Get HU values along a trajectory volume

Question

So, what I am trying to do is to calculate the density profile (HU) along a trajectory (represented by target x,y,z and tangent to it) in a CT. At the moment, I am able to get the profile along a line passing through the target and at a certain distance from the target (entrance). What I would like to do is to get the density profile for a volume (cylinder in this case) of width 1mm or so. I guess I have to do interpolation of some sort along voxels since depending on the spacing between successive coordinates, several coordinates can point to the same index. For example, this is what I am talking about.

Additionally, I would like to get the density profile for different shapes of the tip of the trajectory, for example:

My idea is that I make a 3 by 3 matrix, representing the shapes of the tip, and convolve this with the voxel values to get HU values corresponding to the tip. How can I do this using ITK/VTK?

Kindly let me know if you need some more information. (I hope the images are clear enough).

Answer 1

If you want to calculate the density drill tip will encounter, it is probably easiest to create a mask of the tip's cutting surface in a resolution higher than your image. Define a transform matrix M which puts your drill into the wanted position in the CT image.

Then iterate through all the non-zero voxels in the mask, transform indices to physical points, apply transform M to them, sample (evaluate) the value in the CT image at that point using an interpolator, multiply it by the mask's opacity (in case of non-binary mask) and add the value to the running sum.

At the end your running sum will represent the total encountered density. This density sum will be dependent on the resolution of your mask of the tip's cutting surface. I don't know how you will relate it to some physical quantity (like resisting force in Newtons).

Answer 2

To get a profile along some path, you would use resample filter. Set up a transform matrix which transforms your starting point to 0,0,0 and your end point to x,0,0. Set the size of the target image to x,1,1 and spacing the same as in source image.

I don't understand your second question. To get HU value at the tip, you would sample that point using a high quality interpolator (example using linear interpolator). I don't get why would the shape of the tip matter.