Comparison of quasi-spherical surfaces : application to corneal biometry

In this study, the authors present two new techniques with their own particular advantages dedicated to the authentication of a person based on the three-dimensional geometry of the cornea. A device known as corneal topographer is used for capturing the shape of each cornea. Until now only a few studies on corneal biometry have been conducted and they were limited only to the anterior surface. In this study, since the whole cornea is a tissue layered by two (anterior and posterior) surfaces, the authors propose to use both surfaces to characterise the corneal shape. The first proposed method consists of comparing coefficients from a spherical harmonics decomposition, and this allows to do a fast comparison that can be used to perform many-to-one comparisons. The second approach is based on the minimal residual volume between two corneas after a registration step, this geometry-based method is more accurate but slower, and is thus used to perform one-to-one comparisons. A cascade fusion scheme is also proposed to benefit from the advantages of both methods. The authors’ study demonstrates that corneal shape could be used for biometry. The two proposed methods have been tested and validated on a dataset of 257 corneas

Analyse de maillages surfaciques par construction et comparaison de modèles moyens et par décomposition par graphes s’appuyant sur les courbures discrètes : application à l’étude de la cornée humaine

Réalisé en cotutelle avec Aix Marseille Université.Cette thèse se découpe en trois parties. Les deux premières portent sur le développement de méthodes pour la construction de modèles géométriques moyens et pour la comparaison de modèles. Ces approches sont appliquées à la cornée humaine pour l’élaboration d’atlas et pour l’étude biométrique robuste. La troisième partie porte sur une méthode générique d'extraction d'informations dans un maillage en s'appuyant sur des propriétés différentielles discrètes afin de construire une structure par graphe permettant l'extraction de caractéristiques par une description sémantique. Les atlas anatomiques conventionnels (papier ou CD-ROM) sont limités par le fait qu'ils montrent généralement l'anatomie d'un seul individu qui ne représente pas nécessairement bien la population dont il est issu. Afin de remédier aux limitations des atlas conventionnels, nous proposons dans la première partie d’élaborer un atlas numérique 3D contenant les caractéristiques moyennes et les variabilités de la morphologie d'un organe, plus particulièrement de la cornée humaine. Plusieurs problématiques sont abordées, telles que la construction d'une cornée moyenne et la comparaison de cornées. Il existe à ce jour peu d'études ayant ces objectifs car la mise en correspondance de surfaces cornéennes est une problématique non triviale. En plus d'aider à développer une meilleure connaissance de l'anatomie cornéenne, la modélisation 3D de la cornée normale permet de détecter tout écart significatif par rapport à la "normale" permettant un diagnostic précoce de pathologies ou anomalies de la forme de la cornée. La seconde partie a pour objectif de développer une méthode pour reconnaître une surface parmi un groupe de surfaces à l’aide de leurs acquisitions 3D respectives, dans le cadre d’une application de biométrie sur la cornée. L’idée est de quantifier la différence entre chaque surface et une surface donnée, et de déterminer un seuil permettant la reconnaissance. Ce seuil est dépendant des variations normales au sein d’un même sujet, et du bruit inhérent à l’acquisition. Les surfaces sont rognées et trouées de façon imprévisible, de plus il n’y a pas de point de mise en correspondance commun aux surfaces. Deux méthodes complémentaires sont proposées. La première consiste à calculer le volume entre les surfaces après avoir effectué un recalage, et à utiliser ce volume comme un critère de similarité. La seconde approche s’appuie sur une décomposition en harmoniques sphériques en utilisant les coefficients comme des descripteurs de forme, qui permettront de comparer deux surfaces. Des résultats sont présentés pour chaque méthode en les comparant à la méthode la plus récemment décrite dans la littérature, les avantages et inconvénients de chacune sont détaillés. Une méthodologie en cascade utilisant ces deux méthodes afin de combiner les avantages de chacune est aussi proposée. La troisième et dernière partie