Best-fit Sphere Radius Research Articles

A scapular statistical shape model can reliably predict premorbid glenoid morphology in conditions of severe glenoid bone loss

Knowledge of premorbid glenoid parameters at the time of shoulder arthroplasty, such as inclination, version, joint line position, height, and width, can assist with implant selection, implant positioning, metal augment sizing, and/or bone graft dimensions. The objective of this study was to validate a scapular statistical shape model (SSM) in predicting patient-specific glenoid morphology in scapulae with clinically relevant glenoid erosion patterns. Computed tomography scans of 30 healthy scapulae were obtained and used as the control group. Each scapula was then virtually eroded to create 7 erosion patterns (Walch A1, A2, B2, B3, D, Favard E2, and E3). This resulted in 210 uniquely eroded glenoid models, forming the eroded glenoid group. A scapular SSM, created from a different database of 85 healthy scapulae, was then applied to each eroded scapula to predict the premorbid glenoid morphology. The premorbid glenoid inclination, version, height, width, radius of best-fit sphere, and glenoid joint line position were automatically calculated for each of the 210 eroded glenoids. The mean values for all outcome variables were compared across all erosion types between the healthy, eroded, and SSM-predicted groups using a 2-way repeated measures analysis of variance. The SSM was able to predict the mean premorbid glenoid parameters of the eroded glenoids with a mean absolute difference of 3°±2° for inclination, 3°±2° for version, 2 ± 1 mm for glenoid height, 2 ± 1 mm for glenoid width, 5 ± 4 mm for radius of best-fit sphere, and 1 ± 1 mm for glenoid joint line. The mean SSM-predicted values for inclination, version, height, width, and radius were not significantly different than the control group (P>.05). An SSM has been developed that can reliably predict premorbid glenoid morphology and glenoid indices in patients with common glenoid erosion patterns. This technology can serve as a useful template to visually represent the premorbid healthy glenoid in patients with severe glenoid bony erosions. Knowledge of the premorbid glenoid preoperatively can assist with implant selection, positioning, and sizing.

Wavefront optical spacing of freeform surfaces and its measurement using CGH interferometry

For optical surfaces, the distance between the wavefront at ideal design position and that at real surface testing position along the wavefront propagation direction is an important parameter. It determines the on-axis curvature deviation and best-fit sphere radius of the surface under testing, and thus, affects the optical distance, effective focal length, and tolerance design of the optical system. We define the distance as wavefront optical spacing (WOS or spacing d). The analytical form of the WOS can be utilised in critical tolerance balancing, and its test results can aid in optical system redesign. Aiming at a computer-generated hologram (CGH) interferometric test, in this study, we propose the WOS concept and deduce the coupling relation between the surface error and spacing d, particularly in freeform surface conditions. A cat-eye CGH interferometric method was presented to test the spacing error within a precision of several microns. The simulation and error budget demonstrate that this method can measure the WOS of freeform surfaces. The experimental results indicate that the metrology accuracy is 10.2 ± 4.3 μm (P = 95%) (absolute accuracy), 4.5 μm (repeatability), and 2.1 ppm (relative accuracy).

Three-dimensional geometry of the normal shoulder: a software analysis

Three-dimensional (3D) geometry of the normal glenohumeral bone anatomy and relations is poorly documented. Our aims were (1) to determine the 3D geometry of the normal glenohumeral joint (GHJ) with reference to the scapular body planeand (2) to identify spatial correlations between the orientation and direction of the humeral head and the glenoid. Computed tomographies (CTs) of the normal, noninjured GHJ were collected from patients who had undergone CTs in the setting of (1) polytrauma, (2) traumatic head injury, (3) chronic acromioclavicular joint dislocations, and (4) unilateral trauma with a contralateral normal shoulder. We performed 3D segmentation and measurements with a fully automatic software (Glenosys; Imascap). Measurements were made in reference to the scapular body plane and its transverse axis. Geometric measurements includedversion, inclination, direction, orientation, best-fit sphere radius (BFSR), humeral subluxation, critical shoulder angle, reverse shoulder angle, glenoid area, and glenohumeral distance. Statistical correlations were sought between glenoid and humeral 3D measurements (Pearson correlation). A total of 122 normal GHJs (64 men, 58 women, age: 52 ± 17 years) were studied. The glenoid BFSR was always larger than the humerus BFSR (constant factor of 1.5, standard deviation = 0.2). The mean glenoid version and inclination were -6° ± 4° and 7° ± 5°, respectively. Men and women were found to have significantly different values for inclination (6° vs. 9°, P = .02), but not for version. Humeral subluxation was 59% ± 7%, with a linear correlation with glenoid retroversion (r = -0.70, P < .001) regardless of age. There was a significant and linear correlation between glenoid and humeral orientation and direction (r = 0.72 and r = 0.70, P < .001). The 3D geometry of the glenoid and humeral head present distinct limits in normal shoulders that can be set as references in daily practice: version and inclination are -6° and 7°, respectively, and humeral posterior subluxation is 59%; interindividual variations, regardless of the size, are relative to the scapular plane. There exists a strong correlation between the position of the humeral head and the glenoid orientation and direction.

