scalp-mounted sensors.

During brain MRE, the MEG strength is maximized to provide high sensitivity to dynamic deformation of brain tissue. However, this can cause “phase wrapping.” Phase wrapping occurs when phase, which is proportional to displacement and to MEG strength, exceeds the range from −π to π. Previous work has shown that reducing the MEG strength allows imaging of brain tissue motion without phase wrapping (Badachhape et al., 2017). While it is difficult to measure skull motion directly with MRE (due to the low MR signal in bone) the motion of soft tissue surrounding the skull (scalp) can readily be measured with lower MEG strength, and may provide a reasonable estimate of skull motion. To assess the relationships between and scalp motion and motion of the brain and skull, we estimated displacements and deformations of the scalp and brain by MRE and compared them to skull displacements estimated from three triaxial accelerometers mounted on an instrumented mouth guard.

2. Methods

2.1 Accelerometer and MRE Data Collection

MRE was performed on 6 adult human subjects (5 males and 1 female; median age 28 years) on a Siemens Trio® 3T MRI scanner located at the Center for Clinical Imaging Research at Washington University in St. Louis. All studies were approved by the Institutional Review Board (IRB). The subject was positioned supine within a 12 channel head coil. Skull vibrations were induced at a frequency of 50 Hz through a commercially available system using a “pillow” actuator (Resoundant, Rochester, MN) positioned at the back of the head (Figure 1a,c), as described previously in Badachhape et al., 2017. At 50 Hz, skull motion is effectively transmitted to the brain and multiple shear waves are observed in the brain (Badachhape et al., 2017; Hiscox et al., 2016; Papazoglou et al., 2008). Accordingly, MRE in humans is commonly performed at 50–60 Hz, and 50 Hz excitation facilitates comparison to prior studies. The subject’s head rested on the inflatable portion of the actuator and was stabilized by padding at the temples. Skull kinematics were estimated using three MRI-safe, tri-axial accelerometers (TSD109C2-MRI, BIOPAC©, Goleta, CA) embedded in a mouth guard array (MGA) based on a commercial sports mouth guard and 3D-printed interface (Figure 1b). The RMS amplitudes of acceleration recorded at the accelerometer sites ranged from 2–4 m/s² with the dominant component in the AP direction, similar to Badachhape et al., 2017.

Figure 1.

Overview of human EPI-MRE data collection setup. a) Schematic rendering of the accelerometer mouth guard array (MGA) and its positioning for a human subject lying on the pillow actuator. (b) Three tri-axial accelerometers are embedded within the MGA. (c) The pillow actuator is placed within the 12 channel head coil and the subject’s head is placed on the actuator and preloaded with padding (not shown). (d) Twenty-four axial EPI-MRE slices with 3 mm voxel resolution were acquired with a slice volume centered on the corpus callosum. Due to artifact in the lower slices, only the central twenty slices (outlined by the dotted yellow) were analyzed in this study.

MRE displacement data were acquired using an echo-planar imaging (EPI) sequence augmented with two bipolar MEGs. Images were acquired with 3 MEG directions at four MEG strengths with 8 phase offsets. MEGs were flow-compensated, applied bilateral to the refocusing gradient, with duration matched to vibration period (Johnson et al., 2014). Additional parameters included: TR/TE = 2880/63 ms; GRAPPA = 3; FOV = 240×240 mm²; matrix = 80×80 matrix; 24 axial slices; and 3 mm isotropic voxels. Initially, MEG strengths of 8, 10, 16, and 26 mT/m were selected for this study (1 subject); however some phase wrapping was still observed in scalp tissue voxels at 8 mT/m so the remaining scans (5 subjects) were done with a lower range of MEG strengths: 4, 7, 10, and 26 mT/m. Comparison between data obtained with 4 mT/m and 7 mT/m MEGs in the remaining subjects indicated that 7 mT/m was the best choice for encoding scalp and brain motion without phase wrapping. The highest MEG strength of 26 mT/m was used to quantify brain deformation for all six subjects. MRE phase data were filtered using the “medfilt3” command in MATLAB® (2014a, MathWorks®, Natick, MA). Due to field inhomogeneity artifact at the bases of both brain and scalp, only the central 20 slices were analyzed (Figure 1d).

