Fig. 9.1
Corneal topography
Cornea is responsible for more than 2/3 of the total refractive power of the human eye, so its morphology is of vital importance to determine the quality of the ocular optic system and therefore the vision quality. For this reason it must be understood that quantifying corneal topography is fundamental in clinical practice and helps to decide the corrective (invasive or not) treatment for the corneal disease.
Current corneal topographers are based on three technologies: (1) systems based on the light reflection on the cornea, (2) systems based on the projection of a slit light on the cornea, and (3) systems based on the asymmetric reflection of multicolor LEDs. All of these technologies provide different topographical maps of the anterior and posterior surfaces, as well as pachymetric maps and a series of indices for monitoring and clinic assessment of the corneal topographies.
9.2.1 Systems Based on the Light Reflection on the Cornea
Corneal topographers based on this technology, also called videokeratoscopes , are based on the application of the principles of convex mirrors’ geometrical optics to an instrument in which the rings or Placido discs , with known size and spacing, are reflected on the anterior surface of the cornea. This image is initially captured by a digital camera and then processed by a computer [4]. From identifying the edges of the rings, each topographer uses an algorithm reconstruction of the corneal curvature, which accuracy depends on how the programming architecture is defined. The so-called arc step algorithms are the most used and are based on an iterative process that uses a sequence of arcs from point to point, covering the entire corneal region from the apex to the periphery. This process does not ignore data obtained in the previous step (step i−1) for obtaining current data (step i) [5]. Moreover, this reconstruction algorithm has an error lower than 0.25 μm in the central 3 mm and less than 1 μm for the rest of the corneal surface [6]. This precision is important since the minimum abnormal morphology due to keratoconus may impair the corneal homeostasis [7].
Height and slope data derived from the radial curvature of the corneal surface are presented by topographers as corneal keratometric data of the entire surface by a series of maps that follow a color scale developed by the University of Louisiana [8] (see Fig. 9.1).
Cool colors correspond to flat curves and elevation values below the reference sphere (blue or violet colors).
Mild colors correspond to medium curvature and elevation values equal to the reference sphere (green or yellow colors).
Warm colors correspond to high curvature and elevation values above the reference sphere.
In addition, depending on the size of the Placido disc rings there are two commercial options [4]:
Corneal topographers based on large diameter Placido disc rings . These devices are less susceptible to error associated with the misalignment between examiner and patient because they work at a large distance from the eye. However, because of this distance, it is possible to lose representative points because of the patient’s facial morphology, produced by the shadow of the patient’s nose and eyelashes.
Corneal topographers based on small diameter Placido disc rings . These devices are most susceptible to alignment errors between the examiner and patient because they work in short distances, very close to the human eye. However, it mitigates the loss of information produced by patient’s facial morphology, reducing the shadow that the nose and eyelashes could cause.
However, both systems have an important limitation that results from the use of internal algorithms that do not allow an accurate characterization of the corneal morphology in case of high levels of irregularity. In some cases, it is possible to obtain mistakes up to 4 diopters in corneas that present a very curved morphology, as it occurs in keratoconus disease [9].
9.2.2 Systems Based on the Projection of a Slit Light on the Cornea
Corneal topographers that use this technology are based on the integration of a dual technology. The first process involves projecting a Placido disc, obtaining the mirror image by reflection and representing the curvature and refractive power, which is obtained by an arc-step algorithm. The second phase is the projection of a slit light onto the cornea: due to the transparent structure of the cornea, and using Rayleigh scattering, it is possible to photograph it. These images will provide accurate data of corneal elevations for the entire anterior segment (see Fig. 9.2) [10].
