A New Method to Minimize the Standard Deviation and Root Mean Square of the Prediction Error of Single-Optimized IOL Power Formulas.

Purpose: The purpose of this study was to develop a simplified method to approximate constants minimizing the standard deviation (SD) and the root mean square (RMS) of the prediction error in single-optimized intraocular lens (IOL) power calculation formulas. Methods: The study introduces analytical formulas to determine the optimal constant value for minimizing SD and RMS in single-optimized IOL power calculation formulas. These formulas were tested against various datasets containing biometric measurements from cataractous populations and included 10,330 eyes and 4 different IOL models. The study evaluated the effectiveness of the proposed method by comparing the outcomes with those obtained using traditional reference methods. Results: In optimizing IOL constants, minor differences between reference and estimated A-constants were found, with the maximum deviation at -0.086 (SD, SRK/T, and Vivinex) and -0.003 (RMS, PEARL DGS, and Vivinex). The largest discrepancy for third-generation formulas was -0.027 mm (SD, Haigis, and Vivinex) and 0.002 mm (RMS, Hoffer Q, and PCB00/SN60WF). Maximum RMS differences were -0.021 and +0.021, both involving Hoffer Q. Post-minimization, the largest mean prediction error was 0.726 diopters (D; SD) and 0.043 D (RMS), with the highest SD and RMS after adjustments at 0.529 D and 0.875 D, respectively, indicating effective minimization strategies. Conclusions: The study simplifies the process of minimizing SD and RMS in single-optimized IOL power predictions, offering a valuable tool for clinicians. However, it also underscores the complexity of achieving balanced optimization and suggests the need for further research in this area. Translational Relevance: The study presents a novel, clinically practical approach for optimizing IOL power calculations.

Impact of Single Constant Optimization on the Precision of IOL Power Calculation.

Purpose: The primary objective of this research is to examine how precision in intraocular lens calculation formulas can be impacted by zeroing the mean error through adjustments in the effective lens position value. Additionally, the study aims to evaluate how this modification influences outcomes differently based on the source of the prediction error. Methods: In order to analyze the impact of individual variables on the standard deviation, the study maintained all variables constant except for one at a time. Subsequently, variations were introduced to specific parameters, such as corneal curvature radius, keratometric refractive index, axial length, and predicted implant position. Results: According to our findings, when zeroing the mean error is applied to correct for inaccuracies in corneal power estimation, it results in a significant and exponential rise in standard deviation, thus adversely affecting the formula's precision. However, when zeroing is employed to compensate for prediction errors stemming from axial length measurements or predicted implant position, the effect on precision is minimal or potentially beneficial. Conclusions: The study highlights the potential risks associated with the indiscriminate but necessary zeroing of prediction errors in implant power calculation formulas. The impact on formula precision greatly depends on the source of the error, underscoring the importance of error source when analyzing variations in the standard deviation of the prediction error after zeroing. Translational Relevance: Our study contributes to the ongoing effort to enhance the accuracy and reliability of these formulas, thereby improving the surgical outcomes for cataract patients.

Theoretical Impact of Intraocular Lens Design Variations on the Accuracy of IOL Power Calculations.

To ascertain the theoretical impact of optical design variations of the intraocular lens (IOL) on the accuracy of IOL power formulas based on a single lens constant using a thick lens eye model. This impact was also simulated before and after optimization. We modeled 70 thick-lens pseudophakic eyes implanted with IOLs of symmetrical optical design and power comprised between 0.50 D and 35 D in 0.5-step increments. Modifications of the shape factor resulting in variations in the anterior and posterior radii of an IOL were made, keeping the central thickness and paraxial powers static. Geometry data from three IOL models were also used. Corresponding postoperative spherical equivalent (SE) were computed for different IOL powers and assimilated to a prediction error of the formula due to the sole change in optical design alone. Formula accuracy was studied before and after zeroization on a uniform and non-uniform realistic IOL power distribution. The impact of the incremental change in optic design variability depended on the IOL power. Design modifications theoretically induce an increase in the standard deviation (SD), Mean Absolute Error (MAE), and Root Mean Square (RMS) of the error. The values of these parameters reduce dramatically after zeroization. While the variations in optical design can affect refractive outcomes, especially in short eyes, the zeroization of the mean error theoretically reduces the impact of the IOL's design and power on the accuracy of IOL power calculation.

