## 5 Experiment Analysis
### Quantitative Results of Region-Estimation Algorithm  
In cell quantification, a thresholding process was employed. During the start of processing or in the optimization threshold, images were inspected or visualized manually, and the best set of images (in this case, 2:1) that were visualized were taken in optimizing the threshold value. This might be because of variability in laser power excitation during the acquisition of images, and intensity based image variations had minimal or no effect on the quantification of cellular analysis. Employing one ratio threshold to other cellular ratios did not affect the results, as cellular sizes were uniform in all cellular ratios. Fibroblast (NIH3T3) cell-to-cell interactions are tight and they form tight junctions; therefore, cell boundaries may not be distinguishable. NIH3T3 cells were clustered, and various thresholding values were applied to find the optimal threshold values, as shown in Figure 6. Figure 6 indicates the segmented NIH3T3 cells overlain with binary masks to evaluate the most relevant threshold value. Values were obtained by multiplying a scalar quantity with maximal intensity value in the image, and passing the binary thresholding data. It was important to choose an optimal threshold value because, by choosing a higher threshold value, intensities start merging into another, and for small threshold values, tiny cells seem to appear that are oversegmented. By visual inspection, and from Figure 6 and 7, the value of T = 0.125 corresponded to the best possible results for all image slices. In this way, clustered NIH3T3 cells were converted into their binary masks using the optimal threshold. The binarized mask was then fed into the RE algorithm 1 to count the NIH3T3 cells. The results of the overlain images of HCT-8 and NIH3T3 binary masks on its original images are shown in Figure 8.  
The distribution of NIH3T3 and HCT-8 cells was as shown in Figure 9,b for horizontal cross-sectional views. Figure 9 shows the blue (HCT-8) cell count (BCC), and green (NIH3T3) cell count (GCC); and Figure 9 shows the blue (HCT-8) cell area (BCA) and green (NIH3T3) cell area (GCA) of the _in vitro_ 3D cell spheroid for 2:0.5 ratio images. For other cellular ratios, the distribution pattern is shown in Figures S11-S13. Cell-count distribution gave better observation for HCT-8 cells, whereas the area plot gave better distribution pattern analysis for NIH3T3 cells. The limitation in NIH3T3 cell count can be attributed to the high overlap and the staining procedure of the green cell tracker. After evaluating the count for HCT-8 and NIH3T3 cells (as shown in Figure 9,b), further evaluation for the region-estimation algorithm (Algorithm 1) was performed for each ratio image. The concentration of HCT-8 cells was the maximum in the core region compared to the whole _in vitro_ 3D cell spheroid. The densest region of HCT-8 cells in the _in vitro_ 3D cell spheroid estimated by the RE algorithm 1 (\(R_{dense}\)) was the core region (CR), and the width of the core region was estimated to approximately be 100 \(\upmu\)m.  
Figure 6: Optimal threshold evaluation for NIH3T3 cells using various threshold segmentation results. (**a**) 2:0.5 (2_05_z12), (**b**) 2:1 (2_1_z14), (**c**) 2:2 (2_2_z17), and (**d**) 2:4 (2_4_z10) ratio images. Standalone image analysis software (Image J) was used in comparing the cellular quantification of the results. The procedure to segment and quantify HCT-8 and NIH3T3 cells for all cellular ratio images by ImageJ software was as shown in Figure 10, and the corresponding quantification data was as shown in Figure 11. The process steps during quantification using ImageJ introduce manual biasing: segmentation, thresholding, pixel size, and circularity bias. Briefly, the quantification process was as follows. Slices were input to the ImageJ software, and images were split into three channels: red, green, and blue. After splitting the channels, thresholding was adjusted. A watershed algorithm was then used for segmentation.