porte sur une nouvelle méthode de décomposition en graphes de maillages 3D triangulés. Nous utilisons des cartes de courbures discrètes comme descripteur de forme afin de découper le maillage traité en huit différentes catégorie de carreaux (ou peak, ridge, saddle ridge, minimal, saddle valley, valley, pit et flat). Ensuite, un graphe d'adjacence est construit avec un nœud pour chaque carreau. Toutes les catégories de carreaux ne pouvant pas être adjacentes dans un contexte continu, des jonctions intermédiaires sont ajoutées afin d'assurer une cohérence continue entre les zones. Ces graphes sont utilisés pour extraire des caractéristiques géométriques décrites par des motifs (ou patterns), ce qui permet de détecter des régions spécifiques dans un modèle 3D, ou des motifs récurrents. Cette méthode de décomposition étant générique, elle peut être appliquée à de nombreux domaines où il est question d’analyser des modèles géométriques, en particulier dans le contexte de la cornée.This thesis comprises three parts. The first two parts concern the development of methods for the construction of mean geometric models and for model comparison. These approaches are applied to the human cornea for the construction of atlases and a robust biometric study. The third part focuses on a generic method for the extraction of information in a mesh. This approach is based on discrete differential properties for building a graph structure to extract features using a semantic description. Conventional anatomical atlases (paper or CD-ROM) are limited by the fact they generally show the anatomy of a single individual who does not necessarily represent the population from which they originate. To address the limitations of conventional atlases, we propose in the first part of this thesis to construct a 3D digital atlas containing the average characteristics and variability of the morphology of an organ, especially that of the human cornea. Several issues are addressed, such as the construction of an average cornea and the comparison of corneas. Currently, there are few studies with these objectives because the matching of corneal surfaces is a non-trivial problem. In addition to help to develop a better understanding of the corneal anatomy, 3D models of normal corneas can be used to detect any significant deviation from the norm, thereby allowing for an early diagnosis of diseases or abnormalities using the shape of the cornea. The second part of this thesis aims to develop a method for recognizing a surface from a group of surfaces using their 3D acquisitions in a biometric application pertinent to the cornea. The concept behind this method is to quantify the difference between each surface and a given surface and to determine the threshold for recognition. This threshold depends on normal variations within the same subject and noise due to the acquisition system. The surfaces are randomly trimmed and pierced ; moreover, there is no common landmark on the surfaces. Two complementary methods are proposed. The first method consists of the computation of the volume between the surfaces after performing geometrical matching and the use of this volume as a criterion of similarity. The second approach is based on a decomposition of the surfaces into spherical harmonics using the coefficients as shape descriptors to compare the two surfaces. Each result of the proposed methods is compared to the most recent method described in the literature, with the benefits and disadvantages of each one described in detail. A cascading methodology using both methods to combine the advantages of each method is also proposed. The third and final part of this thesis focuses on a new method for decomposing 3D triangulated meshes into graphs. We use discrete curvature maps as the shape descriptor to split the mesh in eight different categories (peak, ridge, saddle ridge, minimal, saddle valley, valley, pit and flat). Next, an adjacency graph is built with a node for each patch. Because all categories of patches cannot be adjacent in a continuous context, intermediate junctions are added to ensure the continuous consistency between patches. These graphs are used to extract geometric characteristics described by patterns that allow for the detection of specific regions in a 3D model or recurrent characteristics. This decomposition method, being generic, can be used in many applications to analyze geometric models, especially in the context of the cornea

