Kenneth J. Hoffer

The Hoffer Q formula: A comparison of theoretic and regression formulas

ABSTRACT A new formula, the Hoffer Q, was developed to predict the pseudophakic anterior chamber depth (ACD) for theoretic intraocular lens (IOL) power formulas. It relies on a personalized ACD, axial length, and corneal curvature. In 180 eyes, the Q formula proved more accurate than those using a constant ACD (P < .0001) and equal (P = .63) to those using the actual postoperative measured ACD (which is not possible clinically). In 450 eyes of one style IOL implanted by one surgeon, the Hoffer Q formula was equal to the Holladay (P =.65) and SRK/T (P =.63) and more accurate than the SRK (P <.0001) and SRK II (P =.004) regression formulas using optimized personalization constants. The Hoffer Q formula may be clinically more accurate than the Holladay and SRK/T formulas in eyes shorter than 22.0 mm. Even the original nonpersonalized constant ACD Hoffer formula compared with SRK I (using the most valid possible optimized personal A‐constant) has a better mean absolute error (0.56 versus 0.59) and a significantly better range of IOL prediction error (3.44 diopters [D] versus 7.31 D). The range of error of the Hoffer Q formula (3.59 D) was half that of SRK 1(7.31 D). The highest IOL power errors in the 450 eyes were in the SRK II (3.14 D) and SRK I (6.14 D); the power error was 2.08 D using the Hoffer Q formula. The series using overall personalized ACD was more accurate than using an axial length subgroup personalized ACD in each axial length subgroup. The results strongly support replacing regression formulas with third‐generation personalized theoretic formulas and carefully evaluating the Holladay, SRK/T, and Hoffer Q formulas.

Biometry of 7,500 Cataractous Eyes

Summary This biometric analysis of 7,500 eyes of cataract patients gave a mean axial length of 23.65 mm, a mean average keratometric value of 43.81 diopters, a mean preoperative anterior chamber depth of 3.24 mm, and a mean central endothelial cell count of 2,470 cells/mm 2 . There is a statistically significant but clinically insignificant 0.16-diopter flattening of the cornea after cataract surgery without an intraocular lens, but none with an intraocular lens. Pseudophakic eyes do not show a clinically significant increase in corneal flattening over aphakic eyes. Anterior chamber depth increases from 3.24 mm to 3.32 mm (±0.08) in pseudophakic eyes and to 3.67 mm (±0.43) in aphakic eyes. Astigmatism averaged 1.0 diopter in phakic eyes preoperatively, showing a mean increase of only 0.5 diopter in aphakic eyes and 0.65 diopter in pseudophakic eyes. One third of the eyes in this series had axial myopia while slightly less than half had axial hyperopia; the remaining 20% were in the emmetropic range. Preoperative anterior chamber depths were lowest in eyes with short axial lengths and increased with axial length. However, deep (6 mm) and shallow (2 mm) anterior chamber depths were encountered in all three groups. Shorter eyes had steeper corneas than emmetropic eyes by less than 1.0 diopter while myopic eyes had weaker corneas than emmetropic eyes by about 0.5 diopter. Astigmatism was essentially the same in all three groups (1.0 diopter) except that emmetropic eyes showed a small (0.08 diopter) but statistically significant decrease in cylinder from the other groups, as well as a smaller range (6.3 vs. 9.5 diopters). There is a very small but extremely significant increase in endothelial cell count from hyperopic to myopic eyes. There is little correlation between fellow eyes for axial length, average keratometric value, or anterior chamber depth, indicating the need for bilateral examination in calculating intraocular lens power. All other possible correlations of these data were not statistically significant.

Clinical results using the Holladay 2 intraocular lens power formula.

