Computer-Aided Estimate and Modelling of the Geometrical Complexity of the Corneal Stroma

  • Fabio Grizzi
  • Carlo Russo
  • Ingrid Torres-Munoz
  • Barbara Franceschini
  • Paolo Vinciguerra
  • Nicola Dioguardi
Conference paper
Part of the Mathematics and Biosciences in Interaction book series (MBI)


Despite the fact that all anatomical forms are characterised by non-polyhedral volumes, rough surfaces and irregular outlines, it has been suggested that sophisticated computer-aided analytical systems based on the Euclidean principles of regularity, smoothness and linearity can be used in human quantitative anatomy. However, the new fractal geometry is a more powerful means of quantifying the spatial complexity of real objects. The present study introduces the surface fractal dimension as a numerical index of the complex architecture of the corneal stroma, and investigates its behaviour during computer-simulated changes in keratocyte density and distribution, and in the heterogeneous composition of the extracellular matrix. We found that the surface fractal dimension depends on keratocyte density and distribution, as well as on the different concentrations of the constituents making up the extracellular matrix. Our results show that the surface fractal dimension could be widely used in ophthalmology not only because of its ability to quantify drug-correlated architectural changes, but also because it can stage corneal stroma alterations and predict disease evolution.


Fractal Geometry Corneal Stroma Geometrical Complexity Spatial Complexity Human Cornea 
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Copyright information

© Birkhäuser Verlag Basel 2005

Authors and Affiliations

  • Fabio Grizzi
    • 1
    • 2
  • Carlo Russo
    • 1
    • 2
  • Ingrid Torres-Munoz
    • 3
  • Barbara Franceschini
    • 1
    • 2
  • Paolo Vinciguerra
    • 3
  • Nicola Dioguardi
    • 1
    • 2
  1. 1.Scientific DirectionIstituto Clinico HumanitasRozzano, MilanItaly
  2. 2.“Michele Rodriguez” FoundationScientific Institute for Quantitative Measures in MedicineMilanItaly
  3. 3.Istituto Clinico HumanitasOperative Unit of OpthalmologyRozzano, MilanItaly

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