Aberrometry and Topography in the Vector Analysis of Refractive Laser Surgery

Noel A. Alpins, FRACO FROOphth FACS Gemma Walsh, B.Optom

Refractive laser surgery techniques such as laser in situ keratomileusis (LASIK) and photorefractive keratectomy (PRK) are effective methods of treating spherical myopic errors up to 12D and hyperopic errors up to 6D, with good visual outcomes. However, generally more than half of the people who are suitable candidates for refractive surgery have enough astigmatism to warrant its inclusion in the surgical correction. As astigmatism has both direction and magnitude, its incorporation into the treatment makes planning more complex. It has been shown that vector analysis could likely improve the visual outcome of sphero-cylindrical treatments by combining the topographic and refractive astigmatic components to target a reduced level of corneal astigmatism compared to using refractive parameters alone. (1)(2)(5)

Measurement of Astigmatism

There are three differing categories of astigmatism; naturally occurring regular astigmatism, naturally occurring irregular astigmatism and secondary irregular astigmatism associated with ocular trauma, disease, infection or previous ocular surgery.(1) There are many different ways to measure astigmatism, some assessing corneal astigmatism only, and the others measuring refractive astigmatism including the internal optics of the eye. It is important in routine clinical practice to utilize more than one method in the pre-operative examination.

The manifest subjective refraction is a measure of the sphero-cylindrical correction required for the patient’s perception of their best vision. The principal contribution to the cylindrical error is the corneal astigmatism, but also includes astigmatism from the internal optics of the eye (such as the crystalline lens) as well as the interpretation of the image by the cerebral cortex. The measured result depends on many variables such as chart illumination and contrast, test distance and room lighting. The newer technology of wavefront analysis provides a spatially oriented refractive map of the pathway of light through the eye, which provides a greater amount of information on the refractive system than the manifest refraction data alone. It too includes the internal optics of the eye, but unlike subjective responses does not include the conscious percept of the cerebral cortex, thus giving no information regarding the non-optical interpretation of astigmatism images on the retina and visual cortex. This subjective value conventionally forms part of the ablative treatment and is an important component for patient satisfaction.

The application of wavefront analysis in the treatment plan is discussed further on.

Keratometry is a useful objective test to measure average corneal curvature at the paracentral region of the cornea. However, as it requires the manual alignment of optical mires to identify the steepest and flattest corneal meridian, there is a potential problem with reproducing reliable results due to variability between different observers. Corneal topography, or computer assisted videokeratography (CAVK), provides a more detailed quantified view of the corneal astigmatism displayed as a map based on the measurement of refractive power of thousands of separate points over the entire cornea. Average topographical astigmatism can be represented by a simulated keratometry value, which is a mean value derived from a number of constant reference points. It is a best fit compromise, and determined in various ways by the different types of topographers.

Surgical Planning ~ Refraction, Topography, or Both?

In an ideal world the goal of astigmatic refractive surgery is to completely eliminate astigmatism from the eye and its optical correction. However, it has since been recognized that this is not possible in the majority of cases due to the inherent differences between corneal astigmatism (represented by the simulated keratometry value from topography) and refractive astigmatism (represented by lower [second] order aberrations from aberrometry) correcting the eye.(4)(5) Most surgeons traditionally treat the refractive value alone based on the principle that treating what the patient perceives to give their best corrected vision will provide a superior visual outcome.

However, this is not necessarily the case. Disregarding the shape of the cornea while changing it flies in the face of the fundamental principles of corneal surgery. In fact, simple arithmetic analysis shows that an excessive amount of corneal astigmatism may be left if treatment is applied exclusively based on the parameters derived from the refractive cylinder magnitude and axis.(2)(3) This occurs because failing to align the maximum ablation closer to the flattest corneal meridian results in off-axis loss of effect when reducing corneal astigmatism. Consequently, lower (second) order astigmatic aberrations and (third order) coma would not be minimized, with more remaining than otherwise necessary.(1) This may result in post surgical symptoms such as reduced visual acuity and contrast sensitivity, creating difficulty with night driving and thus actually diminishing satisfaction in a proportion of patients.