A Simplified Method to Minimize Systematic Bias of Single-Optimized Intraocular Lens Power Calculation Formulas.

PURPOSE: To provide a simplified method to optimize lens constants to zero the mean prediction error (ME) of an intraocular lens (IOL) calculation formula, without the need to program the formula itself, by exploring the influence of IOL and corneal power on the refractive impact of variations in effective lens position. DESIGN: Theoretical development of an optimized formula and retrospective clinical evaluation on documented datasets. METHODS: Retrospective data from 8878 patients with cataracts with pre- and postoperative measurements available using 4 IOL models and 6 IOL power calculation formulas were examined. A schematic eye model was used to study the impact of small variations in effective lens position (ELP) on the postoperative spherical equivalent (SE) refraction. The impact of keratometry (K) and IOL power (P) on SE was investigated. A theoretical thick lens model was used to devise a formula to zero the average prediction error of an IOL power calculation formula. This was achieved by incrementing the predicted ELP, which could then be translated into an increment in the IOL constant. This method was tested on documented real-life postoperative datasets, using different IOL models and single-constant optimized IOL calculation formulas. RESULTS: For small variations in ELP, there was an exponential relationship between IOL power and the resultant postoperative refractive variation. The ELP adjustment necessary to zero the ME equated to a ratio between the ME and the mean of the following expression: 0.0006*(P2+2K*P) on the considered datasets. The accuracy of the values obtained using this formula was confirmed on documented postoperative datasets, and on published and nonpublished formulas. CONCLUSION: The proposed method allows surgeons without special expertise to optimize an IOL constant to nullify the ME on a documented dataset without coding the different formulas. The influence of individual eyes is proportional to the squared power of the implanted IOL.

Comparison of Low Degree/High Degree and Zernike Expansions for Evaluating Simulation Outcomes After Customized Aspheric Laser Corrections.

Purpose: The purpose of this study was to compare the low degree/high degree (LD/HD) and Zernike Expansion simulation outcomes evaluating the corneal wavefront changes after theoretical conventional and customized aspheric photorefractive ablations. Methods: Initial anterior corneal surface profiles were modeled as conic sections with pre-operative apical curvature, R0, and asphericity, Q0. Postoperative apical curvature, R1, was computed from intended defocus correction, D, diameter zone, S, and target postoperative asphericity, Q1. Coefficients of both Zernike and LD/HD polynomial expansions of the rotationally symmetrical corneal profile were computed using scalar products. We modeled different values of D, R0, Q0, S, and ΔQ = Q1 to Q0. The corresponding postoperative changes in defocus (Δz20 vs. Δg20), fourth order (Δz40 vs. Δg40) and sixth order (Δz60 vs. Δg60) Zernike and LD/HD spherical aberrations (SAs) were compared. In addition, retrospective clinical data and wavefront measurements were obtained from two examples of two patient eyes before and after corneal laser photoablation. Results: The z20, varied with both R0 and Q0, whereas the LD/HD defocus coefficient, g20, was relatively robust to changes in asphericity. Variations of apical curvature better correlated with defocus and ΔQ with SA coefficients in the LD/HD classification. The impact of ΔQ was null on g20 but induced significant linear variations in z20 and fourth order SA coefficients. LD/HD coefficients provided a good correlation with the visual performances of the operated eyes. Conclusions: Simulated variations in postoperative corneal profile and wavefront expansion using the LD/HD approach showed good correlations between defocus and asphericity variations with variations in corneal curvature and SA coefficients, respectively. Translational Relevance: The relevance of this study was to provide a clinically relevant alternative to Zernike polynomials for the interpretation of wavefront changes after customized aspheric corrections.

