Anisotropy

[JohnJ]

Hi All,

I have a question about the Anisotropy algorithm. If I am
understanding the BoneJ code correctly, the more anisotropic a
structure is, the closer the result should be to 1. However, all of
the mouse bone papers I have read use a somewhat different method,
where DA is defined as the length of the longest over the shortest
radii of the MIL ellipsoid. Using that definition, highly anisotropic
structures would have a DA >1.

In trying to compare some recent SR-uCT results to mouse bone
literature, I can't seem to find any papers using the BoneJ
convention. Am I right in assuming that one could calculate DA with
the BoneJ results using the following algebra:

DA_BoneJ = 1 - MIL_short/MIL_long,

DA_alternative = MIL_long/MIL_short,

therefore:

DA_alternative = (1-DA_BoneJ)^-1

Thanks for your input, BoneJ is a great resource for my work.

Cheers,
John

[Michael Doube]

Hi John,

I have a question about the Anisotropy algorithm.  If I am
understanding the BoneJ code correctly,

I'm glad you read it!
The actual DA (1 - min radius / max radius) calculation is done here:
https://github.com/mdoube/BoneJ/blob/master/src/org/doube/bonej/Anisotropy.java#L632
 

the more anisotropic a
structure is, the closer the result should be to 1.

That's correct.
 

 However, all of
the mouse bone papers I have read use a somewhat different method,
where DA is defined as the length of the longest over the shortest
radii of the MIL ellipsoid.  Using that definition, highly anisotropic
structures would have a DA >1.

Yes that's right. When writing the Anisotropy class I decided to report only the 0-1 version of DA, then document the method to avoid any ambiguity. The original document I was working from is the SkyScan CTan manual, which describes in some detail this calculation and gives both options:

"Finally, you can derive from the tensor eigen analysis a single parameter
measuring anisotropy: this is the degree of anisotropy (DA), and is traditionally
expressed as the maximum eigenvalue divided by the minimum eigenvalue.
Values for DA calculated in this way vary from 1 (fully isotropic) to infinity (fully
anisotropic). Mathematically this is a cumbersome scale."

"A more convenient mathematical index of anisotropy is calculated as: DA = 1 - min/max
Here DA is 0 for total isotropy and 1 for total anisotropy. (Both values are
reported by CT-analyser)."

http://www.skyscan.be/next/CTAn03.pdf

 

In trying to compare some recent SR-uCT results to mouse bone
literature, I can't seem to find any papers using the BoneJ
convention.  Am I right in assuming that one could calculate DA with
the BoneJ results using the following algebra:

DA_BoneJ = 1 - MIL_short/MIL_long,

DA_alternative = MIL_long/MIL_short,

therefore:

DA_alternative = (1-DA_BoneJ)^-1

Yes, that's exactly correct. If you would like, BoneJ could report either or both values, but for backwards compatibility, 'DA' must stay as it is and we must make a new label for the traditional method, like tDA. What do you think? It's about 2 lines of code.
 

Thanks for your input, BoneJ is a great resource for my work.

Thanks for using BoneJ, and for your feedback.

Michael

[Michael Doube]

DA_BoneJ = 1 - MIL_short/MIL_long,

DA_alternative = MIL_long/MIL_short,

therefore:

DA_alternative = (1-DA_BoneJ)^-1

Yes, that's exactly correct. If you would like, BoneJ could report either or both values, but for backwards compatibility, 'DA' must stay as it is and we must make a new label for the traditional method, like tDA. What do you think? It's about 2 lines of code.

I committed it already:
https://github.com/mdoube/BoneJ/commit/1b2c6304070d763b001bf69f2bf8486950006e90

Michael

[John Jameson]

Michael,

Thanks very much for the quick response, and for implementing the new code!

Cheers,
John

--

John Jameson
Research Assistant
Orthopaedic & Rehabilitation Engineering Center
Marquette University
Office: ASF Suite 105, Rm 105A

(414) 288-8497 office

(423) 863-1278 cell