Understand the connectivity measurement

Hello everyone, I am reading this article “quantification of connectivity in cancellous bone (Odgaard)” but I don’t understand what is the connectivity of this structure using the variable “deltachi”.
from this page: http://bonej.org/connectivity the connectivity equal to: 1-deltachi
but from the example © fig 3, in the article of Odgaard the deltachi =-1, then I suppose the connectivity =1-deltachi=2??

Can you help me to understand please??

Hi @jaki19,

Short answer, I agree with you that the “connectivity” as defined in your link should be 2. Here’s why I think that:

Step 1: make sure you understand the Euler characteristic.

Step 2: I think that figure means to indicate that those 8 voxels are those under consideration. Those 8 voxels form a torus, which has an Euler characteristic of -1 (see above). This is deltachi which you should interpret as “the amount that this part of the sample (those 8 voxels) contributes to the total Euler characteristic of the entire bone (the 8 voxels plus the “caps” on either side - indicated by dotted lines”

Step 3: if you add the “caps” you end up with something like a hollow sphere which has an Euler characteristic of 2 = 1 - (-1). Also see above. Hooray! :v:

Edit: Okay, I have to be more careful when answering stuff before coffee. A torus has Euler char = 0, not -1, whoops -I’ll look at this a littler more closely

I don’t do bone stuff, but this is my best guess. Does this sound like it could be right to you? You could also try making that 8 voxel shape and doing the analysis in bonej and confirming that you get 2 for the connectivity and -1 for deltachi - that’s what I’d do.

Good luck, and hope this helped.

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