Autologous connective tissue graft or xenogenic collagen matrix with coronally advanced flaps for coverage of multiple adjacent gingival recession. 36-month follow-up of a randomized multicentre trial.

AIM: To report the 36-month follow-up of a trial comparing the adjunct of a xenogenic collagen matrix (CMX) or connective tissue graft (CTG) to coronally advanced flaps (CAF) for coverage of multiple adjacent recessions. MATERIAL AND METHODS: 125 subjects (61 CMX) with 307 recessions in 8 centres from the parent trial were followed-up for 36 months. Primary outcome was change in position of the gingival margin. Multilevel analysis used centre, subject and tooth as levels and baseline parameters as covariates. RESULTS: No differences were observed between the randomized and the follow-up population. Average baseline recession was 2.6 ± 1.0 mm. 3-year root coverage was 1.5 ± 1.5 mm for CMX and 2.0 ± 1.0 mm for CTG (difference of 0.32 mm, 95% CI from -0.02 to 0.65 mm). The upper limit of the confidence interval was over the non-inferiority margin of 0.25 mm. No treatment differences in position of the gingival margin were observed between 6- and 36-month follow-up (difference 0.06 mm, 95% CI -0.17 to 0.29 mm). CONCLUSION: CMX was not non-inferior with respect to CTG in multiple adjacent recessions. No differences in stability of root coverage were observed between groups and in changes from 6 to 36 months. Previously reported shorter time to recovery, lower morbidity and more natural appearance of tissue texture and contour observed for CMX in this trial are also relevant in clinical decision-making.

Wavefront sensing, novel lower degree/higher degree polynomial decomposition and its recent clinical applications: A review.

We are in the midst of a shift towards using novel polynomials to decompose wavefront aberrations in a more ophthalmologically relevant way. Zernike polynomials have useful mathematical properties but fail to provide clinically relevant wavefront interpretation and predictions. We compared the distribution of the eye's aberrations and demonstrate some clinical applications of this using case studies comparing the results produced by the Zernike decomposition and evaluating them against the lower degree/higher degree (LD/HD) polynomial decomposition basis which clearly dissociates the higher and lower aberrations. In addition, innovative applications validate the LD/HD polynomial basis. Absence of artificial reduction of some higher order aberrations coefficients lead to a more realistic analysis. Here we summarize how wavefront analysis has evolved and demonstrate some of its new clinical applications.

Using Artificial Intelligence and Novel Polynomials to Predict Subjective Refraction.

This work aimed to use artificial intelligence to predict subjective refraction from wavefront aberrometry data processed with a novel polynomial decomposition basis. Subjective refraction was converted to power vectors (M, J0, J45). Three gradient boosted trees (XGBoost) algorithms were trained to predict each power vector using data from 3729 eyes. The model was validated by predicting subjective refraction power vectors of 350 other eyes, unknown to the model. The machine learning models were significantly better than the paraxial matching method for producing a spectacle correction, resulting in a mean absolute error of 0.301 ± 0.252 Diopters (D) for the M vector, 0.120 ± 0.094 D for the J0 vector and 0.094 ± 0.084 D for the J45 vector. Our results suggest that subjective refraction can be accurately and precisely predicted from novel polynomial wavefront data using machine learning algorithms. We anticipate that the combination of machine learning and aberrometry based on this novel wavefront decomposition basis will aid the development of refined algorithms which could become a new gold standard to predict refraction objectively.

An Alternative Wavefront Reconstruction Method for Human Eyes.

PURPOSE: To expand upon and clinically demonstrate the results of a new polynomial decomposition method. METHODS: To discuss the theoretical considerations comparing the qualitative and quantitative information produced by the Zernike coefficients and a new polynomial decomposition basis, in a comparative series of theoretical and clinical case studies. RESULTS: These comparative studies validate the novel polynomial basis that decomposes the wavefront, with clear segregation of the higher and lower aberrations. There is no artifactual reduction of some of the higher order aberration coefficients, providing a more clinically relevant retinal image quality prediction. CONCLUSIONS: Some of the inherent limitations of the Zernike polynomials in clinical ophthalmic applications can be solved by a novel set of polynomials forming an alternative higher order basis. The new basis provides a clear separation between modes containing lower order terms versus higher order terms and offers clinicians a more clinically realistic wavefront analysis. [J Refract Surg. 2020;36(2):74-81.].

