A new method for quantifying cranial and cerebral shape and asymmetry fits symmetric superquadric geometric models to three-dimensional coordinate measurements. Asymmetry is quantified as radial residuals of the surface data points from their best-fit superquadric models. Twenty human crania, 10 magnetic resonance imaging (MRI) exocranial surfaces, and 10 corresponding MRI cerebral surfaces as well as two infant head casts were digitized and modeled using superquadrics. Superquadric parameters have simple geometric interpretation, are very reproducible, and demonstrated statistically significant differences between crania of Amerindian ancestry and MRI exocranial surfaces of European ancestry used in this study. Superquadric models demonstrated strong congruence between MRI exocranial and cerebral surfaces. Typical asymmetry was 1-5 mm. Lastly, polar contour plots of radial residuals for head casts before and after orthotic cranioplasty demonstrated the efficacy of using superquadrics to quantify positional plagiocephaly and synostosis of infant crania.
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