Abstract The aim of the present study was to describe the fibre architecture of the fetal heart at mid gestation, and to clarify some persistent controversies concerning the architecture of the myofibres in the right ventricular wall and the muscular ventricular septum. We used quan- titative polarized light microscopy to obtain information about the orientation of myocardial cells in the ventricu- lar mass. These cells, joined into a network by anasto- moses, have at any point in the ventricular mass a princi- pal direction – the fibre direction. We have quantitated this information in the form of maps of the azimuth and elevation angles, in 18 midgestation fetal hearts. Our findings show that the fibre architecture of the heart can be conceptualised as myocardial fibres running like geo- desics on a nested set of warped “pretzels”. This model is an extension to the whole ventricular mass of Krehl’s Triebwerk, and Streeter’s model which was restricted to the left ventricle. A “pretzel” itself can be considered as two doughnuts joined side-by-side, with the tunnel at the center of each doughnut corresponding to the ventricular cavity. Over and above the excellence of the fit between the data and the geodesic representation, three strong ar- guments support this model. First, it is the only existing model that explains the observed rolling over of fibres around the atrioventricular valvar orifices. Second, it ex- plains the trajectory of the fibres from the epicardium to the endocardium at the basal parts of both ventricles and at the apical part of the left ventricle. Third, the predict- ed topological singularities of the model are systemati- cally observed in each of the 18 hearts studied. Key words Myocardium · Heart ventricle · Microscopy · Polarization · Topology Introduction The organization of myofibres has been extensively studied in the mammalian heart, and numerous models have been proposed. In general terms, two different fam- ilies of models can be distinguished (Fig. 1). In the first family, the arrangement of the myocardial fibres is given by analogy with the description of the arrangement of the muscular skeletal fibres. Thus, the fibres are consid- ered to gather in distinct bundles and muscles, with each fibre retaining a close individual relationship with the cardiac fibrous skeleton. These models distinguished from one to four systems of myocardial bundles (Mall 1911; Benninghoff 1931; Robb and Robb 1942; Lev and Simkins 1956; Torrent-Guasp 1975). In the extreme case, Robb and Robb (Fig. 1A) proposed an arrangement of four myocardial bundles anchoring on the fibrous trig- ones and the aortic and pulmonary roots, Torrent-Guasp in contrast (Fig. 1B) considered only one system, which he argued was composed of the unrolled ventricular walls being stretched between the aortic valve at one end and the pulmonary valve at the other. The limitations of these models, mostly based on dissection, have been stressed recently (Lunkenheimer et al. 1997; Schmid et al. 1997; Torrent-Guasp et al. 1997). In the second family of models, the myocardium is viewed as a spe- cialization of the vascular musculature, with myocardial fibres branching from one to another, rather than taking their origin or insertion from the fibrous skeleton. This approach was initiated by Krehl (1891) at the end of the 19 century. It has been considerably reinforced by signif- icant advances that, by means of photonic and electronic microscopy, showed the myocardial fibres to be a net- work of preferentially oriented and branched myocardial cells forming end-to-end cellular junctions (Hort 1960, 1971; Fox and Hutchins 1972). Among these models, some have focused essentially on the architecture of the P.-S. Jouk ( ✉ ) · G. Michalowicz · L. Grossi UF Biologie du développement et Génétique clinique, Centre Hospitalier Universitaire de Grenoble, BP 217, 38043 Grenoble cedex 9, France e-mail: pierre-simon.Jouk@ujf-grenoble.fr Tel.: 33 (0)476765482, Fax: 33 (0)476768850 P.-S. Jouk · Y. Usson · G. Michalowicz Equipe Reconnaissance des Formes et Microscopie Quantitative – Laboratoire TIMC, UMR5525 CNRS, Institut Albert Bonniot, Faculté de Médecine, Université Joseph Fourier, Grenoble I, Domaine de la Merci, 38706 La Tronche Cedex, France Anat Embryol (2000) 202:103–118 © Springer-Verlag 2000 ORIGINAL ARTICLE Pierre-Simon Jouk · Yves Usson Gabrielle Michalowicz · Laurence Grossi Three-dimensional cartography of the pattern of the myofibres in the second trimester fetal human heart Accepted: 23 March 2000