## 5 Experiment Analysis
### Quantitative Results of Region-Estimation Algorithm
After segmentation, images were analyzed by providing the pixel size (30-infinity) and circularity (0.30-1.00). Most biases were eliminated during the TLBO clustering and quantification approach except for thresholding bias. The ImageJ software separately clustered the HCT-8 and NIH3T3 cells along with background noise. Though it was required to perform the segmentation algorithm in both approaches, the watershed algorithm was applied in the ImageJ software, whereas TLBO clustering was applied in the proposed methodology. However, the watershed segmentation technique had the drawback of having excessive oversegmentation [22]. In contrast, TLBO separately clustered the HCT-8 and NIH3T3 cells without any background pixels. Comparative analysis of GCC and BCC using the proposed methodology with the counts of both types of cells obtained from ImageJ software [14] from the peripheral to the core region (slice no. \(z_{0\ldots 49}\)) for 2:0.5 ratio images is shown in Figure 12. Other cellular ratios are presented in Figures S14-S16. Because of circularity and pixel-size bias, there was much observable difference between the BCC and GCC of ImageJ software, and the BCC and GCC obtained after applying the proposed methodology. The counting of cells by the proposed methodology showed that most HCT-8 cells were concentrated towards the core region, whereas NIH3T3 cells were more concentrated towards the peripheral region. The difference between manual cell counting and the proposed methodology was approximately 35%, 40%, 60%, and 80% for 2:05, 2:01, 2:2, and 2:4, respectively. Moreover, the proposed methodology accurately measured the physiological approximation of the cell count for all cell-ratio processes [15]. The difference percentage of the counting results of each ratio was variate, from 35% to 80%. This may be due to two reasons:  
1. Figure 11 shows that the segmentation results of the ImageJ software for the HCT-8 and NIH3T3 cell clusters also included background pixels (noise). This happened for  
Figure 7: NIH3T3 cells count for 2:1 ratio of horizontal cross-sectional images for various threshold values. each ratio image, which were further processed and detected (or counted) as blobs (or cells) by the software. 2. Moreover, the Image] software needed some parameter adjustment (threshold value, circularity, and size) for segmenting and counting the cells. Biasing error affected the final results. Figure 8: Overlain cluster and original images for HCT-8 and NIH3T3 cells: (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. The equation used to evaluate the percentage difference between manual cell counting and proposed-methodology counting is as follows:  
\[Diff(\%)=\frac{\sum_{i=1}^{N}M_{i}-\sum_{i=1}^{N}P_{i}}{T_{c}}\times 100 \tag{4}\]  
where \(\sum_{i=1}^{N}M_{i}\) is the sum of the manual cell count \(\forall i=1\) to \(N\), and N is the number of slices. Similarly, \(\sum_{i=1}^{N}P_{i}\) is the sum of the proposed methodology cell count \(\forall i=1\) to \(N\). \(T_{c}\) is the total number of cells present in the _in vitro_ 3D cell spheroid; \(N=50\). Preliminary data derived from the current nature-inspired clustering algorithm (TLBO) help to understand 3D _in vitro_ systems by the spectrometric location of the extracellular matrix generating protein. Thus, it aids biological scientists in further targeted molecular studies such as polymerase chain reaction (PCR) and Western blot techniques, which are highly selected for treatment planning and diagnostic procedures [23]. Hence, the proposed methodology offers better distribution analysis of HCT-8 and NIH3T3 cells compared to the ImageJ software. Figure 10: Schematic diagram of procedure followed by ImageJ software for segmentation and quantification of HCT-8 and NIH3T3 cells. Figure 9: (**a**) Blue cell count (BCC) and green cell count (GCC) plots. (**b**) Blue cell area (BCA) and green cell area (GCA) from periphery to core of _in vitro_ 3D cell spheroid of 2:0.5 ratio slices.