Fig. 9.2
Systems based on the projection of a slit light on the cornea
Furthermore, this technology has two variants, depending on the spatial arrangement of the photographic system:
System based on the principle of standard or normal photography. Its main feature is that the plane of the camera lens is located in parallel with the image. It means that only a small region is focused (the imaginary extensions of the film planes, the lens, and the focal plane are parallel) (Fig. 9.3) [11, 12]. The most common system is the Orbscan (Bausch & Lomb Incorporated, USA), which was the first commercial device that assessed the posterior corneal surface in a noninvasive and quick way. This system provides different maps of the anterior and posterior corneal surfaces, and also pachymetric data; however, several authors from scientific literature present a strong controversy due to the reliability of the measurements performed by this device on the posterior surface, and also the limited repeatability [8, 13, 14].
Fig. 9.3
Principle of standard photography
Systems based on the principle of Scheimpflug photography . Its main feature is that the plane of the camera lens is placed sideways to the image (the imaginary extensions of the planes of the film, the lens, and the focal plane are not parallel (Fig. 9.4) [12], and therefore the focused region is increased and the image sharpness is improved) [15–17]. The main commercial systems based on this principle are Pentacam (Oculus, USA), Galilei (Ziemer, Switzerland), and Sirius (CSO, Italy), which offer repeatable measurements of the corneal curvature and other anatomical measurements of the anterior segment. However, several authors question the degree of concordance between the measurements provided by these devices [18–20].
Fig. 9.4
Principle of Scheimpflug photography
9.2.3 Systems Based on the Asymmetric Reflection of Multicolor LEDs
These systems are based on the same optical principle than convex mirrors previously described in Sect. 9.2.1, but in this case the emitters are multicolor light-emitting diodes (LEDs).
More specifically, this system uses a panel formed with an asymmetric distribution of more than 700 LEDs in colors red, yellow, and green, which reflection on the cornea provides a more accurate reconstruction of the corneal surface if compared with the lack of detail obtained when projecting a monochromatic light [21–23].
The main novelty of this system is the use of a unique reconstruction algorithm for the reflection of each LED projection; this one being independent of the algorithm used for the other LED projections. This new approach has one main difference with respect to the systems previously described where the rest of them were based on the projection of a monochromatic light and use the same reconstruction algorithm for all the points of the corneal surface. Moreover, the new device permits redefining at the local level, every three points identified in the corneal surface, its curvature or elevation.
9.3 Corneal Topography
Corneal topography is considered a noninvasive exploratory technique that permits to analyze both qualitatively and quantitatively the morphology of the cornea, differentiating standard patterns from those potentially devastating for vision disorders caused by pathological ectatic conditions [1, 7, 15, 24, 25].
Corneal topographers present different maps to represent the measurements that characterize the corneal surface, but previously to the description of these maps, it is fundamental to take into account the dimension or scale to be adopted during the assessment of the topographical test to obtain the maximum information from the clinical point of view. In this regard, two scales can be distinguished [26]:
Absolute scale : the entire dioptric range that the topographer can measure is assigned to a color scale, so sensitivity decreases with small alterations.
The maps currently provided by the topographic devices can be of curvature, sagittal, tangential, elevation, and thickness, as follows:
The curvature keratometric maps provide information about curvature at each point of the corneal surface. They can be axial (or sagittal) and tangential (or instant). Although both types report information about focal curvature, there exist significant differences between them [1, 29]:
Sagittal maps fix the curvature centers on the optical axis and considers the corneal surface to have a spherical geometry, achieving a marked overall smoothing of the corneal periphery. This results in a larger and more peripheral curving area than the actual area of the cone; however, this consideration is erroneous and only true in the paraxial approach since the cornea has a spherical surface. Therefore, it distorts the true picture of the cornea and provides quantitatively inaccurate values [1, 26, 29, 30]. However, this map is useful for a qualitative assessment through colors due to it softens the geometric contours of the cornea and facilitates the interpretation of the results by less-experienced users [26] (Fig. 9.5).
Fig. 9.5
Geometric reconstruction of the corneal sagittal map
Tangential maps do not assume the spherical morphology of the cornea and therefore, the tangential curvature algorithm reconstructs the corneal surface by means of local curvature radii whose centers are not located on the optical axis. These maps represent more accurately the curvature of the peripheral corneal region. This is because at local level the area which best fits the focal curve is considered, which has not been imperatively placed on the optical axis, as occurs in the axial maps (Fig. 9.6) [26]. This map shows a high sensitivity to data obtained, being suitable for monitoring the conical shape of the ectatic disease; however, it is less intuitive than the axial map and its interpretation may be more complex.
