From analysis of the corneal shape change and position of the optical elements, the ratio Δ
Ra/Δ
ACD was calculated for different values of
k, and this relationship is presented in
Figure 3. In this case, the radii of corneal curvatures, the anterior chamber depth, and vitreous chamber depth were changed. The relation between Δ
Ra/Δ
ACD and parameter
k is linear, with a high coefficient of determination (
R2 ≈ 1) (
Figure 3). On the basis of this parameter, changes in ACD, VCD, and corneal curvature that maintain self-adjustment can be deduced. There is one possible relationship between the changes in the values of these parameters that is needed to obtain self-adjustment. For a given value of
k, a single value of Δ
Ra/Δ
ACD will produce and maintain self-adjustment.
Figure 3 shows the conditions required for self-adjustment in cases 1 and 2 (see Methods). In these cases, the condition for self-adjustment will be fulfilled when Δ
ACD/Δ
VCD = –0.487 for case 1 and Δ
Ra/ΔACD = 0.245 for case 2. Case 3 cannot be shown in
Figure 3 because in this case Δ
ACD is constant, and there is no given value of
k.
When self-adjustment required to mitigate IOP fluctuations depends only on the relative positions of the cornea, lens, and retina with no change in the corneal radius (Δ
Ra = 0 and Δ
Rp = 0), the value of parameter
k is equal –0.487 for ∆Φ = 0 D (
Figure 4).This means that displacement of the lens is 49,6% that of the corneal displacement. For ∆Φ = 0 D and a change of Δ
ACD in the range of ±0.5 mm, the axial length of the eye changes by 0.257 mm, and the optical power of the eye changes by 0.35D. These dependencies also remain linear over larger ranges of changes (exemplary up to ∆
ACD = 1.5 mm). Nonlinearities in analyzed characteristics appear far beyond the range of physiological values of the considered variable biometric parameters of the eye.
Figure 4 indicates what is required to estimate the size of changes in optical parameters in order to maintain optical self-adjustment. If the anterior chamber depth changes by Δ
ACD = 0.2 mm, then the vitreous chamber depth should change (Δ
VCD) in the range of –0.231 to 0.035 mm from the initial value in order to maintain image quality. Assuming that self-adjustment is only associated with a change in the anterior chamber depth (Δ
VCD does not change), the self-adjustment condition is fulfilled for Δ
ACD in the range from –0.274 to 0.273 mm. Maintaining Δ
ACD = 0 requires a change of Δ
VCD ranging from –0.134 to 0.133 mm to maintain defocus at less than 0.1 mm.
When simulating the case described in point 1, with self-adjustment assumed to be the result of changes in the cornea radii and the depth of the anterior chamber, the ratios ∆
Ra/∆
ACD and ∆
Rp/∆
VCD were calculated. Simulations showed that, to maintain high-quality optical imagery, the corneal radii should change by 0.243 mm for the anterior surface and 0.205 mm for the posterior surface. Changes in the ACD and the corneal shape caused a change in optical power of 0.96 D for ∆
ACD = –0.5 mm (
Ra = 7.64 mm,
Rp = 6.42 mm) and –0.93D for ∆
ACD = +0.5 mm (
Ra = 7.88 mm,
Rp = 6.62 mm) for ∆Φ = 0 D. The relationship between ∆
Ra and ∆
ACD in the defocus range of ±0.25D is shown in
Figure 5.
Assuming that self-adjustment is only associated with a change in the shape of the cornea (ACD and VCD do not change), the radii of curvature of anterior and posterior corneal surfaces should have the following values:
Ra = 7.83 mm and
Rp = 6.58 mm for a defocus of –0.25D, and
Ra = 7.69 mm and
Rp = 6.46 mm for a defocus of +0.25D. Such corneal shape changes are too large to be plausible physiologically, so such changes cannot be assumed to be involved in optical self-adjustment. The results of this calculations are presented in
Figure 5 as points for Δ
ACD = 0.
The literature reports changes in the axial length of the eye after surgical intervention to reduce IOP with no change in anterior chamber depth (
David et al., 1992). Simulations based on this observation (as described in case 3) were conducted, and the results are shown in
Figure 6. An increase in VCD by ∆
VCD = –0.5 mm caused a change in ocular power of +1.26 D (
Ra = 7.51 mm,
Rp = 6.31 mm), and ∆
VCD = +0.5 mm changed the power of the eye by –1.21 D (
Ra = 8.01 mm,
Rp = 6.73 mm); yet, the image on the retina remained in focus.
In summary, all of the mechanisms of self-adjustment are linked to changes in the optical system of the eye. Specific changes in the biometric parameters may vary in their contribution to preventing defocus. The values of biometric changes required to induce a shift of +0.5 D are shown in
Table 2. A refractive power change of +0.5 D would not produce significant differences between the eyes and hence maintain binocular vision.