To quantitatively measure the goodness of a reconstruction, we propose to use a BSM, which is analogous to mean square error. To calculate the metric, the reconstruction result is first thresholded, such that at each time step, all voxels with amplitudes of at least half of maximum are considered as “valid” voxels, which corresponds to the commonly used FWHM metric in the DOT field.21

After thresholding, the bias term is defined as the Euclidean distance between the center of mass of the valid voxels and the true center. The spread term is defined as the mean-square distance between all valid voxels to the center of mass of the valid voxels, i.e.,

where N() denotes the size of a set, ri is the location vector of the i’th voxel, and rc is the location vector of the center of mass of the valid voxels.

When two spots are simultaneously activated, bias and spread are calculated separately for each of them. In the case where only one region is reconstructed (e.g., two activation spots are indistinguishable in the reconstruction, or one region is missing), if all valid voxels are closer to one activation spot (say, A) than the other (say, B), we report that activation spot B is not detected. Otherwise, the one reconstructed activation is used to calculate bias and spread for both A and B.

Finally, the BSM is defined as

and has the units of distance.

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