Comparison of anterior segment changes after femtosecond laser LASIK and SMILE using a dual rotating Scheimpflug analyzer

BackgroundTo compare the changes in the anterior segment after femtosecond laser in situ keratomileusis (FS-LASIK) and small incision lenticule extraction (SMILE) using a dual rotating Scheimpflug (DRS) analyzer (Galilei®; Ziemer Ophthalmology, Port, Switzerland).MethodsA total of 218 eyes of 109 patients who underwent FS-LASIK or SMILE for myopic correction were retrospectively studied. Ninety-eight eyes of 49 patients who underwent FS-LASIK were compared to 120 eyes of 60 patients treated with SMILE. A DRS analyzer was used for preoperative and 6-month postoperative anterior segment analyses. Measured variables included the central corneal thickness (CCT), anterior chamber depth (ACD), anterior and posterior keratometry (K), anterior and posterior best-fit sphere radius, and maximum posterior elevation (MPE).ResultsAfter the procedure, the amount of CCT decrease was higher in the SMILE group than in the FS-LASIK group, but it was not statistically significant. The MPE was significantly increased after both procedures (p < 0.001 and p = 0.001 in the FS-LASIK and SMILE groups, respectively), with the amount of elevation being higher after FS-LASIK than after SMILE even though it was not statistically significant. And there was a significant change in the steep and average posterior K in the FS-LASIK group (p = 0.006 and 0.001, respectively), but not in the SMILE group.ConclusionsRegarding changes in the MPE and posterior K, changes in the posterior corneal surface were greater after FS-LASIK than after SMILE.Trial registrationThe trial registration number: KCT0003628. Date of registration: 15 March 2019.

Topographic, Tomographic, and Aberrometric Characteristics of Post-LASIK Ectasia.

To report the refractive, topographic, tomographic, and aberrometric characteristics of post-LASIK ectasia; to compare these characteristics with normal post-LASIK controls; and to propose a comprehensive system to grade the severity of post-LASIK ectasia. The refraction, corrected distance visual acuity (CDVA), magnitude, and location of the steepest and thinnest point on the cornea, the highest anterior and posterior surface elevation, the radius of best fit sphere, corneal asphericity, and corneal aberrations were measured in 50 eyes of 29 patients with post-LASIK ectasia. These were compared with corresponding parameters in 50 eyes that did not develop ectasia for more than 1 year after LASIK. A logistic regression analysis was used to create a scoring system to grade the severity. Eyes with post-LASIK ectasia had significantly higher myopia with astigmatism and a lower CDVA than control eyes. Mean topographic toricity was 3.4 ± 1.9D, mean keratometry at the steepest point was 55.32 ± 6.63D, mean highest posterior elevation was 69.72 ± 3 μm, and mean coma was -2.06 ± 1.2 μm. All these parameters were significantly higher than corresponding values in the control group (p < 0.001 in all). Spherical aberration was more negative and the change in asphericity indicated significantly greater prolate shape of the cornea in eyes with post-LASIK ectasia compared to controls. Five parameters, namely, CDVA, spherical equivalent, highest posterior corneal elevation, spherical aberration, and corneal asphericity, were identified as significant predictors of post-LASIK ectasia and used to create a scoring system. Post-LASIK ectasia is characterized by significant changes in refraction, topography, tomography, and aberrometry. The proposed scoring system may be useful in diagnosing, grading, and monitoring post-LASIK ectasia.

Predictive Ability of Galilei to Distinguish Subclinical Keratoconus and Keratoconus from Normal Corneas.

Purpose:To determine the predictive ability of different data measured by the Galilei dual Scheimpflug analyzer in differentiating subclinical keratoconus and keratoconus from normal corneas.Methods:This prospective comparative study included 136 normal eyes, 23 eyes with subclinical keratoconus, and 51 keratoconic eyes. In each eye, keratometric values, pachymetry, elevation parameters and surface indices were evaluated. Receiver operating characteristic (ROC) curves were calculated and quantified by using the area under the curve (AUC) to compare the sensitivity and specificity of the measured parameters and to identify optimal cutoff points for differenciating subclinical keratoconus and keratoconus from normal corneas. Several model structures including keratometric, pachymetric, elevation parameters and surface indices were analyzed to find the best model for distinguishing subclinical and clinical keratoconus. The data sets were also examined using the non-parametric “classification and regression tree” (CRT) technique for the three diagnostic groups.Results:Nearly all measured parameters were strong enough to distinguish keratoconus. However, only the radius of best fit sphere and keratometry readings had an acceptable predictive accuracy to differentiate subclinical keratoconus. Elevation parameters and surface indices were able to differentiate keratoconus from normal corneas in 100% of eyes. Meanwhile, none of the parameter sets could effectively discriminate subclinical keratoconus; a 3-factor model including keratometric variables, elevation data and surface indices provided the highest predictive ability for this purpose.Conclusion:Surface indices measured by the Galilei analyzer can effectively differentiate keratoconus from normal corneas. However, a combination of different data is required to distinguish subclinical keratoconus.

