Reference no: EM133040184

Question: The data correspond to a 3D MRE experiment on human brain.

In the experiments the following MRE sequence parameters were used:

- Field of View (FOV): 240mm x 240mm x 40mm
- Matrix size: 120 x 120 x 20
- Mechanical excitation frequency: 50 Hz
- Motion encoding gradient (MEG) frequency: 50 Hz
- Motion encoding gradient (MEG) shape: sinusoidal.
- Number of MEG cycles: 2
- MEG amplitude: 30 mT/m
- Number of time steps: 8 time-steps
- Shifting of trigger of the x-MEG, the y-MEG and the z-MEG: All over 1 period of the vibration frequency, respectively.
- No phase-difference technique applied Useful parameters

Gyromagnetic ratio of the proton 267.5 10⁶ rad/sT

density of brain tissue ~1000 m³

Task

Process the MRE experiment assigned to you.

In specific, determine the complex wave images for each displacement projection and the spatially filtered complex wave images using a Butterworth low-pass with an 8 pixel filter limit and order 2. All complex wave images need to be scaled to true displacement values.

Perform a 3D Inversion of the Navier Equation, while filtering out compressional properties by applying the Curl-Operator to the spatially filtered complex wave images.
In your solution, present images of a central slice (slice # 10 or 11) of the ...

- spatially-unfiltered images of the complex wave images (real part) for each displacement projection
- spatially-filtered images of the complex wave images (real part) for each displacement projection.
- images of the complex shear modulus G (real and imaginary part) calculated from the filtered complex wave images (use also ‘medfilt2' command for illustration purpose).

Make sure to present a colorbar with units and values for all images.

In the images of the complex shear modulus discard outliers. In our example, outliers shall be defined as:
abs(G) > 20 kPa or abs(G) < 10 Pa. Set these outliers to 0.

Discard all pixels with negative storage modulus Κ{G}. Set these values to 0. Set all loss moduli Κ{G} positive.
Further processing steps as outlined during final project assignment in class: Finally, determine spatially-averaged mechanical properties:
- Calculate Region of Interest (ROI)-averaged values of the storage modulus Κ{G} and of the loss modulus Κ{G}. The ROI shall be defined as the brain tissue excluding fluid-filled ventricles. Also exclude the four slices on both edges of the brain slab.
In addition to the images as specified above submit in your final project:

i. All matlab code that you programmed or used.
ii. The ROI-averaged values as specified above.