|Year : 2015 | Volume
| Issue : 1 | Page : 45-62
Corneal topography and tomography
Sachin Dharwadkar1, BK Nayak2
1 Samartha Clinic Mumbai, Maharashtra, India
2 P. D. Hinduja National Hospital and Medical Research Centre, Mahim, Mumbai, Maharashtra, India
|Date of Submission||08-Dec-2014|
|Date of Acceptance||26-Dec-2014|
|Date of Web Publication||14-Jan-2015|
B K Nayak
P. D. Hinduja National Hospital and Medical Research Centre, Veer Savarkar Marg, Mahim, Mumbai - 400 016, Maharashtra
Source of Support: None, Conflict of Interest: None
Devices that evaluate corneal properties are an indispensible tool in a eye clinic nowadays. With the arrival of new technology in addition to placido based devices, the options available now are many. Cornea based refractive surgery in Indian eyes poses a challenge due to relatively thinner corneas. This is also compounded by lack of well defined, rigid and universal criteria for case selection for the same. In this article we attempt to look at the most common methods of corneal assessment in relation to the selection of candidates for corneal refractive surgery with a review of relevant literature. This is not meant to be exhaustive, but a primer to ease the clinician into understanding and taking up to learn and practice corneal evaluation.
Keywords: Tomography, topography, corneal vertex, corneal apex, saggital curvature, elevation, reference surface
|How to cite this article:|
Dharwadkar S, Nayak B K. Corneal topography and tomography. J Clin Ophthalmol Res 2015;3:45-62
Topography is the study of the shape of the corneal surface. The early devices were limited by their measurements to the central part of the cornea; however, with the explosion of refractive surgical procedures on the cornea and its consequences, the need to know more has led to newer devices and technologies emerging in the market. With the pressures of precise outcomes/results and the plethora of devices available, it can be quite a problem to decide which technology to adopt in clinical practice.
The investigative modalities for studying the corneal shape have undergone a drastic make over in the past few years. The once standard corneal videokeratoscopy has now the company of the scanning slit, optical coherence tomography (OCT), and Scheimpflug imaging to supplement in the assessment of the corneal shape. The addition of these devices has led to the addition of the word "corneal tomography" in the medical jargon as far as corneal imaging is concerned. This is because the images obtained by these devices are essentially a cross section of the cornea, and the elevation data thus obtained being analyzed further. It is in contrast to enface images of concentric rings of the placido-based devices.
Corneal refractive surgery in any form; surface treatment or laser-assisted in situ keratomileusis (LASIK) leads to weakening of the biomechanical strength of the cornea. This especially when dealing with thinner and steeper , Indian corneas need great attention to avert the eventuality of a post-refractive ectasia later in patient's lifetime.
The understanding of corneal topography and tomography along with the advantages/disadvantages of each is fundamental to the assessment of this risk before posting the candidate for refractive surgery. The existing techniques have evolved, new techniques have been added in the last few years. The various techniques give us different information with a different methodology, and it is important that we use the best of each type to give the desired result in our procedures.
In the following article, we would illustrate the use of these corneal imaging techniques in relation to their importance in the pre-refractive surgery screening. The article is not meant to be an exhaustive in content but will seek to look at the topic from the point of view of a comprehensive ophthalmologist wanting to take to learning the art of interpretation of topography maps and using them for decision-making. We also intend to touch upon the basics and bring out certain technical aspects about the available devices citing literature wherever possible, to let the reader make an informed choice about the device (s) he/she would like to use in his/her practice.
Currently, the corneal imaging techniques before refractive surgery involve four main types of devices:
- The videokeratoscope or the Placido-based devices, e. g., Topographic Modeling System (TMS) 4, Keratron, Atlas.
- Scanning slit devices. E. g., Orbscan IIz.
- The Scheimpflug devices. E. g., Pentacam, Sirius, and the Galilei. The latter two have and additional large cone Placido disc incorporated in them.
- OCT-based devices (Visante from Zeiss).
The OCT will not be discussed in this article.
There are certain fundamental differences in the videokeratoscopes, scanning slit, and the Scheimpflug devices and the fact that their data is non-interchangeable has to be kept in mind. They work on totally different principles; have different methods of data acquisition, presentation, and analysis. That apart, the same class of devices from different manufacturers may not strictly compare.  All these devices fundamentally involve simple principles of physics combined with high-end mathematics and statistics (the so-called artificial intelligence or neural networks), to give us a simplistic view of the status of the patient's cornea.
All the devices that are available can be considered to consist of three main parts:
- A projection device (back illuminated Placido rings, Blue light emitting diode (LED)).
- An acquisition device (a Charge coupled device (CCD) camera for Videokeratoscope and scanning slit systems/Scheimpflug camera for Scheimpflug devices), Spectrometer for spectral domain OCT and.
- An analytical device that is a computer with various software (Neural networks/artificial intelligence) and normative database (not in all the machines) to analyze the data that is obtained above.
Let us now consider these techniques and their advantages and drawbacks. The Penatacam printouts would be considered as the prototype Scheimpflug device for the sake of explanation. All other Scheimpflug-based devices offer similar data but differ in their software (machine classifiers) and final data outputs.
The basis of all topography and measurement/quantification of the corneal surface started with the keratometer the optical principle of which is depicted in [Figure 1]. Let us now analyze the transition from these starts into the world of videokeratoscopy.
| Concept of Placido-Based Devices|| |
Curvature measures bending. The more curved the surface the smaller is the radius of curvature and higher the refractive power. It is however important to remember that the radius of curvature is an inherent property of a curved surface, whereas the power [as shown in [Figure 2]] is derived from it with due consideration to the refractive index of the media involved. Also, different shapes can have the same power and hence using the power as the surrogate for shape may not be an ideal situation. The measurement of curvature of a given surface can be done in various methods and with the help of various devices. The keratometer is the reflection of the measurement of the central cornea only, the mid-periphery requiring instruments like the videokeratoscopes. Videokeratoscopes cover the central 7-8-mm zone of the cornea.
The Placido disc invented by Antonio Placido in the late 1800s was the first attempt to qualitatively assess the shape of the entire cornea. This consisted of a disc with concentric dark and light rings in the center of which was a convex lens for visualization of its reflection on the cornea. [Figure 3] The disc in this case would be illuminated by an indirect source and the observer would see the reflections of the rings or "mires" on the examined cornea. The placement and the size of the grid would indicate the kind of corneal problem qualitatively as shown simplistically in [Figure 4].
