Robust estimation of the motile cilia beating frequency

Abstract

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.

Automating the measurement of physiological parameters: A case study in the image analysis of cilia motion

“…Cilia located on biopsy cells are rooted along the surface of the cell. Contrary to the experimental conditions of [8], where cultured ciliated cells are located on an even surface, the beating extremity of cilia form a curve. Since cilia may be of varying lengths, it is useful to consider not just a single curve but several from the root to the tip of the beating region.…”

“…We estimated the power spectrum S = |F | 2 by a power spectral density method, exemplified in [8]. It consists of computing the Fourier transform Fn on each line n of Iv and averaging the square modulus of all the Fn.…”

“…Kymograph analysis [7,8] is a "linescan" method where grey level variations over a line drawn by the user are analyzed semiautomatically. This method is sensitive to illumination, vibrations, proper cell motion and depends on the location of the line, the shape of the ciliated cells, as such it is only really suitable for straight cell borders.…”

Advances in Astrocyte Computational Models: From Metabolic Reconstructions to Multi-omic Approaches

“…Walsh et al (2017) Simplified axonal model Oligodendrocyte Sodium-ion channel number/density has a strong influence on the optimal pattern of myelin and the conduction velocity. Buishas et al (2014) Literature-based, dynamical Ependymal/CSF A computational model for the production of CSF based on experimental evidence of osmotic pressure gradients Meste et al (2015) Computational simulation of CSF based on video-microscopy images from mice brain.…”

A regionalized automated measurement of ciliary beating frequency

“…Moreover, the method is very sensitive to noise and is easily perturbed by cells proper motion. A linescanbased technique is proposed in [12], coupled with the Fast Fourier Transform, and is evaluated on slices on brain ciliated epithelium. It deals with acquisition problems: the removal of artefacts due to the camera sensor, and frame stabilization.…”