Axial motion estimation and correction for simultaneous multi-plane two-photon calcium imaging

Two-photon imaging in behaving animals is typically accompanied by brain motion. For functional imaging experiments, for example with genetically encoded calcium indicators, such brain motion induces changes in fluorescence intensity. These motion-related intensity changes or motion artifacts can typically not be separated from neural activity-induced signals. While lateral motion, within the focal plane, can be corrected by computationally aligning images, axial motion, out of the focal plane, cannot easily be corrected. Here, we developed an algorithm for axial motion correction for non-ratiometric calcium indicators taking advantage of simultaneous multi-plane imaging. Using temporally multiplexed beams, recording simultaneously from at least two focal planes at different z positions, and recording a z-stack for each beam as a calibration step, the algorithm separates motion-related and neural activity-induced changes in fluorescence intensity. The algorithm is based on a maximum likelihood optimisation approach; it assumes (as a first order approximation) that no distortions of the sample occurs during axial motion and that neural activity increases uniformly along the optical axis in each region of interest. The developed motion correction approach allows axial motion estimation and correction at high frame rates for isolated structures in the imaging volume in vivo, such as sparse expression patterns in the fruit fly brain.