Emergence of structure in mouse embryos: Structural Entropy morphometry applied to digital models of embryonic anatomy.

We apply an information-theoretic measure to anatomical models of the Edinburgh Mouse Atlas Project. Our goal is to quantify the anatomical complexity of the embryo and to understand how this quantity changes as the organism develops through time. Our measure, Structural Entropy, takes into account the geometrical character of the intermingling of tissue types in the embryo. It does this by a mathematical process that effectively imagines a point-like explorer that starts at an arbitrary place in the 3D structure of the embryo and takes a random path through the embryo, recording the sequence of tissues through which it passes. Consideration of a large number of such paths yields a probability distribution of paths making connections between specific tissue types, and Structural Entropy is calculated from this (mathematical details are given in the main text). We find that Structural Entropy generally decreases (order increases) almost linearly throughout developmental time (4-18 days). There is one `blip' of increased Structural Entropy across days 7-8: this corresponds to gastrulation. Our results highlight the potential for mathematical techniques to provide insight into the development of anatomical structure, and also the need for further sources of accurate 3D anatomical data to support analyses of this kind.