Processing Stack-of-Stars DCE Data

Image reconstruction

VFA and AFI images

The same reconstruction procedure is used for images acquired by the variable flip angle (VFA) and actual flip angle (AFI) stack-of-stars (SoS) pulse sequences.

1. Apply a Fourier transform in the slice direction to separate slices
2. Shift image in the slice direction to match geometry of reference T2-weighted image
3. Apply the following corrections to each view: 3.1. Center each view in k-space by moving its peak to the center of k-space 3.2. Phase normalize 3.2. Correct for off-resonance frequency using the average phase difference between views in opposite directions
4. Re-grid radial k-space data to a 128x128 Cartesian grid as described by O’Sullivan et al. To summarize, for each slice: 4.1. Multiply signal of each point by its respective area on a Voronoi diagram of the points (including zerofill points) in k-space 4.2. Re-grid each radially defined point to its nearest Cartesian coordinates using its Kaiser-Bessel index
5. Apply Fourier transform to now Cartesian-defined k-space
   Citation

   O'Sullivan, JD 1985 A Fast Sinc Function Gridding Algorithm for Fourier Inversion in Computer Tomography IEEE Transactions on Medical Imaging 10.1109/TMI.1985.4307723

DCE images

The k-space weighted image contrast (KWIC) method described by Song et al (2000 and 2004). was used to reconstruct the DCE images. To summarize, for DCE-MRI, the KWIC method uses radial acquisition's inherent oversampling of the k-space center by only using a subset of the acquired views in that region. By using a sliding window to select the views that are included in that central region, multiple images can be created from a single acquisition of k-space, thus increasing the temporal resolution.

After applying the KWIC, the resulting k-space data is reconstructed using the same method as 1.1- VFA and AFI Images .

B1 field map generation from AFI images

1. Compute pixel-wise actual flip angles using the equation

, where , and , where is the signal intensity from the image acquired at .

2. Divide resulting actual flip angle maps by nominal flip angle to yield normalized pixel-wise B1 field maps.

3. Fit normalized B1 field maps to 3D 3rd degree polynomial using a least-squares fit to yield final B1 field maps used for T1 correction (step 3.1)

T1 map generation from VFA images

1. Compute T1 values using a non-linear least squares fit of the VFA image signal intensity to the Ernst equation

, where , and .

Generate tissue masks for reference region (muscle), kidney and tumor.

1. Open DCE images in an imaging processing software (eg. ImageJ)

   Note: Images immediately following contrast agent injection tend to outline structures well. Anticipating slight movement of the slices either due to respiratory motion or due to other reasons, a T2-weighted scan is usually acquired before the DCE sequence and used for ROI masking.

2. Create a mask accessible by your analysis software which defines skeletal muscle and any other ROIs of interest.

For example, on ImageJ:

1. Create a new empty image with same dimensions as DCE image in File -> New -> Image

2. Draw ROIs by hand and add to ROI Manager by pressing shortcut "t"

3. Set ROIs in empty image to a values for each tissue by Process -> Map -> Set

4. Save as raw image by File -> Save As -> Raw Data

DCE metric map generation from DCE images

Compute contrast agent concentration time-course from signal time-course for each voxel and for spinal muscle (reference region)

For each voxel:

1. Compute actual (B1-corrected) flip angle at voxel using .

2. Normalize signal time course by mean signal prior to bolus injection

3. Compute T1 time-course using equation

, where and is the baseline T1, obtained from the previously generated T1 map (step 3)

4. Estimate contrast agent concentration time-course using equation

, where (check for your specific contrast agent)

Compute spinal muscle (reference region) concentration time-course

1. Using a manually defined tissue mask for the spinal muscle, compute the mean concentration time-course for the entire muscle ROI

Compute quantitative DCE parametric maps

For each voxel:

1. Using the reference region model (Jones et al.) and the muscle as a reference tissue, fit for Ktrans ^trans and ve _e using the following equation:

, where

the reference Ktrans ^trans of muscle, ,

the reference ve _e of muscle, , and

is the concentration of contrast agent, and the subscripts and refer to muscle (the reference region) and the tissue in the voxel being analyzed.

Note: and are reference values, therefore voxel Ktrans ^trans and ve _e values are relative to those assigned when fitting for the equation above. The values of and are from Cardenaz-Rodriguez et al.

Obtaining ROI metrics from maps

While pixel-wise parametric maps allow us to assess heterogeneity of a specific metric within the tumor, we also compute all parameters ( Ktrans ^trans, ve _e) from the ROI of interest (tumor, kidney, and phantom):

1. Extract Ktrans ^trans and ve _evalues for each voxel in the ROI.

2. Compute ROI metrics of choice (eg. mean, median, percentile values, standard deviation)

   Note: To mitigate the impact of pixels whose Ktrans ^trans and ve _evalues are outliers, we prefer median instead of mean of all pixels in the ROI.