Optical Modeling of Schematic Eyes and the Ophthalmic Applications

The objectives of this dissertation are to advance and broaden the traditional average eye modeling technique by two extensions: 1) population-based and personalized eye modeling for both normal and diseased conditions, and 2) demonstration of applications of this pioneering eye modeling.The first type of representative eye modeling can be established using traditional eye modeling techniques with statistical biometric information of the targeted population. Ocular biometry parameters can be mathematically assigned according to the distribution functions and correlations between parameters. For example, the axial dimension of the eye relates to age, gender, and body height factors. With the investigation results from the studies of different population groups, population-based eye modeling can be established. The second type of eye model includes the optical components of the detailed corneal structure. Many of these structures, especially the corneal topography and wavefront aberration, are measured directly from the human eye. Therefore, the personalized eye models render the exact clinical measure and optical performance of the eye. In a sense, the whole eye, other than the identity of the individual, is quantified and stored in digital form for unlimited use for future research and industrial applications. The presentation of this dissertation is: Chapter 1 describes the background of the research in this area, the introduction of eye anatomy, and the motivation of this dissertation work. In Chapter 2, a comprehensive review of the contemporary techniques of measuring ocular parameters is presented and is followed by the review of literature and then the statistical analysis of the ocular biometry parameters. The goal of this chapter is to build a statistical base for population-based schematic eye modeling research. The analysis includes the investigation of the correlations between ocular parameters and ocular refraction, subject age, gender, ethnicity, and accommodation conditions. In Chapter 3, the tools and methods that are used in our optical eye modeling are introduced. The operation of the optical program ZEMAX is discussed. The detail of the optical eye modeling procedure and method of optical optimization, which is utilized to reproduce desired clinical measurement results, are described. The validation functions, which will be used to evaluate the optimization results, are also addressed. Chapter 4 includes the discussion of the population-based eye modeling and the personalized eye modeling. With the statistical information and the clinical measurements presented in Chapter 2 and the computation method described in Chapter 3, the two types of eye modeling technologies are demonstrated. The procedure, difficulty, and validation of eye modeling are included. The considerations of optical opacities, irregular optical surface, multiple reflection, scattering, and tear film breakup effects are discussed and the possible solutions in ZEMAX are suggested. Chapter 5 presents eye modeling applications of the simulations of ophthalmic instrument measurements. The demonstrated simulation results are retinoscopy and photorefraction. The simulation includes both normal eye model and diseased eye model. The close conformity between the simulation results with the actual clinical measurements further validates the eye modeling technique. The ophthalmic simulation application provides the potential for medical training and instrument development. The summary of the dissertation is given in Chapter 6

