A mechanical model of ocular bulb vibrations and implications for acoustic tonometry

• Published in: PloS one Vol. 19; no. 1; p. e0294825
• Main Authors: Tambroni, Nicoletta, Tomassetti, Giuseppe, Lombardi, Silvia, Repetto, Rodolfo
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 18-01-2024; Public Library of Science (PLoS)
• Subjects: Acoustics; Biology and Life Sciences; Contact pressure; Cornea; Determinants; Diagnosis; Elastic shells; Evaluation; Eye; Eye diseases; Finite element analysis; Intraocular Pressure; Iris; Mathematical models; Measurement techniques; Mechanical properties; Medicine and Health Sciences; Nonlinear systems; Ocular accommodation; Physical Sciences; Pressure measurement; Resonant frequencies; Retina; Rheological properties; Rigidity; Sclera - physiology; Spherical harmonics; Spherical shells; Stiffening; Stress-strain curves; Tonometry; Tonometry, Ocular - methods; Vibration; Vibration damping; Vibration mode; Vibrations; Viscoelasticity; Vitreous humor; Vitreous humour; Italy
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0294825

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.