As it becomes more widely recognized that a zero overall astigmatism is mostly unattainable, effective contemporary methods target astigmatism outcomes that combine both the refractive and topographic measurements in the analytical planning process. This should ensure the distribution of the remaining astigmatism to achieve the optimal outcome. That is, choosing a maximal treatment that leaves the minimum amount of astigmatism and in the most favorable orientation. With-the-rule astigmatism is more prevalent in the younger population undergoing laser vision correction, and is thought to be more visually tolerable to refractive perception than against-the-rule astigmatism (Javals rule). (3)(5)(8)

Vector Analysis by the Alpins Method

The surgical planning and analysis process is expedited by the implementation of computer and software technology. Calculations performed for the publication of this chapter utilized the ASSORT program developed by the first author (the Alpins Statistical System for Ophthalmic Refractive surgery Techniques). It employs the principles of vector planning and analysis(1)(2)(3)(4)(5)(6) and can utilize a paradigm that favors with-the-rule astigmatism that minimizes measurable postoperative refractive astigmatism quantified as second order aberrations.

The amount and axis of astigmatic change that the surgeon intends to induce is called the target induced astigmatism vector (TIA). This is determined by using an optimal combination of refractive and topographic data, as seen in the example later on. The surgically induced astigmatism vector (SIA) is the astigmatic change actually induced by the surgery. It is possible to determine whether the treatment was on-axis or off-axis, and also whether too much or too little treatment was applied by examining the various relationships between the SIA and TIA. The correction index (CI) is the ratio of the SIA to TIA and ideally is 1.0. An overcorrection occurs if the CI is greater than 1.0 and less than 1.0 for an undercorrection. The magnitude of error (ME) is the arithmetic difference between the magnitudes of the SIA and TIA. This is positive for overcorrections and negative for undercorrections. The angle of error (AE) is the angle contained by the SIA and TIA vectors. If the achieved correction is orientated counterclockwise (CCW) to where it was intended then the AE is positive. If the achieved correction is clockwise (CW) to the intended axis then the AE is negative.

An absolute measure of success of the surgery is described by the difference vector (DV). This is the induced astigmatic change that would enable the initial surgery to achieve its intended target, and is ideally zero. The DV is a useful dioptric measure of uncorrected astigmatism. A relative measure of success is the Index of success (IOS) which is calculated by dividing the DV by the intended change, the TIA. This is also preferably zero.

As previously mentioned, the corneal and refractive astigmatisms are rarely equivalent. This difference may be represented vectorially by the ocular residual astigmatism (ORA).(9) In other words, the ORA is the noncorneal component of total refractive astigmatism, and quantifies by magnitude and axis orientation the minimum intraocular second order astigmatism aberrations. It is also the amount of corneal astigmatism expected to remain after treatment guided by refractive values alone, to neutralize this intraocular astigmatism.

Aberrometry and Wavefront Guided Treatment

Wavefront technology has added new understanding of the eye’s refractive characteristics. It offers theoretical guidance to reduce spherical aberrations by achieving the most effective prolate aspheric profile and appears to be successful in this endeavor in the initial treatment studies. However, wavefront-assisted LASIK does not address the amount of resultant corneal astigmatism, and therefore is similar to LASIK based on manifest refraction. In addition, as aberrometry includes the internal optics of the eye in its calculations, any changes over time to the crystalline lens may undermine any benefit gained from the wavefront ablation.(1)(7)

Furthermore, if wavefront guided ablation corrects all ocular aberrations at the corneal surface, it would produce an uneven corneal treatment resulting in induced corneal irregularities. This might be an undesirable result when it is widely recognized that a regular cornea with orthogonal and symmetrical astigmatism gives a superior visual result.(1)(6) Permanently changing regional corneal shape in this manner is also complicated by the fact that this form of treatment may in fact be neutralized by epithelial healing.(7)

While wavefront guided ablation may not be the path to “super vision” as it was first thought to be, it does provide useful refractive information. Rather than employing wavefront data exclusively, it can be combined with the vector planning method described in this chapter to produce an optimal treatment with reduced post surgical aberrations.

Combining Wavefront Analysis and Topography with Vector Planning

A typical wavefront analysis is depicted in Figure 1. The sphero-cylindrical refraction as measured by the wavefront device at the spectacle plane is +0.52/-1.83×3. The two dimensional illustration of the wavefront analysis on the left shows a moderate level of mixed astigmatism with a typical saddle appearance. The higher order spherical aberrations are quantified as root-mean-square values in the lower right hand corner of the display. The spherical component of the correction (+0.52) is shown as the defocus. The cylindrical component is displayed beneath this. Third order aberrations (coma and trefoil) are listed separately, with 4th order spherical aberrations. ‘Other terms’ indicates 5th order and higher order aberrations.