PURPOSE To analyze the accuracy of the Holladay 2 formula, which has been proposed as an improvement over the original Holladay formula. METHODS This retrospective analysis comprised 317 eyes operated on by 1 surgeon using 1 technique and 1 intraocular lens style in a specialty practice. Because the Holladay 2 formula has yet to be published, its accuracy can only be analyzed using the commercially available Holladay IOL Consultant computer program to compare it to the Holladay 1, Hoffer Q, and SRK/T formulas. Defined axial length ranges were analyzed individually. RESULTS A lower mean absolute error (MAE) trend was found for the average length eye (22.0 to 24.5 mm) by the Holladay 1 and Hoffer Q formulas. For short eyes (< 22.0 mm), the Hoffer Q and Holladay 2 perform better. The SRK/T consistently showed a trend toward the lowest MAE in all long eyes (>24.5 mm) as well as the subdivisions of medium long (24.5 to 26.0 mm) and very long (>26.0 mm). The Holladay 2 trended toward the least accurate (MAE) of the 4 formulas in all ranges of axial length except the shortest and the very longest. It appears to perform poorer in average and medium long eyes. CONCLUSIONS Although the Holladay 2 formula has improved its MAE accuracy in short eyes, it was not more accurate than the Hoffer Q. The changes made in the formula to effect this improvement in MAE seem to have sacrificed the accuracy of the original Holladay formula in eyes with average and medium long axial lengths.

Intraocular lens power calculation for eyes after refractive keratotomy

BACKGROUND Calculating the intraocular lens (IOL) power for an eye that has previously had refractive keratotomy is a problem because of the difficulty of accurately measuring the central power of the cornea using standard keratometers. METHODS Three methods are proposed to better estimate this parameter. The clinical history method involves subtracting the change in myopia induced by the refractive keratotomy from the average corneal power measured before the keratotomy. The contact lens method determines the difference between the manifest refraction with and without a plano hard contact lens of known base curve and subtracts this difference from that base curve. Videokeratography measures the central corneal power inside the approximately 3-mm zone measured by keratometry, and therefore gives a more accurate power to use in IOL calculation formulas, especially with newer software applications becoming available. RESULTS Published reports have demonstrated that standard keratometers do not accurately measure corneal power after refractive keratotomy and that regression formulas are less accurate than modern third-generation theoretic formulas for eyes that have flatter corneas from refractive surgery. CONCLUSION For eyes that have had refractive surgery, the corneal power derived from clinical history, contact lens refraction, or videokeratography should be used in a third-generation theoretic formula (Hoffer Q, Holladay, SRK/T) to calculate the intraocular lens power used during cataract surgery.

Repeatability of automatic measurements by a new Scheimpflug camera combined with Placido topography

PURPOSE: To assess the repeatability of anterior segment measurements performed by a Scheimpflug camera combined with Placido corneal topography (Sirius) in unoperated, post‐refractive surgery, and keratoconus eyes. SETTING: Private clinical ophthalmology practice. DESIGN: Evaluation of diagnostic test or technology. METHODS: Three consecutive scans were acquired for each eye. The following parameters were evaluated: simulated keratometry, posterior corneal power, mean pupil power (ie, corneal power assessed by ray tracing through the anterior and posterior corneal surfaces), corneal asphericity, thinnest and apex corneal thickness, aqueous depth, anterior chamber volume, and corneal spherical aberration. Repeatability was assessed using test–retest variability, the coefficient of variation, and the intraclass correlation coefficient (ICC). RESULTS: Sixty‐four unoperated eyes, 17 eyes that had myopic excimer laser surgery, and 13 eyes with keratoconus were analyzed. High repeatability was achieved for most parameters in the 3 groups, with an ICC higher than 0.99 for all measurements except posterior corneal power and mean pupil power in keratoconus (ICC, 0.868 and 0.976, respectively), anterior and posterior asphericity in normal eyes (ICC, 0.904 and 0.977, respectively), and spherical aberration in normal eyes (ICC, 0.806), post‐refractive surgery eyes (ICC, 0.980), and keratoconus eyes (ICC, 0.981). CONCLUSION: The anterior segment measurements provided by the new Scheimpflug camera–Placido corneal topography system were highly repeatable and can be relied on in clinical routine and for research purposes. Financial Disclosure: No author has a financial or proprietary interest in any material or method mentioned.

