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The Individual Virtual Eye

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The Individual Virtual Eye The Individual Virtual Eye Dissertation der Fakultät für Informations- und Kognitionswissenschaften der Eberhard-Karls-Universität Tübingen zur Erlangung des Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) vorgelegt von Dipl.-Inform. Jens Einighammer aus Tübingen Tübingen 2008 Tag der mündlichen Qualifikation: 13.2.2008 Dekan: Prof. Dr. Michael Diehl 1. Berichterstatter: Prof. Dr.Ing. Dr.Ing. E.h. Wolfgang Straßer 2. Berichterstatter: Prof. Dr. med. Benedikt Jean Dedication Dedicated to my father Dr. Hans J. Einighammer iii Abstract The individual virtual eye is a computer model of a human eye with respect to the optical properties. Established schematic eyes, as Gullstrand’s model eye, are intended to represent properties of an average eye based on averaged population measurements. In contrast, the individual virtual eye is based on measurements of an individual person. Therefore the geometry of the eye is important, including axial length and topographic measurements of the anterior corneal surface. All optical components of a pseudophakic eye – an eye with an artificial lens – are modeled by means of computer scientific methods. A spline-based interpolation method was developed to efficiently include data from corneal topographic measurements. Based on this virtual eye the geometrical optical properties, such as the wavefront aberration, can be simulated by using Snell’s law of refraction and the method called real ray tracing. Moreover, optical components can be calculated using computer scientific optimization procedures. High value was set on the efficient implementation of the time-critical numerical ray-tracing and optimization procedures to allow for short calculation times in the range of seconds. This leads to clinical application fields in ophthalmology that have been addressed in this thesis. One application is intraocular lens calculation for cataract surgery, with the potential to overcome limitations of current calculation methods like lens calculation after refractive surgery. Also customized aspherical lenses were calculated what shows the capability of the methods to deal with advanced lens geometry. Clinically important issues as the optical effects of intraocular lens dislocation have been investigated. Furthermore, this computer model has been used to assess ablation profiles used in current refractive corneal laser surgery. One possible future enhancement of the model is the simulation of phakic eyes by incorporating a correct model of the human crystalline lens. And, so far, the individual virtual eye focused on geometrical optical properties, but may serve as a basis for including physiological properties of the retina and brain in future. Keywords: Human optics; pseudophakic eye; computer simulation; real ray tracing; Snell’s law; corneal topography; spline interpolation; wavefront aberration; optimization problem; intraocular lens calculation; ablation profiles; refractive surgery v Zusammenfassung Das individuelle virtuelle Auge ist ein Computermodell eines menschlichen Auges zur Simulation der optischen Eigenschaften. Gängige Modellaugen wie das bekannte schematische Auge von Gullstrand basieren auf Daten von vielen Personen und zielen üblicherweise darauf ab, die Eigenschaften eines durchschnittlichen Auges zu repräsentieren. Im Gegensatz dazu basiert das individuelle virtuelle Auge auf Messwerten einer einzelnen Person. Entscheidend dabei sind geometrische Größen, insbesondere die axiale Länge und die Topographie der vorderen Hornhautoberfläche. Alle optischen Komponenten eines pseudophaken Auges – d.h. eines Auges mit einer künstlichen Linse – sind mit computertechnischen Methoden modelliert. Ein auf Spline-Interpolation basierendes Verfahren wurde entwickelt, um eine effiziente Integration von Messwerten einer Hornhauttopographie zu ermöglichen. Anhand dieses virtuellen Auges können unter Anwendung des Snell’schen Brechungsgesetzes und Ray-TracingMethoden geometrisch optische Eigenschaften, wie zum Beispiel die Wellenfrontaberration, simuliert werden. Darüber hinaus können mit computertechnischen Optimierungsmethoden auch optische Komponenten berechnet werden. Großer Wert wurde auf eine effiziente Implementierung der zeitkritischen numerischen Ray-Tracing- und Optimierungsmethoden gelegt, um eine kurze Berechnungszeit im Bereich von Sekunden zu erreichen. Dies führt zu klinischen Anwendungsgebieten in der Ophthalmologie, von denen einige in dieser Arbeit behandelt wurden. Dazu zählt die Intraokularlinsenberechnung für die Kataraktchirurgie, sowohl für normale als auch für schwierige Fälle wie nach refraktiver Chirurgie, bei denen bisherige Berechnungsmethoden unzulänglich sind. Ferner wurden auch individuell zugeschnittene asphärische