The accelerometers induced imaging artifacts, thus the scanning protocol began with a truncated, six-slice version of the EPI sequence (~40 s duration) to record both skull accelerations and signal landmarks during the MRE sequence (Appendix). Skull accelerations and MRE sequence triggers were recorded at 10,000 samples/sec. The accelerometer array was then removed while the subject’s head remained in the head coil. A T1-weighted 3D MP-RAGE sequence with 0.9 mm isotropic voxel resolution was performed followed by four 24 slice EPI-MRE scans, each with increasing MEG strength. The duration of each 24 slice MRE scan was 2.5 minutes; the total time of the scanning procedure was 35–45 minutes.

2.2 Estimation of 3D Skull Motion from Accelerometer Data

Skull kinematics were estimated from accelerometer recordings using methods detailed in Badachhape et al. 2017 (summarized here for convenience). Skull vibration at 50 Hz may be approximated as rigid-body motion (Gurdjian et al., 1970); enabling use of standard 3D kinematic equations (Eq. 1a–c) (Genin and Ginsberg, 1995). Here, a is the linear acceleration vector, α is the angular acceleration vector, r is the position vector from the origin (the posterior clinoid process, a protrusion at the base of the cranial cavity) to the point of interest, and ω is angular velocity. The Cartesian components, denoted by subscripts x, y, and z, represent the right-left (RL), anterior-posterior (AP), and superior-inferior (SI) directions. Thus, ( $a_x^o,a_y^o,a_z^o$) are, respectively, the RL, AP, and SI linear accelerations of the skull origin; (ω_x, ω_y, ω_z) are angular velocities about the RL, AP, and SI directions; and (α_x, α_y, α_z) are the components of angular acceleration. (a_x, a_y, a_z) are the components of linear acceleration a point located at (r_x, r_y, r_z), relative to the skull origin.

$$a_x=a_x^o+({\alpha }_y{r}_z-{\alpha }_z{r}_y)+({\omega }_x({\omega }_y{r}_y+{\omega }_z{r}_z)-r_x({\omega }_y^2+{\omega }_z^2))$$ (1a)

$$a_y=a_y^o+({\alpha }_z{r}_x-{\alpha }_x{r}_z)+({\omega }_y({\omega }_z{r}_z+{\omega }_x{r}_x)-r_y({\omega }_x^2+{\omega }_z^2))$$ (1b)

$$a_z=a_z^o+({\alpha }_x{r}_y-{\alpha }_y{r}_x)+({\omega }_z({\omega }_x{r}_x+{\omega }_y{r}_y)-r_z({\omega }_x^2+{\omega }_y^2))$$ (1c)

These equations contain 9 unknowns (3 components of a, α, and ω), and are solved using the known values of linear acceleration at the positions of the three tri-axial accelerometers. The acceleration signals are harmonic and can be expressed using Fourier coefficients as a sum of sinusoids j. Equations 2a–b demonstrate how displacement, u, can be determined from these Fourier coefficients. Here Ω is frequency, φ is phase shift, A is amplitude, t is time, and the subscript i refers to the three components of motion.

$$a_i={\mathrm{\sum }}_j{A}_{ij}\mathit{sin}({\mathit{\Omega }}_{j}t+{\phi }_j)$$ (2a)

$$\Rightarrow u_i=-{\mathrm{\sum }}_j\frac{A_{ij}}{{\mathit{\Omega }}_j^2}\mathit{sin}({\mathit{\Omega }}_{j}t+{\phi }_j)$$ (2b)

