Randleman et al. [7] demonstrated that the cohesive tensile strength (i.e., how strongly the stromal lamellae are held together) of the stroma decreases from anterior to posterior within the central corneal region (Fig. 13.2). In an experiment in which the cohesive tensile strength was measured for strips of stromal lamellae cut from different depths within donor corneoscleral buttons, a strong negative correlation was found between stromal depth and cohesive tensile strength. The anterior 40 % of the central corneal stroma was found to be the strongest region of the cornea, whereas the posterior 60 % of the stroma was at least 50 % weaker. A number of other authors have reached this conclusion by other indirect means [8–13].

In addition to cohesive tensile strength, tangential tensile strength (i.e., stiffness along the stromal lamellae) and shear strength (i.e., resistance to torsional forces) have both been found to vary with depth in the stroma. Kohlhaas et al. [14] and Scarcelli et al. [15] found that the tangential tensile strength was greater for anterior stroma than posterior stroma, each using different methodology. Petsche et al. [16] found a similar result for transverse shear strength to decrease with stromal depth. The same group have used nonlinear optical high-resolution macroscopy to image the three-dimensional distribution of transverse collagen fibers and have shown that the nonlinearity of tensile strength through the stroma is caused by the greater interconnectivity of the collagen fibers in the anterior stroma compared with the posterior stroma where the collagen fibers lie in parallel to each other [17].

An interesting finding of these studies is the nonlinear nature of the change in tensile strength through the stroma. The cohesive tensile strength appears to decrease rapidly for the anterior-most 30 % [7]. There is then a region between 70 and 20 % depth where the cohesive tensile strength decreases slowly, but then drops off sharply again for the posterior-most 20 %. This nonlinearity may be associated with the known different collagen organizational layers within the stroma [10, 18, 19]. Of note is the remarkable similarity of this curve to that reported for tangential tensile strength by Scarcelli et al. [15] (Fig. 13.3), which demonstrates the strong correlation between corneal biomechanical properties with stromal depth. This finding also agrees with studies that have found other depth-dependent properties of the corneal stroma such as decreasing refractive index [20], greater UV-B absorption in the anterior stroma [21], and varying excimer laser ablation rates [22, 23].

But given that SMILE effectively leaves anterior corneal stroma intact, while the keratomileusis takes place in the deeper and therefore weaker portion of the cornea (as described above), it is reasonable to assume that for any given refractive correction, SMILE will leave the cornea with greater tensile strength than either LASIK or PRK. To take this into account, we need to start thinking more in terms of tensile strength rather than simply in terms of residual stromal thickness. For example, a rough adjustment would be to say that anterior stroma is approximately 50 % stronger than posterior stroma, so a further 50 % of the untouched anterior stromal thickness in SMILE can be added to get an adjusted total uncut stromal thickness value that can be compared to a LASIK residual stromal bed thickness. In reality, we can go further than this by basing the calculation on the real stromal tensile strength data.

We recently developed a mathematical model based directly on the Randleman [7] depth-dependent tensile strength data to calculate the postoperative tensile strength and compare this between PRK, LASIK, and SMILE [24]. Given the similarity between different studies measuring the different types of tensile strength as described above, we made the assumption that cohesive tensile strength is representative of the overall corneal biomechanics. We now suggest that this total tensile strength value should replace residual stromal thickness as the limiting factor for corneal refractive surgery.

To derive the model, first we performed nonlinear regression analysis on the Randleman [7] data and found that a fourth-order curve maximized the fit to the data with an R ² of 0.930 demonstrating the very high correlation achieved by a nonlinear fit. The total tensile strength of the untreated cornea was then calculated as the area under the regression line by integration (see Fig. 13.2). The total tensile strength of the cornea after LASIK was derived by calculating the area under the regression line for all depths below the residual stromal bed thickness (assuming the flap does not contribute to the tensile strength of the postoperative cornea [25]). This value was divided by the total tensile strength of the untreated cornea to represent the relative postoperative total tensile strength (PTTS) as a percentage. Similarly, the total tensile strength of the cornea after PRK was derived by calculating the area under the regression line for all depths below the stromal thickness after ablation. Finally, the total tensile strength of the cornea after SMILE was calculated as the area under the regression line for all depths below the lower lenticule interface added to the area under the regression line for all depths above the upper lenticule interface or within the stromal cap.