Analysis of the human corneal shape with machine learning

Cette thèse cherche à examiner les conditions optimales dans lesquelles les surfaces cornéennes antérieures peuvent être efficacement pré-traitées, classifiées et prédites en utilisant des techniques de modélisation géométriques (MG) et d’apprentissage automatiques (AU). La première étude (Chapitre 2) examine les conditions dans lesquelles la modélisation géométrique peut être utilisée pour réduire la dimensionnalité des données utilisées dans un projet d’apprentissage automatique. Quatre modèles géométriques ont été testés pour leur précision et leur rapidité de traitement : deux modèles polynomiaux (P) – polynômes de Zernike (PZ) et harmoniques sphériques (PHS) – et deux modèles de fonctions rationnelles (R) : fonctions rationnelles de Zernike (RZ) et fonctions rationnelles d’harmoniques sphériques (RSH). Il est connu que les modèles PHS et RZ sont plus précis que les modèles PZ pour un même nombre de coefficients (J), mais on ignore si les modèles PHS performent mieux que les modèles RZ, et si, de manière plus générale, les modèles SH sont plus précis que les modèles R, ou l’inverse. Et prenant en compte leur temps de traitement, est-ce que les modèles les plus précis demeurent les plus avantageux? Considérant des valeurs de J (nombre de coefficients du modèle) relativement basses pour respecter les contraintes de dimensionnalité propres aux taches d’apprentissage automatique, nous avons établi que les modèles HS (PHS et RHS) étaient tous deux plus précis que les modèles Z correspondants (PZ et RR), et que l’avantage de précision conféré par les modèles HS était plus important que celui octroyé par les modèles R. Par ailleurs, les courbes de temps de traitement en fonction de J démontrent qu’alors que les modèles P sont traités en temps quasi-linéaires, les modèles R le sont en temps polynomiaux. Ainsi, le modèle SHR est le plus précis, mais aussi le plus lent (un problème qui peut en partie être remédié en appliquant une procédure de pré-optimisation). Le modèle ZP était de loin le plus rapide, et il demeure une option intéressante pour le développement de projets. SHP constitue le meilleur compromis entre la précision et la rapidité. La classification des cornées selon des paramètres cliniques a une longue tradition, mais la visualisation des effets moyens de ces paramètres sur la forme de la cornée par des cartes topographiques est plus récente. Dans la seconde étude (Chapitre 3), nous avons construit un atlas de cartes d’élévations moyennes pour différentes variables cliniques qui pourrait s’avérer utile pour l’évaluation et l’interprétation des données d’entrée (bases de données) et de sortie (prédictions, clusters, etc.) dans des tâches d’apprentissage automatique, entre autres. Une base de données constituée de plusieurs milliers de surfaces cornéennes antérieures normales enregistrées sous forme de matrices d’élévation de 101 by 101 points a d’abord été traitée par modélisation géométrique pour réduire sa dimensionnalité à un nombre de coefficients optimal dans une optique d’apprentissage automatique. Les surfaces ainsi modélisées ont été regroupées en fonction de variables cliniques de forme, de réfraction et de démographie. Puis, pour chaque groupe de chaque variable clinique, une surface moyenne a été calculée et représentée sous forme de carte d’élévations faisant référence à sa SMA (sphère la mieux ajustée). Après avoir validé la conformité de la base de donnée avec la littérature par des tests statistiques (ANOVA), l’atlas a été vérifié cliniquement en examinant si les transformations de formes cornéennes présentées dans les cartes pour chaque variable étaient conformes à la littérature. C’était le cas. Les applications possibles d’un tel atlas sont discutées. La troisième étude (Chapitre 4) traite de la classification non-supervisée (clustering) de surfaces cornéennes antérieures normales. Le clustering cornéen un domaine récent en ophtalmologie. La plupart des études font appel aux techniques d’extraction des caractéristiques pour réduire la dimensionnalité de la base de données cornéennes. Le but est généralement d’automatiser le processus de diagnostique cornéen, en particulier en ce qui a trait à la distinction entre les cornées normales et les cornées irrégulières (kératocones, Fuch, etc.), et dans certains cas, de distinguer différentes sous-classes de cornées irrégulières. L’étude de clustering proposée ici se concentre plutôt sur les cornées normales afin de mettre en relief leurs regroupements naturels. Elle a recours à la modélisation géométrique pour réduire la dimensionnalité de la base de données, utilisant des polynômes de Zernike, connus pour leur interprétativité transparente (chaque terme polynomial est associé à une caractéristique cornéenne particulière) et leur bonne précision pour les cornées normales. Des méthodes de différents types ont été testées lors de prétests (méthodes de clustering dur (hard) ou souple (soft), linéaires or non-linéaires. Ces méthodes ont été testées sur des surfaces modélisées naturelles (non-normalisées) ou normalisées avec ou sans traitement d’extraction de traits, à l’aide de différents outils d’évaluation (scores de séparabilité et d’homogénéité, représentations par cluster des coefficients de modélisation et des surfaces modélisées, comparaisons statistiques des clusters sur différents