In the later part of the twentieth century, the devices were developed that used a backlit Placido disc and a camera respectively to image the cornea, instead of the indirect illumination and the observers eye, so-called Photokeratoscopy. This again was a qualitative test till sophisticated mathematical software allowed the quantification of the curvature and the shape and as a result of which the videokeratoscopy was born.
| Corneal Videokeratoscopy (CVK)|| |
This is the technique that has now evolved from the initial efforts that started from the Placido disc devised by Antonio Placido and have culminated into a high end gadget with analytical tools. It essentially uses the reflection principle and studies the first Purkinje image from the cornea resulting from the reflection of the illuminated mires of the projection device and its processing by the computer. The pre-corneal tear film being the anterior-most layer of the cornea that reflects the light, its nature has a great effect on the quality of the images that are obtained for analysis. Some devices have also introduced blue-colored mires (Nidek OPD scan 3) to facilitate accurate edge detection by the computer.
The devices are of two types consisting of a large or a small cone Placido projection system [Figure 5]. The large cone Placido can be used slightly away from the patient's face, whereas the small cone device needs to be very near the patient's eye. The advantage of the small cone devices is more complete coverage of the cornea and avoidance of data loss due to the varying nasal bridge anatomy. These areas of absent data are seen as data gaps or hatchings on the final printout in most devices. In some, however, data interpolation is used to give a complete coverage. It would be worthwhile to see the acquired raw image before interpreting the curvature data if not acquiring/selecting a suitable image yourself. One must be aware of this fact, otherwise reports can be misleading [Figure 6]. This probably is also the most important disadvantage of the large cone Placido devices. The theoretical disadvantages of the small cone devices however is that they are more prone to focussing errors, the cone being very near the patient's eye. In clinical use, with modified cone designs and software compensation, the small and large cone devices are pretty much equivalent provided the area of cornea mapped is almost equal. Seventy to ninety percent is the usual coverage in large cone devices. The area covered is mentioned on the printout for most machines.
|Figure 1: Principles of Keratometry (should be scanned from the book page 37 (AB is the object and A' B' is the image. By measuring the size of the object and image, curvature of the convex surface can be calculated|
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|Figure 2: A small radius circle has a large curvature and vice versa. However, power cannot tell shape, different shapes can have same power|
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|Figure 3: This is the schematic diagram of the Placido's disc. There are concentric black and white rings with a convex lens in the center aperture as shown|
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|Figure 4: The images in the top row show normal variations in the corneal shape. The image below shows inferior steepening (mires are closely placed inferiorly) as seen abnormal corneas|
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|Figure 5: This figure shows the different cone designs in Placido systems. The figure on the left side shows a large cone device and the one on the right shows a small cone device where the mires are closely arranged and the cone is smaller in size|
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The measurements of the two types of devices also differ a little bit and the variation should be kept in mind in case one shifts from one type of Placido device to another. Small mire Placido devices represent the maximum curvature in keratoconus at greater magnitude than large mire devices.  The upper lid eyelashes however interfere with acquisition the data in upper part of the cornea both these devices.
Corneal videokeratoscopy (CVK) measures central and mid-peripheral corneal zones as opposed to conventional keratometry that measures the central cornea and is especially useful for evaluating irregular astigmatism compared to the keratometer. Besides screening of refractive surgery candidates, the other applications of CVK include: Diagnosis of corneal irregularities (moderate to advanced ectasias, dystrophies, surface disease, contact lens (CL) warpage, scars, degenerations), evaluating unexplained visual loss, management of surgical patients (planning and monitoring corneal grafts, refractive procedures, cataracts, pterygia), and contact lens fitting.
The data obtained by the CVK is presented usually as four topographic display formats: They are namely curvature (axial and instantaneous/tangential), power (refractive), and recently elevation (difference or relative maps have been added for the analysis of anterior surface), and wavefront maps have also been added. Elevation data, however, when generated from a Placido system has inherent limitations as the systems must make shape assumptions that while reasonable in normal corneas are inaccurate in abnormal or pathologic corneas where there are non-linear changes in curvature.  Many devices also contain qualitative classification systems and quantitative indices and algorithms for data interpretation. A sample printout of one of the Placido-based devices giving an elevation map on the lower left depicted in [Figure 7].
However, CVK does have limitations: There is a lack of standardization between instruments; it depends on reference axis [Figure 8], alignment, and focus; it is susceptible to artefact (distortion, tear film effect); it is based on simplified optics (only applies to central cornea); and there is a smoothing effect as explained below. Also sampling occurs around the circumference of the mires, there is no measurement between mires.
It is important to understand the first limitation more carefully as it will affect all the measurements on Placido-based devices. The figure [Figure 9] explains the relations of the various axes with respect to the apex of cornea and its effect on the image acquisition. According to the American National Standards Institute (ANSI) standard definition, the corneal apex is the point of maximum curvature on the cornea, whereas the vertex is the point nearest to the camera of the Placido instrument located on the corneal topographer axis (CT axis). Before acquisition, the topographer aligns this axis normal to the cornea. Pseudokeratoconus patterns can be created when line of sight (the line passing through the fixation object nodal point and the fovea), the corneal apex, and the videokeratoscope normal (CT axis) do not line up.
Most of us visualize the eye as a Gullstrand-reduced eye, assuming that the eye is symmetric, with the line of sight coinciding with the visual axis, and crossing the center of pupil and corneal apex. This, however, is not always the case. , More so, we assume that the measurement axis of the Placido system also coincides with the above. Most people do not look through the center of their cornea. , A person with pseudo-strabismus due to large angle kappa (angle between pupillary axis and the visual axis) demonstrates these principles. The person looks as though their eyes are not straight (their line of sight does not go through the corneal apex which is the point on the cornea having the maximum curvature), but when you perform a cross-cover test, the eyes are straight (there is no re-fixation movement). When you perform a Hirschberg test, however, the reflected light appears displaced. This is because a reflected image (same as in a Placido videokeratoscope) needs to align normal to the corneal surface to appear straight. When the apex and the line of sight differ, the reflected image appears abnormal (in the adult imaged on a Placido videokeratoscope, this would appear as an asymmetric bowtie [Figure 8]], but the eye is still physically normal. This is the problem with trying to reconstruct shape from a curvature measurement. There are other methods of depicting curvature (i. e., instantaneous or local) that obviate some, but not all, of the above limitations. Sagittal (axial) curvature, however, remains the most commonly used. [Figure 10] shows how the effect of this decentration is less in the elevation-based devices. The standard topographic curvature (axial or sagittal curvature) is a referenced-based measurement. It is not a unique property of the cornea. The same shape can have many different "curvatures" depending on which axis is used to make the measurement.
