# Experimental Study on Multi-Cell Counting Using an Inertial Microfluidic Device
## 3 Results and Discussion
### Statistical Analysis of Percent Recovery  
A multi-factorial ANOVA was conducted to assess the effect of experimental parameters such as the cell size, microscope type, flow rate, channel size, and concentration ratio on percent recovery. Table 4 shows the F-values and significance levels (\(p\)-values) for the main effects and interactions. The results indicate that several experimental parameters significantly influenced the recovery outcomes. Microscope type had a significant effect (F = 79.453, \(p<0.001\)), confirming that the choice of imaging system (inverted vs. fluorescent microscope) meaningfully impacted the counting accuracy. This supports our observations in Figures 6-8, where fluorescent imaging consistently yielded higher particle counts, likely due to improved contrast and visibility. Flow rate was also highly significant (F = 51.007, \(p<0.001\)), validating that lower flow rates improve the counting efficiency. This aligns with our findings that a flow rate of 1 \(\mu\)L/min resulted in the maximum recovery across all channel sizes, as shown in the radar and bar plots. Channel size showed the most dominant effect (F = 131.357, \(p<0.001\)), emphasizing that narrower microchannels (especially 150 \(\mu\)m) provide better focusing conditions and higher detection accuracy. Cell size alone was not statistically significant (F = 0.169, \(p=0.683\)), indicating that the absolute particle diameter did not impact recovery when isolated from other factors. However, when interacted with the concentration ratio, this combination was significant (F = 19.010, \(p<0.001\)), suggesting that the recovery varies when different particle sizes are combined under normal (600:1) or disease (400:1) conditions. The microscope \(\times\) flow rate interaction was also significant (F = 3.322, \(p=0.025\)), indicating that the imaging system's effectiveness is dependent on the flow rate. This supports our conclusion that inverted microscopy is comparable to fluorescent microscopy at higher flow rates, while the latter excels under low flow conditions. Other interactions, including cell size \(\times\) flow rate (F = 2.667, \(p=0.055\)) and flow rate \(\times\) channel size (F = 1.884, \(p=0.097\)), showed marginal effects, suggesting a trend that warrants further exploration in future studies. The ANOVA model yielded a high coefficient of determination (R\({}^{2}\) = 0.899) and an adjusted R\({}^{2}\) of 0.848, indicating that approximately 89.9% of the variability in percent recovery can be explained by the combination of experimental factors included in the model. This high R\({}^{2}\) value confirms that the selected parameters--cell size, flow rate, microscope type, concentration ratio, and channel size--collectively provide a strong and predictive model of the recovery behavior observed. The adjusted R\({}^{2}\) value accounts for model complexity, reinforcing the robustness of the analysis while controlling for overfitting due to multiple interactions. The results of the ANOVA analysis are presented graphically to illustrate the effects of various experimental parameters on the cell recovery percentage, as shown in Figure 10. Each graph displays the mean percent recovery with error bars representing the standard errors and 95% confidence intervals. The data revealed several key trends: mean recovery percentages showed minimal variation between different cell sizes (8 \(\mu\)m: 49.63%; 15 \(\mu\)m: 48.86%), suggesting that this parameter had little influence on the outcome. In contrast, microscope type exhibited a substantial effect, with fluorescent microscopy yielding a significantly higher recovery (57.69%) compared with inverted microscopy (40.80%), likely due to improved cell detection and retention during imaging. Concentration ratio demonstrated only marginal differences between conditions (R1: 48.01%; R2: 50.48%), indicating this factor had limited impact.