# Mueller Matrix-Based Approach for the Ex Vivo Detection of Riboflavin-Treated Transparent Biotissue
## 3 Results
### Mueller Matrix Measurements Ex Vivo
For the calculation of the MM entries, we crop the images as shown in Figure 4. The blue area is the largest continuous rectangle that does not contain the reflection region. Thus, the maximal number of pixels can be evaluated. For the processing, it is beneficial in the current approach to evaluate rectangular areas of the same size only. If only the measurement data from the blue area is used, the entries \(M(2,1)\), \(M(2,2)\) and \(M(3,3)\) show a clear difference between the measurements with and without riboflavin (Figure 6a-c). If only the measurement data from the red area are taken into account, the same difference is less obvious (Figure 6d-f). For the calculated \(R\), \(P\) and \(\Delta\) metrics, a difference between the measurement conditions I, II and III, IV can be found for \(P\) and \(\Delta\) after a reduction in the measurement data to the certain areas specified in Figure 4. The results are displayed in Figure 7.  
This indicates that the signal-to-noise-ratio can be improved by the careful choice of the region of interest segmentation for the input images and that the effect of the CXL is measurable with the MM setup. The polar decomposed MMs can show the effect of CXL after adding riboflavin and treating the samples with UV irradiation as well. This can be derived from the comparison of the matrix entries of \(M_{D}\) and \(M_{\Delta}\). For the entries of \(M_{D}\) (not displayed), the elements \(M(1,2)\), \(M(1,4)\), \(M(2,1)\), \(M(2,4)\), \(M(3,3)\), \(M(3,4)\), \(M(4,1)\), \(M(4,2)\), \(M(4,3)\) and \(M(4,4)\) show differences between the samples with and without riboflavin treatment. Similarly to the results for \(M_{D}\), there is a difference between the samples with and without riboflavin treatment for the entries of \(M_{\Delta}\) in the elements \(M(2,1)\), \(M(2,2)\), \(M(3,3)\) and \(M(4,4)\) as displayed in Figure 8.  
The analysis of the decomposed MMs shows that the difference between measurement conditions I, II, and III, IV can also be derived after the polar decomposition of the MMs. As shown in [20] the degree of orientation of the samples, in this case polymer fibers, is related to the Mueller matrix and its decomposition. In the present work, the changes displayed in Figures 7 and 8 might be attributed to the changes in the orientation of the collagen fibers in the cornea. The structural changes due to the induced corneal collagen cross-linking, leading to a higher degree of orientation, might increase the polarizance and decrease the depolarization power--both of which are observable as macroscopic effects. Figure 5: Mean values of the MM images from a series of measurements on porcine corneas. The measurements were performed on corneas neither prepared with riboflavin nor irradiated with UV (I), not prepared with riboflavin but irradiated with UV (II), prepared with riboflavin but not irradiated with UV (III) and both prepared with riboflavin and irradiated with UV (IV). The error bars represent the standard deviation for the sample size used as derived from multiple measurements. The elements \(M(2,1)\), \(M(2,2)\), \(M(2,3)\), \(M(3,2)\), \(M(3,3)\) and \(M(4,4)\), highlighted by bar plots show a clear difference between the samples with and without riboflavin treatment. Figure 6: MM entries for different regions of interest with an observable difference between the measurements with and without riboflavin: (**a**) mean value of \(M(2,1)\) using the blue area; (**b**) mean value of \(M(2,2)\) using the blue area; (**c**) mean value of \(M(3,3)\) using the blue area; (**d**) mean value of \(M(2,1)\) using the red area; (**e**) mean value of \(M(2,2)\) using the red area; and (**f**) mean value of \(M(3,3)\) using the red area. Figure 4:0 Mean values of \(M_{\Delta}\) from the blue region of porcine cornea images. The errorbars represent the standard deviation for the sample size used, as derived from multiple measurements. Elements \(M(2,1)\), \(M(2,2)\), \(M(3,3)\) and \(M(4,4)\) show the difference between the samples with and without riboflavin treatment.