I have a question about how trilinear interpolation works.

Briefly I am working on perfusion images with a voxel size of 4x4x6 mm. and
T1 images with 1x1x1 mm. I have obtained GM segmentation on T1, I have
the PVE map. I would like to obtain the perfusion value for GM. Therefore I
obtained the linear tranformation matrix from T1 to perfusion image using

I am trying to find percentage volume of GM for a given perfusion image
voxel. I believe it would NOT be very accurate to transform the PVE map to
the perfusion image space using ApplyXFM using trilinear interpolation.

I understand how trilinear interpolation works while reslicing a low
resolution image to get a high resolution image. But I am not sure how/which
the PVE values are combined to obtain the PVE map for a lower resolution
image using trilinear interpolation.

I hope my question is clear enough.

Thank you very much in advance.