Comparison of 2 laser instruments for measuring axial length.

PURPOSE: To compare axial length (AL), anterior chamber depth (ACD), and keratometric (K) measurements of 2 laser biometers. SETTING: Private practices, Lynwood and Santa Monica, California, USA. METHODS: In this prospective comparative observational study of eyes with cataract and eyes with a clear lens, AL, ACD, and K measurements were performed using an IOLMaster biometer, which uses partial coherence interferometry (PCI), and a Lenstar LS 900 biometer, which uses optical low‐coherence reflectometry (OLCR). Intraocular lens (IOL) power calculation was performed using the Haigis formula. The IOL prediction error was calculated for each eye. RESULTS: The study evaluated 50 eyes with cataract and 50 eyes with a clear lens. There was a good correlation between AL, ACD, and K measurements in the cataractous eyes (r = 0.9993, 0.9667, and 0.9959, respectively) and in eyes with a clear lens (r = 0.9995, 0.8211, and 0.9959, respectively). The OLCR unit measured a slightly longer AL in the cataract group and clear lens group (mean difference 0.026 mm and 0.023 mm, respectively), a deeper ACD (0.128 mm and 0.146 mm, respectively), and a flatter K (−0.107 diopter [D] and −0.121 D, respectively). The differences were statistically significant (P<.0001). The mean absolute error in IOL power prediction was 0.455 D ± 0.32 (SD) with the OLCR unit and 0.461 ± 0.31 D with the PCI unit (P>.1). CONCLUSIONS: Measurements were comparable between the OLCR device and the PCI device. A slight decrease (0.050) in the a0 constant is recommended if the Haigis formula is used. Financial Disclosure: No author has a financial or proprietary interest in any material or method mentioned.

Repeatability of automatic measurements performed by a dual Scheimpflug analyzer in unoperated and post-refractive surgery eyes

PURPOSE: To assess the repeatability of the anterior segment measurements performed with a dual Scheimpflug analyzer (Galilei) in unoperated and post‐refractive surgery eyes. SETTING: Private practice. DESIGN: Evaluation of diagnostic test. METHODS: Three consecutive scans were acquired in unoperated eyes and in eyes that had excimer laser surgery for myopia. Unoperated eyes were enrolled from 3 subgroups: younger than 50 years, aged between 50 and 70 years, and older than 70 years. The following parameters were evaluated: simulated keratometry, posterior corneal power, total corneal power, anterior and posterior best‐fit sphere radius, mean and thinnest central corneal thickness, anterior chamber depth and volume, horizontal and vertical corneal diameter, iridocorneal angle in the 4 quadrants, and corneal spherical aberration. Repeatability was assessed using analysis of variance (ANOVA), the coefficient of variation (COV), intraclass correlation (ICC), and test–retest variability. RESULTS: The study evaluated 45 unoperated eyes (n = 45) and 15 post‐refractive surgery eyes (n = 15). Each age subgroup in the unoperated group comprised 15 eyes. The ANOVA did not detect significant differences between the 3 measurements for any parameter. The COV was less than 0.5% for corneal power measurements and less than 3.5% for all remaining parameters except spherical aberration (16.68%). The ICC was more than 0.99 for corneal power measurements and more than 0.94 for all remaining parameters. CONCLUSIONS: The anterior segment measurements provided by the dual Scheimpflug analyzer were highly repeatable. Repeatability did not change with age or after myopic photorefractive keratectomy or laser in situ keratomileusis. Financial Disclosure: No author has a financial or proprietary interest in any material or method mentioned.

