Validation of the Delft Finite Element Model of Orbital Mechanics

Abstract

Purpose: : In the Delft Finite Element Model of Orbital Mechanics, material properties are assigned to the elements based on in-vivo and post mortem measurements. We performed a validation study using high resolution MRI data and the previously measured values for viscoelasticity for a comparison with previous in-vivo measurements of passive rotational stiffness of the eye.

Methods: : High quality MRI data of the deformation of the orbital fat were obtained (see accompanying abstract by Dunning et al.). The orbital fat was segmented (Fig.). To estimate the displacement of the orbital fat, optical flow analysis (OFA) with the Demons and B-splines algorithms was employed. A stiffness matrix was build from finite element 8-node bricks. Material properties of the stiffness matrix were assigned according to post mortem viscoelasticity measurements on calf orbital fat (G’=250-500 Pa and G’’=80-170 Pa; Schoemaker et al. 2006). Local deformations of the orbital fat were first multiplied with the stiffness matrix of the fat to calculate the nodal forces. By multiplying these nodal forces with the deformations again, the energy of the eye movement was calculated. Dividing this energy by the angle of rotation resulted in the rotational stiffness. To validate the OFA, MRI control measurements were done by deformation of a piece of beef.

Results: : Stiffness in horizontal eye rotation was 30 - 480 mNmm/deg, comparable to the stiffness found in in-vivo measurements (120 mNmm/deg). In the OFA validation, translations were within 6% of the applied value, rotation within 3% and strain within 4%.

Conclusions: : Rotational stiffness of the eye could be derived from imaging data. This is a step towards the use of preoperative MRI and OFA to adapt the finite element model to an individual patient.

Keywords: orbit