Figure 2 displays a topographical map of the matching astigmatic eye. The typical bow-tie appearance of the regular corneal astigmatism is evident. In this example the astigmatism measures 2.62 D at the steepest meridian of 96 degrees as quantified by the simulated keratometry values. These parameters can then be examined together with those from the wavefront analysis spherocylindrical (second order) values to produce an optimal treatment by using the Alpins method contained in the ASSORT program. This is shown in the treatment planning screen in Figure 3. In this diagram the treatment has been set to a base of 100% emphasis for correction of refractive astigmatism parameters.

This treatment screen in Figure 3 has been disassembled further for ease of understanding the various components. Figure 4 is the top central section on the ASSORT treatment screen, displaying the preoperative sphero-cylindrical refractive values taken from the wavefront analysis and also the corneal plane conversion. The cylindrical component here is 1.81D of astigmatism at axis 3. This figure also displays the sphero-cylindrical target for the treatment, which in this case is zero.

The treatment vector being employed is shown in the polar diagram in Figure 5. Here the TIA is 1.81D at axis 3. The pre-and-post operative target astigmatism values are shown in Figure 6. The post-operative refractive target value is zero with the target corneal astigmatism value (obtained from Figure 7 below) displayed in blue.

The simulated keratometry values from the preoperative topographical map are shown in Figure 7. Also displayed here are the ORA and the target for the corneal postoperative astigmatism. A vectorial calculation is used to determine the ORA, which in this case is 0.84 D. That is, there is a calculated amount of 0.84 D of intraocular astigmatism that cannot be eliminated from this eye. As the sphero-cylindrical refractive target has already been guided to zero, this can only leave the whole of the remaining astigmatism on the cornea at a near vertical meridian of 103 degrees to neutralize the ORA 90 degrees away, as seen in the target value of Figure 7.

However, as the emphasis is shifted towards the left, the treatment is more closely aligned to the principal corneal meridian. Figure 8 shows the optimal treatment for this eye, with the emphasis placed at 33% topography and 67% refraction. The ORA is still 0.84 D, but now it is apportioned between the refraction and the cornea. Here less corneal astigmatism is targeted and has been reduced to 0.56D at an unchanged meridian 103 (Figure 9). The remaining 0.28 D which is included in the sphero-cylindrical target of a spherical equivalent of zero, is not necessarily detected by the perceptive system at these levels, particularly as it is orientated favorably towards with-the-rule. Thus, with this method of vectorial planning, although the targeted sphero-cylindrical outcome is not zero, but 0.14/-0.28×103 as displayed in Figure 10, the measured postoperative refractive and wavefront astigmatism is likely to be negligible.

 

Despite not targeting a zero sphero-cylindrical outcome, by directing the remaining astigmatism away from the cornea the overall astigmatism is also less, and there are fewer aberrations remaining. This treatment results in an overall higher patient satisfaction.

Treatment of Irregular Astigmatism

Differences in the two opposite superior and inferior hemidivisions of the corneal topographical contour map are widely prevalent. This is known as irregular astigmatism and occurs if the two sides of the bow-tie representation differ in magnitude (asymmetrical) or are not aligned at 180 degrees to each other (nonorthogonal), or most commonly a combination of the two.(1)(6) Irregular astigmatism may also be identified optically using wavefront devices. Unlike other methods of astigmatism analysis, the method described in this chapter may theoretically also be applied independently to each hemidivision in a cornea displaying pre-existing idiopathic irregularity. This would theoretically allow analysis and treatment of this irregular astigmatism to produce an orthogonal, symmetrical cornea.