The relationship between dental implant papilla and dental implant mucosa around single-tooth implant in the esthetic area: A retrospective study.

OBJECTIVE: The aim of the present study was (a) to evaluate the relationship between dental implant mucosa and dental implant papilla levels; and (b) to identify the clinical parameters associated with peri-implant soft tissue stability over time. MATERIALS AND METHODS: This is a retrospective study on a cohort of patients seeking a single-tooth implant therapy in a private practice in the Paris area. Two independent examiners analyzed photographs and radiographs taken the day of definitive crown load (baseline) and the last follow-up visit (at least 12 months later) in order to measure four peri-implant soft and hard tissue parameters. RESULTS: Seventy-four patients corresponding to 90 implants were analyzed. During a mean follow-up of 53.88 months, five implants (5.6%) presented with an apical displacement of the mid-facial marginal mucosal level of at least 1 mm. Changes in the mid-facial mucosa level were explained by changes in (a) the keratinized tissue height over time (p < .0001); (b) changes in the papilla height (p < .0001); and (c) by the periodontal phenotype (p = .007). A significant difference between papillae that gain in height (n = 85) and papilla that lost height (n = 78) was observed concerning (a) the timing of the implant placement (p = .019); and (b) the presence of an incomplete papilla fill (distance from the top of the papilla to the contact point) at baseline (p = .004). CONCLUSIONS: The present findings indicate a dependent association between dental implant mucosa and dental implant papilla levels. Stability of peri-implant soft tissues depends on periodontal phenotype, keratinized tissue height and papilla height.

Xenogenic collagen matrix or autologous connective tissue graft as adjunct to coronally advanced flaps for coverage of multiple adjacent gingival recession: Randomized trial assessing non-inferiority in root coverage and superiority in oral health-related quality of life.

AIM: To evaluate the non-inferiority of the adjunct of a xenogeneic collagen matrix (CMX) or connective tissue graft (CTG) to coronally advanced flaps (CAF) for coverage of multiple adjacent recessions and compare superiority in patient-reported outcomes (PROM). MATERIAL AND METHODS: One hundred and eighty-seven subjects (92 CMX) with 485 recessions in 14 centres were randomized and followed up for 6 months. Patients filled daily diaries for 15 days to monitor patient-reported experience. The primary outcome was changed in position of the gingival margin. Multilevel analysis used centre, subject and tooth as levels and baseline parameters as covariates. RESULTS: Average baseline recession was 2.5 ± 1.0 mm. The surgery was 15.7 min shorter (95%CI from 11.9 to 19.6, p < .0001) and perceived lighter (11.9 VAS units, 95%CI from 4.6 to 19.1, p = .0014) in CMX subjects. Time to recovery was 1.8 days shorter in CMX. Six-month root coverage was 1.7 ± 1.1 mm for CMX and 2.1 ± 1.0 mm for CTG (difference of 0.44 mm, 95%CI from 0.25 to 0.63 mm). The upper limit of the confidence interval was over the non-inferiority margin of 0.25 mm. Odds of complete root coverage were significantly higher for CTG (OR = 4.0, 95% CI 1.8-8.8). CONCLUSION: Replacing CTG with CMX shortens time to recovery and decreases morbidity, but the tested generation of devices is probably inferior to autologous CTG in terms of root coverage. Significant variability in PROMs was observed among centres.

Polynomial decomposition method for ocular wavefront analysis.

Zernike circle polynomials are in widespread use for wavefront analysis because of their orthogonality over a circular pupil and their representation of balanced classical aberrations. However, some of the higher-order modes contain linear and quadratic terms. A new aberration series is proposed to better separate the low- versus higher-order aberration components. Because its higher-order modes are devoid of linear and quadratic terms, our new basis can be used to better fit the low- and higher-order components of the wavefront. This new basis may quantify the aberrations more accurately and provide clinicians with coefficient magnitudes which better underline the impact of clinically significant aberration modes.

