315 The Mouse Model of Myopia
deviation of this procedure is about 1%, with the major source of variability the depth of focus of the video camera.
Axial length measurements and ocular biometry
Perhaps the most important variable in myopia studies is axial length. The type of myopia that is experimentally induced in animal models is almost always axial. Therefore, the first question is about the axial length changes. There were several attempts to measure axial eye lengths in mice: video imaging of freshly enucleated eyes21,22,45; analysis of histological sections of eyes2; highly enlarged photographs of frozen sections15; and eye weight measurements.17 These techniques could be used only post-mortem, and all may have limited resolution to detect experimentally induced axial myopia. Attempts to measure axial eye length in vivo with A-scan ultrasonography (which is typically used in other animal models of myopia) also failed in the small eye of the mouse.22 Major progress was therefore made when a commercial optical low coherence interferometer (OLCI) was adapted to measure short-range optical distances. The initial goal was to measure corneal thickness and anterior chamber depth in humans (the Carl Zeiss “AC Master” (http://www.meditec.zeiss.com/), Jena, Germany). A test showed that this device was also able to measure the intraocular distances in living mouse eyes.46 Unfortunately, the company decided not to market the AC Master so that only prototypes are currently available to a
Figure 6. Measurements of ocular dimensions in a mouse with the “AC Master” (Zeiss-Meditec, Jena, Germany). (A) The slightly anesthetized mouse, positioned on an adjustable platform, which is attached to the chinrest of the device, is encircled. (B) Close-up view used to adjust the eye in the measurement beam. The first Purkinje images of six infrared LEDs, built into the device, are used to align the eye.46
316 F. Schaeffel
few laboratories.21,46,47 Therefore, custom-built low coherence interferometers were introduced,19 or are currently under construction.
The optical principle of optical low coherence interferometry is based on a Michelson interferometer. A low coherence superluminescent laser diode (SLD) that emits an infrared light with a peak emission at 850 nm and a half-band width of 10 nm serves as light source. Due to the broadened bandwidth, the coherence length is rather short (about 10 m), compared to standard laser diodes, in which it is about 160 m. The infrared laser beam emerging from the LED is divided into two perpendicular beams via a semi-silvered mirror. One part is transmitted through the semi-silvered mirror and reaches a stationary mirror. The other part reaches a second mirror that can be moved along the light path with high positional precision. After reflection from both mirrors, the two coaxial beams propagate to the eye, where they are reflected off from the cornea, the lens, and the fundal layers. Interference between both beams can only occur when their optical path lengths are matched with extreme precision, within the coherence length. The occurrence of interference is detected by a photo cell and recorded as a function of the displacement of the movable mirror. Due to the usage of coaxial beams, the measurements are largely insensitive against longitudinal eye movements. The scanning time of the movable mirror is about 0.3 sec. In the human eye, a measurement precision in the range of 2 m has been achieved in corneal thickness measurements, and of 5 to 10 m for the anterior chamber depth and lens thickness measurements (R. Bergner, Carl Zeiss Meditec, Jena, personal communication, 2004). In repeated measurements in mouse eyes, a standard deviation of 8 m was found for axial length — equivalent to less than two diopters.46
It should be kept in mind that optical path lengths are measured with this technique, which need to be converted into geometrical path lengths. This requires that the refractive indices for the ocular media are known. The problem has been analyzed by Schmucker and Schaeffel.46 The errors are generally small even if the refractive indices are not exactly known. Also, in most cases, differences are of interest between the treated and control eyes, rather than absolute axial lengths.
Measurements of the optical aberrations of the mouse eye
In recent years, new optical techniques have been developed to describe the optical quality of the human eye in vivo. Perhaps the currently
317 The Mouse Model of Myopia
most successful technique, the Hartmann–Shack aberrometer, has been adapted for measurements in mice.10 For Hartmann–Shack measurements, a superluminescent diode at 676 nm produces a bright spot on the retina. A fraction of the light is reflected from the fundus and returns from the eye through the pupil. This light reaches a microlens array of 65 × 65 square lenslets with a 400 m aperture and a focal length of 24 mm. The lenslets create a pattern of focal spots on a CCD chip of a video camera. If an eye has no aberrations and is focused at infinity, the spot pattern is perfectly regular and each of the foci is exactly along the optical axes of the lenslets. However, if the wavefront is distorted due to optical aberrations in the cornea and lens, the focal spots are laterally displaced and form irregular patterns (Fig. 7, the left columns show the original HartmannShack images). The displacement of each of the foci is proportional to the
Figure 7. (A) Original Hartmann–Shack images, and reconstructions of the wavefronts recorded from 12 eyes of alert mice. Wave aberration maps are for the third and higher order aberrations, and contour lines are plotted in 0.1 m steps. (B) Calculations of the average modulation transfer functions of the mouse eyes. Note that the contrast transfer drops off steeply with increasing spatial frequency, but that the contrast transfer is still around 20% at 4 cyc/deg (replotted after de la Cera et al., Ref. 10).
318 F. Schaeffel
tilt of the wavefront at the respective position. To reconstruct the threedimensional shape of the wavefront, the centers of the focal spots are detected by image processing software — a demanding task if they are as diffuse, as shown in Fig. 7.10 The shape of the wavefront is typically described as a Polynomial expansion, as proposed by Zernike. The coefficients describe the magnitude of known optical aberrations, like defocus, astigmatism, spherical aberration, and so on. In the measurements in the mouse, defocus was the most dominant term (average hyperopia +10.1 ± 1.4 D), but also astigmatism (3.6 ± 3.7 D) and positive spherical aberration (wavefront error 0.15 ± 0.07 m for a 1.5 mm pupil) were highly significant. At least, the measurements with the Hartmann–Shack sensor provided quite similar spherical refractive errors to the infrared photorefractor (Fig. 1B).
The Zernike coefficients also permit the calculation of how much contrast the optics of the eye transfers at the different spatial frequencies. The transfer function is called modulation transfer function (MTF). It shows that the mouse eye’s optics transfers are still about 20% of the contrast at 4 cyc/deg. Comparing this value to the behavioral limit of spatial resolution of the mouse — around 0.5 cyc/deg, it is unlikely that the optics of the eye is the limiting factor for visual acuity in mice.
It turned out that alert mice could be accurately positioned for Hartmann–Shack aberrometry by just holding their tails, moving the platform, and waiting until they calmed down. It was also attempted to perform measurements under anesthesia. However, the optical quality of the eyes was then much poorer.10 This could explain why such low optical quality was described in rodent eyes in a previous study in mice and rats.48
Remtulla and Hallett7 initially estimated the depth of field of the mouse at as large as +56 D, based on photoreceptor diameters and using the equations provided by Green et al.78 But they also stated that this must be an unrealistic number. They noted that behavioral visual acuity may be five times higher as calculated from anatomical variables,49 and finally estimated the depth of field as +11 D.
Aberrometric techniques permit a more direct estimation of the optical depth of field. De la Cera et al.10 calculated the contrast transfer (modulation) of the mouse optics for a sine wave grating of 2 cyc/deg, at different amounts of defocus. They found that modulation drops to 50% already at about 5 D of defocus. Since the spatial acuity of the mouse is only about a fourth of this value in behavioral studies, the depth of field should be