Mechanical transient-based magnetic resonance elastography

Authors


Abstract

Magnetic resonance elastography (MRE) is a technique for quantifying material properties by measuring cyclic displacements of propagating shear waves. As an alternative to dynamic harmonic wave MRE or quasi-steady-state methods, the idea of using a transient impulse for mechanical excitation is introduced. Two processing methods to calculate shear stiffness from transient data were developed. The techniques were tested in phantom studies, and the transient results were found to be comparable to the harmonic wave results. Transient wave based analysis was applied to the brains of six healthy volunteers in order to assess the method in areas of complex wave patterns and geometry. The results demonstrated the feasibility of measuring brain stiffness in vivo using a transient mechanical excitation. Transient and harmonic methods both measure white matter (∼12 kPa) to be stiffer than gray matter (∼8 kPa). There were some anatomic differences between harmonic and transient MRE, specifically where the transient results better depicted the deeper structures of the brain. Magn Reson Med 53:628–639, 2005. © 2005 Wiley-Liss, Inc.

Magnetic resonance elastography (MRE) is a recently described imaging technique (1, 2) that quantifies material stiffness by measuring cyclic displacements of propagating shear waves. Externally driven MRI-based methods have been described using quasi-static compression methods (3–5) and dynamic shear waves (1). The quasi-static methods measure strain resulting from macroscopic compression of an object and attempt to compute elasticity based on a model of internal stress distribution. Dynamic MRE does not require such a model and is applicable to structures such as the head, which cannot be macroscopically compressed. To date, most work in dynamic MRE has focused on the use of harmonic (1, 6, 7) or steady-state (8, 9) mechanical excitation. Harmonic, in this case, refers to several periods of sinusoidal motion at a single frequency versus continual driving at a single frequency. However, mechanical transients may offer certain advantages in dynamic MRE, such as potentially simplifying the inversion process.

The use of mechanical transients has been introduced in the ultrasound elastography literature as a method for avoiding diffraction biases generated by harmonic excitation (10–12). Transient ultrasound elastography has been used to analyze soft tissues (13–15) including the liver (16), the breast (17), and muscle tissue (18). Ultrasound elastography has the ability to capture motion at much higher frame rates but MRE offers “higher sensitivity and resolution” (12) and has no need for an acoustic window into the skull.

Mechanical transients have been investigated as a method to model traumatic brain injury (19), but there is still debate about the underlying material properties of the in vivo human brain (20, 21). An understanding of the material properties of the in vivo human brain would allow for more accurate mathematical simulations of traumatic brain injury and could potentially be used to study diffuse disease, such as Alzheimer's disease, or to complement fiber tract studies.

The hypothesis of this work is that transient waves can be used as an alternative to harmonic excitation to probe material properties, especially for situations with complex wave patterns and geometries such as in the brain, and will yield results comparable to harmonic MRE for a range of tissue stiffness expected in vivo. The purpose of this work was to develop transient wave mechanical excitation techniques, to develop data acquisition and reconstruction methods providing quantitative stiffness information, to perform comparisons to harmonic wave methods within tissue simulating phantoms, and to test the feasibility of quantitatively assessing the mechanical properties of the human brain in vivo (22–24).

THEORY

The MRE technique consists of a combination of a motion driver, an imaging sequence with motion encoding gradients, and data inversion (Fig. 1). As the driver applies mechanical excitation, the object is imaged with a phase contrast technique to measure displacement patterns. Dynamic MRE typically uses several periods of mechanical excitation in combination with several relative phase offsets between these and the motion sensitization gradients to sample the wave field at different phases in the motion cycle. Reconstruction algorithms then provide an estimate of shear stiffness (the effective shear modulus at the driving frequency) at each point in the image (25). Stiffness reconstruction can be performed on the harmonic wave data using a local frequency estimation (LFE) technique, which is based on the spatial frequency content of the wave image (26), or by direct inversion of the Helmholtz equation from filtered data and its spatial Laplacian (25, 27, 28). However, stiffness reconstruction methods previously described from harmonic wave data (25) assume a complete wave field and are inappropriate for transient wave data, in which the wave is only present in a portion of the image at any given time. Figure 2 shows a comparison of typical harmonic wave and transient wave images.

Figure 1.

Schematic of gradient echo pulse sequence with an additional transient motion-encoding gradient. By varying the phase offset, θ, the transient wave is captured at several depths in the phantom. The motion driver is shown in contact with a phantom.

Figure 2.

Wave images of harmonic wave experiment (left) and transient wave experiment (right) in a phantom.

The processing used in MRE makes the assumption that the captured phase image is indicative of the underlying motion. As explained in Ref. (1), this is a good assumption for harmonic wave motion and was solved directly for sinusoidal motion and rectangular gradients. When using transient motion and time-windowed gradients, the relationship is not as straightforward.

