Mathematical analysis techniques of frontal sinus morphology, with emphasis on Homo

Of all the paranasal sinuses, frontal sinus (FS) morphology, volumes, outlines, and cross-sectional areas vary most and so their statistical noise presents particular challenges. To assess and control this statistical noise requires a suite of mathematical techniques that: model their volume and cross-sectional area ontogeny, determine the uniqueness and fractal dimensions of their outlines (useful in forensics), smooth their outlines via Singular Value Decomposition (SVD), and model their expansion via percolation cluster models (PCMs). Published data sets of FS outlines, cross-sectional areas and volumes of Neanderthal and modern crania (obtained via CT-imaging techniques) are utilized here for application of these novel mathematical methods, which necessitate a modeling approach. Results show that: FS noisiness can be explained as cluster growth, their fractal outlines have properties similar to closed random walks (Brownian bridges) about predefined curves, and the PCMs can simulate the emergence of lamellae. The statistical properties derived from the analysis techniques presented here suggest that an emergence of the lamellae via PCMs (with pinning and quenching-correlated noise) resolves the masticatory stress debate by showing that the lamellae are indeed responses to masticatory stresses, but these are of so low a level that they cannot be measured with strain gauges. PCMs and Brownian bridges, defined by local rules, lead to the emergence of macroscopically observable morphologies. The methodologies presented here contribute to research in emergence phenomena and are not confined to morphological analyses of frontal sinuses.