Variation in the Best Fit Sphere Radius of Curvature as a Test to Detect Keratoconus Progression on a Scheimpflug-Based Corneal Tomographer

2018 ◽  
Vol 34 (4) ◽  
pp. 260-263 ◽  
Author(s):  
Nishant Gupta ◽  
Bruno L. Trindade ◽  
Joobin Hooshmand ◽  
Elsie Chan
Keyword(s):  
Radius Of Curvature ◽  
Sphere Radius ◽  
Best Fit ◽  
Best Fit Sphere

A New Algorithm for Solving the Best-Fit Sphere of Optical Aspherical Surface

2011 ◽  
Vol 418-420 ◽  
pp. 1472-1477 ◽  
Author(s):  
Jie Qiong Lin ◽  
Jin Song Yang ◽  
Ming Ming Lu
Keyword(s):  
Material Removal ◽  
Radius Of Curvature ◽  
Variable Step Size ◽  
Rapid Convergence ◽  
Step Size ◽  
Cubic Surface ◽  
Variable Step ◽  
Speed Up ◽  
Best Fit ◽  
Best Fit Sphere

To solve the best-fit sphere (BFS) accurately is one of the technological keys for the generating and testing of optical aspherical surfaces. This paper presents a new algorithm for solving the BFS of aspherical surfaces to suppress some deficiencies in the existing BFS algorithms. In the proposed approach, a BFS is constructed, which passes through both sides of endpoints in the section of the aspherical surfaces, the center of the BFS is shifted along the x-axis, and its radius of curvature is automatically computed. The variable step size method is proposed to speed up the convergence of the iteration. Through numerically solving the BFS of conic and cubic surface, the advantages of the proposed approach are verified. The results show that the proposed approach is of rapid convergence, and high accuracy; it is not only suitable for the conic surface, but also for higher order aspheres. The obtained asphericity and material removal function is more suitable for the machining and test.

scholarly journals Corneal Elevation Values in Normal Eyes, forme fruste Keratoconus and Keratoconus at Different Stages Measured by Scheimpflug Imaging

2014 ◽  
Vol 3 (1) ◽  
pp. 36-39 ◽  
Author(s):  
Luis Izquierdo ◽  
Maria A Henriquez ◽  
David Dañin
Keyword(s):  
Operating Characteristic ◽  
Predictive Accuracy ◽  
Optimal Cutoff ◽  
Receiver Operating Characteristic Curves ◽  
Scheimpflug Imaging ◽  
Prospective Comparative Study ◽  
Best Fit ◽  
Best Fit Sphere ◽  
Forme Fruste Keratoconus ◽  
Progressive Stage

ABSTRACT Purpose To compare corneal elevation values in normal eyes, forme fruste keratoconus (FFKC) and different stages of keratoconus using Scheimpflug imaging. Materials and methods This prospective, comparative study included 267 eyes (107 normal eyes, 21 FFKC and 139 keratoconus). Keratoconic eyes were divided into four groups according to keratometry values. Maximum posterior elevation (PE) above the (best fit sphere (BFS) at the central 5 mm were measured using the Pentacam (Oculus Optikgeräte GmbH). Receiver operating characteristic curves were used to determine the test's overall predictive accuracy and to identify optimal cutoff points to discriminate between the groups. Results PE had the smallest values in normal eyes and increased in FFKC and each progressive stage of keratoconus. Mean PE was 9.98 ± 5.33 µm in normal eyes, 18.09 ± 9.23 µm in FFKC and 24.97 µm ± 15.89, 37.82 ± 18.64, 46.82 ± 21.41 and 66.07 ± 39.09, in keratoconus stage I, II, III and IV respectively. Conclusion Posterior elevation values increased according to the severity of keratoconus disease. PE can be used as indicator of keratoconus progression. How to cite this article Henriquez MA, Izquierdo L Jr, Dañin D. Corneal Elevation Values in Normal Eyes, forme fruste Keratoconus and Keratoconus at Different Stages Measured by Scheimpflug Imaging. Int J Kerat Ect Cor Dis 2014;3(1):36-39.

Characterization of the Centroidal Geometry of Human Ribs

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
Matthew W. Kindig ◽  
Richard W. Kent
Keyword(s):  
Cross Sections ◽  
Posterior Extremity ◽  
Radius Of Curvature ◽  
Cross Sectional ◽  
Surface Reconstructions ◽  
C1 Continuity ◽  
Best Fit ◽  
Novel Model ◽  
Geometric Primitives