Clinical evaluation of two dental implant macrostructures on peri-implant bone loss: a comparative, retrospective study.

OBJECTIVES: To compare the effect of two implant macrostructures on peri-implant bone level. MATERIAL AND METHODS: This retrospective cohort study was conducted in a private practice. Patients received test (Nobel Speedy Groovy implants) or control implants (Mk III implants) or both. Baseline and corresponding follow-up radiographs, taken with a long-cone technique, were analyzed to evaluate mean bone level changes around implants during a mean follow-up of 69 ± 19 months. A chi-squared test was performed to compare the bone level changes between the two types of implants. A multivariate analysis was used to explain the difference between the two groups. RESULTS: After controlling for inclusion and exclusion criteria, 144 dental implants corresponding to 68 implants in the test group and 76 implants in the control group were placed in 59 patients. Nine dental implants (6.25%) were lost during the observation period: five implants in the test group and four implants in the control group. Consequently, a total of 135 implants placed in 58 patients were available for analysis. Our study shows a significant difference of peri-implant bone level overtime between the test and control groups (P < 0.01). At the end of the observation period, a bone growth was observed in the control group (0.02 ± 0.80 mm), whereas a bone loss was found in the test group (-0.43 ± 1.11 mm). The mean bone level at baseline and the type of periodontal therapy and the maintenance care program were involved in this difference (P < 0.001, P = 0.035, P < 0.001, respectively). CONCLUSION: Our study demonstrates a significant difference in peri-implant bone level between test and control groups. The mean bone level at baseline, the type of periodontal therapy, and the maintenance program may explain peri-implant bone level changes overtime.

Effect of anterior corneal surface asphericity modification on fourth-order zernike spherical aberrations.

PURPOSE: To evaluate the theoretical influence of the change in corneal asphericity (ΔQ) on the change in fourth-order Zernike spherical aberration coefficient (ΔC(4)0) with customized aspheric refractive correction of myopia and hyperopia. METHODS: The initial anterior corneal surface profile was modeled as a conic section of apical radius of curvature R0 and asphericity Q0. The postoperative corneal profile was modeled as a conic section of apical curvature R1 and asphericity Q1, where R1 was computed from defocus D, and Q1 selected for controlling the postoperative asphericity. The corresponding change in fourth-order spherical aberration (ΔC(0)4) was computed within a 6-mm optical zone using inner products applied to the incurred optical path changes. These calculations were repeated for different values of D, R0, Q0, and various intended ΔC(4)0 values. RESULTS: Increasing negative spherical aberration (ΔC(4)(0) < 0) requires a change toward more negative values of asphericity (increased prolateness; ΔQ < 0) for hyperopic and low myopic corrections, but more positive values (ΔQ < 0) for high myopic correction. The larger the intended change in corneal spherical aberration (ΔC(4)(0)), the more myopic the threshold value for which the required change in asphericity, ΔQ, becomes positive. The influence of the magnitude of paraxial defocus correction is less pronounced when larger changes in C(4)(0) are intended. CONCLUSIONS: These results provide a basis for controlling the direction (sign) and the magnitude of spherical aberration changes when using customized aspheric profiles of ablation.

Corneal elevation topography: best fit sphere, elevation distance, asphericity, toricity, and clinical implications.

PURPOSE: To describe the effect of the corneal asphericity and toricity on the map patterns and best fit sphere (BFS) characteristics in elevation topography. METHODS: The corneal surface was modeled as a biconic surface of principal radii and asphericity values of r1 and r2 and Q1 and Q2, respectively. The apex of the biconic surface corresponded to the origin of a polar coordinates system. Minimization of the squared residuals was used to calculate the values of the radii of the BFSs and apex distance (A-values: z distance between the corneal apex and the BFS) of the modeled corneal surface for various configurations relating to commonly clinically measured values of apical radius, asphericity, and toricity. RESULTS: Increased apical radius of curvature and increased prolateness (negative asphericity) led to an increase in BFS radius but had opposite effects on the A-value. Increased prolateness resulted in increased BFS radius and A-value. Increasing toricity did not alter these findings. Color-plot elevation maps of the modeled corneal surface showed complete ridge patterns when toricity was increased and showed incomplete ridge and island patterns when prolateness was increased. CONCLUSIONS: High A-values in patients with corneal astigmatism may result from steep apical curvature and/or high prolateness (negative asphericity). The BFS radius may help in distinguishing between these 2 causes of increased A-values. Increased prolateness and decreased apical radius of curvature (often seen in keratoconus) have opposite effects on the BFS radius but similar effects on the apex distance.