The components of displacement at a point on the skull at position r can then be reconstructed by defining three components of translation ( ${\overline{u}}_x^o,{\overline{u}}_y^o$ and ${\overline{u}}_z^o$) and three components of rotation (θ_x, θ_y, and θ_z) about the skull origin and solving Equations 3a–c:

$${\overline{u}}_x={\overline{u}}_x^o+{\theta }_y{r}_z-{\theta }_z{r}_y$$ (3a)

$${\overline{u}}_y={\overline{u}}_y^o+{\theta }_z{r}_x-{\theta }_x{r}_z$$ (3b)

$${\overline{u}}_z={\overline{u}}_z^o+{\theta }_z{r}_y-{\theta }_y{r}_x$$ (3c)

2.3 Estimation of Brain and Scalp Displacements from MRE

During MRE, oscillating motion-encoding gradients are applied in a specified direction to encode displacement as phase of the MR signal. The resulting MRE phase contrast (Φ), is proportional to the component of displacement in the direction of the gradient (Atay et al., 2008; Muthupillai et al., 1995). The sensitivity of phase measured by an MRE sequence depends on the strength, shape, and number of the MEGs (Atay et al., 2008; Badachhape et al., 2017). For this study, displacement conversions were 10.47μm/rad (7 mT/m), 9.17 μm /rad (8 mT/m), and 2.82 μm /rad (26 mT/m). By applying motion-encoding gradients in three orthogonal directions, the 3D vector displacement field (u) is obtained. The displacement field can be separated into displacements due to (i) rigid-body motion and (ii) dynamic deformation (see Appendix), which includes the contributions of both shear and longitudinal waves,

Phase wrapping occurs when the phase contrast from any component of total displacement exceeds the range −π to π (Figure 2). During MRE, the magnitude of motion-encoded phase measured from scalp voxels was typically larger than the phase measured in brain voxels. With the actuator type and placement used in this study, scalp displacements in the AP direction were usually phase-wrapped at higher MEG strengths (10 mT/m or 26 mT/m). Unwrapped scalp displacements were found by using data obtained at a lower MEG strength of 7 mT/m (in five subjects) and 8 mT/m (in one subject). Similarly, the anterior-posterior (AP) component of brain displacement may also be wrapped (Figure 2d) at higher MEG strengths. Wrapped brain AP displacement data obtained at 26 mT/m MEG strength were spatially unwrapped using FSL PRELUDE (Jenkinson, 2003) and then temporally unwrapped by comparing to MRE data at the same time points obtained at 7 or 8 mT/m MEG strength for the same subject (Figure 2b–c).

Figure 2.

Phase wrapping is a challenge for capturing large motion in an MRE sequence. a) Anatomical T1W image of the central slice of the MRE slice volume. Anatomical data are interpolated to have the same voxel resolution (3 mm) as MRE images. b) MRE data acquisition at a lower MEGS of 7 mT/m provides original unwrapped signal with a lower resulting phase. c) RL (red), AP (green), and SI (blue) components of MRE phase contrast at a single brain voxel in Figure 2b (white circle) are shown with a period of 8 time points. MRE phase contrast is converted to an apparent displacement estimate (u_app) using a phase-to-displacement calibration factor based on the MEGS. d) AP component of MRE phase contrast acquired at 26 mT/m exceeds the principal range of −π:π and is wrapped in some scalp and brain regions. e) Brain displacement encoded at 26 mT/m is spatially and temporally unwrapped. f) Phase wrapping is predominantly seen in the AP component of brain displacement (solid green) at a single brain voxel in Figure 2d. After unwrapping, the original AP component of displacement (dotted green) is recovered for the same brain voxel. MRE phase contrast acquired at 7 mT/m is lower than at 26 mT/m, however apparent displacement is proportional after unwrapping.

