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An approach to constructing a mathematical model for quantifying the dynamics of regeneration of planarian flatworms in biological experiments based on an analysis of a series of digital microscopic images is considered. An approach is proposed to describe the body shape of a planarian using a continuous morphological model, based on the concept of a medial representation of the silhouette of a worm. The silhouette in this case is a polygon approximating the contours of the body of the planarian. The medial representation of the figure includes a median axis and a radial function that describes the width of the figure relative to the median axis. Morphological criteria for assessing the dynamics of regeneration based on a continuous morphological model are proposed and the results of computational experiments are presented.