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Topographical changes of biconvex objects during equatorial traction: an analogy for accommodation of the human lens
  1. R A Schachar1,
  2. D K Fygenson2
  1. 1
    Department of Physics, University of Texas at Arlington, Arlington, Texas, USA
  2. 2
    Department of Physics, University of California, Santa Barbara, California, USA
  1. Dr Ronald A Schachar, PO Box 601149, Dallas, Texas 75229, USA; ron{at}


Aim: To assess and compare the changes in shape of encapsulated biconvex structures undergoing equatorial traction with those changes reported in the human lens during accommodation.

Methods: Equatorial traction was applied to several different biconvex structures: air, water, and gel filled mylar and rubber balloons and spherical vesicles. In the vesicles, traction was applied externally, using optical tweezers, or from within, by the assembly of encapsulated microtubules. The shape changes were recorded photographically and the change in central radius of curvature of water filled mylar balloons was quantified.

Results: Whenever an outward equatorial force was applied to the long axis of long oval biconvex objects, where the minor to major axis ratio was ⩽0.6, the central surfaces steepened and the peripheral surfaces flattened. Similar changes in the shape of the lens have been reported during human in vivo accommodation.

Conclusions: All biconvex structures that have been studied demonstrate similar shape changes in response to equatorial traction. This effect is independent of capsular thickness. The consistent observation of this physical change in the configuration of biconvex structures in response to outward equatorial force suggests that this may be a universal response of biconvex structures, also applicable to the human lens undergoing accommodation.

  • lens shape
  • equatorial traction
  • accommodation

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  • Competing interests: Dr Schachar has a financial interest in the surgical reversal of presbyopia.