Overcoming the partial volume effect#

Each metric extraction method provided by SCT accounts for the partial volume effect in different ways.

Binary mask-based methods#

-method bin: Average within binary ROI#

Because of its simplicity, the traditional method to quantify metrics is to use a binary mask: voxels labeled as “1” (i.e. in the mask) are selected and values within those voxels are averaged.

This method does not account for the partial volume effect whatsoever, and thus the resulting metric could be biased by the surrounding tissues, as demonstrated on the previous page.

-method wa: Weighted average#

Instead, we could turn the binary masks into weighted masks by effectively “weighting” the contribution of voxels at the interface (e.g., mask value = 0.1) vs. voxels well within the tissue of interest (e.g., mask value = 0.9).

This method is only useful if you have an existing binary mask for each region of interest. Also, this method only considers each mask in isolation, rather than considering the relations between adjacent masks. So, while it would help to minimize the partial volume effect, it would not comprehensively solve the problem.

Atlas-based methods#

Instead of using binary masks, we can use the white and gray matter atlas contained within the PAM50 template. In the atlas, each tract is represented using a nonbinary “soft” mask, with values ranging from 0 to 1 at the edges of each tract label that capture the partial volume information. For more information on how the exact partial volume values were determined for each tract, see [Lévy et al., Neuroimage 2015].

-method ml: Maximum Likelihood#

The partial volume information from the atlas can be combined with Gaussian mixture modeling and maximum likelihood estimation to estimate the “true” value within the region of interest (e.g. a white matter tract). This approach assumes that within each compartment, the metric is homogeneous.

-method map: Maximum A Posteriori#

Because Maximum Likelihood estimation is sensitive to noise, especially in small tracts, we recommend using the Maximum a Posteriori method instead. This method adds a prior – specifically, the maximum likelihood estimation computed within either the WM, GM, or CSF compartment of the image, depending on which area the ROI belongs to. (For example, if a metric is extracted for a specific WM tract, the maximum likelihood for the WM as a whole will be used as a prior.)

The map method is the most robust to noise in small tracts. This was further validated using bootstrap simulations based on a synthetic MRI phantom. For more details, see [Lévy et al., Neuroimage 2015] (construction of the phantom, effect of noise, contrast) and [De Leener et al., Neuroimage 2017; Appendix] (effect of spatial resolution).

Note

The methods bin and wa can be used with any binary mask. However, the methods ml and map require you to warp the white matter atlas to the coordinate space of your data, as is shown on the next page.