The relationship among the phase pattern, wave motion, and gradients in the frequency domain is given by (⊗ denotes convolution)

equation image

where f is frequency and Ξ(f), Γ(f), and W(f) are the Fourier transforms of the displacement, the motion sensitizing gradient, and the windowing function, respectively (27). Therefore, the phase shift measured is a convolution of the displacement with the motion sensitizing gradient. In the harmonic case, the result of this convolution is itself a sinusoid at the driving frequency, and since the measured phase shift is the output of a linear filter, the result satisfies the same mechanical equation of motion as the displacement itself. Assuming a nondispersive material, this holds true for the transient case.

In the transient case, the waveform comprises a broad range of frequencies. If the shear stiffness is independent of frequency, the situation is as above. However, if the material is dispersive, the shear stiffness varies with frequency. In this case, the calculations will yield a single shear stiffness that is a weighted average of the stiffness values at different frequencies, and the results from the measured phase data will be a different weighted average than what would have been obtained from the actual displacement. Using different motion sensitization waveforms would yield different weightings, depending on the frequency response of the sensitizing gradient. In practice, shear stiffness will often vary with frequency, but not dramatically, and the average result calculated will closely approximate the value at the central frequency.

Another gradient function that can be considered for capturing wave motion is an impulse function. A sinc function can be modified to approximate an impulse function by shortening its duration and increasing its amplitude to the extent permitted by maximum gradient amplitude, duty cycle, and slew rate limits. A sinc gradient would be equally sensitive across a range of frequencies and would give a more accurate measure of the true displacement compared to a single cycle of a bipolar rectangular gradient. Conversely, a single cycle of a bipolar rectangular gradient would have the greatest motion sensitivity about the center frequency of the gradient, but would distort the shape of the transient pulse, which is illustrated in Fig. 3. Figure 3a shows an example of a time-windowed sinusoidal excitation motion. Figure 3b shows the calculated phase profile that would result from application of a bipolar rectangular motion sensitization gradient. Figure 3b shows the calculated phase profile that would result from application of a sinc motion sensitization gradient. This analysis shows that there is a tradeoff between sensitivity and fidelity of the motion waveform that should be tested.

Figure 3.

(a). Example of a time-windowed sinusoidal excitation motion. (b) Phase profile that would result from application of a bipolar rectangular motion sensitization gradient. (c) Phase profile that would result from application of sinc motion sensitization gradient.

Two independent processing methods to calculate shear stiffness from the transient wave data were tested in this work. The first is a time-of-arrival (TOA) method that tracks a transient wave through the object of interest to estimate wave speed and therefore stiffness. The second is a transient direct inversion (TDI) of the wave equation using spatial and temporal displacement derivatives. In this study, the transient excitation/inversion methods were compared to the harmonic wave excitation/inversion technique to quantify the effectiveness of the new technique. In both cases, the system is modeled as a linearly elastic material with underlying assumptions of isotropy, local homogeneity, and incompressibility (see (25, 27) for a discussion of these assumptions in the harmonic case).

Time Of Arrival

For the time-of-arrival method, simple plane wave propagation is assumed locally, and the shear stiffness within the object of interest is calculated from the wave speed. Wave speed values are derived by tracking a moving transient wavefront within the object through time, somewhat analogous to the study of seismic wave propagation through the earth. A temporal profile indicating the wave motion for every pixel throughout the experiment is determined. In Fig. 4, the temporal profiles for pixels located near the surface and bottom of our phantom are shown from 0 to 25 ms. As indicated by the arrow, the wave absolute maximum passed through the surface pixel near 3.7 ms and continued through to the bottom pixel in an additional 16.3 ms.

Figure 4.

Temporal profiles for pixels located near the surface (solid line) and near the bottom (dashed line) of the phantom of a scale of 0 to 25 ms. The arrows show that it took 3.7 ms for the wave maximum to reach a pixel 2 cm below the surface of the phantom and an additional 16.3 ms to pass a pixel 6 cm below that.

A seventh-order, least squares polynomial fit to the temporal waveform at each pixel location allows an accurate estimation of the time of arrival of the maximum wave amplitude. By doing this for each pixel location, a time-of-arrival image is determined. The inverse speed or “slowness” of the wave was calculated by performing a one-dimensional gradient operation on this image. The shear stiffness μ of the material is calculated from the wave speed c by

equation image(1)

where ρ is the density.

