Abstract

he continuous progress in imaging and computer modelling have increased our understanding of morphogenetic processes at different scales, from organs up to entire organisms. However, in the case of complex animal models (e.g., mouse embryogenesis), is not yet entirely possible to observe in real time the full growth of a developing embryo. Consequently, the current 3D data availability in these cases, even if extensive and detailed, provides only a characterisation of development at discrete moments in time, through single snapshots. To fill this gap, we set up a computer-based approach to describe the evolution in space and time of developmental stages from 3D volumetric images. Specifically, we represent each data into the spherical harmonics space, and we reconstruct the volumes using the values of the spherical harmonics’ coefficients interpolated in time (over the developmental stages). As a result, the reconstruction describes a continuous and smooth changing shape over space and time. We tested this approach using two different data sets: (1) mouse limb buds and (2) mouse hearts. (1) _{100 optical projection tomography (OPT) of mouse limbs were used and the result represents the 4D growth of an ideal limb which considers the common characteristics and features of all the limbs in the data set. We are recreating the growing process starting from E10 (i.e., 10 days after conception) when the limb bud is just a small bump of tissue and finishing at E12 .5 when the limb bud already shows a distinctive “paddle” shape. This approach proved to be robust even in the case of mouse hearts (2) where only a limited number of sample (}30) were used. Also, in this case we were able to create a continuous time-course describing the heart development of a mouse starting from 10 to 29 somites. This approach, able to combine the complexity of different arbitrary shapes over space and time, not only provides a quantitative basis for validating predictive models, but it also increases our understanding of morphogenetic processes from a purely geometrical point of view.