Scalp and brain regions were isolated by thresholding MRE signal magnitude (S) (Figure 3d–e). These regions were validated through comparison with T1-weighted images interpolated onto the MRE slice planes. The scalp is deformable and heterogeneously coupled to the skull. We postulated that scalp voxels with higher amplitudes of harmonic motion are more closely coupled to the skull, and more representative of skull motion. Accordingly, scalp voxels with high motion amplitude and dominant contributions at the fundamental frequency of 50 Hz were selected from MRE data obtained at 7 mT/m and 8 mT/m. First, the head was divided into four quadrants, anterior (A), right (R), left (L), and posterior (P) (Figure 3a); second, scalp voxels in each quadrant were given a composite score (β) as calculated in Equation 4a–c:

$$\overline{\mathrm{\Phi }}=\Vert \mathit{\Phi }\Vert /\Vert {\mathit{\Phi }}_{\mathit{max}}\Vert$$ (4a)

$$\overline{c}=\Vert \mathit{c}\Vert /\Vert {\mathit{c}}_{\mathit{max}}\Vert ;c_i=\frac{\mid c_{1i}\mid }{{\mathrm{\sum }}_{n=0}^7\mid {\mathit{c}}_{\mathit{ni}}\mid }$$ (4b)

$$\beta =0.5\overline{\mathrm{\Phi }}+0.5\overline{c}$$ (4c)

Figure 3.

Scalp voxels for estimation of rigid-body motion are selected by identifying voxels with high MRE phase contrast amplitude and coherent harmonic motion. a) MRE slices are divided into four quadrants to ensure that selected voxels are spatially distributed throughout the scalp. These four quadrants are also used for later analysis of skull, scalp, and brain motion. b) Scalp voxel score β is shown for central MRE slice. Score is computed by equally weighting MRE phase contrast amplitude and the relative power at the fundamental frequency (50 Hz). c) All scalp voxels are shown as 3D points surrounding the MRE slice volume. Voxels selected for scalp rigid-body motion estimation are outlined in red. d) MRE signal magnitude (S) is higher in brain tissue than in scalp. Thresholding the image by signal magnitude enables creation of brain and scalp region-of-interest (ROI) masks. e) Histogram of signal distribution for both scalp (purple) and brain (gray) voxels.

Here, MRE phase contrast amplitude (Φ̄) at each voxel is calculated as the amplitude of phase contrast (||Φ||) scaled by the maximum phase contrast amplitude among all scalp voxels (||Φ_max||) (Eq. 4a). The normalized amplitude of the fundamental harmonic (c̄) at each voxel is then calculated as the relative amplitude at the fundamental frequency (||c||) scaled by its maximum among the scalp voxels (||c_max||). For each component, c_i, the contribution of the fundamental frequency is calculated from amplitude of the FFT at the fundamental frequency (|c_1i|) divided by the sum of the FFT amplitudes at all frequencies ( ${\mathrm{\sum }}_{n=0}^7\mid c_{ni}\mid$) (Eq. 4b). The composite score, β, is then calculated from the sum of the two measures (Figure 3b; Eq. 4c). The N voxels in each quadrant with the highest scores were selected to give a total of 4N scalp voxels (Figure 3c). For the current study, N =100 voxels were chosen per quadrant. MRE data from the brain and selected scalp voxels were then separately fitted to a model of rigid-body motion to estimate rigid-body translation (ū) and rotation (θ) about a common origin located at the posterior clinoid process. This number of voxels (N=100 in each quadrant, ~3–5% of total) provides data from sites spatially distributed throughout the scalp, while limiting the effects of noise and emphasizing the contributions of voxels with strong harmonic displacements (interpreted as tightly coupled to the skull). Estimates of rigid-body motion in the scalp are affected by the number of voxels used; for instance, using all scalp voxels reduces estimates of rigid-body motion amplitude by 25–55% due partly to the effects of fitting noise.

