# Finite Element Analysis of the Epiretinal Membrane Contraction
## 2 Materials and Methods
### Image Acquisition and 3D Model Reconstruction  
The characteristics of the SD-OCT images allows them to be used for a 3D reconstruction based on multiple slice images - as shown in Figure 2, represented by the green lines. Since the objective of the numerical simulations is the analysis of the effects of an ERM contraction, starting from a healthy state, the 3D model was built, based on the healthy eye of Patient 1, as shown in Figure 4.  
The images of interest were initially imported to MIMICS(r), where a manual segmentation was performed on all sequential images, resulting in a 3D reconstruction. The initial model was then imported into 3-matic(r) to be improved, evolving into a more coherent mesh. Ultimately, the improved mesh was imported to FEMAP(r) to generate an interior mesh, necessary for the numerical simulations. The retina finite element model obtained from the OCT images reconstruction is shown in Figure 5 and consists of 17,793 linear tetrahedral elements and 4616 nodes.  
\begin{table}
\begin{tabular}{l c c} \hline \hline  & **Recovered Patient** & **Non-Recovered Patient** \\ \hline Gender & Male & Female \\ \hline Other Eye & Healthy & With Membrane \\ \hline Time between exams [months] & 2 & 13 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Patients characteristics.  
Figure 3: Displacements suffered by the retina, after the membrane emotion. The arrows show the amount of displacement.  
In relation to the 3D modelling of the ERM, there was no available information regarding its initial configuration, since the available OCT images show the ERM on its final, contracted configuration. To overcome this limitation, the initial form of the ERM of both patients was estimated based on the final form and the displacements shown in Figure 3. The model for the ERM was obtained by extruding the projected shape of the enlarged ERM, using linear wedge elements. The thickness of the ERM, was computed in order to maintain the ERM volume constant, after the contraction, since it was possible to obtain the final thickness of the ERM using the OCT scans. From the OCT scans a thickness of 0.14 mm for Patient 1 and 0.07 mm for Patient 2 were measured. An initial thickness of 0.1 mm for Patient 1 and 0.04 mm for Patient 2 were considered for the ERM.  
The final models for both the retina and the ERM were combined in ABAQUS to run the finite elements simulations, as can be seen in Figure 6. For the number of elements along the thickness of the membrane, after several tests conducted, only one element was used along the thickness, for the final model, since it allowed to produce the best results. The final mesh for the ERM, shown in Figure 6 consisted of 130 elements and 90 nodes, for Patient 1 and 657 elements and 480 nodes, for Patient 2.  
The models only differ between patients in the shape and thickness of the ERM, since the same 3D reconstruction of the retina was used in both cases. Boundary conditions were set to simulate the contraction of the retina, similar to the calibration model. As such, the inferior face of the retina was fixed, inhibiting any displacements and the activation level \(\delta\) of the contractile fibres was ramped up to 1.0.  
Figure 4: SLO and OCT images from the healthy eye of Patient 1.  
Figure 5: 3D model of the retina and corresponding finite element mesh obtained from the patient 1 healthy eye.