Corneal Biomechanics

The Deformation Amplitude describes the movement of the apex in vertical direction. This movement depends on the overall corneal stiffness and from the intraocular pressure as well. The higher the corneal stiffness, the smaller the Deformation Amplitude. The Whole Eye Movement describes the movement of the whole eye in vertical direction. It depends on the biomechanical properties of the sclera and the fat tissue behind the eye.

The deflection amplitude describes the movement of the cornea and therefore has a stronger dependency on corneal properties. It is calculated as the difference between Deformation Amplitude and Whole Eye Movement.

This parameter is calculated based on the ratio between the Deformation Amplitude (vertical displacement) at the corneal apex and the Deformation Amplitude at 2 mm nasal and temporal from the apex. In case of a softer tissue the cornea starts to deform only in the center whereas the paracentral part of the cornea deforms much less. Therefore, the DAratio is higher in softer corneas than in stiffer corneas. In stiffer corneas the central and paracentral parts of the cornea are deformed at the same time and the DAratio is relatively small.

During the concave phase of the deformation the central Radius of curvature is calculated. A softer tissue exhibits a smaller radius as stiffer corneas do. The inverse Radius (1 / R) is calculated and the area under this inverse Radius vs. time curve is determined. This area is called integrated Radius and is a very good parameter to quantify the effect of corneal cross-linking. If this parameter gets smaller it indicates a stiffening of the cornea.

Vinciguerra et al. : In Vivo Early Corneal Biomechanical Changes After Corneal Cross-linking in Patients With Progressive Keratoconus : J Refract Surg. 2017 Dec 1;33(12):840-846

The biomechanical properties of the cornea are responsible for its function. Especially, the elastic properties of the cornea are responsible for the stability of the eye globe and a stable refraction as well. Elasticity is defined as the capability of a body to deform reversibly under an external force. The higher the force that is needed to deform an elastic body, the higher is the stiffness.

Analogous to a three point deformation of a beam, the bending stiffness can be defined as the ratio between applied force and the resulting vertical displacement:

For the first time stress-strain curves can be measured in real time on living patients. These measurements were derived by finite element simulations in the lab of Prof. Ahmed Elsheikh from Liverpool and validated both experimentally and clinically¹.

Stress-strain curves describe the intrinsic elastic properties of the cornea. The curves are shifted to the right if the cornea is softer, and shifted to the left if the cornea is stiffer. In comparison to the overall stiffness and rigidity the curves are less dependent on corneal thickness and IOP. The exact physical meaning of stress-strain curves are described here.

The stress-strain index (SSI) describes the position of the curve. A value of one indicates an average elasticity of healthy tissue, a value smaller than one a softer behaviour and a value greater than one a stiffer behaviour than the average. This parameter is one of the first clinical parameter that can indicate stiffening after corneal crosslinking.

¹ Eliasy A et al.: Determination of Corneal Biomechanical Behavior in-vivo for Healthy Eyes Using CorVis ST Tonometry: Stress-Strain Index. Front Bioeng Biotechnol. 2019 May 16;7:105 ff

Applanation tonometry and non-contact tonometry are both based on a simple principle: Applying a mechanical force on the cornea and correlation of the force that is needed to flatten the cornea with the intraocular pressure (IOP). The measured IOP values are influenced by the corneal thickness and the corneal elasticity – and therefore by corneal stiffness. Corneal stiffness is strongly changed for example in case of keratoconus but also after corneal refractive surgery. Moreover, age is known to influence the elastic biomechanical properties. These changes of biomechanical properties can lead to a larger over- or underestimation of the IOP and therefore lead to a wrong management of glaucoma.

The Corvis Biomechanical Index was developed by Riccardo and Paolo Vinciguerra from Italy, in order to detect early keratoconus based on the biomechanical response of the cornea. After a hypothesis of  Cynthia Roberts, PhD and William Dupps, PhD the morphological and geometrical changes in case of  corneal ectasia are only the consequence of earlier biomechanical changes. Changes of corneal curvature or pachymetric changes are therefore only secondary effects. Based on the model suggested by Dubbs and Roberts a local reduction of the elastic modulus occurs first, which causes a cycle of biomechanical decompensation leading to the well-known topographical changes¹. Theoretically, corneal ectasia could be therefore first detected based on corneal biomechanical properties.

The detection of early or subclinical forms of corneal ectasia is gaining more attention as these cases are supposed to be at high-risk for developing iatrogenic ectasia after laser vision correction. In addition, an early detection of the disease is also important in order to perform corneal cross-linking before the vision was already affected.

Currently, screening for subclinical ectasia is mainly done by corneal tomography or corneal topography. Unfortunately, based on these methods a significant amount of cases remains unrecognized, this could represent a high risk when performing refractive surgery in these normal appearing cases. Biomechanical analysis offers a new tool to optimize the screening and to detect cases that are at high risk despite having a normal topography and normal tomography.

Prof. Renato Ambrósio from Brazil developed and index that combines tomographic and biomechanical parameters in order to reach maximal accuracy. Based on a so-called random forest algorithm – a modern machine learning approach – an overall risk score is provided to evaluate ectasia susceptibility.

Pre-operatively, several screening methods exist in order to analyse the risk for developing ectasia after Laser Vision Correction. However, until now limited possibilities exist to evaluate ectasia risk post-operatively.

The CBI_LVC allows an automatic assessment of the biomechanical stability post-operatively. It was developed to differentiate between stable eyes post LVC and eyes that develop ectasia after LVC.

The software also detects automatically whether the examined patient has a treated cornea.

As a final output the CBI-LVC estimates the risk for an ectasia after laser vision correction. This is an aid for clinical decisions such as corneal crosslinking or laser touch-ups.

The new BEST Display (Homburg Biomechanical E-STaging Display) is the ideal solution for monitoring biomechanical changes over time. It enables you to analyze the progression, related to a baseline measurement.

Another important feature is to verify the success of treatment after corneal crosslinking. Whereas topographic changes only occur after several months biomechanical changes can be measured with the Corvis® ST already four weeks after the procedure.

Progression of keratoconus must be detected at a very early stage if a severe loss of vision is to be prevented.

The detection of Normal Tension Glaucoma (NTG) is very challenging in clinical practice. Intraocular pressure measurement will not indicate any elevated risk for glaucoma and also the optic nerve head might appear relatively normal. In Europe up to 30 percent of primary open angle glaucoma patients have a normal intraocular pressure, in Asia the incidence of NTG is even higher.

It has been shown recently that biomechanical properties can serve as an independent risk factor for NTG as the corneas of NTG patients are more deformable than age-matched healthy controls¹. This was the basis for the development of the Biomechanical Glaucoma Factor (BGF)². The BGF is an independent risk factor for normal tension glaucoma and can be used to screen for NTG patients.

¹ Riccardo Vinciguerra et al.: Corneal Biomechanics and Biomechanically-corrected Intraocular Pressure in Primary Open Angle Glaucoma, Ocular Hypertension and Controls;  British Journal of Ophthalmology 2019 April 2019.

² Pillunat KR, Herber R, Spoerl E, Erb C, Pillunat LE.: A new biomechanical glaucoma factor to discriminate normal eyes from normal pressure glaucoma eyes.  Acta Ophthalmol. 2019 Nov; 97(7)