Estimates of skull displacement (reconstructed from accelerometer measurements) were compared to analogous estimates of rigid-body displacement within the brain and scalp (estimated from MRE). In harmonic motion, where the three components of motion are not in phase, the 3D trajectory of each point in the skull, scalp, and brain is an ellipse, which can be represented as a complex coefficient vector, u₀, multiplied by a complex exponential in time, u(t) = u₀exp(iΩt). The elliptical trajectories of material points in skull, scalp, and brain were described by their relative amplitudes and temporal phase. The amplitude of each elliptical trajectory is reported as its mean radius: the circumference of the ellipse divided by 2π.

To describe temporal relationships, consider two 3D complex coefficient vectors u₀ and v₀, corresponding to elliptical trajectories of skull motion and brain rigid-body motion, respectively. As shown in Equation 5, the dot product of the two complex coefficient vectors can be used to calculate temporal phase shift, ϕ (Scharnhorst, 2001).

$$\varphi =\angle ({{\mathit{u}}_0}^{\ast }·{\mathit{v}}_0)$$ (5)

Similarly, the temporal phase shift between scalp and brain rigid-body motion can be calculated. Phase and amplitude differences between the skull, scalp, and brain were compared by analyzing the elliptical trajectories of voxels within corresponding quadrants (Figure 3a). In order to compare phase delay between accelerometer estimates of skull motion and MRE estimates of rigid-body motion, both sets of measurements were referenced to the EPI refocusing gradient (Badachhape et al. 2017).

3. Results

3.1 Comparison of Total Displacement of the Skull, Scalp, and Brain

One period of harmonic motion (period T) is described by eight temporal samples (at t = T/8,2T/8,...,T). In Figure 4, total displacement in the (dominant) AP direction is shown in the skull, scalp, and brain for a representative subject at four time points (an approximate skull “shell” was created from the region between the scalp and brain masks). Here, total displacement in the skull is simply the rigid-body motion estimated from accelerometers. In the scalp and brain, total motion includes contributions from both dynamic deformation and rigid-body motion. (Animations of skull, scalp, and brain motion are in Supplementary Video S1).

Figure 4.

Total displacements (AP-component) of the a) skull, b) scalp, and c) brain for a single subject are shown at four equally-spaced time points within one cycle of harmonic excitation.

3.2 Comparison of Rigid-body Displacement of the Skull, Scalp, and Brain

Rigid-body motion of the scalp and brain were extracted from 7–8 mT/m MRE data and compared with rigid-body motion of the skull estimated from accelerometers (Figure 5). The skull typically has the largest estimated rigid-body motion amplitude, followed by the scalp and the brain, respectively. Significant phase differences exist between rigid-body motions of each region. The amplitude and phase of rigid-body motion across all six subjects are compared in Figure 6. The largest component of translation for all three regions is in the AP direction, though the skull often exhibits a relatively large SI component of translation. The highest component of rotation is typically about the RL axis. The brain exhibits lower rotations than the skull and scalp. As shown in Figure 6c, the mean temporal phase shift between skull and brain motion (ϕ_Sk/Br) is similar to the phase shift between scalp and brain motion (ϕ_Sc/Br), however there are much larger variations in estimated phase shift between skull and brain motion compared to the variations of estimates of phase shift between the scalp and brain. Table 1 lists the mean and standard deviation for ϕ_Sk/Br and ϕ_Sc/Br across each of the four quadrants. (Animations of rigid-body motion are in Supplementary Videos S2).

Figure 5.

Rigid-body displacements (AP-component) for a single subject are shown at the time point corresponding to the maximum displacement of the a) skull (t=5T/8), b) scalp (t=6T/8), and c) brain (t=4T/8). d) Time course of representative voxels in each region near the anterior of the head (Skull-cyan, Scalp-magenta, Brain-black) shows differences in amplitude and phase of AP rigid-body motion. The location of the representative voxels are shown on panels a), b), and c) respectively.

Figure 6.

Comparison of RMS amplitude of rigid-body motion: a) translation and b) rotation for the skull (red), scalp (green), and brain (blue) at the posterior clinoid process. Error bars indicate standard deviation (n=6). C) Phase shift [ϕ_Sk/Br] between harmonic displacements of anterior points on the skull and brain (red); phase shift [ϕ_Sc/Br] between harmonic displacements of anterior points on the scalp and brain (green). Mean phase delay is plotted as a vector and scaled by deviation. Individual observations are shown for each subject.