A retrospective study of root coverage procedures using an image analysis system.

AIM: To investigate the efficacy of root coverage procedures and factors that may affect the clinical outcomes in non-experimental patients. MATERIAL AND METHODS: Two hundred and eighty-seven root coverage surgical procedures in 215 adult patients were evaluated retrospectively. Descriptive statistics were used to determine the patient profile. Comparisons between surgeries were assessed, and the impact of different parameters on the probability of mean/complete root coverage and gingival augmentation was explored. RESULTS: The mean percentage of root coverage was 72.29 (+/- 28)%. Complete root coverage was observed in 35.56% of the defects. The difference between the surgical procedures was not significant. The mean percentage of gingival augmentation was 106.18 (+/- 260)%. The difference between non-submerged grafts and the other techniques was significant (p<10(-3)). A significant negative impact of smoking, and maxillary teeth for both mean and complete root coverage were found. A significant positive impact of the tuberosity donor site was found for complete root coverage. Maxillary teeth and Miller's Class II and III were positive predictive factors for gingival augmentation. CONCLUSIONS: Under non-experimental conditions, root coverage procedures are effective. Smoking, maxillary teeth, donor site, and Miller's Classes are prognostic factors that may affect the results.

Root coverage assessment: validity and reproducibility of an image analysis system.

AIM: The aim of this methodological study was to validate a new method for root coverage evaluation following periodontal plastic surgery. MATERIAL AND METHODS: Thirty recessions were treated in 21 consecutive patients, using a subepithelial connective tissue graft technique. Clinical measurements and photographs were taken at baseline and 12+/-6 months after treatment. The mean percentage of root coverage for linear and surface area measurements was calculated using conventional clinical evaluation, and compared with ImageJ, a public domain Java image processing program. Bland-Altman plots were used for assessing repeatability and agreement between clinical and ImageJ measurements. The strength of the relationship was calculated using the Pearson product moment correlation coefficient. RESULTS: The repeatability of ImageJ was excellent for both linear and surface area measurements. The agreement between clinical and ImageJ measurements was good for the linear evaluation, showing lower and upper limits of -13.14% and 17.42%, respectively. Significant correlations (p<0.001) were found between clinical and ImageJ measurements, ranging from 0.93 to 0.94 for linear evaluation, and from 0.89 to 0.90 for surface evaluation. CONCLUSIONS: The outcomes of this study show that the ImageJ analysis is a reliable, reproducible method to evaluate the percentage of root coverage after periodontal plastic surgery, when a midfacial linear measurement is used.

Corneal asphericity change after excimer laser hyperopic surgery: theoretical effects on corneal profiles and corresponding Zernike expansions.