paramètres cliniques). Les résultats obtenus par la meilleure méthode identifiée, k-means sans extraction de traits, montrent que les clusters produits à partir de surfaces cornéennes naturelles se distinguent essentiellement en fonction de la courbure de la cornée, alors que ceux produits à partir de surfaces normalisées se distinguent en fonction de l’axe cornéen. La dernière étude présentée dans cette thèse (Chapitre 5) explore différentes techniques d’apprentissage automatique pour prédire la forme de la cornée à partir de données cliniques. La base de données cornéennes a d’abord été traitée par modélisation géométrique (polynômes de Zernike) pour réduire sa dimensionnalité à de courts vecteurs de 12 à 20 coefficients, une fourchette de valeurs potentiellement optimales pour effectuer de bonnes prédictions selon des prétests. Différentes méthodes de régression non-linéaires, tirées de la bibliothèque scikit-learn, ont été testées, incluant gradient boosting, Gaussian process, kernel ridge, random forest, k-nearest neighbors, bagging, et multi-layer perceptron. Les prédicteurs proviennent des variables cliniques disponibles dans la base de données, incluant des variables géométriques (diamètre horizontal de la cornée, profondeur de la chambre cornéenne, côté de l’œil), des variables de réfraction (cylindre, sphère et axe) et des variables démographiques (âge, genre). Un test de régression a été effectué pour chaque modèle de régression, défini comme la sélection d’une des 256 combinaisons possibles de variables cliniques (les prédicteurs), d’une méthode de régression, et d’un vecteur de coefficients de Zernike d’une certaine taille (entre 12 et 20 coefficients, les cibles). Tous les modèles de régression testés ont été évalués à l’aide de score de RMSE établissant la distance entre les surfaces cornéennes prédites (les prédictions) et vraies (les topographies corn¬éennes brutes). Les meilleurs d’entre eux ont été validés sur l’ensemble de données randomisé 20 fois pour déterminer avec plus de précision lequel d’entre eux est le plus performant. Il s’agit de gradient boosting utilisant toutes les variables cliniques comme prédicteurs et 16 coefficients de Zernike comme cibles. Les prédictions de ce modèle ont été évaluées qualitativement à l’aide d’un atlas de cartes d’élévations moyennes élaborées à partir des variables cliniques ayant servi de prédicteurs, qui permet de visualiser les transformations moyennes d’en groupe à l’autre pour chaque variables. Cet atlas a permis d’établir que les cornées prédites moyennes sont remarquablement similaires aux vraies cornées moyennes pour toutes les variables cliniques à l’étude.This thesis aims to investigate the best conditions in which the anterior corneal surface of normal corneas can be preprocessed, classified and predicted using geometric modeling (GM) and machine learning (ML) techniques. The focus is on the anterior corneal surface, which is the main responsible of the refractive power of the cornea. Dealing with preprocessing, the first study (Chapter 2) examines the conditions in which GM can best be applied to reduce the dimensionality of a dataset of corneal surfaces to be used in ML projects. Four types of geometric models of corneal shape were tested regarding their accuracy and processing time: two polynomial (P) models – Zernike polynomial (ZP) and spherical harmonic polynomial (SHP) models – and two corresponding rational function (R) models – Zernike rational function (ZR) and spherical harmonic rational function (SHR) models. SHP and ZR are both known to be more accurate than ZP as corneal shape models for the same number of coefficients, but which type of model is the most accurate between SHP and ZR? And is an SHR model, which is both an SH model and an R model, even more accurate? Also, does modeling accuracy comes at the cost of the processing time, an important issue for testing large datasets as required in ML projects? Focusing on low J values (number of model coefficients) to address these issues in consideration of dimensionality constraints that apply in ML tasks, it was found, based on a number of evaluation tools, that SH models were both more accurate than their Z counterparts, that R models were both more accurate than their P counterparts and that the SH advantage was more important than the R advantage. Processing time curves as a function of J showed that P models were processed in quasilinear time, R models in polynomial time, and that Z models were fastest than SH models. Therefore, while SHR was the most accurate geometric model, it was the slowest (a problem that can partly be remedied by applying a preoptimization procedure). ZP was the fastest model, and with normal corneas, it remains an interesting option for testing and development, especially for clustering tasks due to its transparent interpretability. The best compromise between accuracy and speed for ML preprocessing is SHP. The classification of corneal shapes with clinical parameters has a long tradition, but the visualization of their effects on the corneal shape with group maps (average elevation maps, standard deviation maps, average difference maps, etc.) is relatively recent. In the second study (Chapter 3), we constructed an atlas of average elevation maps for different clinical variables (including geometric, refraction and demographic variables) that can be instrumental