Three-dimensional assessment of the dimensions of the osteoarthritic glenoid

Osteoarthritis results in changes in the dimensions of the glenoid. This study aimed to assess the size and radius of curvature of arthritic glenoids. A total of 145 CT scans were analysed, performed as part of routine pre-operative assessment before total shoulder replacement in 91 women and 54 men. Only patients with primary osteoarthritis and a concentric glenoid were included in the study. The CT scans underwent three-dimensional (3D) reconstruction and were analysed using dedicated computer software. The measurements consisted of maximum superoinferior height, anteroposterior width and a best-fit sphere radius of curvature of the glenoid. The mean height was 40.2 mm (SD 4.9), the mean width was 29 mm (SD 4.3) and the mean radius of curvature was 35.4 mm (SD 7.8). The measurements were statistically different in men and women and had a Gaussian distribution with marked variation. All measurements were greater than the known values in normal subjects. With current shoulder replacement systems using a unique backside radius of curvature for the glenoid component, there is a risk of undertaking excessive reaming to adapt the bone to the component resulting in sacrifice of subchondral bone or under-reaming and instability of the component due to a 'rocking horse' phenomenon.

Comparison of Posterior Corneal Imaging Before and After LASIK Using Dual Rotating Scheimpflug and Scanning Slit-Beam Corneal Tomography Systems

To compare the maximum posterior elevation (MPE) measurements before and after LASIK using a dual rotating Scheimpflug (DRS) imaging system (Galilei, Ziemer Ophthalmic Systems, Port, Switzerland) and a scanning slit-beam (SSB) imaging system (Orbscan IIz, Bausch & Lomb, Rochester, NY). This retrospective study included 78 eyes from 78 patients who underwent myopic LASIK. Preoperative and postoperative data collected included anterior and posterior best-fit sphere radius and axial curvature readings, posterior central elevation (PCE), and MPE relative to a best-fit sphere using a 7.8-mm region of interest. Data were compared using paired t test analysis. Mean preoperative PCE (5.06 ± 2.29 μm with the DRS system and 12.78 ± 6.90 μm with the SSB system) and MPE (4.87 ± 4 μm with the DRS system and 15.44 ± 9.78 μm with the SSB system) were statistically different (P < .001). Mean postoperative PCE (4.55 ± 2.34 μm with the DRS system and 20.59 ± 8.11 μm with the SSB system) and MPE (4.90 ± 3.35 μm with the DRS system and 24.95 ± 10.15 μm with the SSB system) were statistically different (P < .001). The difference between preoperative and postoperative MPE measurements by DRS was not statistically significant (P = .953), whereas the difference measured by SSB was statistically significant (P < .001). The consistency of DRS measurements suggests that the posterior surface of the cornea does not change appreciably after keratorefractive surgery and is imaged more accurately using DRS compared with SSB. The DRS system affords confidence in interpreting data that are useful for discerning morphologic abnormalities of the cornea, both before and after keratorefractive surgery.

Corneal Elevation Topography: Best Fit Sphere, Elevation Distance, Asphericity, Toricity, and Clinical Implications

To describe the effect of the corneal asphericity and toricity on the map patterns and best fit sphere (BFS) characteristics in elevation topography. 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. 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. 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.

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

To assess the repeatability of the anterior segment measurements performed with a dual Scheimpflug analyzer (Galilei) in unoperated and post-refractive surgery eyes. Private practice. Evaluation of diagnostic test. 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. 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. 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.

Dynamics in longitudinal eye movements and corneal shape

The magnitude and character of longitudinal movements of the eye were studied in the context of high speed videokeratoscopy. It was of interest to determine whether these dynamic changes in the eye movements can affect the corneal shape and its estimation. A high speed videokeratoscope with a sampling frequency of 50 Hz was used for measuring the corneal apex movements as well as for measuring variations in the best-fit sphere radius and central radius of curvature. The magnitude of the measured longitudinal apex movements could reach over 200 microm showing a slow trend. The estimated local changes of the apex movements that could be associated with the cardiopulmonary system were about 40-50 microm. The temporal variations in the equivalent estimated central radius of curvature ranged between 10 and 15 microm. Spectral analysis of the longitudinal eye movements revealed strong signatures of the pulse and respiration signals as well as the assumed blink control signal. No clear association between the longitudinal apex movements and the corneal curvature was found. However, very slow significant changes in the corneal shape were observed. The central radius of curvature of the cornea revealed slow changes of up to 120 microm. Understanding the nature of such changes will be of benefit in ophthalmic applications requiring highly accurate measurements of corneal shape, such as contact lens design and refractive surgery.