|Figure 6: Large cone and small cone Placido mires in same eye. Note the difference in the number of mires and the data loss due to nasal anatomy in large cone Placido. Also note that the small cone mires have less distinct edges|
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|Figure 7: A typical printout of the Placido-based device showing axial (upper left), tangential/ instantaneous (upper right), elevation (lower left), and wave front maps (lower right)|
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|Figure 8: Curvature topography is reference axis dependent. The figure on the left shows an on axis topography showing a symmetric bow tie pattern. This measurement when repeated with slight decentration with respect to the line of sight (black line) shows an asymmetric bowtie. Courtesy Prof Belin|
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|Figure 9: In figure, the line of sight is different from the corneal apex A, this would result in an artifact on Placido-based imaging and explains the displaced apex syndrome|
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|Figure 10: The sagittal curvature map (upper right) shows a gross asymmetric bowtie pattern (which is considered abnormal) but the front and the back elevation maps shown below are normal. This is characteristics of displaced apex syndrome in which the line of sight and the corneal apex do not coincide leading to asymmetric bow tie pattern in otherwise normal corneas. Courtesy Prof Belin|
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"Keratoconus" maps can be created on Placido devices in normal aspherical surfaces with angular decentrations as small as 5 degrees. This again underlines the need to have more information about the corneal surface through multiple technologies and also without forgetting basic clinical examination like the Hirschberg tests and cover tests. The important differentiating feature among the normal and the abnormal corneas in this scenario would be the orthogonality of astigmatism, normal pachymetry, stable refractions, and best corrected acuity of 20/20 in spite of having an asymmetric bowtie pattern.  Because clinicians are less familiar with interpreting curvature data, these devices convert this information to power values with the paraxial formula (P = (n-1)/r; where P = corneal power, n = 1.3375 (compensates for negative power of posterior cornea by incorporating a fixed correction in the refractive index to compensate for posterior corneal power), and r = radius of curvature in meters). This ignores spherical aberration but is a good approximation for the power of the central cornea.
Curvature maps are usually displayed in one of two formats - axial or tangential - depending upon what method is used to calculate the radius of curvature. For the axial curvature map, r = the distance from the corneal surface to the optical axis along the normal (vertex normal) and all radii are measured from this axis. Due to this common reference axis, small irregularities may not be visible or "smoothened out" as they are very small as compared to the large corneal diameter. The axial maps represent a running average of scaled curvatures. Extreme values are averaged out of the calculation. These maps are spherically biased and are calculated on the assumption that all rays of light striking the corneal surface are refracted, forcing a focal point through the optical axis as a reference axis [Figure 11]a. This is similar to a keratometer and assumes that the center of rotation of the best fit sphere lies on the optical axis. It is a good approximation for the paracentral cornea (2-mm zone).
The axial map is the most commonly used and provides a good estimate of overall corneal shape, which appears smooth with little noise because it provides an average of adjacent curvature values. This is useful for evaluating corneal optics (i. e., central power of cornea, calculating intraocular lens (IOL) power, and screening for pathology). Axial map, also referred to as sagittal maps and can be converted to "Refractive" maps applying the refractive index, Snells law, and ray tracing instead of Gaussian optics that is used for the axial map. This map plots the refractive power of the cornea at each point.  This accounts for spherical aberration outside the central zone, and provides information about the imaging power of the cornea. This is helpful for correlating curvature to vision and analyzing surgical effects.
On the other hand, for the tangential (local, instantaneous) map, r = the instantaneous radius of curvature at each point on the cornea. This is the true "r," independent of the defined central axis, and is therefore a more accurate measure of curvature at a particular point. As a result, the tangential (instantaneous) map is noisy because it is more sensitive to local changes and accentuates focal abnormalities. This is useful for evaluating corneal shape (i.e., ectasia, assessment of refractive surgery candidates, surgically induced changes, and contact lens fitting). The difference in the two types of maps is illustrated with example in [Figure 11]b.
|Figure 11: (a) This figure shows the difference in the concept of the sagittal and the tangential curvature. As seen in the figure the radii of curvature in the axial map on left are derived from the distances from the reference (optical axis) and the derivation of the tangential curvature is independent of the reference axis as shown in figure on right (b) This shows actual maps to illustrate the principles explained in 11 a. The maps belong to the same eye of the same patient but differ in values and appearance as the derivation is in a different manner. Tangential map on the right makes localized elevation look more obvious|
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[Figure 12] is an elevation map for one of the Placido-based device. These maps are however may not be very accurate and reliable as the assumptions (sphero-cylindrical optics) used in their construction do not perform well in the setting of non-linearly altered corneal shape (ectasia/post-surgery).  These devices derive the elevation maps using the angle of reflection, whereas true elevation can only be measured accurately by triangulation method employed in slit scan and Scheimpflug devices.
|Figure 12: Figure shows the elevation map for the anterior surface in Placido-based device the left upper corner indicated the reference body and its dimensions that are used for the current calculations|
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In addition to the type of map display, the map scale (dioptric range, step size, number of colors) is also very important because it affects sensitivity. An absolute scale is constant for all exams and is useful for comparisons over time and between patients. A relative or normalized scale adapts to the range of powers on the corneal surface and differs for each cornea. Thus, the power range and step size may be narrow or broad, which magnifies or minifies significant changes. Sensitivity is also affected by the step size (dioptric range for each map color). The recommended step size is 1.5 D (Universal standard scale).  Small steps increase sensitivity by adding more colors and exaggerate minor or normal changes, which can cause confusion (i. e., pseudo keratoconus) and misdiagnosis. Large steps decrease sensitivity and mask significant changes due to smoothing of points between rings. Topographic artefact can occur with inappropriate step size, misalignment with the CT axis, pressure on the globe, and altered tear film.
Most CVK instruments also contain quantitative measures, indices, and algorithms to aid in data evaluation. The most commonly used machine classifiers (artificial intelligence) are the KISA devised by Rabinowitz and Rehman, the keratoconous prediction index (KPI) by Maeda et al., Cone location and magnitude index (CLMI) among the many others that are commercially available. The classical Rabinowitz system and the Klyce and Maeda systems are available on most commercial Placido devices (e. g, TMS). They have different methods of assessment, in that the Rabinowitz system has sharp defined cut-offs and is made with data from keratoconus patients to differentiate it from normals and relies on examination of both eyes. It does not account for other causes of topographic abnormalities.  KISA is a composite index calculated as KISA% = (K) × (I-S) × (AST) × skewed radial axis index (SRAX) × 100. In this case, only absolute values are used without sign, any K value less than 47.2 was substituted by 1 and only ones in excess of 47.2, difference used (if K is 57.2, the value input is 10). SRAX is the difference between 180 and smaller of the two angles between the radii and the AST index quantifies the degree of regular corneal astigmatism (Sim K1-Sim K2). Using this index set at 100 percent in eyes with no other pathology in their study, Rabinowitz et al., detected no overlap between normal eyes and keratoconus.  According to the authors, this score also has a range for suspects with minimum overlap to the normal population. Sixty to one hundred percent values are considered to be suspect. The KPI index developed by Maeda and Klyce consider eight different indices together to give a result and help differentiate keratoconus from other corneal irregularities.  The CLMI is a novel index in that it is platform independent and can be used with any machine. It can track the location and magnitude of cone over time to assess progression. It showed 100% specificity and 100% sensitivity in separation of cones and normal eyes when used on a validation set.  All these software however are no substitute for history and thorough clinical examination and also an independent validation in new set of population.