Transient Direct Inversion

This method is more fundamentally based on the mechanical equation of motion (25, 27). With the assumptions stated above, but not assuming a single plane shear wave, the wave equation can be locally inverted to solve for shear stiffness,

equation image(2)

where μ is shear modulus, ρ is density (assumed 1), and Ψ is displacement. In the harmonic case, the numerator further reduces to −ω 2, where ω is the mechanical frequency. If the shear stiffness varies with frequency, as discussed above, this equation will yield a weighted average of the shear stiffness values at different frequencies. The denominator of Eq. [2] is the spatial Laplacian of the image, with the second derivatives along x and y calculated as simple finite differences. The numerator in Eq. [2] is the second temporal derivative of displacement and is calculated similarly for each pixel location through time.

In the transient reconstruction, stiffness is calculated from the spatial Laplacian and second temporal derivatives at each point in time. The stiffness values are then combined through time utilizing an amplitude-weighted least squares method. The amplitude weighting is necessary because when the wave amplitude is close to zero (except for noise), Eq. [2] is no longer valid. Thus, the calculation yields a useful estimate only when the wave is present and therefore the amplitude weighting emphasizes times of maximum displacement in the stiffness calculation.

MATERIALS AND METHODS

For all experiments, gradient echo based phase contrast sequences were run on a 1.5-T GE Signa MRI scanner (GE Medical Systems, Milwaukee, WI). Figure 1 illustrates the experimental setup for imaging shear waves and a representative wave image. An electromechanical driver (a coil of wire pulsed with alternating current) was synchronized with the motion encoding gradients and provided shear motion (29). This experimental setup was used to determine the efficacy of transient mechanical wave excitation techniques as well as to compare them to harmonic wave techniques. The frequencies in the harmonic experiments were limited to a maximum of 200 Hz.

In order to study data acquisition methods and their effects on the inversion results, both sinc and bipolar rectangular gradients were used in separate experiments on the same agarose gelatin phantom with tissue simulating properties. A line profile through the phantom was analyzed to determine what effect the differently shaped gradients would have on the measured phase displacement as explained under Theory and then tested again on the full inversions.

The agarose gelatin phantoms were then used to test the relative abilities of transient and harmonic MRE to detect and measure shear wave propagation. In each experiment the motion-encoding gradient was applied in the same direction (left–right) as the applied motion and orthogonal to the direction of the wave propagation.

The technique was tested on a 12-cm-deep 2% agarose gelatin phantom with two 3% (stiff) and two 1% (soft) agarose gelatin cylindrical inclusions. The cylindrical inclusions measured 25 and 10 mm in diameter (Fig. 5a–d). The seven regions of interest chosen for analysis are also shown in Fig. 5.

Figure 5.

Twelve-centimeter-deep agarose gelatin phantom with two 3% (stiff: b, d) and two 1% (soft: a, c) agarose gelatin cylindrical inclusions. The cylindrical inclusions measure 25 and 10 mm in diameter. Seven regions of interest were chosen for analysis: (1) top layer, (2) middle layer, (3) bottom layer, (4) large soft inclusion, (5) large stiff inclusion, (6) small stiff inclusion, and (7) small soft inclusion.

Using the described phantom, a harmonic wave data set was acquired with 64 temporal offsets equally spaced around a cycle of a 200 Hz sinusoidal mechanical excitation. The amplitude of the shear motion was calculated to be 70 μm near the surface of the phantom. Because the entire object of interest does not contain wave displacement at one time in the transient case, as in Fig. 2, it is necessary to use enough temporal offsets to cover the entire object (64 in this case). A typical harmonic wave acquisition uses fewer offsets (such as 8), so a harmonic acquisition with 64 offsets was obtained to allow direct comparison with the transient techniques. Acquisition parameters were TR/TE = 150/30 ms, 60° flip angle, 20 cm FOV, 5 mm slice thickness, and 256 × 64 resolution. Six motion cycles of the wave were used for harmonic MRE, sensitized to by two rectangular bipolar gradients. A sample harmonic wave image for this object is also shown in Fig. 2.

Transient wave data were acquired from the same phantom using 64 temporal offsets of a single cycle of a sinusoidal transient with a 5-ms period; this corresponds to one period of a 200-Hz sine wave. One motion cycle of the wave was used for transient MRE sensitized to by one rectangular bipolar gradient. Acquisition parameters were otherwise the same. Four temporal offsets from these data are shown in Fig. 6, where each frame is separated by 3.6 ms. These data were analyzed with both the TOA and TDI algorithms. For the TDI method, derivative window lengths of seven pixels and seven time points were chosen as most appropriate for this data set. After analysis of the harmonic and transient wave techniques was complete, the results were compared between methods.

Figure 6.

Four offsets from a 64-offset transient acquisition using a single cycle of a sinusoidal transient with a 5-ms period. Each frame is separated by 3.6 ms and the white line indicates the points for which the wave has a maximum value at this temporal offset.

