• Rigid-body registration (linear) - 6 degrees of freedom (dof)

• Pitch - Think of nodding (“yes”)
• Yaw - Think of shaking head (“no”)
• Roll - Think of shoulder shrugging (“I don’t know”)
• x – left/right
• y – forward/backward
• z – jump up/down

• Rigid-body registration (linear) - 6 degrees of freedom (dof)
  • Co-registration (within the same person)
    • Cross-sectional between-sequences
    • Longitudinal between-sequences
    • Longitudinal within-sequence

• Rigid-body registration (linear) - 6 degrees of freedom (dof)
  • Co-registration (within the same person)
    • Cross-sectional between-sequences
    • Longitudinal between-sequences
    • Longitudinal within-sequence

• Rigid-body registration (linear) - 6 degrees of freedom (dof)
  • Co-registration (within the same person)
    • Cross-sectional between-sequences**
    • Longitudinal between-sequences
    • Longitudinal within-sequence

• Affine registration – 12 dof (scaling)
• Non-linear (> 12 dof): sually requires a prior affine registration
  • Across-subject registration
  • Registration to a template: There are many different templates

For a voxel \(v\), the rigid transformation can be written as:

\[T_{\rm rigid}(v) = Rv + t\] where \(R =\) \[\left[\begin{array}{ccc} \cos\beta\cos\gamma& \cos\alpha\sin\gamma + \sin\alpha\sin\beta\cos\gamma & \sin\alpha\sin\gamma - \cos\alpha\sin\beta\cos\gamma \\ -\cos\beta\sin\gamma & \cos\alpha\cos\gamma - \sin\alpha\sin\beta\sin\gamma & \sin\alpha\cos\gamma + \cos\alpha\sin\beta\sin\gamma \\ \sin\beta & -\sin\alpha\cos\beta & \cos\alpha\cos\beta \end{array}\right]\]

• 6 degrees of freedom
• \(3\) associated with the translation vector: \(t=(t_x, t_y, t_z)\)
• \(3\) associated with the rotation parameters: \(\theta=(\alpha, \beta,\gamma)\).

• Initialize an empty list and add two elements to it

l = list()
l[[1]] = c(1, 2, 4, 5)
l[[2]] = matrix(1:10, nrow = 2)
print(l)

[[1]]
[1] 1 2 4 5

[[2]]
     [,1] [,2] [,3] [,4] [,5]
[1,]    1    3    5    7    9
[2,]    2    4    6    8   10

• Subsetting uses double brackets:

print(l[[1]])

[1] 1 2 4 5

If a vector has names, you can also put the - Initialize an empty list and add two elements to it

x = c(one = 1, three = 14, two = 5)
print(x)

  one three   two 
    1    14     5 

x[c("three")]

three 
   14 

If a list has names, you can subset with the $

• Subsetting with double brackets:

names(l) = c("V", "m"); l[["V"]]

[1] 1 2 4 5

If a list has names, you can also subset with the $

l$V

[1] 1 2 4 5

• get_image_filenames_list_by_subject - returns a list, each element is a subject, and each subject has a vector of filenames, named for each modality

library(ms.lesion)
all_files = get_image_filenames_list_by_subject()
class(all_files); names(all_files)

[1] "list"

[1] "test01"     "test02"     "test03"     "training01" "training02"
[6] "training03" "training04" "training05"

files = all_files$training01; class(files); names(files)

[1] "character"

[1] "T1"    "T2"    "FLAIR"

t1_fname = files["T1"]
t1 = readnii(t1_fname)
rt1 = robust_window(t1, probs = c(0, 0.975))

The registration function from extrantsr can register 2 images. The main arguments are:

• filename - either nifti object or filename of image to be registered (moving)
• template.file - either nifti object or filename of target image (fixed)
• typeofTransform - transformation of moving to fixed image (Rigid/Affine/SyN)
• interpolator - how are voxels averaged in fixed space (Linear/NearestNeighbor/LanczosWindowedSinc)

It can also perform bias correction if correct = TRUE.

For example, if we wanted to register the FLAIR to the T1 image, we would run:

library(extrantsr)
reg = registration(
  filename = files["FLAIR"], template.file = files["T1"],
  typeofTransform = "Rigid", interpolator = "Linear", verbose = FALSE)
names(reg)

[1] "outfile"             "fwdtransforms"       "invtransforms"      
[4] "interpolator"        "other_interpolator"  "invert_interpolator"
[7] "typeofTransform"     "retimg"             

The output in reg would contain the transformed image and paths to the estimated transformations.

double_ortho(rt1, reg$outfile)

We would like to perform registration within a visit for all modalities. The extrantsr function within_visit_registration will do the following steps:

1. Inhomogeneity correction (N3 or N4): could also use images from previous lecture
2. Registration to a fixed image (T1)

The function within_visit_registration arguments take in:

• fixed image - the image to be registered to
• moving images - images to register to the fixed
• typeofTransform - transformation of moving to fixed image (Rigid/Affine)
• interpolator - how are voxels averaged in fixed space
• correct - should correction be done, if so, specify correction = "N4"

and outputs a list of transformations (fwdtransforms) and output filenames (outfile)

With lists and vectors, there are apply functions. These apply a function to every element of the list. In this course, we will use:

