## 4 Discussion  
The results of the present study can be summarized as follows. First, the propofol dose was not associated with PIHF in older individuals. Second, our proposal model (\"model N\") was more accurate than the previously reported model (\"model P\"). Third, the propofol dose at induction of anesthesia decreased by 0.1 mg/kg for every 10 years of aging. This is the first study to focus on quantifying the relationship between aging and the propofol dose utilizing a neural network model. PIHFs are more likely to occur with aging, and propofol has the adverse effect of dose-dependent hypotension [15; 16; 17]. However, the effect of higher or lower propofol doses on the frequency of hypotension after the induction of anesthesia in older patients has not been determined, with one report suggesting an increase in the frequency of hypotension [18] and another suggesting no change [19]. Since propofol theoretically causes hypotension in a dose-dependent manner, it is reported that the reason the frequency of hypotension did not change with higher or lower doses is that anesthesiologists adjust the propofol doses according to the frailty of older patients and not just their age [19]. In the data collected in this study, the propofol doses were compared between groups of older patients aged 65 years or older who developed PIHF and those who did not, but there was no significant difference. These results suggest that the anesthesiologists at our hospital adjust the propofol dose according to the apparent vigor of older individuals and their frailty, including ADL, as mentioned earlier. According to previous reports, the induction of anesthesia with propofol using target-controlled infusion (TCI) instead of manual induction increases the induction time, but post-induction hypotension is less frequent [20]. It has also been reported that remimazolam is less likely to cause hypotension than propofol [21]. In cases where hypotension is expected to occur, TCI or remimazolam is a better choice. However, it is difficult to accurately predict whether hypotension will occur after the induction of anesthesia. Although several methods have been reported to predict hypotension after the induction of anesthesia [22; 23], and patients with cardiac disease are prone to hypotension [24], there are no absolute indicators. A comprehensive judgment must be made by the anesthesiologist, including the history, laboratory findings, and patient frailty. Figure 7: Simulation utilizing model N: pairwise decadal change in the propofol dose per kilogram. Each boxplot represents the distribution of the dose differences (mg/kg) between two adjacent hypothetical ages (e.g., 20 and 30, 30 and 40,..., up to 80 and 90 years). The \(x\)-axis indicates the paired hypothetical ages used in the simulation, and the \(y\)-axis shows the difference in the predicted propofol dose per body weight. Boxes represent interquartile ranges; red horizontal lines indicate medians; green triangles indicate means; whiskers denote 1.5 \(\times\) IQR; and circles represent outliers. The model N developed in this study was more accurate in predicting the propofol dose than the previously reported model P. In contrast, the model P article reported that PIHFs were likely to occur when the actual propofol dose administered had an error of 5 mg or higher from the model P prediction [12]. To exclude the possibility that the propofol dose in our hospital may likely produce PIHF, we performed the following validation. The data from our hospital were divided into two groups, those with residual errors of \(\geq\)5 mg and those with residual errors of \(<\)5 mg from the model P prediction, and the proportions of PIHF were compared using a chi-square test. The results were not significantly different, indicating that the propofol dose at our hospital was not likely to cause PIHF. We believe that the main reason why model N, which was created using a smaller number of cases than model P, had better prediction accuracy was that the models were compared using data from our hospital.