in the evaluation of ML task inputs (datasets) and outputs (predictions, clusters, etc.). A large dataset of normal adult anterior corneal surface topographies recorded in the form of 101×101 elevation matrices was first preprocessed by geometric modeling to reduce the dimensionality of the dataset to a small number of Zernike coefficients found to be optimal for ML tasks. The modeled corneal surfaces of the dataset were then grouped in accordance with the clinical variables available in the dataset transformed into categorical variables. An average elevation map was constructed for each group of corneal surfaces of each clinical variable in their natural (non-normalized) state and in their normalized state by averaging their modeling coefficients to get an average surface and by representing this average surface in reference to the best-fit sphere in a topographic elevation map. To validate the atlas thus constructed in both its natural and normalized modalities, ANOVA tests were conducted for each clinical variable of the dataset to verify their statistical consistency with the literature before verifying whether the corneal shape transformations displayed in the maps were themselves visually consistent. This was the case. The possible uses of such an atlas are discussed. The third study (Chapter 4) is concerned with the use of a dataset of geometrically modeled corneal surfaces in an ML task of clustering. The unsupervised classification of corneal surfaces is recent in ophthalmology. Most of the few existing studies on corneal clustering resort to feature extraction (as opposed to geometric modeling) to achieve the dimensionality reduction of the dataset. The goal is usually to automate the process of corneal diagnosis, for instance by distinguishing irregular corneal surfaces (keratoconus, Fuch, etc.) from normal surfaces and, in some cases, by classifying irregular surfaces into subtypes. Complementary to these corneal clustering studies, the proposed study resorts mainly to geometric modeling to achieve dimensionality reduction and focuses on normal adult corneas in an attempt to identify their natural groupings, possibly in combination with feature extraction methods. Geometric modeling was based on Zernike polynomials, known for their interpretative transparency and sufficiently accurate for normal corneas. Different types of clustering methods were evaluated in pretests to identify the most effective at producing neatly delimitated clusters that are clearly interpretable. Their evaluation was based on clustering scores (to identify the best number of clusters), polar charts and scatter plots (to visualize the modeling coefficients involved in each cluster), average elevation maps and average profile cuts (to visualize the average corneal surface of each cluster), and statistical cluster comparisons on different clinical parameters (to validate the findings in reference to the clinical literature). K-means, applied to geometrically modeled surfaces without feature extraction, produced the best clusters, both for natural and normalized surfaces. While the clusters produced with natural corneal surfaces were based on the corneal curvature, those produced with normalized surfaces were based on the corneal axis. In each case, the best number of clusters was four. The importance of curvature and axis as grouping criteria in corneal data distribution is discussed. The fourth study presented in this thesis (Chapter 5) explores the ML paradigm to verify whether accurate predictions of normal corneal shapes can be made from clinical data, and how. The database of normal adult corneal surfaces was first preprocessed by geometric modeling to reduce its dimensionality into short vectors of 12 to 20 Zernike coefficients, found to be in the range of appropriate numbers to achieve optimal predictions. The nonlinear regression methods examined from the scikit-learn library were gradient boosting, Gaussian process, kernel ridge, random forest, k-nearest neighbors, bagging, and multilayer perceptron. The predictors were based on the clinical variables available in the database, including geometric variables (best-fit sphere radius, white-towhite diameter, anterior chamber depth, corneal side), refraction variables (sphere, cylinder, axis) and demographic variables (age, gender). Each possible combination of regression method, set of clinical variables (used as predictors) and number of Zernike coefficients (used as targets) defined a regression model in a prediction test. All the regression models were evaluated based on their mean RMSE score (establishing the distance between the predicted corneal surfaces and the raw topographic true surfaces). The best model identified was further qualitatively assessed based on an atlas of predicted and true average elevation maps by which the predicted surfaces could be visually compared to the true surfaces on each of the clinical variables used as predictors. It was found that the best regression model was gradient boosting using all available clinical variables as predictors and 16 Zernike coefficients as targets. The most explicative predictor was the best-fit sphere radius, followed by the side and refractive variables. The average elevation maps of the true anterior corneal surfaces and the predicted surfaces based on this model were remarkably similar for each clinical variable

