Robust estimation of the motile cilia beating frequency

The estimation of the cilia beating frequency (CBF) is of great interest in understanding how the CBF modulates liquid fluxes and how it is controlled by the ciliated cell intra- and/or extracellular medium composition in physiological processes. Motion artifacts and camera defaults may hinder the computation of the frequency variations during long-lasting experiments. We have developed a new analysis approach consisting of a preliminary corrective step (removal of a grid pattern on the image sequence and shift compensation), followed by a harmonic model of the observed cilia using a maximum likelihood estimator framework. It is shown that a more accurate estimation of the frequency can be obtained by averaging the squared Fourier transform of individual pixels followed by a particular summation over the different frequencies, namely the compressed spectrum. Robustness of the proposed method over traditional approaches is shown by several examples and simulations. The method is then applied to images of samples containing ciliated ependymal cells located in the third cerebral ventricle of mouse brains, showing that even small variations in CBF in response to changes in the amount of oxygenation, pH or glucose were clearly visible in the computed frequencies. As a conclusion, this method reveals a fine metabolic tuning of the cilia beating in ependimocytes lining the third cerebral ventricle. Such regulations are likely to participate in homeostatic mechanisms regulating CSF movements and brain energy supply.