Fig. 9.6
Geometric reconstruction of the corneal tangential map
Elevation maps do not represent data directly measured by the corneal topographer, but are obtained by comparing the reconstruction of the anterior or posterior corneal surface to the best fitted surface, typically a sphere, a toroid, a revolution ellipsoid or a non-revolution ellipsoid. The difference between both surfaces is provided by altimetry data that correspond to the elevation maps (Fig. 9.7) [4, 31, 32]. Furthermore, typical dimensions of the reference surface are around 8 mm in diameter, thereby scenarios that may influence the data acquisition process, such as shadows generated by eyelashes, are avoided [33]. These maps present several advantages: data are presented quantitatively in μm, so they are highly accurate and have a high sensitivity to small changes that can occur in the corneal morphology as a result of keratoconus [1]; also, topographers allow the selection of the best suited surface to perform the elevation map, which results in a sensitivity increase of the clinical diagnosis. This map provides, for both corneal surfaces, the elevation of the corneal apex, the elevation of the minimum thickness point [34] and the elevation of the center of the central region [35]. As the posterior surface is not altered by the excimer laser photoablation or by the generation of the corneal flap, nor is adulterated by the hyperplastic effect of corneal epithelium, data from the posterior surface could be very useful for the clinical diagnosis of keratoconus [1, 8, 26, 34, 35].
Fig. 9.7
Altimetry elevation map
The thickness map does not show data directly measured by the corneal topographer, but must be precisely reconstructed using the anterior and posterior corneal surfaces. This map gives information of the minimum thickness point and its position on the center of the cornea. This point is essential for maintaining the corneal structure and determining the progressive thinning of the cornea when the severity of keratoconus progresses [36, 37]. Some studies in the scientific literature evaluate the pachymetric profile from the center to the periphery depending on the average thickness of the concentric rings separated by 0.1 mm and centered at the minimum thickness point. This profile presents a more abrupt change in a pathological stage than in a healthy scenario [29, 38, 39].
9.4 New Diagnosis Systems
The development of new technologies in the ophthalmology field permits to improve the clinical diagnosis capability providing an accurate analysis of the corneal shape and the possibility of quantifying patients’ visual quality. Furthermore, these technologies have increased and improved the sensitivity and specificity of the assessment and diagnosis of keratoconic cornea [40]. The diagnosis of keratoconus has gained importance during the last years because of two fundamental reasons:
The need to contraindicate the practice of refractive surgery techniques that can speed up the development of keratoconus [41, 42]. In this case, it is fundamental to carry to an extreme the sensitivity of the diagnosis process even at the cost of sacrificing specificity, which most negative consequence would be to contraindicate a suitable candidate for a refractive surgery.
The different analysis methods based on assessment indices of the corneal surface that are available in the clinical practice try to diagnosis the presence of the keratoconus disease by using a quantitative and qualitative detection of this deformation in the cornea. Although the methods that are going to be referenced do not achieve individually a diagnostic accuracy of 100 % (real positives + real negatives/number of cases), the sum of all of them does provide the ophthalmologist a diagnostic accuracy of 100 %.
These evaluation indices are obtained from the topographical maps previously described, and for this reason several clinical studies have proposed determined cutoff values to distinguish between normal corneas and corneas with keratoconus [40]. However, the main problem with these indices lies in the fact that each index has a high degree of specificity for the corneal topographer for which it has been developed, and cannot be directly extrapolated to other devices. Even in some cases, the results obtained from those devices do not coincide with the published equations [40, 46].
For the above-mentioned reasons, it is important to know the systems for the diagnosis of keratoconus disease, distinguishing between univariate quantitative diagnosis systems, multivariate quantitative diagnosis systems, diagnosis systems based on graphical geometry, diagnosis systems based on mathematical models, diagnosis systems based on biomechanical models, and diagnosis systems based on neural networks.