Accommodation: optical function and crystalline lens imaging

Esta tesis se centra en el estudio, por medio de varias técnicas in vivo, del proceso de acomodación del ojo humano. En primer lugar, haciendo uso de un sistema de Óptica Adaptativa, muestra que las aberraciones de alto orden disminuyen la precisión acomodativa, al mismo tiempo que tienden a incrementar las fluctuaciones de la acomodación. Por último, con un sistema de Tomografía de Coherencia Óptica de alta resolución, se hace imagen estática tridimensional del cristalino para diferentes demandas acomodativas. Del mismo modo, también se hace imagen dinámica bidimensional del cristalino durante la acomodación. El análisis de las imágenes permite obtener información de la respuesta acomodativa del ojo

Tonometry:a study in biomechanical modelling. Appraisal and utility of measurable biomechanical markers.

Goldmann Applanation Tonometry (GAT) is the recognised ‘Gold Standard’ tonometer.However this status is refuted by eminent authors. These contradictory views have driventhe initial goal to assess, from first principles, the evolution of GAT and to experimentallyevaluate its utility and corrections. Subsequently, an important caveat became theevaluation of Corneal Hysteresis and Corneal Resistance Factor.Chapter 1. Biomechanical building blocks are defined and constitutive principlesincorporated into continuum modelling. The Imbert-Fick construct is re-interpreted asimple biomechanical model. GAT corrections are also appraised within a continuumframework; CCT, geometry and stiffness. These principles enable evaluation ofalternative tonometer theory and the evolving biomechanical markers, CornealHysteresis (ORA-CH) and Corneal Resistance Factor (ORA-CRF).Chapter 2 appraises corneal biomechanical markers, CCT, curvature, ORA-CH andORA-CRF in 91 normal eyes and the impact these have on three tonometers: GAT,Tonopen and Ocular Response Analyser (ORA). Tonopen was the sole tonometer notaffected by biomechanics. CCT was confirmed the sole measurable parameter affectingGAT. ORA did not demonstrate improved utility. ORA-CH and ORA-CRF do not appearrobust biomechanical measures.Chapter 3 assessed agreement between GAT, the ORA measures and Tonopen.Tonopen is found to measure highest and raises the question should a development goalemphasise GAT agreement or improvement?Chapter 4 assessed repeatability of the three tonometers and biomechanical measureskeratometry, pachymetry, ORA-CH and ORA-CRF on 35 eyes. Coefficients ofRepeatability (CoR) of all tonometers are wide. Effects assessed in Chapter 5 may bemasked by general noise. ORA does not appear to enhance utility over GAT.Isolation of corneal shape change via Orthokeratology (Chapter 5) demonstrate ORACHand ORA-CRF reflect, predominantly, a response to corneal flattening. It is proposedthey do not significantly reflect corneal biomechanics.After reviewing models for tear forces (Chapter 6), a refined mathematical model ispresented. Tear bridge attraction is minimal and cannot explain under-estimation of IOPby GAT in thin corneas. CCT corrections and the Imbert-Fick rules are incompatible.Chapter 7 summarises findings. The supremacy of GAT is likely to remain for some time,reflecting the sheer magnitude of overturning 60 years of convention, historicalprecedent, expert opinion as well as the logistical and educational difficulties ofredefining standards and statistical norms

Birefringent properties of the human cornea in vivo : towards a new model of corneal structure

The fundamental corneal properties of mechanical rigidity, maintenance of curvature and optical transparency result from the specific organisation of collagen fibrils in the corneal stroma. The exact arrangement of stromal collagen is currently unknown but several structural models have been proposed. The purpose of the present study is to investigate inconsistencies between current x‐ray derived structural models of the cornea and optically derived birefringence data. Firstly, the thesis reviews the current understanding of corneal structure, particularly in relation to corneal birefringence. It also reviews and develops the different analytical approaches used to model optical biaxial behaviour, particularly as applied to predict corneal optical phase retardation. The second part develops a novel technique of elliptic polarization biomicroscopy (EPB), enabling study of corneal birefringence in vivo. Using EPB, the pattern of corneal retardation is recorded for a range of human subjects. This dataset is then used to investigate both central and peripheral corneal birefringence as well as the corneal microstructure. A key finding is that the central parts of the cornea exhibit a retardation pattern compatible with a negative biaxial crystal, whereas the peripheral corneal regions do not. Furthermore, within the central regions of the cornea, orthogonal confocal conic fibrillar structures are identified which resemble the analytically derived contours of equal refractive index of an ideal negative biaxial crystal. The third part of this work presents a synthesis of previous published experimental, anatomical and theoretical findings and the experimental results presented in this thesis. Based on these findings, a novel corneal structural model is proposed that comprises overlapping spherical elliptic structural units. Finally, ensuing biomechanical and clinical consequences of the spherical elliptic structural model and of the EPB technique are discussed including their potential diagnostic and surgical applications

Caracterización óptica de lentes intraoculares = Optical characterization of intraocular lenses