Two reference phantoms were also made from the same batches of the 1% agar and 3% agar gelatin. These phantoms were studied using the same methods as described for the complex phantom.

Harmonic and transient mechanical shear waves were then used to examine the brains of six healthy volunteers. All imaging was again performed using standard gradient echo imaging on a 1.5-T GE Signa whole-body imager with additional motion encoding gradients used to detect and measure the shear wave propagation. The 120-μm maximum amplitude motion was induced by a bite bar, electromechanically shaken in the left-right or “nay” motion, as illustrated in Fig. 7. Thirty-two images of the shear wave were acquired as it propagated through the head for both the harmonic and the transient motions each in both the right/left (R/L) and anterior/posterior (A/P) motion sensitizations. The harmonic experiments utilized 80 Hz sinusoidal motion, shaking the head left, then right, and a 6.25-ms rectangular impulse to one side was used for the transient experiments.

Figure 7.

For the in vivo experiments, motion was induced through a bite bar, pivoting the head in a left-to-right or “nay” motion about the back of the head with an amplitude of 120 μm.

Acquisition parameters were TR/TE = 98/30 ms, 60° flip angle, 24 cm FOV, 5 mm slice thickness, and 256 × 64 resolution. Five motion cycles of the wave were used for harmonic MRE, sensitized to by two rectangular bipolar gradients. One motion cycle of the wave was used for transient MRE sensitized to by one rectangular bipolar gradient. Acquisition parameters were otherwise the same. These data were analyzed with the TDI algorithm, where the derivative window lengths of four pixels and two time points were chosen as most appropriate for this data set. Anatomic correlation and shear stiffness were then compared between the harmonic and transient wave techniques.

RESULTS

Figure 8 illustrates experimental results comparing phase accrual using sinc and rectangular gradient sensitizations to a mechanical transient. Figure 8a shows two spatial line profiles of phase accrual through the center of a phantom for sinc gradient sensitization (solid line) and bipolar rectangular gradient sensitization (dashed line). The same single period of sinusoidal motion was used for motion actuation in each case. The sinc gradient more accurately captured the shape of the motion but the bipolar rectangular gradient provides a higher signal to noise ratio in the resulting phase image. Figure 8b shows the transient inversions of the data along the two profiles for the sinc and rectangular encodings. Figures 12 and 13 show complete inversions for both methods to be discussed below.

Figure 8.

(a) Spatial line profiles of phase accrual through the center of the phantom for sinc gradient sensitization (solid line) and bipolar rectangular gradient sensitization (dashed line). The same single period of sinusoidal motion was used for motion actuation in each case. Note that the sinc gradient more accurately captures the shape of the motion (a sinusoid), but the bipolar rectangular gradient provides a higher signal to noise ratio in the resulting phase image. (b) Transient inversion of data along the two profiles for the sinc and rectangular encodings measuring similar stiffness values.

Figure 12.

MR Elastograms obtained using the transient direct inversion method (TDI) using rectangular gradient motion sensitization (a) and sinc motion sensitization (b), showing shear stiffness on a scale of 0 to 80 kPa. There is a subtle degradation in image quality when using the sinc motion sensitization.

Figure 13.

Bland-Altman plot showing difference versus mean for the harmonic and time-of-arrival methods using five regions of interest chosen from the three layers and the two large inclusions (regions 1–5 in Fig. 6). The mean difference of the two techniques is −0.71 kPa with the 95% confidence interval between −8.51 and 7.09 kPa.

Harmonic wave methods were first performed on the phantom for comparison to transient methods. The harmonic wave data were processed using a previously published direct inversion algorithm (25) and the results are shown in Fig. 9. The stiff and soft inclusions are clearly depicted and there is variation among the three layers. The phantom was made in three layers over 3 days and each background layer was designed to have the same stiffness. It is possible that some variance between the layers does exist.

Figure 9.

The results from harmonic wave processing for shear stiffness are shown using the described phantom. Shown on a scale of 0 to 80 kPa, the two stiff and two soft inclusions have been highlighted with dashed lines.

The first of the two transient reconstruction methods developed was the TOA technique, which determines the time when the wave “arrives” at each pixel as shown in Fig. 6. The white line indicates the points for which the wave has a maximum absolute value at this temporal offset. The image is sensitized to particle motion in the left–right direction and the downward propagation of transverse waves is clearly evident. The calculated TOA, using bipolar gradient sensitization, for each pixel is shown in Fig. 10. The gradient of this image in the vertical direction was then used to calculate wave speed and the resulting elastogram is shown in Fig. 11a. The large inclusions are distinct from the background and the small inclusions are visible, although with less clear margins. There are artifacts located beneath the large soft inclusion and very near the bottom of the phantom, to be discussed in the next section. Figure 11b, the result of sinc gradient sensitization, shows the overall unevenness in the inversion and the effects of the decreased wave SNR in the lower left of the phantom when compared to the rectangular gradient inversion.