9.4.1 Univariate Quantitative Diagnosis Systems
These indices are based on a unique variable and are used to characterize the corneal irregularity from corneal topographies. Some of the most used indices are the following:
Asphericity coefficient (Q) . It is an index that describes how the corneal curvature changes from the central region to the peripheral region. Its value depends on the diameter of study, so it is necessary to indicate it when expressing a particular index [47]. The most common parameter used in literature is Q. In a natural or non-pathological stage, the section of the cornea is a prolate ellipse with an average Q value setting –20 ± 0.12 DS [48, 49]. This is physically interpreted as the cornea is more curved in the center than at the periphery. For keratoconic corneas, Savini et al. [19] reported Q values in the corneal region that comprise a 8 mm diameter of −0.84 for the anterior surface and −1.10 for the posterior surface [19]. Another study comprising the same diameter and the same corneal region reports Q values of the anterior surface between −0.65 and −1.18 and between −1.17 and −0.66 for the posterior surface [50], according to the severity of keratoconus using the Amsler–Krumeich classification [51]. The values of asphericity describing the geometry of the cornea showed that the central and paracentral regions are more curved than the peripheral region, and this difference is greater in keratoconus disease than in normal corneas. Moreover, these values are higher when the severity of keratoconus increases. However, due to asphericity is measured in the central region (4–5 mm), if protrusion is located in the peripheral region, topographer may provide normal or even positive values of asphericity. Therefore, this quantitative index is not very specific for the diagnosis of keratoconus, and must be considered in relation to the apex position in the cone.
Inferior–Superior Value (I–S) . This index is defined as the power difference between five points of the inferior hemisphere and five points of the superior hemisphere of the corneal region located at 3 mm from the corneal apex at spatial intervals of 30°. A positive value indicates higher inferior curvature, while a negative value indicates higher superior curvature. I–S values between 1.4 and 1.8 D are defined as cutoff points for suspected keratoconus and I–S values higher than 1.8 D as cutoff points for clinical keratoconus [52, 53].
Simulated keratometry (SIMK) . This index provides information on the diopter power of the flattest and most curved meridians in the so-called useful region of the topographer (ring diameters between 3 and 9 mm). Numerically, it is expressed as K1 and K2, and the difference between the two values provides a quantitative value of corneal astigmatism. A clinical study provided SIMK mean values of 43.53 ± 1.02 D for a group of normal corneas, and established a cutoff value for keratoconus group twice the value of the standard deviation of the control group [4, 54].
Central Keratometry (K Central) . This is the average value of corneal power for the rings with diameter of 2, 3, and 4 mm. Values below 47.2 D are considered normal, while values between 47.2 and 48.7 D are considered probable keratoconus. Values above 48.7 D are clinical keratoconus [4, 53].
Average corneal power (ACP) . This index indicates an average power value of various points in the central region [53].
Effective refractive power (EffRP) . Index averaging the power in the central area of 3 mm diameter. It considers Styles–Crawford effect [47].
Apex curvature (AK) . It corresponds to an index that provides a value of the instantaneous curvature in the corneal apex. Values below 48 D indicate normality, values between 48 and 50 D are suspect, and values above 50 D denote abnormally high curvature [40].
Surface asymmetry index (SAI) . It is an index that indicates an average value of the power differences between the points spatially located at 180° from 128 equidistant meridians. A radially symmetrical surface has a value of zero, and this value increases as the degree of asymmetry is greater [4, 40, 55].
Surface Regularity index (SRI) . It is a local descriptor of regularity in a central area of 4.5 mm diameter (it comprises the central ten rings of Placido Disc). It quantifies power gradient differences between successive pairs of rings in 256 equidistant semimeridians. It correlates well with the value of visual acuity (p = 0.80, P < 0.001), assuming the cornea as the only limiting factor for vision. A normal cornea presents SRI values below 0.56 (this value would be 0 in a perfectly regular cornea) [4, 40, 56].