Comparison of Pentacam and Orbscan IIz on Posterior Curvature Topography Measurements in Keratoconus Eyes

To compare the measurements of posterior elevation above the best-fit sphere and of pachymetry in established keratoconus patients using 2 different technologies--Scheimpflug imaging with the Pentacam and scanning slit combined with Placido imaging with Orbscan IIz. Retrospective comparative case series. Patients with confirmed keratoconus by biomicroscopy and Placido topography who had corneal topography scans by the Pentacam and Orbscan IIz on their visit from April 2004 to April 2005. These scans were obtained routinely for patient diagnosis, treatment, and progression. The mean difference, standard deviation (SD), and 95% limits of agreement (LOA) were calculated, and Bland-Altman plots were constructed for best-fit sphere radius of curvature, posterior elevation above the best-fit sphere, and pachymetry of the thinnest point. Thirty-six eyes of 29 patients were analyzed. The average radius for posterior best-fit sphere was 5.97 microm (range, 4.69-6.79) for the Pentacam and 6.00 microm (range, 4.97-6.55) for Orbscan IIz. The mean difference (Pentacam - Orbscan IIz) for the radius generated for the best-fit sphere was -0.03+/-0.22 SD with a 95% confidence interval (CI) of -0.11 to 0.04 and a 95% LOA of -0.46 to 0.40 (P = 0.362). The mean posterior elevation by best-fit sphere fixed to the apex was 34.86 microm (range, 3-120) for the Pentacam and 48.50 microm (range, 11-118) for Orbscan IIz. The mean difference was -13.64+/-26.08 SD (95% CI, -22.46 to -4.81; 95% LOA, -64.75 to 37.48; P = 0.003). The average thinnest point for the Pentacam was 443.6 microm (range, 164-587), and that for Orbscan IIz was 445.9 microm (range, 204-597). The mean difference in the thinnest point for the Pentacam and Orbscan IIz was -2.28+/-35.55 (95% CI, -14.31 to 9.75; 95% LOA, -71.95 to 67.39; P = 0.703). Both the Pentacam and Orbscan IIz determine similar thinnest points but have a measurable difference in posterior elevations above the best-fit sphere, despite similar radii of curvature. This difference may be important in the screening of patients for refractive surgery to avoid surgery on patients with early keratoconus. This study cannot determine if the Pentacam is underestimating the posterior vault or if Orbscan is overestimating this height, and further studies with a standardized test object are needed.

Contact Lens-Induced Corneal Swelling and Surface Changes Measured with the Orbscan II Corneal Topographer

The purpose of this study was to measure central and topographical corneal swelling in response to contact lens wear and eye closure, to determine whether the swelling induced by soft and polymethyl methacrylate (PMMA) lenses is different, and to determine whether the anterior and/or posterior corneal shape alters with corneal swelling. An Orbscan II corneal topographer was used to measure corneal swelling and the shape of the anterior and posterior corneal surfaces of 16 neophytes before and after wearing soft and PMMA contact lenses with near-zero oxygen transmissibility. The lens-wearing eye was patched for 3 h. The mean 15.1% +/- 3.8% (+/- SD) central corneal swelling with soft lenses was significantly >12.6% +/- 4.1% with PMMA lenses. Topographical corneal swelling was significantly greater with soft vs. PMMA lenses. However, the difference between central and peripheral corneal swelling was much greater with PMMA lenses. With both lenses, the cornea swelled significantly more in the center than the periphery. The anterior best-fit sphere radius remained unchanged in response to soft lenses (0.00 +/- 0.04 mm) and steepened slightly but significantly with PMMA lenses (-0.04 +/- 0.05 mm). The posterior best-fit sphere radius flattened significantly with both lenses (0.12 +/- 0.07 mm with soft and 0.14 +/- 0.08 mm with PMMA lenses). Corneal swelling (greater centrally than peripherally) flattens the posterior surface of the cornea and is independent of lens type. Although the anterior best-fit sphere radius steepened with PMMA, the magnitude is probably clinically unimportant. Both lens types produced greater central vs. peripheral corneal swelling. However, the soft lens induced significantly greater overall swelling than PMMA. Because their oxygen transmission was the same, these results suggest that there is lateral diffusion of oxygen from the peripheral area of the cornea (that is not covered by the lens) toward the center.