These softwares calculate the probability of the patients map resembling a keratoconic or other known patterns of anterior curvature by comparing it using a pre-defined mathematical model fed into the machine. [Figure 13] shows a model flow chart for the data acquisitions to calculations of a Placido-based device for sake of explanation. The performances of these classifiers in clinical practice are tested and evaluated depending on their receiver operating characteristics curves involving their parameters and indices. The specificity and the sensitivity of these classifiers in detecting true keratoconus should be known for each one individually, before one starts to use these in clinical practice and would be well-advised to examine these before hand in case a device purchase is contemplated, as they vary with each machine.
|Figure 13: This figure illustrates the flow chart for the prototype Placido-based device from the image acquisition to the neural network and the final outcome|
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However, the importance of looking at the raw data, its quality and the topographic map can never be undermined and is most important before the interpretation of any report is started. Machine classifiers use mathematical models developed from the regression analysis of the patients with keratoconus and other irregularities and try to fit the data acquired for every patient into them, to give a spontaneous response in relation to the acquired data. Caution must be exercised in the stand-alone use of these indices for interpretation of topography printouts.
| Relevance of Elevation-Based Devices: (Tomographers)|| |
The occurrence of iatrogenic keratectasia after uneventful LASIK on normal eyes with no traditional risk factors (age, pre-op corneal thickness, ablated depth, residual stromal bed, normal Placido reports, and single point corneal thickness values) has demonstrated the need to know more about the cornea undergoing refractive surgery.  In addition, several recent studies have demonstrated the role of the epithelium in masking the cone on Placido-based devices. ,, The accuracy of multiple standard point ultrasound pachymetry in predicting change in corneal shape is found wanting as pointed out by Rabinowitz et al., Epithelial changes around the cone tend to mask the early ectatic changes on the anterior surface. Inability of the Placido topographers to give accurate anterior elevation maps in all scenarios as cited before definitely necessitates a need to search for new and accurate tools to obtain more information on the cornea. Modifications in the curvature, asymmetry, and elevation differences in the posterior surface have been well-documented in keratoconus eyes ,, These studies using different instruments reported greater posterior astigmatism, posterior elevation, and prolacity in suspect eyes as compared to normal. The consensus around the discriminant values is however lacking, highlighting the fact that the patterns are to be more relied upon than the actual "values" derived. Hence, the current weight of evidence suggests that the study of the posterior surface appears to be invaluable to the decision-making in refractive surgery. These facts without doubt stress the vital role of elevation-based devices in corneal evaluation pre-refractive surgery.
| Elevation-Based Devices (Tomographers)|| |
Elevation-based topographers are the relatively new entrants into the market and use different principles for acquisition and calculation vis a vis the Placido-based devices. These devices are basically of three types: The Slit scanning devices, the Scheimpflug devices, and the OCT-based devices. In these devices, the machine usually provides a composite printout display. The most common maps that are provided in their display include the anterior elevation map, the posterior elevation map, sagittal power display, and the pachymetric map. The posterior elevation and the pachymetry map are the valuable additions as compared to the Placido-based devices.
The understanding of the elevation-based devices should start with the concepts of elevation and reference surface.
| Concept of Elevation|| |
In terrain topography, the surface elevation is surveyed in reference to sea level which is fixed. The localized elevations in the cornea being small relative to the cornea itself, to unmask these irregularities the global curvature must first be eliminated akin to the pattern standard deviation calculations in visual fields. This can be achieved by fitting the cornea with a surface with features most resembling it, the so-called reference surface. This reference surface can be a sphere, asphere, ellipsoid, toric aspheroid, etc. Although the cornea is not exactly spherical in shape, the most commonly used reference surface used is a sphere. Not many studies in literature have addressed the best choice of reference shape to detect ectatic change but it should be remembered that this choice can affect the final image/output significantly. In one study, the use of the toric ellipsoid was associated with decreased risk of masking the cone as compared to the best fit sphere (BFS).  Another group using the Galilei analyzer has recommended the use of the toric aspheroid had the ability to differentiate in between the Forme fruste keratoconus (FFKC) and the normal corneas using the Galilei analyzer.  The rationale behind this finding is that by virtue of being very close to the natural corneal shape, it will highlight the abnormalities better which otherwise would be hidden in the ridge pattern normally generated by the BFS. Familiarity with the different outputs obtained with the respective reference surfaces in varying scenarios would help us identify suspicious patterns in each of them over a period of time. Individual effort on the part of each refractive surgeon is desired to use each of the reference surfaces in the best possible way.
| Elevation and its Relation to Slope and Curvature|| |
These are three different measurements of a surface. Corneal elevation is the measurement of height between points at two different elevations and is primary source data for tomographers. For the Placido-based devices, it is the "Slope" which measures steepness or incline between two points that is derived by the analysis of reflections of rings on the cornea. Slope is the first derivative of elevation and can be used to either calculate elevation or curvature. Curvature is calculated from slope data in Placido topography system and elevation is calculated from it using integral mathematics. The Scheimpflug prototype (tomographers) Pentacam uses elevation as primary data and calculates curvature by differential mathematics. Since surgically altered surfaces can have non-linear changes in curvature, a method that "calculates" and not actually measures elevation may be inaccurate due to multiple elevation (mathematical) solutions available for these surfaces. 
| Float|| |
The reference surfaces can be fitted in the two ways as depicted in [Figure 14]. The float is a method of unconstrained fit where no pre-condition are defined for the position/locations of the reference surface. Here, the reference surface fits the surface to be measured with minimum square difference that is minimum difference above as well as below the measured surface. In the pinned or apex fit, the center of the reference is pinned on the view axis and the apex of the reference surface is located on/pinned to the surface to be studied as shown in the [Figure 14]b. This is in short a "constrained" fit, where conditions are imposed on the reference surface. As a result the pinned fit being located with its apex on/pinned to the surface to be studied and not elevated about it lowers the central hill (for prolate surfaces ) seen on the float fitting due to its different methodology. The float method is the commoner of the two and what is normally shown by all elevation instruments nowadays. This method basically fits the reference surface to the surface in question with minimum square difference. The fitting type should be kept in mind while looking at different instruments as it makes a difference in the output as shown in [Figure 15]. One should bear in mind that the "float" is not synonymous with "elevation" or elevation map and is actually a method of fitting of a reference surface in elevation-based devices.
|Figure 14: Types of fitting methods for a reference surface. 1 Apex fit/center + pinned - Center of reference object is constrained on the view axis and it intersects data surface on the view axis. This flattens the central hill as it centers on it, Float - Center is unconstrained. Reference fits the corneal surface with minimum square difference. Almost all devices use this method as it has the least error|
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|Figure 15: The figure illustrates the effect of the fitting methods on the final result. The figure on the left utilized the float and the one on the right did not|
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| Best Fit (BF) Surface|| |
The actual raw data obtained by the elevation-based topographers lacks qualitative patterns that would allow the clinician to easily separate normal from abnormal corneas. In other words, raw elevation data for normal eyes look very similar to the raw elevation data in abnormal eyes as shown in the [Figure 16].
