Estimation of the mechanical properties of the eye through the study of its vibrational modes

Measuring the eye's mechanical properties in vivo and with minimally invasive techniques can be the key for individualized solutions to a number of eye pathologies. The development of such techniques largely relies on a computational modelling of the eyeball and, it optimally requires the synergic interplay between experimentation and numerical simulation. In Astrophysics and Geophysics the remote measurement of structural properties of the systems of their realm is performed on the basis of (helio-)seismic techniques. As a biomechanical system, the eyeball possesses normal vibrational modes encompassing rich information about its structure and mechanical properties. However, the integral analysis of the eyeball vibrational modes has not been performed yet. Here we develop a new finite difference method to compute both the spheroidal and, specially, the toroidal eigenfrequencies of the human eye. Using this numerical model, we show that the vibrational eigenfrequencies of the human eye fall in the interval 100 Hz - 10 MHz. We find that compressible vibrational modes may release a trace on high frequency changes of the intraocular pressure, while incompressible normal modes could be registered analyzing the scattering pattern that the motions of the vitreous humour leave on the retina. Existing contact lenses with embebed devices operating at high sampling frequency could be used to register the microfluctuations of the eyeball shape we obtain. We advance that an inverse problem to obtain the mechanical properties of a given eye (e.g., Young's modulus, Poisson ratio) measuring its normal frequencies is doable. These measurements can be done using non-invasive techniques, opening very interesting perspectives to estimate the mechanical properties of eyes in vivo. Future research might relate various ocular pathologies with anomalies in measured vibrational frequencies of the eye.Comment: Published in PLoS ONE as Open Access Research Article. 17 pages, 5 color figure

Toroidal vibrational modes.

<p>Six different patterns of toroidal vibration at the lowest frequencies in our model S0 of the eye that correspond to the same transversal cut as shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0183892#pone.0183892.g001" target="_blank">Fig 1</a>. Light and dark blue (red and yellow) shades indicated a motion towards (away from) the reader and normal to the drawn plane. <i>Left panels</i>: eigenfunctions with even parity in <i>l</i>: (<i>n</i> = 1, <i>l</i> = 2) vibrating at 318 Hz, (1, 4) at 648 Hz and (2, 2) at 909 Hz. <i>Right panels</i>: eigenfunctions with odd parity: (1, 3) at 492 Hz, (2, 1) at 1159 Hz and (1, 5) at 797 Hz.</p

Simplified mechanical model of the eyeball.

<p>Left: transversal cut of the human eye with the different structural parts annotated in it (source: Wikipedia). Right: spherically symmetric, homogeneous and isotropic eyeball model employed in this work.</p

Calibration of the method.

<p>Comparison between the analytic (panels with black background) and numerical (white background) solutions of vibrational patterns. Because of the symmetries, only one quadrant of the full equatorial plane of an spherical body is shown. Modes of odd and even parities are displayed in the upper and lower panels, respectively. In this case, we are using 100 points in the radial direction and 50 in the angular one. We can also observe a good agreement in their corresponding frequencies (listed below each panel), that improves as we increase the resolution.</p

Frequencies of selected normal modes of improved eyeball models.

<p>Frequencies of selected normal modes of improved eyeball models.</p

Frequencies of selected normal modes of the simplified human eye.

<p>Frequencies of selected normal modes of the simplified human eye.</p