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A toolbox of geometric elements for labyrinth model design and analysis


  • The author has no funding, financial relationships, or conflicts of interest to disclose.

  • For my granddaughter, Elaia Danielle, with love.



To develop a toolbox of defined geometric shapes that can aid in the emulation of the architecture of the labyrinthine membranes.

Study Design:

Analytical review of geometric shapes that are candidates for inclusion in the toolbox.


The mammalian labyrinth appears to have an overall tubular configuration. The bulges, bends and constrictions manifest by these chambers and conduits may be construed to be variations on an underlying core cylindrical structure. Four geometries that embrace the cylindrical shape are identified, namely the cylinder itself, the ellipsoid, the hyperboloid, and the torus. These can be exploited as model design tools and used to approximate the individual components of the labyrinth.


A toolbox of geometric elements is identified for use in modeling the mammalian labyrinth. The toolbox includes cylindrical, ellipsoidal, hyperboloidal, and toroidal elements, their figures and mathematical definitions, as well as derivative characteristics that relate to contour and curvature.


This analysis suggests that there is a heuristic value in considering the underlying structure of the mammalian labyrinth to be cylindrical. Four principal geometric shapes that are based on the cylinder have been identified for use in a toolbox of design elements. This toolbox can be used to model any mammalian labyrinth. Laryngoscope, 2012