TITLE: Processing Stack-of-Stars DCE Data
AUTHORS: Rong Zhou

[DESCRIPTION]
Step-wise protocol for reconstruction of Stack-of-stars acquired DCE series, T1 and B1 maps and PK (pharmacokinetic) modeling of DCE data using a reference region model is provided. 

[STEPS]
SECTION: Reconstruction of Stack-of Stars (SoS) radial k-space sampled DCE data
1. Image reconstruction

1.1. 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. 

Apply a Fourier transform in the slice direction to separate slices
Shift image in the slice direction to match geometry of reference T2-weighted image
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
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
Apply Fourier transform to now Cartesian-defined k-space
 

1.2. 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. 
 

 



2. 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)

3. 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

  .

5. DCE metric map generation from DCE images


5.1. 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)

4. 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
5.2. 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

5.3. 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 and ve using the following equation:

 , where

the reference Ktrans of muscle,          ,
the reference ve 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 and ve values are relative to those assigned when fitting for the equation above. The values of   and   are from Cardenaz-Rodriguez et al.

 

 

6. 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,ve ) from the ROI of interest (tumor, kidney, and phantom):
1. Extract Ktrans and ve values 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 and ve  values are outliers, we prefer median instead of mean of all pixels in the ROI.