Figure 10.

By tracking the wave through the phantom, the time of arrival of the wave absolute maximum is calculated for each pixel, shown on a scale of 0 to 30 ms. A gradient of this image yields wave slowness, which then may be used to calculate shear stiffness.

Figure 11.

MR Elastograms obtained using the TOA method using rectangular gradient motion sensitization (a) and sinc motion sensitization (b) showing the calculated shear stiffness values for the agar phantom (scaled from 0 to 80 kPa). (a) The wave was not permitted to travel completely though the phantom and caused artifacts seen as the areas of apparent decreased stiffness at the bottom of the phantom. The area of apparent increased stiffness in the lower left of the phantom is due to low signal to noise in that region and will also be visible in other methods. (b) Note the overall unevenness in the inversion and the effects of the decreased wave SNR in the lower left of the phantom when compared to the rectangular gradient inversion.

The result of the second of the two transient reconstruction methods developed, the TDI method, is shown in Fig. 12. For the bipolar gradient sensitization as shown in Fig. 12a, all four of the inclusions are easily seen, as well as the separation among the three individually poured layers, which each appear internally homogeneous. There is a subtle degradation in image quality when using the sinc motion sensitization.

The harmonic wave and transient wave methods, using bipolar gradients, were then compared by statistical analysis of several regions of interest (ROI). Seven ROIs from the 64 offset harmonic wave, transient time-of-arrival, and transient direct inversion data sets were chosen and their calculated mean shear stiffnesses are summarized in Table 1. The seven ROIs, as indicated in Fig. 5, included the four inclusions and three regions in the 2% agar background area selected to represent the three pouring layers of the phantom construction.

Table 1. Shear Stiffness Measurements for Seven Regions of Interest and Reference Phantoms as Calculated by Harmonic Wave, Transient Time-of-Arrival, and Transient Direct Inversion Methods
Region of interestShear stiffness (kPa) measured using
Harmonic waveTOATDI
  • a

    Data were not included in Bland–Altman plots.

1. Top layer 2% agar31.59 ± 0.8532.99 ± 1.0228.36 ± 0.35
2. Middle layer 2% agar27.54 ± 1.1130.94 ± 0.4125.80 ± 0.38
3. Bottom layer 2% agar37.64 ± 2.8536.08 ± 2.5027.79 ± 1.00
4. 25 mm 1% agar5.40 ± 0.985.17 ± 0.344.50 ± 0.20
5. 25 mm 3% agar66.07 ± 1.7567.39 ± 5.1854.78 ± 3.11
6. 10 mm 3% agara58.56 ± 5.6843.51 ± 0.9954.71 ± 5.31
7. 10 mm 1% agara8.84 ± 0.6717.27 ± 0.788.84 ± 0.65
1% agar reference7.78 ± 1.317.07 ± 0.324.76 ± 0.12
3% agar reference107.62 ± 3.6688.85 ± 6.2572.24 ± 3.00

Figure 13 is a Bland–Altman (30)plot showing the difference versus the mean for the harmonic and the transient TOA methods. The points plotted represent data in the regions of interest from the three background layers and the two large inclusions. The mean difference of the two techniques (harmonic minus time of arrival) is −0.71 kPa with the 95% confidence interval between −8.51 and 7.09 kPa.

Figure 14 is a Bland–Altman plot showing the difference versus the mean for the harmonic and the transient direct inversion methods. The mean difference of the two techniques (harmonic minus transient direct inversion) is 5.32 kPa with the 95% confidence interval between −3.78 and 14.41 kPa. Although there is a greater overall difference between the two techniques in this case, the data are more tightly clustered, indicating higher correlation but with an overall systematic effect toward lower estimates in stiff regions for TDI as opposed to the harmonic method.

Figure 14.

Bland–Altman plot showing difference versus mean for the harmonic and transient direct inversion methods using five regions of interest (regions 1–5 in Fig. 6) chosen from the three layers and the two large inclusions. The mean difference of the two techniques is 5.32 kPa with the 95% confidence interval between −3.78 and 14.41 kPa.

The small stiff inclusions were not included as part of the Bland–Altman plots because their values were considered less reliable in comparison to the larger inclusions and backgrounds regions. The filter lengths chosen for the processing techniques were designed to optimize the results as a whole and were on the order of the size of the small inclusions. This will be further addressed below.

