Having shown that the modeling was representative of real eyes, it can be used to investigate the question of why increased higher-order aberrations make refracting difficult in keratoconus. As mentioned in the Introduction, there is an inherent challenge in trying to compensate for elevated higher-order aberrations with a lower-order correction. This process is made more difficult because, unlike normal eyes, eyes with keratoconus do not necessarily have one unique area of optimal dioptric correction (
Figure 4) (
Marsack et al., 2014) and visual image quality used by patients to guide the subjective refraction is poorer in keratoconus. Because subjectively refracting an eye is a sequential process in which the practitioner seeks the optimal correction based on the starting point, as well as the binary better or worse responses by the patient, this modeling illustrates how the process can direct the practitioner to a local, rather than the global, maximum. This is seen in both spectacle and scleral lens corrections (in 10 of 20 and 5 of 20 SyntEyes, respectively), with a considerably larger dioptric distances for the spectacles. Consequently, depending on their starting point (e.g., Seidel or Zernike refraction, autorefraction, retinoscopy, or habitual correction), practitioners can easily reach a local maximum focus rather than the globally optimal correction. In many cases, it is plausible that the global maximum may never be reached because one must traverse a dioptric space with worsening visual image quality between the foci before it improves as one approaches the global maximum (
Figure 3). Moreover, it is important to remember that, although the best possible spectacle corrections are often inferior to the visual quality that can be accomplished with scleral lenses, patients cannot continuously wear scleral lenses and will need spectacles for the times between lens wear.
In essence, the patterns in the scatterplots are a series of through-focus spherical scans in the presence of a cylindrical correction oriented along a certain axis. As such, any vertical line through these patterns likely represents something similar to the interval of Sturm, the distance between the horizontal and vertical foci of an astigmatic eyes. This finding is supported by the observations that keratoconic SyntEyes with two regions of highest VSX find those regions on opposite sides of the pattern, both in the vertical direction (sphere) and in the horizontal direction (cylinder and orientation). This reasoning is not the entire explanation, however, as in typical eyes with a regular corneal astigmatism there was only one compact region of highest VSX. Meanwhile, the shell-like shape is probably related to how the different regions of the keratoconic cornea sequentially gain dominance in the through-focus scans using only a spherocylinder correction. As the spherical power of the correction moves from more positive to more negative, the position where a given ray is effectively incident on the cornea changes. One can see how the lower part of the pattern would correspond with the negative spherical corrections required to correct the high power of the steep cone area, whereas positive or low-negative corrections would correct the flatter superior cornea. The scleral lens corrections, in contrast, lead to highly compact patterns, but the focus can be extended under the influence of the residual corneal astigmatism (see
Supplement A). In this sense, VSX is a useful visual image quality metric for the current purpose as it uses all visually relevant information of the light passing through the limiting aperture of the eye. Using VSX is also advantageous in rotationally asymmetric cases, such as keratoconus, because one can be more confident about the correct centration and application of neural weighting functions in the spatial domain (VSX) rather than in the Fourier domain. Nevertheless, changes in pupil size might affect the appropriateness of the objectively optimal correction, which is a topic of ongoing investigation.
Note that these results also have several limitations toward translation into clinical applications. The first is the use of VSX to assess the visual image quality. On its own VSX does not predict absolute visual acuity, but changes in its logarithm (logVSX) are strongly correlated with changes in logarithm of the minimum angle of resolution visual acuity (
Schoneveld, Pesudovs, & Coster, 2009;
Ravikumar et al., 2013). As such, the patterns in
Figures 2,
3, and
4 should be considered as qualitative indications of where in correction space the best foci of those eyes would be under a spherocylindrical correction, rather than actual visual acuity that these eyes might be able to reach. VSX is able to do this in a very robust way, but is conceivable that better, more suitable visual image quality metrics will be developed that outperform VSX in the future. Further, although the upper bound of VSX for spherocylindrical correction in normal eyes has been defined (
Hastings, Marsack, Thibos, & Applegate, 2018), the lower bound where VSX is meaningful has not. This finding is relevant to many of the VSX values reported here for the keratoconic eyes.
Next, the analysis used SyntEyes rather than real eyes. Although the results were in agreement with real eyes and the methods described could be applied to real eye data, the challenge is that clinical data are too often incomplete to make a reliable personalized whole-eye model because parts of the lens biometry are missing. SyntEyes solve this issue by making several assumptions that work on the population level, but might lead to errors if used to estimate the lens biometry of an individual eye (
Rozema, Rodriguez, Navarro, & Tassignon, 2016) that could lead to incorrect estimates of the lenticular wavefront. Given that the wavefront aberrations of the crystalline lens interact with those of the cornea to minimize the total wavefront (
Artal, Berrio, Guirao, & Piers, 2002), the known lenticular aberrations of the SyntEyes may be beneficial for this current proof-of-concept analysis. In a clinical setting, and in the absence of a clinical way to reliably estimate of the crystalline lens aberrations (
Atchison et al., 2016), one might use a crystalline lens power calculation instead, if necessary, in an iterative algorithm. Another limitation of the current model is that the corrective lenses are assumed to be stable, on-axis and with a generic vault, thickness, and form. Moreover, the pupil size of 5 mm used here is rather large, which might have reduced VSX. The influence of these variables is part of currently ongoing studies. Finally, the calculation times are too long to be used in daily practice (3–8 hours per eye), even when using parallel computing on a high-end computer, which might become a moot point as computational processing technology advances.