Quantifying structure regularity in fluorescence microscopy cell images using a novel multi-dimensional approximate entropy metric

Techniques such as fluorescence microscopy reveal in three dimensions the complex mechanical structure of the cell cytoskeleton, made up of actin filaments, microtubules and intermediate filaments. Methods to quantify the degree of order in this structure could prove useful in classifying cells and may be related to the structural integrity of the cell. Approximate Entropy (ApEn) is a regularity statistic that has previously been used to quantify randomness in 1D time series data. We have extended the ApEn concept to define a multi-dimensional parameter suitable for application to three dimensional image data. This 3D ApEn parameter was applied to fluorescence microscopy images showing actin filaments in normal and cancerous human prostate cells. Differences between the ApEn calculated from the different images were observed, with cancer cells tending to have higher values indicating a lower degree of order.