To give a qualitative definition to the elevation data the machine using the above concepts of elevation and float, identifies the dimensions of a selected reference shape that can best fit to the examined surface for each eye tested depending on its individual characteristics. This calculated reference shape varies in dimensions for each eye and its shape and curvatures are indicated on the printout. This is called as the best fit reference surface. This surface is fitted in a pre-defined "Fit zone" which is usually 8 mm in diameter is used in most machines. Most of the software in different machines have their specific reference surface setting (e. g., the Belin Ambrosio display (BAD) has the BFS). In other situations, one can use different references depending on individual choice and experience.
|Figure 16: Figure shows that the raw elevation data from normal as well as abnormal eyes lacks quality and looks same if not compared to reference body (Courtesy Prof Belin)|
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| Scanning Slit System|| |
Orbscan is the prototype machine of this type.
This was the first attempt at the study of the posterior surface of the cornea which started in 1995 with the introduction of Orbscan I. Later the Placido was added in the second version of the device. The scanning slit system was introduced for the first time with the Orbscan that used the theorem of slit scan triangulation for the calculation of the corneal power. Triangulation is a highly accurate mathematical concept in use in satellite navigation and land topography to calculate distances using fixed known reference and is used in this device. The diagram [Figure 17] highlights the principle of scanning slit imaging and triangulation.
|Figure 17: This figure shows the principle of scanning slit imaging and triangulation|
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The device uses the projection of a slit of light [Figure 18]a at various positions on the vertical meridian on the cornea, takes images at pre-specified positions using the video camera, and calculates the curvature at these positions using triangulation. The entire cornea is covered with 40 vertical slits, 20 on each side normal to the surface at each position of acquisition, capturing the backscattered light with the video camera. Each of the slits has 240 data points.  The data for the area between these slits is interpolated. The approximate acquisition time is 1.5 seconds. In addition, the device has a Placido disc for the calculation of the anterior curvature [Figure 18]b. This Placido disc however is not circular and cannot get data from the upper and lower parts of the cornea consistently.
|Figure 18: Orbscan which uses the projection of a slit of light, (a) shows the projected slit of light on the cornea and b shows the Orbscan machine in side view and front view|
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Many ophthalmologists and researchers have proposed their own scales and indices for interpretation of the Orbscan images. The readers are advised to refer to specific literature on the device for the same. [Figure 19] shows a prototype Orbscan quad map image that is most commonly used and the basic parts of the printout are explained here.
|Figure 19: shows the various indices that need to be seen while inspecting an Orbscan map for evidence of keratoconus. All four maps 1. Anterior elevation 2. Posterior elevation 3. Keratometric map (Power map) 4. Thickness map (pachymetry) need to be seen in detail along with the indices 5. anterior and posterior best fit sphere 6. various Indices (sim Ks, keratometric asymmetry in 3- and 5-mm zone, pupil diameter, angle kappa, etc.)|
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In many of the instrument reviews and research, certain problems with the Orbscan have been highlighted vis a vis the Scheimpflug devices. In normal corneas, the pachymetry lags in accuracy and reproducibility to the Scheimpflug devices  and the readings were not interchangeable. , The Orbscan inaccurately identifies the post-operative posterior corneal surface and routinely locates the surface too anteriorly. As a result, its pachymetry reading is too thin, and its topography suggests ectasia. The inability of the Orbscan to identify the posterior corneal surface on post-LASIK eyes promoted the false beliefs that changes to that surface were commonplace after LASIK and that most patients exhibited subclinical ectasia. ,,,,
Although pre-operative pachymetry is repeatable and correlates well with ultrasound after a built-in "fudge factor," the Orbscan IIz's measurements of the central corneal thickness after myopic LASIK are less than those measured by ultrasonic pachymetry. This difference decreases with time and may not be significant after 1 year. [Figure 20] shows some common drawbacks on the Orbscan printout.
|Figure 20: Shows the drawback of the keratometric map lower left in that the map is truncated above and below due to the horizontal shape of the mires (as shown in the photo of the device in Figure 18). The pachymetric readings of the upper and lower parts have not been acquired and there is no quality score for the image in this particular device. One should refrain from interpreting images with incomplete data|
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Edge-detection algorithms that are the heart of the scanning slit-based Orbscan IIz system are vulnerable to interference from artifacts introduced by the corneal reshaping. The Orbscan IIz in particular exaggerates the posterior corneal surface's contour, and clinicians must be careful to avoid an over-interpretation of this topographic analysis for several months following refractive surgery. 
Due to the above reasons, the Scheimpflug technology appears to supercede scanning slit devices in their accuracy and usage in refractive surgery clinics nowadays.
| Scheimpflug Imaging|| |
The concept of Scheimpflug photography was started by an Austrian naval forces officer, who was a cartographer by profession, Theodore Scheimpflug. This was initially used for the purpose of topographic imaging for military purposes with cameras attached to the gliders or hot air balloons with the prototype devices. His method of photography could correct for the perspective distortion of the aerially acquired photographs [Figure 21].
|Figure 21: (a) Photo graph of the original Scheimpflug camera (b)180/360-degree rotation of the camera around the cornea imaging the perpendicular illuminated corneal slits|
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The initial concept used multiple fixed cameras that used to capture images. This was replaced by the moving charge-coupled device (CCD) camera in the ophthalmic devices to serve the same purpose as illustrated in [Figure 21]b. The images so acquired are subjected to analysis and reconstruction to give the information for the surface studied. [Figure 22] illustrates the principle of Scheimpflug imaging vis a vis the conventional camera.
