38 ± 10 (22–55)
−5.96 ± 1.9 (−1.25 to −10)
−0.95 ± 1.0 (0 to −4.0)
SEQ of the correction (Dpt)
Cylinder of the correction (Dpt)
Lenticule thickness/ablation depth
−5.70 ± 1.95 (−1.25 to −10)
−0.79 ± 1.04 (0 to −4.0)
118 ± 3.8 (100–120)
7.8 ± 0.1 (7.5–8.0)
120 ± 27 (48–164)
6.7 ± 0.2 (6.2–7.0)
14.3 Angle K and the Pattern of the Achieved Centration
A very important issue regarding the achieved centration is its pattern in regard to the visual axis. The visual axis is the line which connects the fovea with the fixation point via the nodal point of the eye. The line of sight is defined as the line connecting the fixation point with the center of the entrance pupil. The pupillary axis is the line passing through the EPC perpendicular to the cornea. The definition of angle kappa (angle K) is the angular distance between visual and pupillary axis [19–21], which is in myopic eyes approximately 2.0° and is mostly positive [19, 22]. As a result of positive angle K the first image of Purkinje is located nasal to the pupillary center or temporal in cases of a negative angle K. Studies conducted in order to assess the distribution of angle K in myopic eyes showed a prevalence of positive angle K in the majority of the tested subjects, while a negative angle K or no angle K was identified in substantially less cases [19, 23].
For our study purposes the degree of angle K was estimated indirectly by the coordinates of the CV on the preoperative pachymetry maps of Pentacam. When the patient fixates on the red spot, in the middle of the monochromatic slit light source (blue LED at 475 nm), then the reference axis of the instrument (measurement axis) and the patient’s visual axis would be coaxial. In this case the intercept of the instrument’s reference axis and the cornea would be the CV [19, 24]. This point is called corneal apex (CA) in the Pentacam software, which is a misnomer for vertex [19, 25], as the CA should academically refer to the point of greatest corneal curvature or shortest radius  (Fig. 14.1). Knowing the location of the CV, we can estimate the location of the preoperative CSCLR and also evaluate the angle K, because the CSCLR is a good approximation of the point where the visual axis intersects the cornea.
In order to assess the angle K of the examined eyes, the points corresponding to the preoperative CSCLR were depicted on a Cartesian system in relation to the EPC (Fig. 14.2). Regarding the angle K of the right eyes (blue dots), the points with positive x-coordinates correspond to positive angle K, while the points having negative x-coordinates correspond to negative angle K. Regarding the angle K of the left eyes (red dots), the points with negative x-coordinates correspond to positive angle K, while the points with positive x-coordinates correspond to negative angle K. When the points were located on the y-axis (0, y), the angle K was 0°. The preoperative CSCLR demonstrated a nasalization pattern, since in most eyes angle K was positive. The mean distance of the preoperative CSCLR from the EPC was 0.227 ± 0.121, ranging from 0.014 to 0.602.
Corneal landmarks as being identified by Altas (Carl Zeiss Meditec AG, Germany) and Pentacam™ (Oculus, Germany) for the same patient. The first two images (videokeratoskopy and axial curvature) were created by Atlas. The corneal vertex (CV) is depicted with an X, the entrance pupil center (EPC) with ⊗ and the corneal apex (CA) with △. The last image represents a postoperative pachymetry map of Pentacam. The EPC is depicted with a cross, the pupil edge with a white dotted circle and the CA with a white dot. Note that the point identified as CA by Pentacam has the same displacement in relation to the EPC as the CV on Atlas images. This example further supports the observation that the CA in Pentacam software is actually the CV
In order to evaluate the pattern of the achieved centration in regard to the visual axis, we located on each eye the coordinates of the point of maximum pachymetrical difference (PMPD) on the differential pachymetry maps and depicted it on a Cartesian system in relation to the EPC (Fig. 14.3). The PMPD corresponds to the maximum refractive power and the center of mass of the lenticule and therefore represents the achieved centration. The results were compared to the preoperative pattern of the CSCLR in relation to the EPC (Fig. 14.2). We examined for each eye the displacement of the PMPD on the x-axis in relation to the preoperative CSCLR. The achieved centration would follow the pattern of angle K if the x-coordinate of the PMPD maintained the same sign (+ or −) as the x-coordinate of the preoperative CSCLR. We concluded that 26 out of 34 right eyes (76.47 %) and 26 out of 35 left eyes (74.28 %) follow the pattern of angle K (Table 14.3), with the achieved centration showing a nasalization pattern. In a recent study presented by Lazaridis et al. , the pattern of the achieved centration was evaluated in a similar group of patients treated with femtosecond laser assisted-LASIK (FS-LASIK). In that case the reference point of centration was the EPC. The results showed a random distribution pattern of the achieved centration in regard to the visual axis (Figs. 14.4 and 14.5).
Depiction of the points of the preoperative CSCLR (attempted centration) in relation to the EPC (0,0) in SMILE group. The degree of angle K could be evaluated by the location of the preoperative CSCLR, because the CSCLR is a good approximation of the point where the visual axis intersects the cornea
Mean distance between PMPD and preoperative CSCLR
Preoperative pattern of angle K (no. of eyes)
Achieved centration following the preoperative pattern of angle K
0.315 ± 0.211 (0.0 to –1.131)
26/34 (76.47 %)
26/35 (74.28 %)
52/69 (75.36 %)
14.4 Evaluation of the Achieved Centration
The estimation of the eccentricity of the treatment zone after refractive surgery is crucial in order to evaluate its visual impact and distinguish decentrations from pseudodecentrations, especially when attempting a retreatment. It is therefore essential to define a standard method of centration analysis. Refractive surgeons have previously attempted to estimate the extent of decentration by manipulating sheets of transparency film placed on the computer screen to point the apparent center of the treated area and measure its decentration . Other groups proposed as method of centration analysis the estimation of the intersecting point of the four farthest edges of the treatment zone in the x- and y-axes and defined the decentration as the distance of this point from the EPC [28, 29]. This approach however is according to the author’s calculations not accurate because in cases of pseudodecentration or by peripheral abnormalities, it does not point the actual center of the treatment zone. Many studies of centration analysis were based on subjective visual estimates by trained observers on topography maps, with most of them being conducted on tangential maps, axial maps, or elevation maps . An objective approach of centration analysis was presented by Qazi et al. , using a custom software on Orbscan topography in order to determine the topographic functional optical zone and the centroid of this zone on refractive maps.