The model was then applied to a variety of different scenarios and a number of conclusions could be drawn from the analyses:

These results can be quantified in the example scenario represented in Fig. 13.6 which shows the relative total tensile strength after LASIK (purple), photorefractive keratectomy (PRK) (blue), and small incision lenticule extraction (SMILE) (green) plotted against a range of ablation depths for a fixed central corneal thickness of 550 μm, a LASIK flap thickness of 110 μm, and a SMILE cap thickness of 130 μm. The orange lines indicate that the postoperative relative total tensile strength reached 60 % for an ablation depth of 73 μm in LASIK (approximately −5.75 diopters [D]), 132 μm in PRK (approximately −10.00 D), and 175 μm in SMILE (approximately −13.50 D), translating to a 7.75 D difference between LASIK and SMILE for a cornea of the same postoperative relative total tensile strength. The red lines indicate that the postoperative relative total tensile strength after a 100 μm tissue removal would be 54 % in LASIK, 68 % in PRK, and 75 % in SMILE.

In this model, there are some factors that have not been considered. First, this model only considers the central point on the cornea. A full model of the cornea, for example, by finite element analysis, that can take into account the stromal thickness progression and the volume of the ablation profile would be a significant improvement but is likely to provide the same data qualitatively, albeit perhaps more accurately in terms of absolute tensile strength changes. Indeed, one study has used finite element modeling to compare the stress distribution after SMILE and LASIK and found that there was a greater increase in the stress in the residual stromal bed in the LASIK model than in the SMILE model [27].

In the model, we have made the assumption that the stromal lamellae in the LASIK flap do not contribute to the total tensile strength of the cornea at all, an assumption that is supported by published studies demonstrating negligible contribution. Schmack et al. [25] found that the mean tensile strength of the central and paracentral LASIK wounds was only 2.4 % that measured in the control eyes. As described earlier, Knox Cartwright et al. [5] experimentally demonstrated a LASIK flap depth-dependent increase in corneal strain, reporting an increase in strain of 9 % for a 110 μm flap and 33 % for a 160 μm flap. This result is predicted by our current model which showed that the remaining relative total tensile strength would be less for thicker flaps, as would be expected.

Another factor not considered is that Bowman’s layer remains intact after SMILE, which is not true in either LASIK or PRK. Bowman’s layer has been shown to have very different biomechanical properties to stromal tissue as demonstrated by Seiler et al. [26] who showed that removing Bowman’s layer with an excimer laser reduced Young’s modulus by 4.75 %. Leaving Bowman’s layer intact may further increase the corneal biomechanical stability after SMILE compared with LASIK and PRK. Finally, the present model in addition does not consider the effect of the tunnel incision on tensile strength changes which although small will not be zero.

In summary, considering the safety of subtractive corneal refractive surgical procedures in terms of tensile strength represents a paradigm shift away from classical residual stromal thickness limits. The residual thickness-based safety of corneal laser refractive surgery should be thought of at least in terms of total residual uncut stroma. Ideally, a parameter such as total tensile strength, which takes the nonlinearity of the strength of the stroma into account, seems more appropriate. For example, the residual stromal bed thickness under the interface in SMILE could easily be less than 250 μm due to the additional strength provided by the untouched stromal lamellae in the cap, as long as the total remaining corneal tensile strength is comparable to that of the post-LASIK 250 μm residual stromal bed thickness standard. In this new case of using remaining total tensile strength, the minimum would evidently be defined as the total tensile strength remaining after LASIK with a residual stromal bed thickness of 250 μm.

As described earlier, spherical aberration induction is largely due to peripheral stromal expansion outside the ablation zone. Peripheral stromal expansion is caused by the relaxation of severed stromal collagen lamellae, so it would be expected to find less stromal expansion after SMILE as fewer lamellae are cut, and hence, it would be expected for less spherical aberration to be induced.

In a recent study [33], we compared the induction of spherical aberration between SMILE, where the refractive lenticule is only minimally aspheric, and LASIK using the MEL80 with the Laser Blended Vision module [29], which uses a nonlinear aspherically optimized ablation profile. The LASIK group was matched by refraction to within ±0.25 D and all eyes were treated with a 6 mm optical zone in both groups. Corneal spherical aberration (Atlas, Carl Zeiss Meditec) was analyzed for a 6 mm diameter and no difference was found between the two groups. Therefore, SMILE though minimally aspheric produced similar spherical aberration induction to the highly aspherically optimized myopic Laser Blended Vision profile. This indicates that the femtosecond flapless procedure leads to less induction of spherical aberration than expected for a non-aspheric conventional excimer myopic profile. These results are similar to other published studies: two studies have shown that there are less aberrations induced by SMILE than LASIK [30, 31], and one study showed that induction of aberrations was similar [32].

Following this study, we also investigated how the induction of spherical aberration after SMILE changed for optical zones of 6, 6.5, and 7 mm. The induced spherical aberration decreased as expected for larger SMILE optical zones; the regression line slope was 0.081 for 6 mm, 0.059 for 6.5 mm, and 0.030 for 7 mm (Fig. 13.7).