Different sector index (DSI) . It is an index that quantifies the average power difference between sectors of 45° with the highest and lowest power [40, 53].
Opposite industry index (OSI) . This is another index indicating in terms of average power difference between opposing sectors of 45° [40, 53].
Irregular astigmatism index (IAI) . It is a measure of dioptric variables along each semimeridian, which is normalized by the mean power of the cornea and the number of measured points [40, 53].
Corneal Irregularity Measurement (CIM) . This is a numeric index representing the degree of irregularity in the morphology of the corneal surface. It quantifies the standard deviation between the corneal surface and the best-fit reference surface, which in this case is a toric surface. High values of this ratio indicate a greater possibility of the cornea to present a pathology related to a morphological abnormality. A healthy cornea has CIM values from 0.03 to 0.68 μm, while a value from 0.69 to 1 μm is considered as suspect or normal limit, and a value from 1.10 to 5.00 μm as pathological or unusual [4].
Analyzed area (AA) . It is the ratio of the data area interpolated by the area circumscribed by the outermost peripheral ring [40, 53] area.
Centre Surround index (CSI) . It is an index that quantifies the average power difference between the central zone of 3 mm diameter and a half-peripheral ring comprised between 3 and 6 mm diameters [40, 53].
Corneal uniformity index (CU) . It corresponds to an index that quantifies the distortion uniformity in the central area with 3 mm diameter. It is expressed as a percentage, that is, a value of 100 % indicates that the cornea has a perfect consistency [47].
Predicted Corneal Acuity (PC Acuity) . It quantifies the optical quality in Snellen units (with a range of 20/10 to 20/200) in the central zone of the cornea with 3 mm diameter [40, 47].
Skew of steepest radial axis (SRAX) . It measures the angle between the more curved superior semimeridian and more curved inferior semimeridian. The more curved semimeridian for each hemisphere is determined by averaging the powers of the rings from 5 mm to 16 mm diameter. The smallest angle between these semimeridians is subtracted from 180º, and the result, in degrees, is the SRAX index. A value greater than 20° is considered indicative of keratoconus, but due to the high dispersion of values in some astigmatic corneas, this value is only valuable if corneal astigmatism is greater than 1.5 D [40].
Topographic irregularity (TI) . It is the root mean square (RMS) value of the difference between the actual topography data and a geometric reference surface, which in this case is a spherical cylinder that best fits the corneal surface of the study [40].
Calossi–Foggi Apex curvature gradient (ACG) . This index quantifies the average difference per length unit of the corneal power in relation to the apical power. Values greater than 2 D/mm can indicate keratoconus, between 1.5 and 2 suspect, and less than 1.5 is considered a normal value [40].
Calossi–Foggi Inferior-Superior Index . It is a vertical asymmetry index similar to I–S value, but this indicates the difference in terms of average power between the superior area and a inferior area. This last is determined according to a major probability of presence of the cone. A positive value means that inferior area is more curved, and vice versa. A value less than 1.5 is considered normal, a value between 1.5 and 2 considered suspect, and values greater than 2 are considered abnormal [40].
Orbscan surface irregularity . It is a coefficient calculated from the standard deviations of the mean curvature and mean astigmatism in the zones comprised between the center rings of 3 mm and 5 mm diameters. Values greater than 1.5 in the area of 3 mm and/or 2 in the area of 5 mm are indicative of high irregularity. This value is not specific for keratoconus, but merely indicates irregularity [40].
Mean toric keratometry (MTK) . This index is obtained from the data of the elevation map of the cornea. It compares and analyzes the elevation values of the cornea calculated by means of the best adjustment to a toric reference surface. If the MTK value is high, the cornea acquires a geometrical behavior similar to a toric surface, which is clinically interpreted as a major probability of suffering ectatic alterations. The MTK index follows a Gaussian probability distribution, with an average value of 44.5 D, and the range defined for the values from 41.25 D to 47.25 D contains 96 % of the population . [57]
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