Department of Civil, Chemical and Enivironmental Engineering, University of Genoa, Genoa, Italy.
Department of Industrial, Electronic, and Mechanical Engineering, Roma Tre University, Rome, Italy.
PLoS One. 2024 Jan 18;19(1):e0294825. doi: 10.1371/journal.pone.0294825. eCollection 2024.
In this study, we propose a comprehensive mechanical model of ocular bulb vibrations and discuss its implications for acoustic tonometry. The model describes the eye wall as a spherical, pre-stressed elastic shell containing a viscoelastic material and accounts for the interaction between the elastic corneoscleral shell and the viscoelastic vitreous humor. We investigate the natural frequencies of the system and the corresponding vibration modes, expanding the solution in terms of scalar and vector spherical harmonics. From a quantitative point of view, our findings reveal that the eyebulb vibration frequencies significantly depend on IOP. This dependency has two origins: "geometric" stiffening, due to an increase of the pre-stress, and "material" stiffening, due to the nonlinearity of the stress-strain curve of the sclera. The model shows that the second effect is by far dominant. We also find that the oscillation frequencies depend on ocular rigidity, but this dependency is important only at relatively large values of IOP. Thus close to physiological conditions, IOP is the main determinant of ocular vibration frequencies. The vitreous rheological properties are found to mostly influence vibration damping. This study contributes to the understanding of the mechanical behavior of the eye under dynamic conditions and thus has implications for non-contact intraocular pressure measurement techniques, such as acoustic tonometry. The model can also be relevant for other ocular pathological conditions, such as traumatic retinal detachment, which are believed to be influenced by the dynamic behavior of the eye.
在这项研究中,我们提出了一个全面的眼球振动力学模型,并讨论了其对声振眼压测量的影响。该模型将眼球壁描述为一个含有粘弹性材料的预加应力的弹性壳,并考虑了弹性角膜巩膜壳与粘弹性玻璃体之间的相互作用。我们研究了系统的固有频率和相应的振动模式,通过标量和矢量球谐函数展开解。从定量的角度来看,我们的发现表明眼球振动频率显著依赖于眼压。这种依赖性有两个来源:由于预应增加引起的“几何”变硬,以及由于巩膜的应力-应变曲线的非线性引起的“材料”变硬。该模型表明,第二个效应远占主导地位。我们还发现,振动频率取决于眼球刚性,但这种依赖性仅在相对较高的眼压值时才重要。因此,在接近生理条件下,眼压是眼球振动频率的主要决定因素。玻璃体的流变性质主要影响振动阻尼。这项研究有助于理解眼球在动态条件下的力学行为,因此对非接触眼压测量技术(如声振眼压测量)具有重要意义。该模型对于其他眼部病理情况也可能具有相关性,例如外伤性视网膜脱离,据信其受到眼球动态行为的影响。