Intraoperative optical refractive biometry for intraocular lens power estimation without axial length and keratometry measurements

PURPOSE: To correlate intraoperative aphakic autorefraction to conventional emmetropic intraocular lens (IOL) calculations and derive an empiric predictive model for IOL estimation based on optical refractive biometry without axial length and keratometry measurements. SETTING: Institutional Review Board of the University of Southern California, Los Angeles County General Hospital, Los Angeles, California, USA. METHODS: A pilot group of 22 eyes of 22 patients scheduled for cataract surgery were enrolled in a prospective trial. All patients had a standard preoperative workup with subsequent cataract extraction and IOL implantation according to conventional biometric measurements and IOL calculations. Intraoperative autorefractive retinoscopy was used to obtain aphakic autorefraction and to measure the aphakic spherical equivalent before lens implantation. A linear regression analysis was used to correlate the aphakic spherical equivalent to the final adjusted emmetropic IOL power to empirically derive a refractive formula for IOL calculation (optical refractive biometry method). A second validation series of 16 eyes was used in a head‐to‐head comparison between the optical refractive biometry and the conventional IOL formulas. A subset of 6 eyes from the validation series were post‐refractive cases having subsequent cataract surgery. RESULTS: Intraoperative retinoscopic autorefraction was successfully obtained in all 22 patients in the pilot group and all 16 patients in the validation group. The spherical equivalent of the aphakic autorefraction correlated linearly with the final adjusted emmetropic IOL power (P<.0001, with adjusted r2 = .9985). The relationship was sustained over an axial length range of 21.43 to 25.25 mm and an IOL power range of 12.0 to 25.5 diopters (D). In a subsequent validation series of 10 standard and 6 post‐laser in situ keratomileusis (LASIK) cataract cases, the optical refractive biometry method proved to be a better predictive model for IOL estimation than conventional formulas; 83% of the LASIK eyes and 100% of the normal eyes were within ±1.0 D of the final IOL power when aphakic autorefraction was used, compared with 67% of LASIK eyes and 100% of the normal eyes, using the conventional methodology. CONCLUSIONS: A new model for IOL power calculation was derived based on an optical refractive methodology that breaks away from the conventional art introduced by Fyodorov in the 1960s. A purely refractive algorithm is used to predict the power of the IOL at the time of surgery without the need for axial length and keratometry measurements. This method bypasses some limitations of conventional biometry and shows promise in the post‐refractive cataract cases.

Comparison of anterior segment measurements by 3 Scheimpflug tomographers and 1 Placido corneal topographer.

PURPOSE: To compare the anterior segment measurements provided by 3 Scheimpflug tomographers and a Placido corneal topographer. SETTING: Private clinical ophthalmology practice. DESIGN: Evaluation of diagnostic test or technology. METHODS: In a sample of 25 consecutive patients having either refractive or cataract surgery, the anterior eye segment was analyzed by means of a rotating Scheimpflug camera (Pentacam), 2 devices with a Scheimpflug camera combined with a Placido disk (Sirius and TMS‐5), and a Placido disk corneal topographer (Keratron). Measurement results were compared using analysis of variance. Agreement was assessed using Bland‐Altman plots. RESULTS: The mean simulated keratometry (K) was different between the 4 instruments (P<.0001), with Keratron providing the highest value (44.43 diopters [D] ± 1.28 [SD]). The Pentacam and Sirius provided the lowest values (44.05 ± 1.21 D and 44.05 ± 1.27 D, respectively), without statistical difference (posttest). The mean posterior corneal power and minimum corneal thickness were statistically different between the 3 Scheimpflug cameras (P<.0001 and P=.0210, respectively); 95% limits of agreement, however, were narrow for posterior corneal power and large for corneal thickness. The only 2 devices measuring the distance between the corneal endothelium and the anterior lens surface showed a statistically but not clinically significant difference (2.90 ± 0.48 mm and 2.94 ± 0.47 mm, respectively). There were no statistically significant differences in anterior corneal asphericity between the 4 instruments. CONCLUSION: Although the measurements of some parameters by different instruments were similar, caution is warranted before using them interchangeably. Financial Disclosure: No author has a financial or proprietary interest in any material or method mentioned.

Intraocular lens power calculation after previous laser refractive surgery

Methods to attempt more accurate prediction of intraocular lens power in refractive surgery eyes are many, and none has proved to be the most accurate. Until one is identified, a spreadsheet tool is available and can be used. It automatically calculates all the methods for which data are available on a single sheet for the patients chart. The various methods and how they work are described.