Figure 15 shows example wave images from one volunteer of the collected in vivo data. White indicates anterior displacement while black indicates posterior displacement for the A/P sensitizations. In the R/L sensitizations, white indicates leftward displacement and black indicates rightward displacement. Figure 15a represents anterior to posterior shear waves traveling toward the center of the brain from harmonic motion, or shearing off of the left and right sides of the skull. Note the drop off of wave amplitude toward the center of the brain. Figure 15b is an image of right to left displacement shear waves from harmonic motion. Anterior to posterior shear waves from a transient impulse are shown in Fig. 15c. Figure 15d shows right to left displacement shear waves from a transient impulse. All motion is shown on a scale of −60 to 60 μm.

Figure 15.

Example wave images from the collected in vivo data. White indicates anterior displacement while black indicates posterior displacement for the A/P sensitizations. In the R/L sensitizations, white indicates leftward displacement and black indicates rightward displacement. (a) Anterior to posterior shear waves traveling toward the center of the brain from harmonic motion. Note drop off of wave amplitude toward the center of the brain. (b) Right to left displacement shear waves from harmonic motion. (c) Anterior to posterior shear waves traveling toward the center of the brain from a transient impulse. (d) Right to left displacement shear waves from a transient impulse All motion is shown on a scale of −60 to 60 μm.

The harmonic wave (Fig. 16b) and transient wave (Fig. 16c) elastograms are presented, adjacent to the fast spin echo anatomic image (Fig. 16a) for a single volunteer. On a scale of 0 to 20 kPa, the harmonic case shows apparent trend that white matter is stiffer than gray. The white/gray matter difference is more subtle in the transient elastogram but more accurately depicts certain anatomic features. The more peripheral white matter correlates anatomically as shown in anterior region (1). This white/gray matter difference is particularly evident in the corpus callosum, the most highly structured region of white matter in the brain, as shown in the genu (2) and splenium (3) of the corpus callosum.

Figure 16.

Harmonic wave (b) and transient wave (c) elastograms, adjacent to the fast spin echo anatomic image (a) for a single volunteer. On a scale of 0 to 20 kPa, the harmonic case shows apparent trend that white matter is stiffer than gray. The white/gray matter difference is more subtle in the transient elastogram but more accurately depicts certain anatomic features. The more peripheral white matter correlates anatomically as shown in anterior region (1). This white/gray matter difference is particularly evident in the corpus callosum, the most highly structured region of white matter in the brain, as shown in the genu (2) and splenium (3) of the corpus callosum.

Figure 17a and b are the elastograms of Fig. 16 overlayed onto the FSE image, where Fig. 17a is the harmonic case and Fig. 17b is the transient case. Again, note the strong correlation in the transient elastogram of the some of the deeper structures, such as the corpus callosum (3, 4). Outlines of the sulci in the transient case are clear as in 1, 2, and 5.

Figure 17.

Harmonic (a) and transient (b) elastograms of Fig. 16 overlayed onto the FSE image. Again, note the strong correlation in the transient elastogram of the some of the deeper structures, such as the corpus callosum (3, 4). Outlines of the sulci in the transient case are clear as in 1, 2, and 5.

The harmonic wave and transient wave methods for the six in vivo volunteers were then compared by analysis of six ROI. The mean shear stiffness values for the ROIs (three gray matter, three white matter, both peripheral and deep) from the harmonic wave and transient direct inversion data sets are summarized in Table 2. Gray matter is reported as 5.3 ± 1.3 and 7.5 ± 1.6 kPa for the harmonic and transient inversions, respectively. White matter was measured at 10.7 ± 4.4 kPa for the harmonic inversion and 11.6 ± 2.4 kPa for the transient direct inversion.

Table 2. Shear Stiffness Measurements in Six Volunteers for Six Regions of Interest (both Gray and White Matter) as Calculated by Harmonic Wave and Transient Direct Inversion Methods
 Shear stiffness (kPa) measured using
Harmonic waveTDI
Gray5.3 ± 1.37.5 ± 1.6
White10.7 ± 1.411.6 ± 2.4

DISCUSSION

Mechanical transient excitations were successfully implemented and both a sinc and a bipolar rectangular gradient were shown to be viable options for motion sensitization. The inversion results are similar but the rectangular encoding inversion should be more accurate since it averages stiffness values over a smaller frequency range and it has higher SNR. The use of a bipolar rectangular gradient is preferred for the TOA analysis as the use of a sinc gradient makes robust determination of the wave arrival difficult.