Table 1.

(i) Temporal phase shift, ϕ_Sk/Br, between harmonic motion of the skull (estimated by accelerometers and brain (estimated by MRE) and (ii) phase shift, ϕ_Sc/Br, between scalp and brain motion (both estimated from MRE). Results are shown for each of the four quadrants.

	ϕSk/Br (rad)	ϕSc/Br (rad)
Ant.	5.52 ± 1.18	5.02 ± 0.32
Right	5.51 ± 1.20	5.00 ± 0.30
Left	5.49 ± 1.19	5.08 ± 0.38
Post.	5.48 ± 1.20	5.03 ± 0.34

3.3 Comparison of Dynamic Deformations of the Scalp and Brain

Dynamic deformation, ũ, in the scalp and brain was estimated from the difference between total motion and rigid-body motion at 7 mT/m for scalp data and 26 mT/m for brain data. Figure 7 shows each component of dynamic deformation for the full scalp region and a single slice of brain tissue at a single time point. (Supplementary Video S3 illustrates dynamic deformation in the scalp and brain).

Figure 7.

RL, AP, and SI components of dynamic deformation for a) scalp and b) central slice of brain tissue. Note difference in color scale between scalp and brain figures, reflecting the difference in deformation amplitude.

3.4 Comparison of Rigid-body and Deformation Amplitudes in the Skull, Scalp, and Brain

Amplitudes of displacements due to rigid-body motion (skull, scalp, and brain) and deformation (scalp and brain) were calculated from the mean elliptical radius for voxels within the four quadrants shown in Figure 3a. All available voxels were used for both the skull and brain while for the scalp only the 400 voxels with the highest β scores were used. Scalp and brain rigid-body and deformation amplitudes were compared across the six subjects for each quadrant (Figure 8). Estimated rigid-body displacements of the skull are larger than those of the scalp or brain. Dynamic deformation is larger in scalp than in brain (Figure 7). Brain tissue displacement due to deformation was consistently smaller than rigid-body displacement in the skull and rigid-body displacement in the scalp.

Figure 8.

Ratios of rigid-body displacement amplitude for the a) scalp and skull, b) brain and skull, and c) brain and scalp followed by ratios of dynamic deformation amplitude to rigid-body displacement amplitude for the d) scalp and skull, e) brain and skull, and f) brain and scalp.

4. Discussion

MRE estimates of scalp and brain tissue motion were compared to accelerometer-derived estimates of skull motion to illuminate the relationship between scalp motion (which can be measured readily with external sensors in a variety of situations) and brain motion (which can only be measured with sophisticated imaging technology under controlled conditions). Under excitation at 50 Hz using the pillow actuator, rigid-body translation in the AP direction was dominant in all regions. Rigid-body displacements of the brain and scalp, estimated by MRE, are smaller than skull displacement estimated from accelerometers (Figure 5). The scalp also appears to experience relatively high dynamic deformations. In contrast, the brain experiences low amplitudes of dynamic deformation compared to its rigid-body displacement.

The motions of scalp and skull are qualitatively similar, with large AP translations and large rotations about the RL axis relative to other displacement components. In contrast, while the brain experiences high AP translation (Figure 6), it undergoes relatively little rotation. The average estimated phase shift between skull and brain is similar to the phase shift between scalp and brain, though the former has a larger variability across subjects. The large phase shifts suggest that the skull-brain interface is quite compliant. The higher variability between skull and brain phase shift may arise because skull motion is measured with a different sensor (scalp and brain are both measured by MRE), and the coupling between the accelerometer array and skull is more variable from subject-to-subject.

