# Physical Simulation-Based Calibration for Quantitative Real-Time PCR
## 4 On-Machine Test
### Uniformity Test  
The uniformity test is used to verify the consistency of detection results obtained from different well positions when amplifying samples with the same initial concentration using  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Probe Position** & **Pre-Set Simulated Ct Value** & **Experimentally Measured Ct Value** \\ \hline A7 & 15 & 15.369 \\ B7 & 18 & 18.592 \\ C7 & 21 & 21.509 \\ D7 & 24 & 24.795 \\ E7 & 27 & 27.676 \\ F7 & 30 & 30.882 \\ G7 & 33 & 33.973 \\ H7 & 36 & 36.831 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Experimentally measured Ct values of calibration device.  
Figure 14: Experimentally measured amplification plot of the calibration device.  
Figure 15: Experimentally measured standard curve of the calibration device.  
a qPCR instrument. In theory, the measured Ct values should be identical; however, in practice, they may be influenced by differences in the amount of excitation light received by each reaction well. Some qPCR instruments utilize halogen lamps as their excitation light source, which may experience degradation over time during usage. This degradation could potentially exacerbate the edge effects of the instrument, leading to differences in the amount of excitation light received by reaction wells at different positions. Without re-calibration of the region of interest (ROI), this may impact experimental results.  
The calibration device can also be used for uniformity calibration. When testing the uniformity of qPCR instruments using the developed calibration device, the eight probes of the calibration device were set to simulate identical Ct value, all set to 24. The calibration device was then placed in the seventh column and run method settings was set to the same as in Section 4.1.  
After running the qPCR process, the amplification curves obtained are shown in Figure 16. The uniformity of Ct values (\(\Delta C_{tu}\)) can be calculated according to Equation (4), and the precision of Ct values (\(RSD_{Ct}\)) can be calculated according to Equation (5). The results of the uniformity test are presented in Table 8. The results indicate that when the calibration device simulates identical Ct values, the measured results from the probe within individual reaction wells are not entirely consistent. This discrepancy is caused by inherent differences in the instrument. When analyzing Ct value results for nucleic acid detection in practical use, it is essential to consider the differences introduced by the non-uniformity between reaction wells.  
\[\Delta C_{tu}=C_{tqmax}-C_{tqmin} \tag{4}\]  
\[RSD_{Ct}=\frac{1}{\frac{\sum_{i=1}^{n}C_{tqi}}{n}}\times\sqrt{\frac{\sum_{i= 1}^{n}\left(C_{tqi}-\frac{\sum_{i=1}^{n}C_{tqi}}{n}\right)^{2}}{n-1}}\times 1 00\% \tag{5}\]  
where the \(C_{tqi}\) represents the experimentally measured Ct value of the number \(i\) probe position; \(C_{tqmax}\) represents the maximum value among the experimentally measured Ct values of all probe positions; \(C_{tqmin}\) represents the minimum value among the experimentally measured Ct values of all probe positions; and \(n\) represents the number of probes, \(n=8\).  
Figure 16: Experimental amplification plot when simulate identical Ct values.  
In this test, although the calibration results obtained from the standard curve simulation demonstrated a linear correlation of one, a uniformity test on eight wells at the same position revealed discernible differences between the wells. The measured Ct values exhibited variations and deviated from the preset values. It is evident that in standard curve calibration, due to the normalization of linearity calculations, such differences are easily obscured in the final results. Therefore, it is recommended that a comprehensive approach or multiple methods be employed for calibrating and analyzing qPCR instruments.