The four inclusions were clearly demarcated for the harmonic wave results as shown in Fig. 9. As noted in Table 1, the three layers were measured at three varying stiffnesses. Although the inclusions measured significantly stiffer or softer in comparison to the background, with the exception of the small soft inclusion, the stiffness values of the inclusions do not agree well with the reference phantoms. The stiffness of the small inclusions varies considerably from that of the larger inclusions. The motion frequency, motion amplitude, and processing techniques were chosen to give the best overall results and were not optimized for the small inclusions; therefore, those inclusions were not part of the analysis. The inconsistency of the results from the small inclusions even within the harmonic wave technique would make comparison with transient techniques inconclusive. The bright areas in the lower left region of the phantom are artifacts due to insufficient wave amplitude in this region.

The time-of-arrival method was the first of the two transient methods developed. Figure 6 shows an example of the wave tracking, which was part of the TOA analysis. The first frame of that figure shows a miscalculation of the arrival of the wave just near the large soft inclusion due to the planar nature of the wave and the bowing of the wave around the inclusion. Because of this effect, there was very little displacement in regions just below the inclusion and it was possible find secondary waves with larger amplitudes. This resulted in a miscalculation of the time of arrival of the wave in that and following regions, as indicated in Fig. 10. Because the wave propagation is assumed to be planar, discontinuities along boundaries of materials with varying wave speed cause errors in the TOA method. This occurs as the gradient operation is performed and appropriate gradient filters or smoothing must be applied. Figure 11a shows the calculated stiffness map where the effect of the error, in this particular case, had been lessened by applying a median filter to the TOA elastogram. An additional artifact is visible in near the bottom of the phantom because not enough time was permitted for the wave to fully penetrate. Ringing of the mechanical driver causing a smaller secondary wave also added to the difficulty of tracking the primary wave. As in the harmonic case, there is an artifact in the lower left region of the phantom due to poor wave penetration.

The TOA were then compared to the established harmonic wave technique. The calculated values for the TOA method as indicated in Table 1 were comparable to that of the harmonic technique, with similar stiffness values in the three layers. The Bland–Altman plot of Fig. 13 yielded a mean difference between the two techniques in the seven ROIs of −0.71 kPa. The TOA method estimated a similar stiffness for the soft inclusion to that of the harmonic method with a moderately increased variance within its measurement. The variance of the calculated stiffness within each layer is similar to that of the harmonic measurements. The mean difference between the TOA and harmonic methods for the stiff inclusions was relatively small, but had a large variance because of the lower signal-to-noise within these inclusions.

The second of the two transient reconstruction techniques developed, the TDI method, has calculated stiffness values comparable to those of the harmonic technique but appear to be systematically lower for the TDI method, as indicated in Table 1. There was significant agreement in stiffness among all three layers. The measured stiffness of the soft inclusion agreed with its reference. Although the stiff inclusion did not agree with its reference, there was good agreement between the large and small stiff inclusions. The Bland–Altman plot of Fig. 14 yielded a mean difference between the two techniques in the seven ROIs of 5.32 kPa. Due to the noise sensitivity of the second derivative in the denominator, there was considerable variance in the stiff inclusion using both the transient and the harmonic wave direct inversion methods, resulting from the low SNR there. In addition to SNR, derivative window length was an important factor in the calculation of stiffness for direct inversion. Because of the relatively long wavelength of shear waves in the stiff objects, adaptive derivative window lengths would be more appropriate for calculation of stiffness, especially in the small inclusions.

Both the harmonic and the transient results clearly depict the inclusions against the background regions. To better illustrate this, line profiles were drawn through the large soft and large stiff inclusions for the TDI and harmonic techniques and plotted together. Figure 18 shows the line profiles through the soft inclusion. Both methods yield similar values within the soft inclusion as well as similar profiles in the transition region from inside the inclusion to the background, as indicated by the boundary lines of the inclusion. The TDI method provides a slightly sharper transition on the bottom of the inclusion. Similar features may be seen in Fig. 19 through the stiff inclusion.

Figure 18.

Line profiles of stiffness versus position for the harmonic wave and TDI methods drawn through the soft inclusion. Both methods have similar values measured within the soft inclusion as well as similar profiles in the transition region from inside the inclusion to the background, as indicated by the boundary lines of the inclusion. The TDI method provides a slightly sharper transition on the bottom of the inclusion.

Figure 19.

Line profiles of stiffness versus position for the harmonic wave and TDI methods drawn through the stiff inclusion. Both techniques show comparable transition profiles from the inclusion to the background.