Aptly called as corneal "tomography," this imaging modality involves the acquisition of slices of the cornea (each one passing diametrically through the center) by a rotating camera and their analysis. The technology of these devices is totally different from the Placido-based devices and they derive the elevation data as their primary raw data. This data can be converted by means of advanced mathematical algorithms into curvature data. As opposed to attempting to generate elevation data from curvature (integral), the calculation of curvature from elevation data provides a unique solution (differential).
Of the Scheimpflug devices that are available in India, the Pentacam is the only "purely Scheimpflug" device and the other two, the Sirius and the Galilei are bimodal devices that combine the large cone Placido with the Scheimpflug. The Galilei has 2 Scheimpflug cameras for faster image acquisition and image averaging, whereas the Pentacam and the Sirius have 1 each [Figure 23]. The commonalities of the devices are that they acquire the cross-sections of the surface illuminated by slit beams in various meridians with the help of rotating Scheimpflug cameras and analyse them. As all the illuminated slits projected pass through the center of the cornea, the central measurements are accurate.
|Figure 22: This is an illustration to show how the Scheimpflug camera principle works (right) with respect to the conventional camera (left). This method of image acquisition enhances the depth of focus|
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|Figure 23: These are the various Scheimpflug devices commonly available. 1) Pentacam with single Scheimpflug camera 2) Sirius with Placido (large) and the Single camera (yellow) 3) The Galilei- Dual camera device with a large cone Placido|
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One pertinent difference between the Pentacam and the other two devices is that these two derive the anterior curvature by a combination of Placido and the Scheimpflug data by the use of proprietary software and by incorporating the refractive index value that is mentioned on the printouts. The Pentacam derives the curvature purely form the elevation data using mathematical methods and readings may not strictly be always interchangeable between these devices for the sheer difference in the technology they use. This has been documented by various comparative studies to that effect. The curvature data derived by the Pentacam has compared well with the Placido in the studies done till date in normal as well as abnormal eyes. , The Galilei and the Pentacam HR (The version of Pentacam with high-resolution Scheimpflug camera and uses 1, 20, 000 points) are devices capable of analyzing more than 1,00,000 data points from high definition images. The other available devices use fewer data points.
The most important advantage of the tomographic devices (Scheimpflug, OCT, and slit scan imaging) is the global pachymetric map and the posterior elevation map. [Figure 24] This data is possible only with the above technologies (and the OCT that is not discussed here). The Scheimpflug scores over the slit scanning devices due to better edge identification and reproducibility of data as has been proved by various publications. ,,, Commonly, the clinician views elevation data not in its raw form (actual elevation data) but compared to some reference shape. [Figure 25] shows the Scheimpflug raw data (images).
|Figure 24: Global pachymetry map (left) and the back elevation map- (right) important advantages of the elevation-based devices over the Placido-based systems|
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[Figure 26] shows the concept of the reference surface (in bold) located under the surface to be evaluated. In these elevation maps, it is important to remember that the colors represent the elevation data. Any point on the cornea that is higher than the best-fit reference surface will be shown as a peak - in the "hotter" colors, and any point that is lower than the best-fit sphere will be shown as a valley - in the "cooler" colors. [Figure 26]. In the printouts, the reference surface, its diameter/s, method of fitting used, and the fitted area are mentioned in addition to the color scales used as shown in [Figure 27]. The elevated points are given (+) values and the depressed points are given (−) values as shown in [Figure 28].
|Figure 26: This figure illustrates the color coding in elevation-based topography in a simplified way. The level of the reference surface is shown as a yellow line. The area elevated above the reference surface is shown in red and the area depressed below is shown in blue|
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|Figure 27: The figure shows the notation for reference objects being used for the calculation. The ellipsoid reference (BFTEF) is used in this case and has a max and min curvature defined. The fitting method is float and the area fitted is 8 mm|
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|Figure 28: The plus sign with hot colors and the minus sign with cool colors indicates the location of the points above and below the reference surface, respectively|
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These reference shapes as discussed before can be spheres, aspheres, toric aspheroids, and ellipsoids with multiple options available and customisable in every device. The maps typically display how actual corneal elevation data compares to or deviates from this known shape. The map is obtained for the anterior as well as the posterior elevations. The output data will depend on the choice of the reference surface [Figure 29] and one may well follow the manufacturers' guideline and personal experience to set the reference surface and interpret the results accordingly.
|Figure 29: This shows back elevation of the same astigmatic eye with different reference surfaces. The toric ellipsoid to left of the sphere to the right. The pattern of astigmatism is best seen on the spherical reference surface. The scale on the left shows the color coding used for the above maps. As seen here the toric surface more snuggly fits the surface in question leading to smaller values of elevation/ depression|
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Fitting a reference surface to the central 8.0-mm zone appears best, as most of the pathology lie inside this zone, this provides adequate data points and most users should be able to obtain maps without extrapolated data. Most of the instruments have their acquisition set within the 9-mm zone. Since the normal eye is a surface aspherical prolate fitting the central 8-mm zone allows for subtle identification of both ectatic disorders and astigmatism. Use of larger zones leads to more artefacts due to the aspheric prolate nature of the corneal surface.
Ectasia and keratoconus are diseases that involve thinning of the cornea and hence the pachymetric maps are invaluable evidence to that effect. The value of pachymetric progression has been demonstrated by Luz et al., where it is seen that the pachymetric variation from limbus to the thinnest point in normal eyes is distinct from eyes with keratoconus.  Indices of curvature and thickness that are generated centered around the thinnest point can detect mild forms of keratoconus undetected by Placido-based neural network program.  The Belin Ambrosio (Enhanced ectasia) display [Figure 30] in the Pentacam incorporates these novel parameters as percentage thickness increase (PTI) from thinnest point and the Corneal thickness spatial profile (CTSP) This map has a normal and a hyperopic database in its latest version. Another feature of this software is the ability to enhance the cone location. This is done by subtracting the 4mm area around the thinnest point and calculating the new BFS for the rest of the cornea (which would be flatter if the cone is located in the excluded area). As a result when the excluded area is compared with the flatter "new" BFS, it stands out if abnormal in the "enhanced map" that is shown at the bottom of the printout for both the anterior and the posterior surface. In addition to these features, the display in its current third version (BAD3) incorporates the K max, maximum front, and back elevation in microns, a pachymetry map, thin point location, displacement of the thin point from apex, and a pachymetry-based classifier the ART max. Besides this machine classifier, the main classifier, the "D" value, incorporates 9 parameters for its calculation and has been independently validated in a retest population. 
|Figure 30: Belin Ambrosio enhanced ectasia display (BAD) version 3. E. g., Keratoconus map|
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The curvature maps are the indirect/surrogate indicators to thinning and protrusion and may not match the accuracy of the elevation devices in predicting the change of corneal shape as they do not image the posterior cornea and do not provide a thickness map. According to some researchers also, the anterior curvature changes are initially masked by the thinning/heaping of the epithelium forming a typical donut pattern (Central thinning over the cone with peripheral ring of thick epithelium) and hence the posterior elevation and thickness profile assumes peculiar importance. 
