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Chord mu: a new reference marker and its clinical relevance
It denotes two-dimensional displacement of the entrance of the pupil center from the subject-fixated coaxially sighted corneal light reflex.
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Angle kappa has long been a point of consideration for adequate centration of multifocal IOLs. Good centration is important to maximize the visual quality and minimize the visual side effects. Proper centration of multifocal IOLs has always been a point of contention as the successful outcome of the surgery depends on it. There are some patients who undergo a successful multifocal IOL implantation and are unhappy despite good Snellen visual acuity. This has been attributed to a comparative decrease in contrast sensitivity along with the appearance of halos and glare. Clinically, the centration of a multifocal IOL is checked with its concentricity of the rings to the pupil but rarely an effort is made to check its alignment with the visual axis.
Various ocular axes and angles have been defined to explain the concept, and it is essential to understand the reasoning behind all of these concepts.
Source: Priya Narang, MS, and Amar Agarwal, MS, FRCS, FRCOphth
Optical axis has been defined as a line that connects all four Purkinje images that originate from a coaxial source of light (Figure 1), whereas line of sight passes through the fixation point to the center of the entrance of the pupil (Figure 2). The visual axis connects the point of fixation with nodal points and the fovea, whereas the pupillary axis is defined as a line perpendicular to the surface of cornea that passes through the center of the entrance of the pupil (Figure 3).
Measurement of chord mu
As suggested by Chang and colleagues, chord mu is considered to be the new reference marker. It denotes two-dimensional displacement of the entrance of the pupil center from the subject-fixated coaxially sighted corneal light reflex.
The value of chord mu (µ) can be calculated with the help of an IOLMaster (Zeiss), Lenstar (Haag-Streit), Pentacam (Oculus) or another device. With a mathematical calculation using the x and y coordinates of the pupillary axis and with the application of Pythagoras formula, the chord length can be obtained by the square root of the sum of the squares of the x and y coordinates: C = (x2 + y2). The resultant value C denotes the value of chord mu.
Clinical significance
The importance and clinical application of chord mu along with the concept of actual and apparent chord mu have been clearly delineated by Jack Holladay. The values of chord mu change as the frame of reference moves from the corneal plane to the iris-lens plane. The IOLMaster measures the apparent chord mu, whereas Pentacam and OCT measure the actual chord mu. The apparent chord mu is contemplated to be the distance between Purkinje image 1 and the apparent pupil center when viewed coaxially from the light source at the cornea. The mean apparent chord mu has been calculated as 0.3 ± 0.15 mm. Actual chord mu is the actual distance between the visual axis and the pupil center, which is less because it is not magnified by the cornea. The values of actual chord mu range from 0.2 ± 0.11 mm.
Peer studies have put forward that apparent chord values greater than 0.6 mm and actual values greater than 0.42 mm are suggestive of a higher incidence of glare and halos with diffractive multifocal IOLs. The placement of an IOL is ideal if it is placed on the visual axis with the pupillary center or in between them, and this happens when the chord mu is minimal.
Multifocal IOLs should be avoided in patients with large chord mu and higher-order root mean square corneal wavefront error greater than 0.5 mm over a 6-mm zone. A study by McCormick depicted that the average higher-order root mean square wavefront error for a normal cornea was 0.38 ± 0.14 µm over a 6-mm zone.
Angle kappa and chord mu
Angle kappa is the angular value between the pupillary axis and the visual axis (Figure 4), whereas chord mu is the two-dimensional distance between the center of the pupil and the subject-fixated coaxially sighted corneal light reflex (Figure 5). The mean value of angle kappa has been determined to be 3° ± 0.13°, and values greater than 3.26° are considered to be abnormally high. In cases with high astigmatism and hypermetropia, these values are often reported to be 10° or more. The chord length values are reported in millimeters or microns, and a standard conversion formula of 1 mm to 7.5° can be applied when measured along the surface of the cornea.
PPP and pinhole optics
Pinhole pupilloplasty (PPP) is a surgical maneuver performed in cases of higher-order aberrations, and it has been documented to enhance the visual potential by inducing a pinhole effect. The pupillary aperture is targeted to be 1.5 mm. Studies have documented that with the decrease in the size of the pupillary aperture, the chord mu values also decrease.
In PPP, coaxially sighted corneal light reflex was employed, and the Purkinje 1 reflex emanating from the coaxial tube of a Lumera microscope was enveloped by the pupillary margin. Ideally, a subject-fixated coaxial light reflex should be employed, but as the PPP procedure was performed under local anesthesia a coaxially sighted corneal light reflex was employed.
- References:
- Basmak H, et al. J Refract Surg. 2007;doi:10.3928/1081-597X-20070501-06.
- Brodie SE. Invest Ophthalmol Vis Sci. 1987;28(4):736-742.
- Chang DH, et al. Am J Ophthalmol. 2014;doi:10.1016/j.ajo.2014.06.028.
- Holladay JT. J Cataract Refract Surg. 2019;doi:10.1016/j.jcrs.2019.03.029.
- Holladay JT, et al. J Cataract Refract Surg. 2017;doi:10.1016/j.jcrs.2016.11.049.
- McCormick GJ, et al. Ophthalmology. 2005;doi:10.1016/j.ophtha.2005.04.022.
- Narang P, et al. J Cataract Refract Surg. 2019;doi:10.1016/j.jcrs.2018.12.007.
- Narang P, et al. J Cataract Refract Surg. 2019;doi:10.1016/j.jcrs.2019.02.037.
- For more information:
- Amar Agarwal, MS, FRCS, FRCOphth, is director of Dr. Agarwal’s Eye Hospital and Eye Research Centre. Agarwal is the author of several books published by SLACK Incorporated, publisher of Ocular Surgery News, including Phaco Nightmares: Conquering Cataract Catastrophes, Bimanual Phaco: Mastering the Phakonit/MICS Technique, Dry Eye: A Practical Guide to Ocular Surface Disorders and Stem Cell Surgery and Presbyopia: A Surgical Textbook. He can be reached at 19 Cathedral Road, Chennai 600 086, India; email: aehl19c@gmail.com; website: www.dragarwal.com.
- Priya Narang, MS, can be reached at Narang Eye Care & Laser Centre, Ahmedabad, India; email: narangpriya19@gmail.com.
Disclosures: Agarwal and Narang report no relevant financial disclosures.