The required scan time is often longer for transient data acquisition due to the number of temporal offsets. Using typical acquisition parameters such as 8 time offsets, 4 gradient pairs, 200 Hz excitation frequency, and a TR of 80 ms, a harmonic wave scan will take approximately 4 min. To acquire a comparable transient scan and ensure full coverage of the test object, the scan would require 32 min. Experiments were performed on a similar phantom to reduce scan time by taking more than one gradient snapshot of the wave during each acquisition (Fig. 20). By using two gradient pairs with one mechanical excitation (top right), the single transient wave motion is captured at two depths simultaneously (bottom right), effectively halving scan time. There is very little difference in the depiction of shear stiffness with this technique, as calculated using the TDI method (Fig. 21). It may be possible to extend this idea and thereby significantly reduce transient scan time by using several gradients, only limited by the echo time and desired frequency of sensitization.

Figure 20.

Normally, one gradient pair is used to sensitize to a mechanical transient, as shown on the left. By using two gradient pairs (indicated on the right) and still only one mechanical excitation, the single transient wave motion is captured at two depths, allowing the number of repetitions (and total acquisition time) to be reduced by one half.

Figure 21.

Shear stiffness maps using one sensitizing gradient pair (left) and two sensitizing gradient pairs (right) as calculated using the transient direct inversion method. Although scan time has been halved, there is very little difference in the in the results.

The in vivo images of Fig. 16 illustrate that for both harmonic and transient methods white matter is stiffer than gray matter. In the harmonic case, the image may be a bit misleading, as the difference is not as striking as it appears. There was a lack of wave penetration toward the midline of the brain in the harmonic case. The inversion of this low amplitude data artificially raises the calculated shear stiffness in this area. There was much better wave penetration in the transient experiments, and therefore the shear stiffness values and structure of the deeper brain are more reliable. Also, while the white/gray matter difference is more subtle in the transient elastogram, certain anatomic features are much better depicted. This is best seen in the genu and splenium of the corpus callosum. When the elastograms of Fig. 16 are overlayed onto the FSE image, as in Fig. 17, the structural similarities and differences are clearer, such as along the sulci. The better driver response and resulting better wave penetration in the transient case, combined with the lack of reflection and standing waves, allow for a complete analysis on the interior of the brain. Both methods indicate that white matter is stiffer than gray matter, as well as comparing favorably with each other, while the harmonic results are more variable for white matter. Because of the complex structure of gray and white matter, particularly when bounded by one another, the reported ROIs show a high variability in general.

As scan time is a more significant factor for in vivo cases when using the transient method, an analysis of a volunteer data set for fewer offsets was made. The 32 offset data as shown in Figs. 16 and 17 were reduced to 16 and 8 offsets and analyzed again using transient direct inversion. Figure 22 shows the results of this time comparison for transient wave elastograms of 32 (Fig. 22a), 16 (Fig. 22b), and 8 (Fig. 22c) temporal offsets. Note that the 16 offset data are nearly identical to the 32-offset example. Even reducing scan time to that of a harmonic acquisition (8 offsets, Fig. 22c) does not appreciably corrupt the anatomic features of the transient elastogram. The stiffness values of the deeper white matter do elevate when shortening to 8 offsets. Therefore, for the longer transient impulses used for in vivo brain analysis, time is much less of a factor than initially anticipated, possibly being equal to that of the harmonic case.

Figure 22.

Transient wave elastograms of same volunteer for 32 (a), 16 (b), and 8 (c) temporal offsets. Note that the 16 offset data are nearly identical to the 32-offset example. Even reducing scan time to that of a harmonic acquisition (8 offsets, c) does not appreciably corrupt the anatomic features of the transient elastogram. The stiffness values of the deeper white matter are apparently elevated when shortening to 8 offsets.

CONCLUSION

Theory and experiments showed that the use of transient wave mechanical excitations is possible, several acquisition and reconstruction methods exist, and the transient techniques provide an alternative and quantitatively comparable method for the estimation of stiffness values representative of tissues. The TDI reconstruction technique seems to have been less sensitive to the low wave amplitude region and therefore had fewer artifacts compared to both the TOA technique and the harmonic results. The increase in acquisition time may be reduced by the proposed extension to multiple gradients. Increasing the detected motion of the waves by exploring more optimal combinations of excitation motion and sensitizing gradient waveform will improve accuracy in tracking the transient wave front.

In in vivo results demonstrate the feasibility of measuring brain stiffness using a transient mechanical excitation. Although there were some differences between the harmonic and transient analyses, the measured stiffness values compared favorably. There was better depiction of the deeper structures of the brain for the transient inversion. Preliminary studies show that transient imaging time may be less of a factor for in vivo experiments. It is possible that the transient and harmonic methods may be used as complementary techniques in future experiments. The positive results indicate further investigation to determine the stiffness of the in vivo brain for a larger population with possible applications to disease analysis.

Acknowledgements

The authors thank the members of the Radiology Research Lab, particularly Kevin Glaser, for their assistance and guidance.

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