Mitigating Jacobian overestimation in SyN for near-zero brain volume change

[ChristineFarrugia]

Hi,

I am estimating brain volume change from pairs of MRIs using Jacobian-based morphometry. The image pairs can differ in contrast and SNR. I'm doing this as follows (using ANTsPY):

reg = ants.registration(fixed=fix, moving=mov, type_of_transform='SyNOnly', initial_transform=workdir+'/output_transform.mat', mask=icv_fix, moving_mask=icv_mov, singleprecision=False)
and then extract the Jacobian:
jac = ants.create_jacobian_determinant_image(fix,reg['fwdtransforms'][0],do_log=False,geom=False)

To find the volume in moving space, I multiply the Jacobian field by the volume of a voxel in fixed space and sum over a brain parenchyma mask (also in fixed space). I then subtract the volume in fixed space to find the change, repeat everything with moving and fixed images interchanged, and calculate the average.

The problem is that the volume change I'm getting is consistently higher than what I'm expecting, which should be close to zero. Of course, the fact that I'm using images with different contrasts, SNRs etc undoubtedly contributes to that, but from the literature, I understand that deformation-based methods using Jacobian determinants tend to overestimate small volume changes, and that a Kullback–Leibler penalty on the log-Jacobian can reduce this bias (https://www.sciencedirect.com/science/article/pii/S1361841509000462?via%3Dihub)

As far as I'm aware, ANTs does not implement this directly, so I wonder if you could provide some advice on:

• SyN parameter settings that could help to improve Jacobian stability when true change is near zero.
• Post-registration strategies, e.g., smoothing Jacobians, or masking/eroding regions prone to artifacts.

Thanks in advance for any guidance.

[gdevenyi]

Hi, https://github.com/CoBrALab/optimized_antsMultivariateTemplateConstruction/ implements a complete unbiased DBM pipeline using ANTs tools. You can take a look at how various steps are implemented, or directly use it.

[ChristineFarrugia]

Hi @gdevenyi
Thanks very much for your feedback. I’ve taken a look at the DBM pipeline you mentioned, and while it goes beyond the simple use case I currently need, I’m interested in incorporating it into my workflow.
Suppose I have two images from the same subject, A and B, and I’d like to register A to B and extract the Jacobian of the resulting transformation. Is it possible to do this by running twolevel_modelbuild and twolevel_dbm with only a single subject?

[gdevenyi]

Its a bit overkill to use it for a single subject, but it would just be a single level, with a single subject, with a single iteration.

The basics of registration and jacobians for ANTs is covered in their documentation, https://github.com/ANTsX/ANTs/wiki/Forward-and-inverse-warps-for-warping-images,-pointsets-and-Jacobians

[cookpa]

There's not a direct Jacobian penalty but regularization can be added in the registration, eg total_sigma=1 (default is 0)