Significant attenuation of motion transmitted from the skull to brain was observed, which was mirrored by the ratio between scalp and brain motion. The relatively consistent ratio between the amplitude of rigid-body displacement of the scalp (from MRE) to the amplitude of deformation in brain tissue (from MRE) indicates that MRE alone can be used to approximately describe head biomechanics. Similarities in the amplitude of AP-translation and θ_RL-rotation in the scalp and skull, relative to other components of rotation, also support this conclusion (Figure 6b). The differences between brain rigid-body motion and brain deformation are consistent with previous work (Badachhape et al., 2017).

In the scalp, motion imparted from the skull is somewhat attenuated, and dynamic deformations are comparable in amplitude to rigid-body motion. In monitoring athletes for head impact, sensors may be embedded in helmets (Broglio et al., 2012), attached to mouth guards (Camarillo et al., 2013), or mounted to the scalp, (Wu et al., 2016a, 2016b). The current data confirm that scalp-based measurements are not precise measurements of underlying skull motion, but that consistent relationships between scalp motion, skull motion, and brain deformation may be exploited using multiple, spatially-distributed scalp sensors.

Some experimental limitations are acknowledged. Estimates of skull motion assume perfect coupling between the skull and accelerometers. Additionally, the spacing between accelerometers is small compared to the size of the head, which can limit the precision of rigid-body motion estimates in the skull. Large deformations in the scalp might affect estimates of scalp rigid-body motion, though scalp voxels for rigid-body motion estimation are selected from areas postulated to be well coupled to the skull. The MRE sequence used in this study is not optimized for imaging the scalp; some measurement uncertainty may arise due to lower signal-to-noise.

5. Conclusion

This study demonstrates the feasibility of MRE to simultaneously measure scalp motion and brain tissue deformation for characterizing the biodynamics of the human head. Results suggest that reasonable estimates of skull motion and brain deformation can be obtained from suitable arrays of scalp-mounted sensors, although such data must be interpreted with care (Wu et al., 2016b). Estimates of rigid-body displacement of the scalp are typically 20–50% lower than corresponding estimates of rigid-body displacement of the skull. Brain displacements due to deformation are generally an order of magnitude smaller than skull displacements, consistent with earlier observations (Badachhape et al., 2017). Differences in rigid-body translation and rotation of the brain relative to the skull and scalp show quantitatively the mechanical effects of the skull-brain interface. The current measurements of simultaneous skull, scalp and brain motion in vivo will inform future experimental studies of head kinematics and lead to improved simulations of TBI biomechanics.

Supplementary Material

2. Supplementary Video S1.

Three-dimensional animations of a) skull, b) scalp, and c) brain total displacement for a single subject are shown. While total displacement in all three directions (RL, AP, SI) is animated, only the AP component of displacement is measured by the color scale. Animation displacement is scaled by 300x.

3. Supplementary Video S2.

Three-dimensional animations of a) skull, b) scalp, and c) brain rigid-body displacement for a single subject are shown. While rigid-body displacement in all three directions (RL, AP, SI) is animated, only the AP component of displacement is measured by the color scale. Animation displacement is scaled by 300x.

4. Supplementary Video S3.

Animations of the RL, AP, and SI components of dynamic deformation for a) scalp and b) central slice of brain tissue. Note difference in color scale between scalp and brain figures, reflecting the difference in deformation amplitude. Scalp animation displacement is scaled by 300x while brain animation displacement is scaled by 3000x.

Appendix. Characterizing Brain Tissue Displacement and Dynamic Deformation with MRE

