Diffusion (Image3d)

Diffusion allows the mapping of channels or structures (here biological tissues). It creates a vector field based on all voxels and its surroundings.

First used for:
Kupczik K, Stark H, Mundry R, Neininger F, Heidlauf T, Röhrle O (2015). Reconstruction of muscle fascicle architecture from iodine-enhanced microCT images: a combined texture mapping and streamline approach. Journal of Theoretical Biology 382 (7): 34–43. DOI:10.1016/j.jtbi.2015.06.034 / ISSN:0022-5193

In this example, we use a part of an image stack from Julian Sartori (Thanks for the support!), which shows the achilles tendon of a rat.

Download: Image stack

To convert Dicom to the Nifti (nii) file format you can use dcm2niigui from Chris Rorden’s Neuropsychology Lab.

First step
Load a image stack and show its content.

▸ Image3d


image.load stack.nii.gz
image.info stack.nii.gz stack-info.txt
image.analysis stack-analysis.png // more under the topic 'Histogram'
image.setrange
image.setcrop
image.gradient stack-gradient.png // more under the topic 'View'

image.load

image.analysis

image.gradient

Second step
Calculate the vector field and reduce it.

▸ Image3d


image.load stack.nii.gz
vector := image.make.vector
vector.use vector
// thread.max := 2 // here you can reduce the number of threads
// image.diffusion 16
image.diffusion.adaptive 16 // if structure simple, do one step per 8 voxels
vector.save "stack_vector.nii"
vector.save "stack_vector.txt" // for cloud2

newvector := vector.copyscale 0.1
vector.use newvector
vector.save "stack_reduce.nii"
vector.save "stack_reduce.txt"

▸ More details


// image.diffusion.map map.pgm 16 // calculate diffusion map from one voxel with scan length at center point
// image.diffusion.map map.pgm 16 <0,0,0> // calculate diffusion map from one voxel with scan length at center point
// image.diffusion.map map.pgm 16 <10,10,10> // calculate diffusion map from one voxel with scan length at point <10,10,10>
// image.diffusion.map map.pgm 16 <10,10,10> < -3,-3,-3> // calculate diffusion map from one voxel with scan length at point <7,7,7>
// image.diffusion.map map.pgm 16 <0,0,0> < -3,-3,-3> // calculate diffusion map from one voxel with scan length at center point plus < -3,-3,-3>
// image.diffusion.colormap map.ppm 16 ... // calculate diffusion map from one voxel with scan length at center point / ... see above
// image.diffusion.dump dump.txt 16 ... // dump diffusion from one voxel with scan length at center point / ... see above
// image.diffusion.histogram ... // calculate length histogram from one voxel at center point / ... see above
// image.diffusion.sd ... // calculate sd's from one voxel at center point / ... see above

// image.diffusion.method 5 // 1=stark2013 2=stark2014a 3=stark2014b 4=stark2015a 5=stark2015b(default) // algorithm for image.diffusion
// image.diffusion.max 0.25 // (%)
// image.diffusion.angle 0.08726 // (rad) - 5*(pi/180) = 5°
// stark2013 = only the single best vector
// stark2014a = mean the two best vectors, if distance < r/2
// stark2014b = mean (same SD) best vectors, only for diffusion.max (%)
// stark2015a = mean (same SD) best vectors (around diffusion.angle (rad)), only for diffusion.max (%)
// stark2015b = mean the best vectors (around diffusion.angle (rad)), only for diffusion.max (%)
// image.diffusion 16 // calculate vector field from image with scan length
// image.diffusion.adaptive 16 // calculate vector field from image with scan length - only for image div 2 and if fails for subpixels

Third step
Evaluation (with cloud2 please use *.txt).

stack_vector.txt (x,y view)

stack_reduce.txt (x,y view)

▸ Cloud2


edit.vectors.invert

stack_vector.txt (x,y view)

▸ Cloud2


edit.vectors.norm

stack_vector.txt (x,y view)

stack_reduce.txt (x,y view)

▸ Cloud2


edit.global.mean.vectors

stack_vector.txt (x,y view)

Third step / Advanced
Projection and Evaluation (with cloud2 please use stack_reduce.txt).

▸ Cloud2


edit.vectors.norm
transform.clear.z // transform.clear.x
edit.local.mean.vectors

stack.nii (x,y view)

stack_reduce.txt (x,y view)

stack.nii (y,z view)

stack_reduce.txt (y,z view)