# RTK/Examples/4DROOSTERReconstruction

RTK provides a tool to reconstruct a 3D + time image which does not require explicit motion estimation. Instead, it uses total variation regularization along both space and time. The implementation is based on a paper that we have published (article. You should read the article to understand the basics of the algorithm before trying to use the software.

The algorithm requires a set of projection images with the associated RTK geometry, the respiratory phase of each projection image and a motion mask in which the region of the space where movement is expected is set to 1 and the rest is set to 0. Each piece of data is described in more details below and can be downloaded from MIDAS. It is assumed that the breathing motion is periodic, which implies that the mechanical state of the chest depends only on the respiratory phase.

## Contents

# Projection images

This example is illustrated with a set of projection images of the POPI patient. You can download the projections and the required tables of the Elekta database, FRAME.DBF and IMAGE.DBF. The dataset is first used to reconstruct a blurry image:

```
# Convert Elekta database to RTK geometry
rtkelektasynergygeometry \
-o geometry.rtk \
-f FRAME.DBF \
-i IMAGE.DBF \
-u 1.3.46.423632.141000.1169042526.68
# Reconstruct a 3D volume from all projection images. It implicitly assumes that the patient's chest is static, which is wrong. Therefore the reconstruction will be blurry
rtkfdk \
-p . \
-r .*.his \
-o fdk.mha \
-g geometry.rtk \
--hann 0.5 \
--pad 1.0
# Keep only the field-of-view of the image
rtkfieldofview \
--reconstruction fdk.mha \
--output fdk.mha \
--geometry geometry.rtk \
--path . \
--regexp '.*.his'
```

You should obtain something like that with VV:

# Motion mask

The next piece of data is a 4D deformation vector field that describes a respiratory cycle. Typically, it can be obtained from the 4D planning CT with deformable image registration. Here, I have used Elastix with the sliding module developed by Vivien Delmon. The registration uses a patient mask (red+green) and a motion mask (red) as described in Jef's publication:

The registration can easily be scripted, here with bash, where each phase image of the POPI 4D CT has been stored in files 00.mhd to 50.mhd:

```
for i in $(seq -w 0 10 90)
do
mkdir $i
elastix -f 50.mhd \
-m $i.mhd \
-out $i \
-labels mm_50.mha \
-fMask patient_50.mha \
-p Par0016.multibsplines.lung.sliding.txt
done
```

Deformable Image Registration is a complex and long process so you will have to be patient here. Note that the reference frame is phase 50% and it is registered to each phase from 0% to 90%. One subtle step is that the vector field is a displacement vector field, i.e., each vector is the local displacement of the point at its location. Since I ran the registration on the 4D planning CT, the coordinate system is not that of the cone-beam CT. In order to produce the vector field in the cone-beam coordinate system, I have used the following bash script that combines transformix and several "clitk" tools that are provided along with VV:

```
# Create 4x4 matrix that describes the CT to CBCT change of coordinate system.
# This matrix is a combination of the knowledge of the isocenter position / axes orientation
# and a rigid alignment that has been performed with Elastix
echo "-0.0220916855767852 0.9996655273534405 -0.0134458487848415 -83.6625731437426197" >CT_CBCT.mat
echo " 0.0150924269790251 -0.0131141301144939 -0.9998000991394341 -4.0763571826687057" >>CT_CBCT.mat
echo " 0.9996420239647088 0.0222901999207823 0.0147976657359281 77.8903364738220034" >>CT_CBCT.mat
echo " 0.0000000000000000 0.0000000000000000 0.0000000000000000 1.0000000000000000" >>CT_CBCT.mat
# Transform 4x4 matrix that describes the transformation
# from planning CT to CBCT to a vector field
clitkMatrixTransformToVF --like 50.mhd \
--matrix CT_CBCT.mat \
--output CT_CBCT.mha
# Inverse transformation. Also remove upper slices that are outside the
# planning CT CBCT_CT.mat is the inverse of CT_CBCT.mha
clitkMatrixInverse -i CT_CBCT.mat \
-o CBCT_CT.mat
clitkMatrixTransformToVF --origin -127.5,-107.5,-127.5 \
--spacing 1,1,1 \
--size 256,236,256 \
--matrix CBCT_CT.mat \
--output CBCT_CT.mha
# Go over each elastix output file, generate the vector field with
# transformix and compose with the two rigid vector fields
for i in $(seq -w 0 10 90)
do
transformix -in 50.mhd \
-out $i \
-tp $i/TransformParameters.0.txt \
-def all -threads 16
clitkComposeVF --input1 CBCT_CT.mha \
--input2 $i/deformationField.mhd \
--output $i/deformationField.mhd
clitkComposeVF --input1 $i/deformationField.mhd \
--input2 CT_CBCT.mha \
--output $i/deformationField.mhd
done
```

This is a bit complicated and there are probably other ways of doing this. For example, Vivien has resampled the planning CT frames on the CBCT coordinate system before doing the registrations, in which case you do not need to do all this. Just pick one of your choice but motion-compensated CBCT reconstruction requires a 4D vector field that is nicely displayed on top of a CBCT image, for example the fdk.mha that has been produced in the first step (the vector field is downsampled and displayed with VV):

The elastix output files and the transformed 4D DVF are available here.

# Respiratory signal

The motion model requires that we associate each projection image with one frame of the 4D vector field. We used the Amsterdam shroud solution of Lambert Zijp (described here) which is implemented in RTK

```
rtkamsterdamshroud --path . \
--regexp '.*.his' \
--output shroud.mha \
--unsharp 650
rtkextractshroudsignal --input shroud.mha \
--output signal.txt
```

in combination with Matlab post-processing to get the phase signal. Note that the phase must go from 0 to 1 where 0.3 corresponds to 30% in the respiratory cycle, i.e., frame 3 if you have a 10-frames 4D DVF or frame 6 if you have a 20-frames 4D DVF. The resulting phase is in green on top of the blue respiratory signal and the detected end-exhale peaks:

# Motion-compensated cone-beam CT reconstruction

We now have all the pieces to do a motion-compensated reconstruction. Gathering all these pieces is probably the main difficulty. If you have set everything correctly, you now only have to run the following commands

```
# Reconstruct from all projection images with motion compensation
rtkfdk \
-p . \
-r .*.his \
-o fdk.mha \
-g geometry.rtk \
--hann 0.5 \
--pad 1.0 \
--signal sphase.txt \
--dvf deformationField_4D.mhd
# Keep only the field-of-view of the image
rtkfieldofview \
--reconstruction fdk.mha \
--output fdk.mha \
--geometry geometry.rtk \
--path . \
--regexp '.*.his'
```

At this stage, you should have the time to drink a coffee (several for some computers). A neat solution to appreciate the improvement is to toggle between uncorrected and motion-compensated reconstruction:

You should be aware that we have constructed the 4D vector field with phase 50% as a reference. Therefore, the image is compensated towards that position. However, any other phase can be reconstructed by modifying the reference image of your 4D vector field. We usually like to reconstruct towards the time-average position.