MRE phase contrast, Φ describes tissue displacement during harmonic actuation. Phase contrast images of displacement are obtained by using time-varying (square wave) motion-encoding gradients, G(t) to encode the harmonic displacement field u(r,t):

$$\mathrm{\Phi }(\mathit{r})=N\gamma {\int }_0^T\mathit{G}(t)·\mathit{u}(\mathit{r},t)dt$$ (A.1)

where γ is the gyromagnetic ratio of ¹H, T is the period, N is the number of motion-encoding gradients, and u(r,t) = u_oe^i(Ωt−ψ) is the vector of displacement at position r and time t. Here, Ω is angular frequency (rad/s) and ψ = ψ(r) is the temporal phase shift of the displacement at that voxel. Evaluation of this integral yields an expression for the MRE phase contrast Φ, including the temporal phase shift:

$$\mathrm{\Phi }=\frac{4N\gamma G{u}_G{e}^{-i\left(\psi -\frac{\pi }{2}\right)}}{\mathit{\Omega }}$$ (A.2)

Here, u_G is the component of u_o in the direction of the gradient: u_G = G · u_o/G and G is the motion encoding gradient strength. The sensitivity of the sequence is doubled by computing the phase difference between acquisitions using positively (P) and negatively (N) polarized motion-encoding gradients, which also serves to remove static background phase from imaging gradients.

$${\mathrm{\Phi }}_T={\mathrm{\Phi }}_P-{\mathrm{\Phi }}_N=2{\mathrm{\Phi }}_P=\frac{8N\gamma G{u}_G{e}^{-i\left(\psi -\frac{\pi }{2}\right)}}{\mathit{\Omega }}$$ (A.3)

The magnitudes of the total (reported) phase Φ_T and of the displacement u_G are linearly related to each other by the ratio u_G/Φ_T = Ω/(8NγG). For the echo-planar imaging (EPI) sequence used in this study, Ω = 2π(50 s⁻¹), N = 2, and γ of ¹H is 2.68(10⁵)rad/(s·mT), so that u_G/Φ_T = 2.82 μm/rad at a motion-encoding gradient strength of G = 26mT/m.

As shown in Badachhape et al., 2017, clear artifacts (spikes) in the recorded accelerometer signal correspond to specific events in the MRE pulse sequence. A pulse sequence diagram for the EPI-MRE sequence, annotated with the timing of the RF pulse, refocusing gradient, and motion-encoding gradients relative to the acceleration signals, is shown in Figure A1a. The sequence is repeated six times, sequentially applying positive and negative polarity motion-encoding gradients along three orthogonal directions (G_x,G_y,G_z) to record three-dimensional displacement vector fields. The timing of the RF pulse and refocusing pulse are then shifted by 1/8 of the cycle duration (2.5 ms) relative to the actuation to estimate the displacement field at 8 time points during each cycle of harmonic motion (T = 20 ms). To relate the phases of skull motion and brain motion, the center of the 180° refocusing pulse is chosen as a common landmark for synchronizing both accelerometer and MRE signals.

Total harmonic displacement of tissue encoded as MRE phase (Φ) can be separated into two contributions: rigid-body displacement and dynamic deformation. For biological tissue, the bulk modulus, κ, is typically large enough that shear waves are the dominant components of dynamic deformation (Manduca et al., 2001). In MRE of the brain, the tissue is often assumed to be isotropic and the curl of the displacement field is used to isolate only shear wave contributions (Clayton et al., 2012). For our analysis, we subtract rigid-body displacement, ū, from total displacement, u, at each of the eight time points of our harmonic displacement signal in order to estimate displacement due to dynamic deformation, ũ (Figure A1b–c) (Badachhape et al., 2017).

Figure A1.

Characterization of brain tissue displacement and deformation using an EPI-MRE sequence. a) Artifacts (spikes) in the accelerometer signal trace correspond to “landmark” events in the EPI pulse sequence, such as the RF pulse and refocusing gradient. Bipolar motion-encoding gradients (gray lines) are applied sequentially in the x, y, or z direction on each side of the refocusing gradient. b) MRE phase (Φ) encodes total displacement, which includes displacements due to both rigid-body motion and dynamic deformation. c) Representative AP-components of displacement fields for a single axial slice of brain tissue at time point 5T/8: (i) T1-weighted image, (ii) total displacement (u), (iii) rigid-body displacement (ū), (iv) displacement due to dynamic deformation (ũ).