Quantifying elasticity of the brain using Magnetic Resonance Elastography

1. Quantifying elasticity of the brain using Magnetic Resonance Elastography A review of “Mechanical Transient-Based Magnetic Resonance Elastography”, McCracken, 2005 Presenter: Brian Sweetman Advisor: Andreas Linninger, Ph D Date: October 12, 2006

2. Questions/Comments • Shearing input • Is there a way to calculate elastic modulus from shear modulus? • White matter with higher shear modulus than gray matter? • Better depiction of deeper brain structures for transient inversion vs. harmonic excitation • Technical differences in the way transient MRE is performed; yield different results

3. Mechanical input • 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. • -60 µm to 60 µm

4. Calculating elastic modulus from shear modulus http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/elastic_constants_G_K.cfm When subjected to pure shear strains defined as: It follows that… Because G has to be positive, v has to be greater than -1.

5. Further restrictions on the Poisson ratio When subjected to hydrostatic pressure, strains defined as: It follows that… Because K has to be positive, v has to be less than 0.5 Poisson ratio Upper and lower bound therefore are -1<v<0.5

6. Justification for ∆V/V equal to sum of strains Products of strain measures will be much smaller than individual strain measures (when overall strain is small)

7. Elastograms: harmonic vs. transient • 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.

8. Elastograms with FSE background • 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.

9. Experimental Setup • 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.

10. Comparison of harmonic and transient wave images • Harmonic (left); transient (right)

11. Phase profiles • 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.

12. Temporal profiles • 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.

13. ROI in phantom (agarose gel) • 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.

14. Four offsets • 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.

15. Phase accrual • 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.

16. Harmonic wave processing • 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.

17. Calculate shear stiffness • 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.

18. TOA method using RGMS and SMS • Figure 11. MR Elastograms obtained using the TOA method using rectangular gradient motion sensitization(RGMS) (a) and sinc motion sensitization (SMS) (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.

19. TDI method using RGMS and SMS • 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.

20. Comparison of Shear Stiffness using different methods

21. Harmonic vs. TOA • 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.

22. Harmonic vs. TDI • 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.

23. Wave images • 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 m.

24. Soft inclusion (fig 5) • 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.

25. Stiff 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.

26. One vs. Two gradients • 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.

27. One vs. two gradients • 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.

28. 32, 16, and 8 temporal offsets • 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.