Connectome normalisation - volume product instead of sum?

Hi MRtrix community,

I know there have been some previous discussions on this, but I haven’t seen reference to these particular points.

Using the scale_invnodevol option in tck2connectome, will “scale each contribution to the connectome edge by the inverse of the two node volumes”. Based on the paper that @rsmith referenced here the normalization term is the sum of the volumes of the two nodes.

As @rsmith explained here, I understand that normalizing by node volume might not be appropriate after running SIFT2, when the connectome is interpreted in terms of tract density.

Still, I’m wondering about two points:

  1. Why use the sum of volumes, rather than their product? Under the interpretation of probability of connection, wouldn’t multiplying the two volumes be more closely related to the probability of finding such a connection (of course, this doesn’t take into account many other effects, but still).
  2. Wouldn’t it be more appropriate to mask the atlas file by the seeding mask (e.g., by the WM/GM interface, if using ACT)? This would be especially important for sub-cortical regions, where most of the volume does not contain streamline endpoints.

I would love to hear your thoughts on this.

Many thanks,
Roey