The sagittal or axial curvature maps are poor indicators of the location of the cone in keratoconus and commonly exaggerate its peripheral appearance. Both anterior elevation maps, posterior elevation maps, and pachymetric maps more accurately locate the true cone position.
The various devices incorporate various type of machine classifiers that can give a mathematical representation of the acquired data and classify it into normal and abnormal patterns as is [Figure 31]a and b. The classifiers would be as good as the data that is presented to them for calculation. Hence, the quality and the technique of acquisition of images would be of paramount importance for a good result.
|Figure 31: The figures a and b shows the examples of various machine classifiers for the different devices and different types of printouts. There is a large variety of printouts possible depending on the software installed in the machine|
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| Interpretation of Topography/Tomography Reports|| |
Regular astigmatism shows a classic pattern where the flat meridian is depressed with respect to reference surface and the steep meridian is above or elevated with respect to the reference surface in tomography maps and shows a symmetric bowtie with orthogonal axes on topography. The larger the astigmatism the greater the difference between corresponding points on the principal meridians. Additionally, the further you go out from the center or apex the greater the deviation from the reference surface. Irregular astigmatism is by definition where the principal meridians are non-orthogonal. This is readily apparent in the maps. Mild changes may still be associated with good best spectacle corrected vision (BSCVA), but larger amounts of irregular astigmatism are typically associated with a reduction in BSCVA.
Irregularly, irregular corneas are so distorted that the principal meridians can often not be identified. These corneas are almost always pathologic, associated with a significant reduction in BSCVA and may be seen in conditions such as advanced keratoconus, Pellucid degeneration, anterior dystrophies, and corneal scarring.
In screening for refractive surgery cases, in addition to a keen sense of detail in topographic patterns, it is important to have sensitive and specific indices to minimize the false positives as well as false negatives for detecting problematic corneas. Each technology and software has advantages as well as limitations. Different technologies alone or in combination that study the various aspects of the cornea to the fullest will offer the greatest sense of security for selecting a proper case. Given the constraints of all currently available devices and classifiers examination of a doubtful case with more than one system would be prudent choice. A complete overview of the technology and the mathematics used is paramount to select a good method/s for our practice. Population validations of machines and their different statistical tools that are published in literature add authenticity to them and inspire confidence in their usage.
Before looking at the interpretation of the maps we have to understand what we are looking for.
| Keratoconus and FFKC|| |
Keratoconus is a clinical diagnosis and FFKC is a subtle topographic abnormality before clinical manifestation of the disease.
The aim of topography and tomography in refractive surgery clinic is to rule out keratoectatic disease either in form of frank keratoconus or subtle FFKC as they are contraindications to the procedure. There are certain topo and tomographic criteria for both obtained through the work of various researchers and it would be worth a mention just before proceeding to interpret the reports. The suspicious signs for keratoconus include:
Axial map abnormalities
- K greater than 48 D.
- SRAX greater than 21 degrees.
- I-S greater than 1.42D.
- Corneal astigmatism on anterior odr posterior surface greater than 6 D.
- Against the rule astigmatism.
- S-I difference at the 5-mm zone >2.5 D.
On the elevation maps
- Isolated island or tongue-like extension on either surface (BFS mode).
- Elevation values greater than 12 microns on the anterior elevation map in the central 5 mm (BFTE mode).
- Elevation values greater than 15 microns on the posterior elevation map (BFTE mode).
Pachymetry/corneal thickness map: On Scheimpflug devices
- Thinnest location less than 470 microns.
- Displacement of the thinnest point >500 microns from the center.
- Pachymetry difference asymmetry in two eyes at thinnest point >30 microns.
- S-I difference at the 5 mm circle >30 microns.
- Cone-like pattern on the thickness map.
| Steps in Interpretation of the Topographic Maps for Refractive Surgery Screening|| |
The ideal protocol will depend on the devices and their availability, whether a Placido or a Scheimpflug scanning slit or both are available. Since the global pachymetry and the elevation of the posterior surface are available only on the Scheimpflug, OCT or scanning slit they would provide more information and would logically even be superior if the curvature maps obtained from them are comparable to the Placido-based devices. Hence, the elevation-based devices especially the Scheimpflug-based ones would be a better choice, after all the publications and the physics discussed above. Besides, there are more false positives and negatives in Placido-derived images also. The devices like the Pentacam have demonstrated to have not only comparable but also interchangeable  results (with Placido) for the anterior surface and can be used as standalone device and so can be the bimodal devices (Sirius, Galilei) that contain both technologies.
Interpretation of topography printouts is NOT all about pattern identification but also looking in between the lines. An important error to be avoided in all instances is to jump to the machine classifier results directly and basing your clinical decision on them. The step wise interpretation of the reports would include:
Follow the sequence of GRADES:
G- General information.
R- Reliability (Quality).
S- Subsequent test.
- Patient demography, eye, date of procedure, and which eye is being examined.
- Look at the basic data on the map, note the quality of raw data (mires in Placido and the edges in Scheimpflug), so also the quality scores that are available in the devices. On the display, correlate this to the acquisition area and watch for areas of missing data (data gaps), indicated by hatchings or absent data. If poor quality is seen (in terms of image appearance or a poor quality score), repeat the images or select a better image. In case one does not procure the images himself/herself, it is prudent to see the Placido raw image selected for calculations especially if abnormal. The edges of the Scheimpflug map should be seen for hatchings that come within the central 8-mm zone/areas of absent data (as the case may be depending on the instrument make).
- It is pertinent to start by looking at the reference scales that are in use on your machine unless the steps are kept constant (using absolute scales/universal scale, etc.) as a rule. If the current data has to be compared to a previous report done elsewhere, similar scales can be used to get an approximation preferably on a device with similar technology. Steps of 1.5 D are the usual standard for curvature data/2.5 µm for pachy/10 µm for eleviation (contour). Absolute scales allow comparison between successive examinations of same patients and over different patient groups.
