The geometric correction of position changes and shape distortion in digital fluorescence images of living cells

Digital imaging fluorescence microscopy of living cells is a valuable method for studying the dynamics of cellular processes. We are interested in distinguishing different pathways for uptake of fluorescently labeled compounds by living cells on the basis of the differences in their kinetics and location within the cell. The rate constants are calculated on a pixel by pixel basis from a series of images taken at intervals over the course of the experiments. This calculation is meaningful only if, during the time course of reaction, the pixels remain spatially invariant. Because the cells are alive during the experiment, the cells changes shape and position in the interval between image acquistion and thereby destroys the spatial invariability of the pixels. Quantitative studies of uptake processes in cells are limited to well behaved systems, i.e., nonmoving or fixed cells. Such experiments with fixed cells provide estimates of the rates of passive uptake processes, part but not all of the information needed to intrepret the image data about the active transport processes. It is obvious that, for quantitative interpretation of uptake studies, it is essential to perform a geometric correction operation, by which each cell image in the time series is mapped to the same shape in order to restore spatial invariability of pixels. The objective of this paper is to develop and test the numerical method for mapping the changes in position and shape of the cell back to the initial geometry. Subsequently, uptake rates or other pixel by pixel based calculations can be performed and the results correlated with cell structure. We have used the recursive procedure based on two dimensional polynomials of arbitrary degree using the least squares method, and as a final step, the interpolation method by Akima. There is a significant improvement in pixel by pixel calculations after correction, although some problems, notably edge effects, still remain.