During embryogenesis, a mammalian heart develops from a simple tubular shape into a complex 4-chamber organ, going through four distinct phases: early primitive tubular heart, emergence of trabeculations, trabecular remodeling and development of the compact myocardium. In this paper we propose a framework for standardized and subject-independent 3D regional myocardial complexity analysis, applied to analysis of the developmentevolution of the mouse left ventricle. We propose a standardized subdivision of the myocardium into 3D overlapping regions (in our case 361) and a novel visualization of myocardial complexity, whereupon we: 1) extend the fractal dimension, commonly applied to image slices, to 3D and 2) use volume occupied by the trabeculations in each region together with their surface area, in order to quantify myocardial complexity. The latter provides an intuitive characterization of the complexity, given that compact myocardium will tend to occupy a larger volume with little surface area while high surface area with low volume will correspond to highly trabeculated areas. Using 50 mouse embryo images at 5 di erent gestational ages (10 subjects per gestational age), we demonstrate how the proposed representation and complexity measures describe the developmentevolution of LV myocardial complexity. The mouse embryo data was acquired using high resolution episcopic microscopy. The complexity analysis per region was carried out using: 3D fractal dimension, myocardial volume, myocardial surface area and ratio between the two. The analysis of gestational ages was performed on embryos of 14.5, 15.5, 16.5, 17.5 and 18.5 embryonic days, and demonstrated that the regional complexity of the trabeculations increases longitudinally from the base to the apex, with a maximum around the middle. The overall complexity decreases with gestational age, being most complex at 14.5. Circumferentially, at ages 14.5, 15.5 and 16.5, the trabeculations show similar complexity everywhere except for the anteroseptal and inferolateral area of the wall, where it is smaller. At 17.5 days, the regions of high complexity become more localized towards the inferoseptal and anterolateral parts of the wall. At 18.5 days, the high complexity area exhibits further localization at the inferoseptal and anterior part of the wall.

B. Paun is supported by the grant FI-DGR 2014 (2014 FI B01238) from the Generalitat de Catalunya. The research leading to these results has received funding from the EU FP7 for research, technological development and demonstration under grant agreement VP2HF (no. 611823) and from the Spanish Ministry of Economy and Competitiveness (grant TIN2011-28067, TIN2014-52923-R, the Maria de Maeztu Units of Excellence Programme MDM-2015-0502) and FEDER. C. Butakoff is supported by the grant from the Fundació La Marató de TV3 (20154031), Spain. The HREM datasets used in this manuscript were provided and collected by Dr. T. J. Mohun, Emily Hardman and Fabrice Prin from the Francis Crick Institute, London.