Nature's Secret Code: Fibonacci Sequence and 3D Modelling the Growing Rib
Presenter Status
Undergraduate Student
Abstract Type
Clinical Research
Primary Mentor or Principal Investigator
Richard Schwend, MD
Presentation Type
Poster
Start Date
20-5-2026 12:00 PM
End Date
20-5-2026 1:00 PM
Abstract Text
Hypothesis: Pediatric ribs that contribute to thoracic volume expansion follow a logarithmic spiral geometry, exhibiting scale enlargement while overall spiral shape is preserved.
Design: Retrospective cross-sectional morphometric analysis of pediatric CT scans.
Introduction: Efficient biological growth of solid structures often follows logarithmic spiral geometry. Rib shape is clinically relevant because curvature and orientation directly influence thoracic volume and mechanics during growth. Prior qualitative work suggested that pediatric ribs may approximate a spiral-based growth pattern, but the fidelity of this geometry across ages and rib levels has not been rigorously quantified.
Methods: Chest CT scans from 180 children aged 0–18 years (sex-balanced), 3,884 ribs, were analysed. Rib centerlines were segmented in 3D and fit to a logarithmic spiral using optimized rotation, translation, and isotropic scaling. Fit quality was assessed with R² and surface-distance metrics (Chamfer and Hausdorff), while spiral geometry was described by angular span and scale factor. Rib-level and age effects were analysed using mixed-effects regression with subject as a random effect.
Results: Ribs (2-11) contributing most to thoracic volume expansion showed excellent conformity to a logarithmic spiral across all pediatric ages, with uniformly high median fit (median R² ≈ 0.99 and narrow interquartile ranges), whereas ribs 1 and 12 exhibited lower and more variable fit, likely due to different function. Surface-distance error was low, with median Chamfer distances corresponding to approximately 1–3% of rib length, well under 5% geometric error for ribs 2–11. Middle ribs (ribs 3–6), which contribute most to thoracic volume, had the closest fit. There was preservation of rib shape during growth. No meaningful sex-based differences were observed.
Conclusion: Pediatric ribs 2-11 closely follow a logarithmic spiral geometry, with geometric error typically under 5%. Growth occurs primarily through scale enlargement rather than changes in spiral form, linking preserved rib geometry to the progressive increase in thoracic volume across childhood.
Nature's Secret Code: Fibonacci Sequence and 3D Modelling the Growing Rib
Hypothesis: Pediatric ribs that contribute to thoracic volume expansion follow a logarithmic spiral geometry, exhibiting scale enlargement while overall spiral shape is preserved.
Design: Retrospective cross-sectional morphometric analysis of pediatric CT scans.
Introduction: Efficient biological growth of solid structures often follows logarithmic spiral geometry. Rib shape is clinically relevant because curvature and orientation directly influence thoracic volume and mechanics during growth. Prior qualitative work suggested that pediatric ribs may approximate a spiral-based growth pattern, but the fidelity of this geometry across ages and rib levels has not been rigorously quantified.
Methods: Chest CT scans from 180 children aged 0–18 years (sex-balanced), 3,884 ribs, were analysed. Rib centerlines were segmented in 3D and fit to a logarithmic spiral using optimized rotation, translation, and isotropic scaling. Fit quality was assessed with R² and surface-distance metrics (Chamfer and Hausdorff), while spiral geometry was described by angular span and scale factor. Rib-level and age effects were analysed using mixed-effects regression with subject as a random effect.
Results: Ribs (2-11) contributing most to thoracic volume expansion showed excellent conformity to a logarithmic spiral across all pediatric ages, with uniformly high median fit (median R² ≈ 0.99 and narrow interquartile ranges), whereas ribs 1 and 12 exhibited lower and more variable fit, likely due to different function. Surface-distance error was low, with median Chamfer distances corresponding to approximately 1–3% of rib length, well under 5% geometric error for ribs 2–11. Middle ribs (ribs 3–6), which contribute most to thoracic volume, had the closest fit. There was preservation of rib shape during growth. No meaningful sex-based differences were observed.
Conclusion: Pediatric ribs 2-11 closely follow a logarithmic spiral geometry, with geometric error typically under 5%. Growth occurs primarily through scale enlargement rather than changes in spiral form, linking preserved rib geometry to the progressive increase in thoracic volume across childhood.
Comments
Full text not provided by primary author
Poster Board Number: 6