While a number of studies have quantified overall ribcage morphology (breadth, depth, kyphosis/lordosis) and rib cross-sectional geometry in humans, few studies have characterized the centroidal geometry of individual ribs. In this study, a novel model is introduced to describe the centroidal path of a rib (i.e., the sequence of centroids connecting adjacent cross-sections) in terms of several physically-meaningful and intuitive geometric parameters. Surface reconstructions of rib levels 2–10 from 16 adult male cadavers (aged 31–75 years) were first extracted from CT scans, and the centroidal path was calculated in 3D for each rib using a custom numerical method. The projection of the centroidal path onto the plane of best fit (i.e., the “in-plane” centroidal path) was then modeled using two geometric primitives (a circle and a semiellipse) connected to give C1 continuity. Two additional parameters were used to describe the deviation of the centroidal path from this plane; further, the radius of curvature was calculated at various points along the rib length. This model was fit to each of the 144 extracted ribs, and average trends in rib size and shape with rib level were reported. In general, upper ribs (levels 2–5) had centroidal paths which were closer to circular, while lower ribs (levels 6–10) tended to be more elliptical; further the centroidal curvature at the posterior extremity was less pronounced for lower ribs. Lower ribs also tended to exhibit larger deviations from the best-fit plane. The rib dimensions and trends with subject stature were found to be consistent with findings previously reported in the literature. This model addresses a critical need in the biomechanics literature for the accurate characterization of rib geometry, and can be extended to a larger population as a simple and accurate way to represent the centroidal shape of human ribs.

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

Cornea ◽  
2011 ◽  
Vol 30 (5) ◽  
pp. 508-515 ◽  
Author(s):  
Damien Gatinel ◽  
Jacques Malet ◽  
Thanh Hoang-Xuan ◽  
Dimitri T Azar
Keyword(s):  
Clinical Implications ◽  
Best Fit ◽  
Best Fit Sphere

Best-Fit Sphere

2018 ◽  
pp. 244-244
Author(s):  
Oliver K. Klaproth
Keyword(s):  
Best Fit ◽  
Best Fit Sphere

Proximal Interphalangeal Joint Dimensions for the Design of a Surface Replacement Prosthesis

1996 ◽  
Vol 210 (2) ◽  
pp. 95-108 ◽  
Author(s):  
H E Ash ◽  
A Unsworth
Keyword(s):  
Sagittal Plane ◽  
Middle Finger ◽  
Proximal Interphalangeal Joint ◽  
Sagittal Profile ◽  
Radius Of Curvature ◽  
Surface Replacement ◽  
Articular Surfaces ◽  
Phalangeal Bone ◽  
Best Fit ◽  
Replacement Prosthesis

The bones from 83 proximal interphalangeal joints (PIPJs) were dissected in order to determine the shape and size of the articular surfaces. The bones were modelled in acrylic dental bone cement and the original bones and replicas were then sectioned and shadow-graphed. Dimensions were taken from these shadowgraphs to be used in the design of a surface replacement prosthesis for the PIPJ. It was found that the bi-condylar heads of the proximal and middle phalanges were circular in the sagittal plane as was the base of the middle phalanx. However, the radius of curvature of the middle phalangeal base was greater than that of the proximal phalangeal head indicating that the PIPJ is not a conforming joint. The alignment of the radial and ulnar condyles of the proximal phalangeal bones was investigated and it was found that the index and middle finger bones tended to have a more prominent ulnar condyle while the ring and little finger bones tended to have a more prominent radial condyle. This was due to a slight difference in diameters of the two condyles. The proximal phalangeal bone lengths L ranged from 29–52 mm, maximum head widths W from 8.5–15.5 mm and maximum diameters D of the best-fit circles to the sagittal profile of the bone head from 6–11 mm. The middle phalangeal bone lengths ranged from 16–35 mm, maximum head widths from 8.5–12 mm and maximum diameters from 5–7.5 mm. The relationships and ratios between these dimensions for the proximal and middle phalanges have been calculated.

scholarly journals Diagnostic Sensitivity of Different Reference Bodies When Using Scheimpflug Tomography in a Myopic Population with Keratoconus

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Daniel Garcerant ◽  
Ignacio Jiménez-Alfaro ◽  
Nicolás Alejandre
Keyword(s):  
Observational Study ◽  
Receiver Operating Characteristic ◽  
Normative Data ◽  
Operating Characteristic ◽  
Roc Curves ◽  
Mean Square ◽  
Cutoff Points ◽  
Reference Body ◽  
Best Fit ◽  
Best Fit Sphere

Purpose. To establish which reference body offers the greatest sensitivity in keratoconus (KC) diagnosis, obtain normative data for the myopic population with toric ellipsoid reference bodies, and determine the cutoff points for a population with KC.Methods. A retrospective, observational study of the entire Scheimpflug tomographer database of the Fundación Jiménez Díaz in Madrid was conducted to identify a normal myopic and a KC myopic population. Three different reference bodies were tested on all patients: best fit sphere (BFS), best fit toric ellipsoid with fixed eccentricity (BFTEFE), and best fit toric ellipsoid (BFTE). Anterior and posterior elevation measurements at the apex and thinnest point were recorded, as well as the root mean square of posterior elevations (RMS-P). Normative data were extracted, and receiver operating characteristic (ROC) curves were generated to obtain cutoff points between the normal and KC population.Results. A total of 301 eyes were included, comprising 219 normal myopic and 82 myopic KC eyes. BFS and BFTEFE produced the best results when measuring posterior elevation at the thinnest point. BFTE had better sensitivity with the RMS-P. From all measurements, best sensitivity (100%) was achieved with a cutoff point of 8 μm of posterior elevation at the thinnest point using the BFTEFE. BFTE was found to hide the cone in certain patients.Conclusions. Posterior elevation measured at the thinnest point with a BFTEFE is the best-performing parameter and, therefore, is recommended to discriminate between normal and KC patients within a myopic population.

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