• lapply - apply function and return the elements as a list
  • lapply(LIST, FUNCTION, OTHER_ARGUMENTS_TO_FUNCTION)
• sapply - apply function and return a “simplified” version
  • if all elements returned are a one-element vector, return a vector
  • if element 1 is a vector of length 3 and element 2 is a vector of length 1, return a list

res = within_visit_registration(
  fixed = files["T1"], moving = files[c("T2", "FLAIR")],
  correct = TRUE, correction = "N4",
  typeofTransform = "Rigid", interpolator = "Linear")
output_imgs = lapply(res, function(x) x$outfile)
out = c(T1 = list(t1), output_imgs)

# Running Bias-Field Correction on file

# Running Registration of file to template

# Applying Registration output is

$fwdtransforms
[1] "/var/folders/1s/wrtqcpxn685_zk570bnx9_rr0000gr/T//RtmpN4MXsP/file12bc91f0b4b400GenericAffine.mat"

$invtransforms
[1] "/var/folders/1s/wrtqcpxn685_zk570bnx9_rr0000gr/T//RtmpN4MXsP/file12bc91f0b4b400GenericAffine.mat"

$prev_transforms
character(0)

# Applying Transformations to file

 [1] "-d"                                                                                              
 [2] "3"                                                                                               
 [3] "-i"                                                                                              
 [4] "<pointer: 0x7fdb04b572c0>"                                                                       
 [5] "-o"                                                                                              
 [6] "<pointer: 0x7fdb04a70fa0>"                                                                       
 [7] "-r"                                                                                              
 [8] "<pointer: 0x7fdb04b61880>"                                                                       
 [9] "-n"                                                                                              
[10] "linear"                                                                                          
[11] "-t"                                                                                              
[12] "/var/folders/1s/wrtqcpxn685_zk570bnx9_rr0000gr/T//RtmpN4MXsP/file12bc91f0b4b400GenericAffine.mat"

# Writing out file

[1] "/var/folders/1s/wrtqcpxn685_zk570bnx9_rr0000gr/T//RtmpN4MXsP/file12bc910bbbbfa.nii.gz"

# Removing Warping images

# Reading data back into R

# Running Bias-Field Correction on file

# Running Registration of file to template

# Applying Registration output is

$fwdtransforms
[1] "/var/folders/1s/wrtqcpxn685_zk570bnx9_rr0000gr/T//RtmpN4MXsP/file12bc961de5f840GenericAffine.mat"

$invtransforms
[1] "/var/folders/1s/wrtqcpxn685_zk570bnx9_rr0000gr/T//RtmpN4MXsP/file12bc961de5f840GenericAffine.mat"

$prev_transforms
character(0)

# Applying Transformations to file

 [1] "-d"                                                                                              
 [2] "3"                                                                                               
 [3] "-i"                                                                                              
 [4] "<pointer: 0x7fdb04959bc0>"                                                                       
 [5] "-o"                                                                                              
 [6] "<pointer: 0x7fdb04b4b650>"                                                                       
 [7] "-r"                                                                                              
 [8] "<pointer: 0x7fdb0493e220>"                                                                       
 [9] "-n"                                                                                              
[10] "linear"                                                                                          
[11] "-t"                                                                                              
[12] "/var/folders/1s/wrtqcpxn685_zk570bnx9_rr0000gr/T//RtmpN4MXsP/file12bc961de5f840GenericAffine.mat"

# Writing out file

[1] "/var/folders/1s/wrtqcpxn685_zk570bnx9_rr0000gr/T//RtmpN4MXsP/file12bc9153222ab.nii.gz"

# Removing Warping images

# Reading data back into R

$T2
NULL

$FLAIR
NULL

double_ortho(out$T1, out$T2 )

The multi_overlay function takes in a list of images and then plots one slice across modalities (assumes center slice):

multi_overlay(out)

• Overall, there seems to be good overlap after registration
• It is usually beneficial to do inhomogeneity correction before registration.
  • just set correct = TRUE or pass in the bias-corrected images

Applying a Brain mask to all registered images

Now that the images are in the same space as the T1, if we skull-strip the T1 image (we did with MALF), we can apply this mask to those images to extract brain tissues using the neurobase::mask_img command:

mask = readnii("../output/training01_01_t1_mask.nii.gz") # MALF mask 
masked_imgs = lapply(out, mask_img, mask)

ortho2(masked_imgs$FLAIR)

ortho2(masked_imgs$T2)

• Registration within a subject can be done in R
  • registration wraps around the reading/writing of images and applying transformations (uses ANTsR functions)
  • double_ortho, ortho2, and multi_overlay can provide some basic visual checks to assess registration quality
  • within_visit_registration is a registration wrapper function
  • preprocess_mri_within - wraps multiple steps above (inhomo, reg, extract)
• Once images are registered in the same space, operations can be applied to all the images, such as:
  • Masking with a brain mask
  • Transforming images to new spaces with one modality

• Co-registration requires a few degrees of freedom (usually 6)
  • sequences from the same individual/brain are more alike than images from different subjects
• Example analyses that do not require a reference template
  • Identify location-specific longitudinal changes within an individual
  • Tissue class or structural segmentation
  • Analysis of indvidual-subject change in intensities

We have only done registration within a subject, but many times you want to perform a population-level analysis. This requries registration to a template:

• The registration can be done for this as well, just the template.file is now the template image and filename is the subject image.
  • other files (in the same space) can be transformed using the other.files and other.outfiles arguments. Or:
  • ants_apply_transforms can be used to apply this transformations to the other files

http://johnmuschelli.com/imaging_in_r