When Virchow's law fails: Crouzon syndrome as a test case for quantitative suture closure–endocranial shape relationships

Crouzon syndrome is a syndromic craniosynostosis characterized by premature fusion of cranial sutures and variability in cranial phenotype, which is poorly explained by classical growth rules such as Virchow's law. This study tested whether quantitative, continuous assessment of calvarial suture patency can help explain endocranial shape variability when categorical suture descriptions fail. We retrospectively analyzed preoperative cranial CT scans from children with FGFR2-related bicoronal craniosynostosis and age-matched controls (birth to 4 years). Endocasts were reconstructed using a semiautomated pipeline and analyzed with three-dimensional geometric morphometrics. Suture patency of major calvarial sutures was quantified as a continuous measure and converted into age-adjusted residuals, allowing deviations from control closure dynamics to be assessed independently of age. Intracranial volume increased with age at comparable rates in both groups, indicating preserved global endocranial growth. However, endocranial shape and its allometric relationship to growth differed between groups. While age-adjusted suture patency showed only weak associations with shape in controls, suture residuals covaried strongly with coherent, system-level endocast shape changes in Crouzon patients, including alterations in anteroposterior proportions and cranial fossa configuration. Morphological clusters did not map one-to-one onto suture closure patterns, indicating nonlocal and context-dependent effects. These findings suggest that suture-based models such as Virchow's law fail to predict cranial shape in syndromic craniosynostosis. By treating suture patency as a continuous, age-adjusted variable embedded within a coupled brain-skull growth system, this study suggests that Crouzon syndrome could act as a test case for quantitative, system-level models of craniofacial development.