The effects of material properties and equatorial stretching forces on the stress distribution and shape profile of human lenses were investigated to see whether support could be found for either or both current theories of accommodation. Finite element analysis was used to create models using shape parameters and material properties from published data. Models were constructed for two lenses of different ages. Material properties were varied to show differences between models with a single elastic modulus and those with different moduli for the cortex and the nucleus. Two levels of stretching forces were applied at the equator. Comparisons between experimental and model profiles were made, and stress distribution patterns were constructed. In all models, stretching produces a flattening in the peripheral curvature of the lens. In the younger lens, model and experimental results show that central curvature at some points is steeper for stretched than for unstretched profiles. In the older lens, gradients are flatter at all central points for stretched model and experimental profiles compared to the unstretched profile. In all models, there is a region of higher stress distribution within the lens that corresponds with the position of an inflection point that appears on the anterior surface and, in the older lens, also on the posterior surface. The results show that equatorial stretching forces can produce shape changes in support of both current theories of accommodation depending on the lens age, shape, and applied force.

*F*

_{t}, was divided equally into smaller forces,

*F*

_{ n}, and each was applied from 124 equally spaced loading points located around the lens located at 2.0 mm from the edge of the equator. Each loading point was linked to fives nodes on the capsule, one node on the equator, and two nodes on either side ( Figure 2). Hence, each

*F*

_{ n}was, in turn, subdivided into five smaller forces pulling on the capsule.

Equatorial radius (mm) | Anterior sagittal thickness (mm) | Posterior sagittal thickness (mm) | Total sagittal thickness (mm) | |
---|---|---|---|---|

27-year-old lens | 4.26 | 1.67 | 2.40 | 4.07 |

46-year-old lens | 4.41 | 1.44 | 2.61 | 4.05 |

Capsule | Cortex | Nucleus | ||||
---|---|---|---|---|---|---|

27 years | 46 years | 27 years | 46 years | 27 years | 46 years | |

Single-modulus lens | ||||||

Young's modulus (N/m ^{2}) | 5 × 10 ^{6} | 3.9 × 10 ^{6} | 3 × 10 ^{3} | 4 × 10 ^{3} | 3 × 10 ^{3} | 4 × 10 ^{3} |

Poisson ratio | 0.47 | 0.47 | 0.47 | 0.47 | ||

Two-modulus lens | ||||||

Young's modulus (N/m ^{2}) | 5 × 10 ^{6} | 3.9 × 10 ^{6} | 3 × 10 ^{3} | 4 × 10 ^{3} | 6 × 10 ^{2} | 10 ^{3} |

Poisson ratio | 0.47 | 0.47 | 0.47 | 0.47 | 0.47 | 0.47 |

*y*-axis to generate a solid of revolution (representing the anterior or posterior sections of the lens separately) and using the method of cylindrical shells to calculate the volume generated (Thomas, 1973).

^{2}× 10

^{6}). The annulus of maximum stress is surrounded by progressively lower stress levels, marked in orange and then yellow, which extend into the center of the lens. With the higher level of applied force (

*F*

_{t}= 0.120 N, Figure 4b), the stress concentration spreads toward the center of the lens and the maximum stress region decreases in size.

*R*

^{2}≥ .995. The coefficients of

*x*

^{2}and

*x*are shown in Table 3 together with the gradients at 0.2, 0.4, 0.6, and 1.0 mm radial distance from the center.

Coefficient
of x ^{2} | Coefficient
of x | Gradient at x = 0.2 mm | Gradient at x = 0.4 mm | Gradient at x = 0.6 mm | Gradient at x = 1.0 mm | |
---|---|---|---|---|---|---|

27-year-old single-modulus lens | ||||||

Unstretched | −0.0748 | −0.0134 | −0.0433 | −0.0732 | −0.1032 | −0.1630 |

Model 0.065 N | −0.0627 | −0.0230 | −0.0481 | −0.0732 | −0.0982 | −0.1484 |

Experimental 0.6 mm | −0.0873 | −0.0017 | −0.0366 | −0.0715 | −0.1065 | −0.1763 |

Model 0.120 N | −0.0533 | −0.0198 | −0.0411 | −0.0624 | −0.0838 | −0.1264 |

Experimental 1.0 mm | −0.0562 | 0.0043 | −0.0182 | −0.0407 | −0.0631 | −0.1081 |

27-year-old two-modulus lens | ||||||

Unstretched | −0.0748 | −0.0134 | −0.0433 | −0.0732 | −0.1032 | −0.1630 |

Model 0.065 N | −0.0589 | −0.0247 | −0.0483 | −0.0718 | −0.0954 | −0.1425 |

Experimental 1.0 mm | −0.0562 | 0.0043 | −0.0182 | −0.0407 | −0.0631 | −0.1081 |

Model 0.100 N | −0.0426 | −0.039 | −0.0560 | −0.0731 | −0.0901 | −0.1242 |

Experimental 2.0 mm | −0.0349 | 0.0011 | −0.0129 | −0.0268 | −0.0408 | −0.0687 |

46-year-old single-modulus lens | ||||||

Unstretched | −0.0317 | −0.0592 | −0.0719 | −0.0846 | −0.0909 | −0.1226 |

Model 0.065 N | −0.0362 | −0.0343 | −0.0488 | −0.0633 | −0.0777 | −0.1067 |

Experimental 1.0 mm | −0.0414 | 0.0017 | −0.0149 | −0.0314 | −0.0480 | −0.0811 |

Model 0.120 N | −0.0336 | −0.0266 | −0.0400 | −0.0535 | −0.0669 | −0.0938 |

Experimental 2.0 mm | −0.0307 | −0.0457 | −0.0580 | −0.0703 | −0.0825 | −0.1071 |

46-year-old two-modulus lens | ||||||

Unstretched | −0.0317 | −0.0592 | −0.0719 | −0.0846 | −0.0909 | −0.1226 |

Model 0.100 N | −0.0248 | −0.0353 | −0.0452 | −0.0551 | −0.0651 | −0.0849 |

Experimental 2.0 mm | −0.0307 | −0.0457 | −0.0580 | −0.0703 | −0.0825 | −0.1071 |

Experiment
(mm ^{3}) | Model
(mm ^{3}) | Deviation (%) | |
---|---|---|---|

Anterior section | |||

27-year-old single-modulus lens | |||

Experimental 0.6 mm, model 0.065 N | 37.4 | 39.4 | 5.3 |

Experimental 1.0 mm, model 0.120 N | 34.63 | 34.625 | 0.01 |

27-year-old two-modulus lens | |||

Experimental 1.0 mm, model 0.065 N | 34.63 | 36.93 | 6.6 |

Experimental 2.0 mm, model 0.100 N | 34.66 | 32.82 | 5.3 |

46-year-old single-modulus lens | |||

Experimental 1.0 mm, model 0.065 N | 46.79 | 44.8 | 4.25 |

Experimental 2.0 mm, model 0.120 N | 39.71 | 40.9 | 3.06 |

46-year-old two-modulus lens | |||

Experimental 2.0 mm, model 0.100 N | 39.71 | 38.81 | 2.3 |

Posterior section | |||

46-year-old two-modulus lens | |||

Experimental 2.0 mm, model 0.100 N | 50.07 | 49.63 | 0.88 |