# Numerical Simulation on Corneal Surface Behavior Applying Luminous Beam Levels
## 3 Results
### Model Validation  
It was essential to validate the proposed model; the cornea is considered a regular geometry. Therefore, it is possible to view a proportional fraction to validate a specific area. Hence, 25% of the corneal surface was considered for the analysis. This was mainly to reduce the computational resources and the time to solve. Figure 5 shows a free-body diagram in different views. The boundary conditions had three constraints, shown in Figure 5, marked by a gray shadow; where it exists, they were applied in each of the three views of the figure. These conditions belonging to the nodes involved in the numerical analysis program are shown \begin{table}
\begin{tabular}{c c c c} \hline
**Case No.** & **Wavelength** & **Frequency** & **Electromagnetic Spectrum** \\ \hline
1 & 300 nm & 999.31 THz & UV-B \\
2 & 350 nm & 856.55 THz & UV-A \\
3 & 460 nm & 651.72 THz & Visible Spectrum (Blue) \\
4 & 1000 nm & 299.79 THz & Near Infrared \\
5 & 1500 nm & 199.86 THz & Medium Infrared \\ \hline \end{tabular}
\end{table} 
Table 2: Cases of study. Figure 5: Free-body diagram, (**a**) base constraint, (**b**) lateral constraint, and (**c**) adjacent lateral constraint. in Figure 6. As a result of this validation, 26 nodes (blue dots) were assigned at the base of the corneal structure. Several researchers contemplated comparing the data from the necessary mechanical properties to be used. The following parameters were selected for a K (modulus of compressibility) of 100 \(\upmu\), shear modulus of 0.282 MPa, and elastic modulus of collagen fibers (EFIB) of 38.950 MPa [30]. The values assigned were compared with an experimental investigation from 1972. In this specific case, the displacement carried out at the specific moment of the incidence of an amount of load, the whole process was quantifiable in an experiment with the corneas of 15 specimens of different persons [31]. The results of the comparison are shown in Table 3.  
The error was calculated in each of the seven payloads; cases 1 to 4 exhibit less than 1%, and the last three no more than 10%, averaging a total error of 3.4%, which is an acceptable value to proceed with the analysis of the cases; from the data of Table 3 and by applying the general equation of error percent it is possible to estimate the error per case. \[\%error=\left(\frac{analysis\ result-experimental\ value}{analysis\ result}\right)\ *\ 100\]  
In each case, the error was calculated for each of the seven references: case 1 = 0%; case 2 = 0%; case 3 = 0%; case 4 = 0.83%; case 5 = 5.35%; case 6 = 8.68%; case 7 = 8.97%. Applying an average to the above percentage error results in a \(\%error=3.40\%\). Figure 7 shows the comparative values from Table 3; age-related health conditions and the solution method (numerical or experimental) contribute to the difference between each curve displayed in the graph. However, there is an approximation between outcomes. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **Load (mmHg)** &
\begin{tabular}{c} **Deformation** \\ **(\(\upmu\)m)** \\ \end{tabular} & **Experimental Values Range (\(\upmu\)m)** \\ \hline
1 & 10 & 10.7 & 1.7–11.8 \\
2 & 15 & 17.989 & 9.59–18.4 \\
3 & 20 & 23.1 & 12.3–23.7 \\
4 & 25 & 27.8315 & 14.4–27.6 \\
5 & 30 & 33.387 & 16.4–31.6 \\
6 & 35 & 37.4516 & 17.8–34.2 \\
7 & 40 & 39.01 & 18.5–35.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Correlation of results. Figure 6: Corneal section; anchorage and movement node assignment. The analysis of the cases to be studied was based on the procedure applied in the validation, but in this case, the whole model was contemplated for greater assertiveness in the results; thus, we were able to consider a more significant number of decimal places in the calculations. Also, the complete model (corneal surface) in the program, its exportation to STL, the tetrahedral mesh's application, and the assignation of the boundary conditions were used and configured. Figure 8 shows the free-body diagram into 2 views; (a) 3D view and (b) wireframe view.