PURPOSE: To determine the theoretical relationships between the changes in corneal paraxial power, asphericity, and the corresponding Zernike polynomial expansion after conventional and customized excimer laser correction of hyperopia. METHODS: The initial corneal profile was modeled as a conic section of apical radius of curvature R1 and asphericity Q1. The theoretical value of the postoperative apical radius of curvature R2 was computed by using a paraxial formula from the value of R1 and hyperopic defocus D. The postoperative asphericity Q2 of the corneal surface was computed within the optical zone of diameter S after the delivery of a Munnerlyn-based profile of ablation for hyperopia using conic section-fitting and minimization of the squared residuals. These calculations were repeated for different values of defocus, initial apical radius of curvature, and asphericity. Taylor series expansions were also used to provide an approximation aimed at predicting change in asphericity. The coefficients of a Zernike polynomial expansion of the rotationally symmetrical corneal profile (defocus C2(0), spherical aberration C4(0), secondary spherical aberration C6(0)) were also computed, by using scalar products applied to the considered corneal profile modeled as a conic section and were expressed as a function of both its apical radius and asphericity. This allowed approximation of the variations of the Zernike polynomial expansion of the corneal profiles by subtracting the postoperative coefficient weighting a particular aberration from that of the preoperative one in different theoretical situations, after both conventional and customized hyperopia treatments aimed at controlling the postoperative corneal asphericity and delivered over a normalized pupil diameter. RESULTS: Conical least-squares fitting was unambiguous, allowing approximation of the postoperative corneal profile as a conic section of apical radius R2. After a Munnerlyn-based hyperopia treatment, the sign of the asphericity of this profile remains theoretically unchanged, but its value decreased for initially oblate and increased for initially prolate corneas, respectively. A similar trend was noted with the approximation obtained by the Taylor series expansion. The alteration of the apical radius and/or of the asphericity of the corneal surface resulted in variations of both the corneal profile Zernike coefficients C2(0) and C4(0). The former was essentially dependent on the variation of the apical radius and the latter essentially on the variation of both apical radius and asphericity. CONCLUSIONS: Conventional and customized profiles of ablation for hyperopia alter the postoperative corneal asphericity and the Zernike coefficients of the corneal profile. The results of this study may be useful in the interpretation of the postoperative variations of the corneal profile and their impact on corneal wavefront expansion variations after both conventional and customized profiles of ablation.

Analysis of customized corneal ablations: theoretical limitations of increasing negative asphericity.

PURPOSE: To determine the ablation depths of customized myopic excimer laser photoablations performed to change corneal asphericity after laser in situ keratomileusis (LASIK) and photorefractive keratectomy (PRK). METHODS: A mathematical model of aspheric myopic corneal laser surgery was generated. The initial corneal surface was modeled as a conic section of apical radius R(1) and asphericity Q(1). The final corneal surface was modeled as a conic section of apical R(2) and asphericity Q(2), where R(2) was calculated from the paraxial optical formula for a given treatment magnitude (D), and Q(2) was the intended final asphericity. The aspheric profile of ablation was defined as the difference between the initial and final corneal profiles for a given optical zone diameter (S), and the maximal depth of ablation was calculated from these equations. Using the Taylor series expansion, an equation was derived that allowed the approximation of the central depth of ablation (t(0)) for various magnitudes of treatment, optical zone diameters, and asphericity. In addition to the Munnerlyn term (M), incorporating Munnerlyn's approximation (-D small middle dot S(2)/3), the equation included an asphericity term (A) and a change of asphericity term (Delta). This formula (t(0) = M + A + Delta) was used to predict the maximal depth of ablation and the limits of customized asphericity treatments in several theoretical situations. RESULTS: When the initial and final asphericities were identical (no intended change in asphericity; Q(1) = Q(2); Delta = 0), the maximal depth of ablation (t(0) = M + A) increased linearly with the asphericity Q(1). To achieve a more prolate final asphericity (Q(2) < Q(1); dQ < 0; Delta > 0), the maximal depth of ablation (M + A + Delta) was increased. For treatments in which Q(2) was intended to be more oblate than Q(1) (Q(2) > Q(1); dQ > 0; Delta < 0), the maximal depth of ablation was reduced. These effects sharply increased with increasing diameters of the optical zone(s). Similarly, in the case of PRK, the differential increase in epithelial thickness in the center of the cornea compared with the periphery resulted in increased oblateness. CONCLUSIONS: Aspheric profiles of ablation result in varying central depths of ablation. Oblateness of the initial corneal surface, intentional increase in negative asphericity, and enlargement of the optical zone diameter result in deeper central ablations. This may be of clinical importance in planning aspheric profiles of ablation in LASIK procedures to correct spherical aberration without compromising the mechanical integrity of the cornea.