![]() ![]() ![]() Such formalism allows us to identify connections that are not ‘expected’ to occur in the context of the entire topology of the network. A common feature of the topology of complex networks such as the skull is that one can identify groups of nodes (bones) that have well-defined patterns of connections (i.e., craniofacial articulations or synarthrosis) with other groups of nodes 17. We infer the susceptibility of craniofacial articulations to close prematurely using the reliability formalism developed for network models 17. A recent comparison of network models of craniosynostosis conditions showed that, despite the associated abnormal shape variation, skulls with different types of craniosynostosis share a same general pattern of network modules 16. Anatomical network models have been used before, for example, to identify developmental constraints in skull evolution 12, 13, analyze the evolution of tetrapod disparity in morphospace across phylogeny 14, and model the growth of human skull bones 15. This network model is thus a mathematical representation of the entire pattern of structural relations (i.e., physical contacts or articulations) among skull bones. Here, we address the susceptibility of articulations to close from a theoretical standpoint, by modeling the skull as a network in which nodes and links formalize bones and their articulations at birth (Fig. ![]() Non-genetic factors are even less specific than genetic ones and include, among many others, bio-mechanical stress, hypoxia, and use of drugs or smoking during pregnancy 5, 8, 9, 10, 11. The number of genes identified to be carrying mutations associated with craniosynostosis has grown in the last two decades 7 for example, more than 60 genes have been shown to carry mutations associated with craniosynostosis 7: some of them show specificity for a suture in the context of a syndrome (e.g., ASXL1 and metopic suture in the Bohring-Opitz syndrome), others predispose to more than one type of craniosynostosis (e.g., FGFR2 in coronal, sagittal, and multi-suture synostoses), while most of them are not specifically associated with suture development, but to osteogenesis in general (e.g., ALX4, EFNA4, and TGFBR2). It is known that both genetic and non-genetic factors participate in the formation and maintenance of craniofacial articulations through life. In general, it is not well understood which factors predispose some articulations but not others to close prematurely. Craniosynostosis can occur in isolation, as non-syndromic craniosynostosis 4, 5, or as part of a variety of congenital disorders, such as Apert and Crouzon syndromes 6. This premature fusion of bones, if not treated surgically, can cause head malformations due to compensatory growth of other joints 2, sometimes provoking severe brain damage due to an increase of intracranial pressure 3. Craniosynostosis is a pathological condition with an estimated prevalence of about 5 in 10,000 live births 1, in which one or more articulations between cranial bones (frontal, parietal, temporal, and occipital) close prematurely, leading to the fusion of these bones. The timely closure of bone articulations is a normal process that takes place during skull development. Our findings suggest that the topological arrangement of skull bones might act as a structural constraint, predisposing some articulations to closure, both in normal and pathological development, also affecting the long-term evolution of the skull.Ĭraniofacial articulations are sites of primary bone growth and remodeling adequate formation and maintenance of these articulations is therefore important for a healthy development of the head and brain. These results indicate a relationship between the architecture of the skull and the specific articulations that close during normal development as well as in pathological conditions. In a similar way, articulations that close during the normal postnatal development of the skull have also lower reliability scores than those articulations that persist through adult life. We show that, of the 93 human skull articulations at birth, the few articulations that are associated with non-syndromic craniosynostosis conditions have statistically significant lower reliability scores than the others. To assess the susceptibility of each craniofacial articulation to close prematurely, we used a network model of the skull to quantify the link reliability (an index based on stochastic block models and Bayesian inference) of each articulation. Craniosynostosis, the premature fusion of cranial bones, affects the correct development of the skull producing morphological malformations in newborns. ![]()
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