Intraokularlinsen berechnet, und somit die Leistungsfähigkeit des Ray-Tracing- Verfahrens im Hinblick auf aufwendigere Linsengeometrien demonstriert. Als klinisch relevante Fragestellung wurde der optische Effekt einer Verdrehung oder Verkippung von Intraokularlinsen evaluiert. Darüber hinaus wurden Ablationsprofile untersucht, wie sie derzeit in der refraktiven kornealen Laserchirurgie eingesetzt werden. Eine zukünftige Erweiterungsmöglichkeit wäre die Einbeziehung eines Modells der natürlichen kristallinen Linse des Menschen, so dass auch phake Augen simuliert werden können. Auch konzentriert sich das virtuelle Auge bislang auf geometrisch optische Eigenschaften, könnte aber als Basis dienen für die Einbeziehung von physiologischen Eigenschaften von Netzhaut und Gehirn. Schlüsselbegriffe: Optik des menschlichen Auges; pseudophakes Auge; Computer- simulation; Ray Tracing; Snell’sches Gesetz; Hornhauttopographie; Spline-Interpolation; Wellenfrontaberration; Optimierungsproblem; Intraokularlinsenberechnung; Ablationsprofile; refraktive Chirurgie vii Main Contributions This is an interdisciplinary thesis combining scientific fields. The main contribution field and key discipline is computer science: computer technical structures and methods were developed and implemented for the realization of an individual virtual eye to allow for realistic simulation regarding the optical properties and furthermore allow for calculation of optical components. This leads to substantial contributions to a second discipline, medicine, as there are clinically relevant applications of the individual virtual eye in ophthalmology. Computer Science Contributions to computer science are located in chapter 3 that describes the computer technical development and implementation of the individual virtual eye: • Modeling of optical components (spectacles, cornea and lens) of the virtual eye with mathematical surfaces that are feasible regarding physiology and optical properties as well as efficiently usable for computational ray tracing (section 3.1 on page 33 ff.) • Development of a spline-based interpolation schema for corneal elevation and surface normals obtained from corneal topography measurements, especially regarding an efficient usage for ray tracing (section 3.1.1 on page 34 ff.) • Simulation of optical performance by real ray tracing through the virtual eye based on Snell’s law resulting in the geometric optical criterions spot size and wavefront aberration (section 3.2 on page 41 ff.) • Calculation of optical components (e.g. intraocular lenses) by the formulation of optimization problems taking the geometry as input and optical quality criterions as output; solving by numerical minimization in one or more dimensions (section 3.3 on page 46 ff.) • Implementation of the virtual eye in a way that allows for an integration into medical devices leading to practicable medical applications (Figure 1-1) Medicine Contributions to medicine are found in chapter 5 that shows the ophthalmological applications of the individual virtual eye: • Calculation of intraocular lenses with the potential to overcome limitations of current calculation methods like the correct handling of refractive treated eyes what is of particular clinical interest (section 5.1 on page 55 ff.) • Calculation of customized toric aspherical intraocular lenses what is not possible so far in clinical practice (section 5.2 on page 67 ff.) • Analysis of ablation profiles currently used in refractive laser surgery (section 5.3 on page 98 ff.) ix Software Architecture The individual virtual eye is embedded in the real ray tracing module of the OphthaTOP (OphthaSWISS AG, Switzerland) videotopometer software developed in cooperation with the Division “Experimental Ophthalmic Surgery”, University Eye Hospital Tübingen. An overview of the software architecture showing the main components is shown in Figure 1-1. All calculations performed in this thesis were done with this real ray tracing module. Main Application • Operating System: Microsoft Windows XP Grabber- • Programming Language: C++ Module • Developer Environment: Microsoft Visual Video display: Studio .NET 2003 DirectX 9 • Architecture: Microsoft Foundation Classes (MFC) Internal data exchange between modules: Viewer-Module(s) Class TopometerData Display: Windows Graphics Device Interface (GDI) Data Exchange: Patient- & Elevation- & • DirectX WDM Examination- Real Ray Tracing (Windows driver model) • USB 2.0 Manager Module Module 3D-View: DirectX 9 Data Exchange: Data Exchange: ODBC/SQL OLE Automation Hardware Database Data Analysing including Management System Environment CMOS IBM DB2 Express-C V9 Microsoft Excel camera Figure 1-1: Software architecture xi Contents Dedication .................................................................................................................................iii
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