The target refractive and corneal astigmatism values must be considered separately for each hemimeridian, with individual treatment plans required for both the superior and inferior topographic magnitudes and meridian values with the common refractive astigmatism value. From this, minimum target astigmatism values may be calculated for each part of the cornea, and their orientations are used to guide the choice for the optimal TIA for that side.(6)

The vectorial difference between the two opposite semimeridian values for magnitude and axis in each corneal part is called the topographic disparity (TD). When displayed on a 720 degree double-angle vector diagram, the TD quantifies the irregular astigmatism of the cornea in dioptres, and the treatment required to reduce or eliminate the irregular astigmatism can be determined from this.(6)

The information gained from computerized topography regarding the corneal height (either directly such as the Z dimension on the Orbscan device, or indirectly inferred from slope measurement) may be translated into planned tissue ablation patterns using the Munnertyn formula. This ablative pattern may then be applied at specific points on the corneal surface to reduce the irregularity.(1) There are various methods to link topographical information with tailored ablation, though a real time preoperative link is yet to be achieved.

In this way, the corneal shape may be manipulated by asymmetrical surgical treatment to the irregular hemidivisions of the cornea, allowing the achievement of any corneal shape (thus producing regular astigmatism where selected). In cases of irregular astigmatism a rearrangement rather than a reduction of the corneal astigmatism may be of benefit, as regularizing the cornea may improve best corrected visual acuity to better approach the goal of supernormal vision.

Summary

Due to natural differences in the vast majority of eyes between total astigmatism as measured by refraction and corneal astigmatism, it is impossible to completely eliminate astigmatism from the eye’s optical system and its correction. It can therefore be beneficial to combine both these elements when considering the plan for refractive laser surgery to produce an optimal, individualized outcome. If the treatment plan utilizes manifest refraction data alone, it may actually increase the postoperative aberrations, thereby reducing the final visual result.

The Alpins method of vector planning utilizes information from both corneal topography and manifest refraction/wavefront data to target less postoperative corneal astigmatism and minimize postoperative aberrations. Though this often means that the postoperative refractive astigmatism target is not zero, this minor refractive error (with a spherical equivalent of zero) that remains postoperatively in a favorable orientation may not be significant enough for patient perception. In fact, overall the patient satisfaction is potentially higher due to the lesser amount of lower order aberrations.

This method of vector planning and analysis may also be used to optimize treatment for each separate hemimeridian of the cornea in cases of irregular astigmatism. This would enable the surgeon to rearrange the corneal astigmatism and regularize the cornea, thus producing a potential increase in the best corrected visual acuity. Though a real time preoperative link to the topographical and wavefront information for this specialized ablation is yet to be formed, this integration of these diagnostic modalities utilizing vector planning may be a reality in the future.

REFERENCES

1. Goggin M, Alpins N, Schmid, L, Management of irregular astigmatism. Current Opinion in Ophthalmology 2000, 11:260-266
2. Alpins, NA. Astigmatism by the Alpins Method. J Cataract Refract Surg 2001; 27:31-49
3. Croes, KJ. The Alpins Method: A breakthrough in astigmatism analysis. Medical Electronics, September 1998
4. Alpins, NA. A new method of analyzing vectors for changes in astigmatism. J Cataract Refract Surg 1993; 19: 524-533
5. Alpins, NA. New method of targeting vectors to treat astigmatism. J Cataract Refract Surg 1997; 23:65-75
6. Alpins, NA. Treatment of irregular astigmatism. J Cataract Refract Surg 1998; 24:634-646
7. Alpins, NA. Wavefront technology: A new advance that fails to answer old questions on corneal vs refractive astigmatism correction. J of Refractive Surg; November/December 2002: 737-39 Discusses wavefront technology and the benefits of incorporating it into the refractive laser surgery plan.
8. Javal, E. Memoirs d’Ophthalmometrie. 1890, G Masson, Paris
9. Duke-Elder, S, ed. System of Ophthalmology. Vol 5: Ophthalmic optics and refraction. St Louis, Mosby, 1970: 275-278

Dr. Noel Alpins FRACO. FROOphth. FACS
Medical Director NewVision Clinics Melbourne
Founding Member, Melbourne University Excimer
Laser Group; Protocol and Ethics Committee.
Published widely-Techniques for Treatment and Analysis of Astigmatism.
Developer: ASSORT Computer Program Cataract & Refractive Surgery Planning and Outcomes

Gemma Walsh, B.Optom.
University of Melbourne;
Senior Optometrist
New Vision Clinics, Melbourne, Australia.
Postgraduate Diploma in Advanced Clinical Optometry.

Dr Alpins has a financial interest in the ASSORT ® program used in this chapter for calculating treatment parameters.