Abstract

Craniosynostosis, the premature fusion of cranial bones, affects the correct development of the skull producing morphological malformations in newborns. 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. 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. 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. 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. 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.

Highlights

  • We investigated the relationship between the link reliability score and the susceptibility of an articulation to close during normal development or due to craniosynostosis

  • We find that sutures that normally close have significantly slightly lower reliability scores than those that do not (Mann-Whitney-Wilcoxon: one sided, W = 368, p-value = 0.047; Cohen’s d = −0.52) (Fig. 2); which is in agreement with our hypothesis that during normal development there is a tendency to close articulations that are topologically rare in the newborn skull

  • We find that while the reliability scores of articulations that close in craniosynostosis conditions tend to have lower scores than those that close during normal development, this difference is not statistically significant at a 5% significance level (Mann-Whitney-Wilcoxon: one sided, W = 15.5, p-value = 0.087; Cohen’s d = −0.964)

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Summary

Introduction

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. 1) This network model is a mathematical representation of the entire pattern of structural relations (i.e., physical contacts or articulations) among skull bones. If the architecture of the skull is driving (or influencing) the closure of articulations, we surmise that there is a relationship between the susceptibility of a pair of bones to fuse and the ‘topological unexpectedness’ of their articulation To quantify such ‘unexpectedness’, we use the link reliability score, that is the probability that a connection exists in the network given the observed (neonatal) topology of the skull[17]. We use the reliability formalism to investigate whether the topological arrangement of bones predicts which articulations are more susceptible to close in development; in other words, we want to assess if the architecture of the skull acts as an agent that constrains the fusion of bones

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