While using the Placido-based devices stand alone, the basic patterns for the anterior curvature on the axial map need to be compared to the standard patterns provided by Rabinowitz et al.,  and Levy et al.,  [Figure 32]. The map patterns can be classified into circular, oval, steepening (superior or inferior), bowtie (symmetric and asymmetric), and with or without skewing of the radial axes, J and the inverted J as shown in the [Figure 32] template. The symmetrical bowtie, round, and the oval are considered normal, the asymmetric bowtie, skewed axes, inferior steepening, and J and inverted J pattern, and their various permutations as suspicious. The Pellucid (crab claw), butterfly, and the keratoconus (D) patterns are examples of abnormal patterns.
|Figure 32: These are the basic shape templates given by Rabinowitz and Levy to depict the changes in the axial maps in various corneas. Levy studied the families of patients of keratoconus to see the pattern in first degree relatives. (J and inverse j patterns) asymmetric bow tie with skewed radial axes and inferior steepening; and Jinv, asymmetric bow tie with skewed radial axes and superior steepening|
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Look for the maximum keratometry of the anterior surface ( Kmax) and correlate with the ultrasound corneal thickness values (measured at multiple points).
Use the instantaneous map to look for the location of maximum power/cone location. The corneal thickness above this location can be mapped with ultrasound and compared to a symmetric location on the other side of the pupil. The difference more than 30 microns is suspicious.  This is followed by examining the machine classifiers like the KISA, KPI, etc. available with the Placido-based devices. If available, the wavefront maps and the modulation transfer function can be correlated at this stage along with the history of patients refractive changes over the years.
4. Look at the elevation maps (for elevation-based Scheimpflug and scanning slit devices) - If a Scheimpflug or scanning slit is being used, the elevation data and the global pachymetry can be obtained from the Scheimpflug or the slit scan device itself. The important points to be noted in the elevation maps are the posterior elevation patterns, thinnest point location, the peripheral corneal thickness values (and the percentage thickness increase (PTI) if available as in Pentacam) in addition to the anterior curvature data (acquired independently in bimodal devices through Placido or derived mathematically as in Pentacam).
5. The most elevated points on the anterior and the posterior elevation maps should be correlated to the highest power on Axial/Saggital curvature map and the thinnest point on the global pachymetry map. If all the above match, it is called as the "fourpoint touch" and is a hallmark of suspect cornea, especially if the apex is decentered by more than 500 microns and the peripheral thickness readings of the upper and lower half at the 7-mm zone also show a significant difference of greater than 100 microns. Look over each index and the values provided by the device like the K max and other specific indices.
6. These indices should be used with clinical correlation to the patients' demographics (i. e., Younger patient with suspect topo/tomography more significant as compared to an older individual with same changes), inter eye asymmetry (in patterns, axes, elevations, pachymetric behavior, maximal corneal power), and the refractive error and put into perspective for consideration in refractive surgery.
7. After examining all the above, the statistical statement (or machine classifier report eg, KISA, KPI, BAD "D value," etc.) provided by the respective machines can be seen and correlated to the above findings. Some of these indices have undergone independent validation in population-based studies and are more robust than others. The maps will also provide a final comment on its analyses of the presented data and flag it (as normal or abnormal or as percentage probability of abnormalcy) depending on the softwares that are built into them.
8. If it is a repeat test, compare it with the previous tests and note the changes, especially if a suspect cornea is being followed up. Most of the machines have an in-built program to generate comparative difference map to highlight the changes.
It is important to remember that these machine classifiers have their own limitations in terms of specificity and sensitivity and are not to be considered as the gospel truth. A thorough search of validation of these classifiers by the individual physician by looking up peer reviewed journals is recommended before putting them into practice.
Decision-making with the topography/tomography reports
Putting corneal evaluation into refractive surgery practice.
Having interpreted the reports carefully and seen the various indices with the available technology to evaluate the topographic risk, the further assessment would include patient factors like desired correction, age, inter eye asymmetry, calculated residual stromal bed following ablation, and the pre-operative corneal thickness. One such system to predict the risk of an individual eye and allot a risk score was proposed and validated by Randlemann in 2008.  It contained the use of five parameters (Topography, residual stromal bed, Age, Corneal thickness pre-op, and Manifest refraction spherical equivalent (MRSE) and led to a cumulative score that would be predictive of the risk. This system however had its own share of criticism and shortcomings about the sensitivity, , its accuracy in the setting of normal topography result  and scoring design. But till such a time that a new system becomes available by continued research and incorporation of other risk factors like tomographic indices it may used as a reasonable guide for decision making.
In one of the recent published literature, the percentage of the (preoperative) corneal thickness ablated (including thickness of the flap) was the risk factor most predictive of ectasia risk among all others.  Thus, the knowledge of topography and its correct application forms the vital cog in the wheel of successful refractive surgery practice.
| Important Glossary|| |
- Curvature axial: This is the commonest map used in topography it is a running average of the corneal power and used more commonly in IOL power calculations.
- Curvature tangential (instantaneous): This map measures local irregularities better and is commonly used in refractive surgery to detect suspect corneas.
- Refractive power map: IT is a map depicting the various points in diopteric power.
- Elevation Map (anterior and posterior elevation) maps that show the deviation of the examined surface from the utilised reference surface.
- Raw elevation data: It is the data which is not usually displayed in elevation base devices but used for calculations due to its lack of qualitative nature.
- Best fit surface: It is that surface that is used for generating elevation maps and can be manually or automatically fitted to the surface in question using different algorithms like float or apex fit.
- Best fit sphere: It is a spherical reference surface that best fits the measured surface by the different fitting algorithms.
- Float: It is an algorithm to fit the reference surface to the surface in question using minimum square difference.
- Apex fit: Is the constrained fitting of the reference surface with the center on the view axis and intersecting the examined surface on the axis.
- Wave front map: It is Zernike or a fourier analysis of the examined surface and is available in most of the topographer devices and helps in understanding higher order aberrations.
Above in [Figure 32], [Figure 33], [Figure 34], [Figure 35], [Figure 36] e. g. are given for exercise.
|Figure 33: Keratoconus map exemplifying the 4 point touch. In this figure, the thinnest point of the cornea coincides with the highest power on the tangential map and the most elevated point on the anterior and posterior surfaces. This is classical of ectatic disease|
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|Figure 34: This figure shows a front surface curvature map a corneal thickness map and front elevation map. Sagittal map shows nearly symmetric bowtie with minimal skewing of the axis which is also reflected on the elevation map. This is characteristics of the astigmatism|
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|Figure 35: Asymmetric bowtie with skewing of axes and steepening. This map shows central elevated area with asymmetric bowtie pattern and skewing of the radial axis AB (SRAX)|
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[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8], [Figure 9], [Figure 10], [Figure 11], [Figure 12], [Figure 13], [Figure 14], [Figure 15], [Figure 16], [Figure 17], [Figure 18], [Figure 19], [Figure 20], [Figure 21], [Figure 22], [Figure 23], [Figure 24], [Figure 25], [Figure 26], [Figure 27], [Figure 28], [Figure 29], [Figure 30], [Figure 31], [Figure 32], [Figure 33], [Figure 34], [Figure 35], [Figure 36]
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