## 4 Discussion
### Adjusting the Preset Initial Values  
Although the initial values incorporated into the self-developed program run in MATLAB could also be adjusted to comply with the clinical conditions of the in-vivo scanning procedure, zero values in the beginning of computation were used to simplify the procedure. Patients' kidneys and bladders always have I-131 counts even at the first trial of scan in the practical data survey (e.g., in Figure 2, the preset elapsed time was 1 h). Thus, the I-131 concentration in the kidney or bladder that presumably existed at the initial time can be interpreted as a nonzero initial value in the computation program. If the initial values of either kidney or bladder are reset to zero and the MATLAB program is re-run, the results change significantly. As illustrated in Figure 4, in cases 2 and 8, the initial values for kidney and bladder were reset to 0.0 and 0.0. Then, both the theoretical concentrations decrease in the initial time compared with the real outcome from the in vivo gamma camera scanning. Specifically, AT\({}_{\text{kidney}}\) for cases 2 and 8 increased from 0.002 and 0.002 to 0.010 and 0.004, while AT\({}_{\text{bladder}}\) increased from 0.001, 0.019 to 0.010, 0.036 (ref. Table 4). In addition, the average initial values for kidney and bladder were 0.028 \(\pm\) 0.022 and 0.025 \(\pm\) 0.026, respectively. The original preset biokinetic model could not account for the radioactive I-131 concentrations that already existed in the kidney and the bladder. However, changing the initial values in running the computational program could simulate the respective physical phenomena in the numeric analysis.  
Figure 4: Cases 2 and 8 with the zero initial values for kidney and bladder; the outcome differs from the experimental data from in vivo gamma camera scanning. (**A**) Cases 2 and (**B**) case 8 with the zero initial values for kidney and bladder; the outcome differs from the experi-mental data from in vivo gamma camera scanning.  
\begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**References**} & \multicolumn{2}{c}{**Biological Half-Life (h)**} & \multicolumn{1}{c}{**Patient**} & \multirow{2}{*}{**Approach**} \\  & \multicolumn{2}{c}{**Thyroid Whole Body**} & & \\ \hline
[1] & \(38.7\pm 13.8\) & \(12.4\pm 1.9\) & 9 & Gamma camera in-vivo survey \\
[2] & \(15.8\pm 12.0\) & \(12.5\pm 5.5\) & 5 & Gamma camera in-vivo survey \\
[7] & **10.9–30.1** & **16.8–43.3** & 57 & SPECT/CT image \\
[18] & & 45.5 & 1 & OLINDA theoretical simulation \\
[19] & \(63.2\pm 44.9\) & \(13.7\pm 2.5\) & 36 & Gamma camera in-vivo survey \\
[20] & & \(30\pm 17\) & 19 & Gamma camera in-vivo survey \\
[21] & 480 & 6 & & Theoretical simulation according to ICRP-53 \\
[22] & 33 & 110 & N/A & Practical survey combined theoretical \\ This work & & & & simulation according to ICRP-128 \\  & \(37.0\pm 14.3\) & \(12.3\pm 1.7\) & & 4 compartments model \\  & \(36.0\pm 15.6\) & \(15.0\pm 5.6\) & 12 & standard 9 compartments model \\  & \(34.3\pm 15.4\) & \(14.8\pm 5.9\) & & simplified 9 compartments model \\ \hline \end{tabular}
\end{table}
Table 5: The biological half-lives in the major compartments, whole body (BF + WB), and thyroid calculated in this and other studies. The calculations via different practical methods and simulations are quite controversial.