Model of the isolated Ex-Vivo human crystalline lens using cosine functions

R. Urs, A. Ho, F. Manns, J. M. Parel

Research output: Chapter in Book/Report/Conference proceedingConference contribution


The purpose of this study is to develop an age dependent model of the whole isolated ex-vivo human crystalline lens shape using a single mathematical function. Contours of whole isolated human crystalline lenses were obtained from shadow-photogrammetric images. 28 lenses (PMT=1 to 5 days) ranging in age from 6 to 90 years were used for this study. Lens contours were extracted using MATLAB's morphological and edge detection functions. The contours were first fit to a 10th-order even Fourier series containing tilt and decentration terms in a polar coordinate system using MATLAB's curve fitting toolbox to determine the position of the lens center and the tilt angle. To ensure axis-symmetry, phase terms were excluded from the Fourier series. This preliminary analysis was used to correct for tilt and decentration. The corrected profiles were resampled and the first 11 coefficients of the Fourier decomposition were calculated and analyzed as a function of age. The root mean squared error between the original lens contour and the lens profile reconstructed using the coefficients of the Fourier decomposition ranged from 13 to 66 μm. Only the coefficient of the zeroth-order term (i.e. diameter of the 'equivalent' fitted circle) showed a significant increasing trend with age (a0 = 0.007 x Age + 2.675; p<∈0.0001). From this study it can be concluded that the shape of the whole human crystalline lens can be accurately modeled with 10thorder Fourier series within a polar coordinate system.

Original languageEnglish (US)
Title of host publication25th Southern Biomedical Engineering Conference 2009
Number of pages2
StatePublished - 2009
Event25th Southern Biomedical Engineering Conference 2009 - Miami, FL, United States
Duration: May 15 2009May 17 2009

Publication series

NameIFMBE Proceedings
ISSN (Print)1680-0737


Other25th Southern Biomedical Engineering Conference 2009
Country/TerritoryUnited States
CityMiami, FL


  • Accommodation
  • Finite Element Modeling
  • Lens Model
  • Presbyopia

ASJC Scopus subject areas

  • Biomedical Engineering
  • Bioengineering


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