The optical characterization of an intraocular lens (IOL) provides objective and quantitative information that is essential to fully understand its performance as an implant that replaces the crystalline lens in the human visual system. Additionally, it can be used to predict the performance of the new IOL designs. This thesis analyses the main sources of uncertainty in the calculation of the IOL power and the compensation of the residual refractive errors by using some unconventional degrees of freedom. The thesis focuses on the in vitro characterization of a variety of commercially available IOLs (monofocal, multifocal, spherical, aspherical, apodized, full-­-aperture, and of different materials, powers and additions) in optical bench. To this end, we have designed and implemented the necessary methods of measurement and an experimental setup that, according to the international standard regulation, reproduces the conditions of such implants in the human eye. We have developed a method to measure the energy efficiency of IOLs. This method has allowed us to explain the clinical results obtained in the evaluation of the stereoscopic acuity when using two tests based on different principles. The optical imaging quality of IOLs has been quantified through the experimental measurement of the modulation transfer function and the fringe visibility (contrast). We have developed and implemented a method to characterize some artifact, named halo, that can be perceived by those patients implanted with multifocal IOLs. Finally, all the experimental results have been used as a basis for the comparison of the IOL performances.La caracterización óptica de las lentes intraoculares (IOLs del inglés Intraocular Lenses) proporciona una información objetiva y cuantitativa que es necesaria para comprender su funcionamiento como implante que sustituye al cristalino en el sistema visual humano. Además, permite predecir el rendimiento de los nuevos diseños. Dicha caracterización se debe llevar a cabo mediante pruebas in vivo en pacientes ya implantados así como con pruebas in vitro en banco óptico o mediante simulación teórica. Esta tesis analiza las fuentes de error en el cálculo de la potencia de las lentes intraoculares y la compensación de los errores refractivos residuales mediante el uso de grados de libertad no convencionales. Se centra, fundamentalmente, en la caracterización in vitro de una variedad de lentes comercialmente disponibles (monofocales, multifocales, esféricas, asféricas, apodizadas, no-­-apodizadas, y distintos materiales, potencias y adiciones) en un banco óptico. Para ello se ha diseñado y puesto a punto los métodos de medida, un montaje experimental que reproduzca las condiciones en las que las lentes se implantan en el ojo y de acuerdo con la normativa internacional. Se ha medido la calidad óptica a través de la Función de Transferencia de Modulación o la visibilidad de franjas (contraste). Se ha desarrollado e implementado un método para la cuantificación experimental de la eficiencia energética de los distintos modelos de IOLs. Este método ha servido para explicar algunos resultados clínicos obtenidos al evaluar la visión estereoscópica con dos tests con diferente principio de funcionamiento. Se ha desarrollado e implementado un método para caracterizar el halo que perciben algunos pacientes implantados con IOLs multifocale

Corneal biomechanical properties : Measurement, modification and simulation

Esta tesis aborda la medición de las propiedades biomecánicas de la córnea. Se desarrollaron técnicas para medir la rigidez de la córnea in vitro con el fin de estudiar el comportamiento de la córnea como una función de diferentes factores (tales como la hidratación, la geometría, la presión intraocular y la rigidez de la córnea). Los datos experimentales se utilizaron para construir modelos numéricos capaces de reproducir la respuesta biomecánica observada de la córnea. Se aplicaron modelos numéricos para recuperar los parámetros biomecánicos de mediciones de deformación in vivo y para estudiar el efecto de la implantación de segmentos de anillos intraestromales. En particular, se utilizaron el método de inflación en ojos enteros y botones córneales, la extensiometría bídimensional, un soplo de aire combinado con tomografía de coherencia óptica (OCT), microscopía de Brillouin y OCT-vibrografía para las mediciones experimentales. Para el análisis numérico, se construyeron modelos de elementos finitos para estudiar la inflación de ojos enteros y botones córneales, la respuesta de la córnea después de un soplo de aire, el comportamiento del ojo bajo vibración y los cambios refractivos después de la implantación de anillos intraestromales. This thesis addresses the measurement of the corneal biomechanical properties. Techniques were developed to measure the corneal stiffness in vitro in order to study the corneal behavior as a function of different factors (such as hydration, geometry, intraocular pressure, corneal stiffness). Experimental data were used to build numerical models, which were able to reproduce the observed biomechanical response of the cornea. Numerical models were applied to retrieve biomechanical parameters from in vivo deformation measurements and to study the outcome with implantation of intrastromal ring segments. In particular whole-eye / corneal inflation, 2D extensiometry, an air-puff technique combined with optical coherence tomography (OCT), Brillouin microscopy and OCT-vibrography were used for the experimental measurements. For the numerical analysis, finite element models were built for eye inflation, corneal response following an air-puff, ocular vibration behavior and refractive changes after ICRS implantation