A reduced whole eye model to estimate in vivo biomechanical properties of the human cornea

Abstract

 

Purpose

 

To develop a reduced whole eye model for inverse estimation of corneal biomechanical properties

 

Methods

 

Figure 1 shows a cross-section of the model. The corneal limbus was supported by a parallel network of spring (Kz, Kx) and dashpot (μ) to account for globe, muscles and fat viscoelasticity. The cornea itself was modeled as a fiber dependent, hyperelastic and incompressible material. Depth dependent properties were incorporated to model shear resistance (Petsche et al., 2013). Corneal deformation from Corvis-ST (OCULUS Optikgerate Gmbh, Germany) was used in the inverse finite element (iFE) method. Transient air-puff pressure and a constant intraocular pressure (IOP) were applied as loads. 10 eyes of 10 normal subjects were measured. The optimized function was defined as the difference between the displacement of the anterior edge of the cornea estimated by iFE and obtained after image processing of Corvis-ST images. The iFE was solved using Abaqus v.6.12 (Simulia Inc., USA) and custom python scripting. Further IOP was varied from a normal of 15 mmHg to 13 and 17 mmHg to assess sensitivity of property parameters to measured IOP.

 

Results

 

Figure 2 shows the apical rise of the corneas vs. simulated increase in pressure applied to the posterior surface using the estimated biomechanical properties. The non-linear response of the cornea was evident and the regression was excellent (R²=0.98). Figure 3 shows the regressed data for IOP=13, 15 and 17 mmHg for all the 10 corneas averaged together for each IOP. The average difference in estimated apical rise was ~5% at 15±2 mmHg. The mean biomechanical properties of the cellular matrix were 73±22.8 kPa and 4.81±9.97MPa at IOP=15 mmHg. Similarly, the mean properties of collagen network were 0.39±0.05 kPa and 308±76 at IOP=15 mmHg.

 

Conclusions

 

A novel reduced whole eye model was developed which significantly reduced the computation time from the previous whole eye model developed by the authors. The model also incorporated depth dependent shear properties and demonstrated its application to estimate in vivo properties.  

 

Figure 1 shows a cross-section of the model<br /> Figure 2 shows the apical rise of the corneas vs. simulated increase in pressure applied to the posterior surface using the estimated biomechanical properties<br /> Figure 3 shows the regressed data for IOP=13, 15 and 17 mmHg for all the 10 corneas averaged together for each IOP<br />