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intraocular lenses. Another promising modeling direction is the populationbased eye modeling that can be established using traditional eye-modeling techniques with the statistical information and correlations of the ocular parameters of the targeted population. Simulating ocular device measurements including eye models could be useful, for not only rapid prototyping and sensitivity evaluations of ocular instruments, but also for the teaching and training of medical personnel. Computational personalized eye modeling techniques also allow the integrated information to be quantitatively evaluated for disease development studies without the repetitive examination of human subjects. The revelations that the ocular optics may be clinically altered have sped the renovation of physiological optics from an observational to a quantitative, and possibly even a predictive, science.

The optical elements of an anatomically accurate eye model include the cornea, the anterior chamber, the iris (pupil stop), the posterior chamber, the crystalline lens, the vitreous chamber, and the retina. Schematic eye models in the early 20th century used spherical ocular elements and constant indexes of refraction.1 Later in the 1980s, aspherical ocular elements and complex models of the eye lens were incorporated to represent better than average ocular monochromatic and chromatic imaging properties of the eyes. These general eye models were important to evaluate optical performance, to investigate ocular properties, and to design new ophthalmic corrections, including spectacles and contact lenses. Among the current published generic eye models, the wide-angle Navarro model2 was built by incorporating published anatomical values of conic constant into the Gullstrand-Le Grand spherical surfaces3 and by updating the values of the anterior radius and refractive index of the cornea. This model has been shown to produce on-axis image quality, as well as off-axis aberrations that are in agreement with mean human measurements, and, therefore, this model will be used in this chapter as the initial base emmetropic model for demonstration purposes.

13.1.1. Ocular Measurements for Optical Eye Modeling

The numerical measurement of the ocular biometry and optical parameters are essential for mathematical eye modeling. The ophthalmic measurements that are useful for modeling are briefly reviewed below.

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13.1.1.1.Curvature, dimension, thickness, or distance parameters of ocular elements

Because of the difficulty and intrusiveness of reaching the internal ocular tissues in vivo, the noninvasive reflection signals of light or sound waves from the interfacial surfaces of different ocular layers are typically used to provide information about the ocular dimensions and locations. These techniques include the ultrasoundgraphy A- and B-scans, the pachymeter, which measures corneal thickness, partial coherence interferometry (PCI) techniques, such as the IOL mater, OCT devices including Cirrus™ HD-OCT, the RTVue-100 Fourier-Domain OCT, the Visante OCT, and the Spectral OCT/SLO, MRI devices, spectacular microscopy, and keratometer.

13.1.1.2. Three-dimensional (3D) corneal topography

Corneal topography, also known as photokeratoscopy or videokeratography, is a noninvasive technique for imaging the surface curvature of the cornea. Since the cornea is typically responsible for about 70% of the eye’s refractive power, its surface condition, especially the anterior interface, is of critical importance in both determining the quality of vision and in eye modeling work. The topographic techniques include the Placido disk imaging, such as Humphrey® Atlas™ corneal topography systems and TMS-4a Topographer, the slit-scanning system of Orbscan, and the Scheimpflug imaging of Pentacam. The Orbscan and the Pentacam devices provide both anterior and posterior corneal elevation maps as well as mapping the thickness of cornea, and, therefore, are especially valuable for the eye modeling.

13.1.1.3. Crystalline lens parameters

The crystalline lens can be measured in vitro or in vivo. Ultrasound, OCT, and Purkinje images are the most popular in vivo methods. Though the first two methods can measure curvatures and thicknesses, they have the disadvantages of touching the cornea and being slow in measurement. Purkinje images are the sequence of reflections from the refracting surfaces of the eye elements. PI, PII, PIII, and PIV indicate the refraction images formed at the boundary of air/cornea (or tear), posterior cornea/aqueous, aqueous/anterior

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lens, and posterior lens/vitreous, respectively. The Purkinje images method can measure curvatures while the eye is viewing a target and can, therefore, monitor accommodation variations.

13.1.1.4. Refractive index

Refractive indexes of ocular elements are not often measured in clinical environments. However, they do not vary significantly across individuals. The human lens has a gradient refractive index. The Liou and Brennan eye model4 uses a gradient index to mimic the measured data. For simplified computation, an “equivalent” constant index is often used instead of the actual gradient index. The Navarro 1985 model used 1.42 for relaxed eye, and this model describes the index as a function of accommodation. The Atchison 2008 study used Purkinje imagery to describe a lens equivalent refractive index as a function of age and applied the parameter in the four-surface eye model.5 Unless age or accommodation factors are encountered, most eye-modeling work simply adapts the constant values of refractive index.

13.1.1.5. Wavefront aberration

In recent years, WFA has become a popular method for evaluating monochromatic performance of the human eye and is sometimes described as “the fingerprint of the individual eye.” In physical optics, the wavefront represents the surface locus of points that have the same optical path or phase from the light source. The 2D function of WFA describes the point-to-point departure from perfect wavefront, normally a spherical surface, in the exit pupil. In ocular optics, WFA becomes an important addition to the conventional refractive error measurement. The second-order WFA corresponds to the refractive error, and high-order WFA is responsible for reduced visual acuity (VA) in spite of an optimal correction from spherical or cylindrical refractive lens. VISX WaveScan Wavefront System and the Allegro Analyzer are examples of commercial devices of the Shack-Hartmann and the Tscherning types of aberrometer, respectively. The clinically measured WFA of an eye can be used for customized eye modeling.

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