# Prediction of Blood Pressure after Induction of Anesthesia Using Deep Learning: A Feasibility Study
## 2 Materials and Methods
We take only the latest observed blood pressure, but not the blood pressure values for \(W\) timesteps because the inconsistent sampling rate (e.g., every minute) of the blood pressure may harm the results of the RNN. Third, we define the blood pressure value of the timestep \(t+G\) as an output \(o_{t}\). It is important that the output \(o_{t}\) is not the blood pressure at the timestep \(t\), but the future blood pressure at the timestep \(t+G\). Through the steps above, for each timestep \(t\), we generate a triple of the input \(i_{t}\), the supplementary input \(si_{t}\), and the output \(o_{t}\). Assuming that \(t=100\), \(W=60\), and \(G=20\). The input \(i_{100}\) will be a \((K-2)\times 60\) matrix and the \(si_{100}\) will be a real-number of the normalized blood pressure at the 100-th timestep. The output \(o_{100}\) will be a blood pressure value at the 120-th timestep. This can be interpreted that it predicts the blood pressure of one minute later (i.e., after 20 timesteps) given the lastly observed vital signs for three minutes (i.e., 60 timesteps). As we generate the triple \((i_{t},si_{t},o_{t})\) for every timestep, the total number of triples for the \(r\)-th operation will be \(T_{r}/3-W-G+1\). We conduct the above transformation process to the three blood pressures (e.g., MBP, DBP, and SBP) independently, and got the triples for each of them. The transformation process is summarized in Figure 3. In short, the input consists of \(W\) vital signs \(i_{t}\) and a current blood pressure \(si_{t}\), while the output is a future blood pressure \(o_{t}\) after \(G\) timesteps. We observe that different operations exhibit different sequential patterns (e.g., different aspect of heart-rate changes). To incorporate such diversity of sequential patterns, we design an RNN model followed by fully connected layers as shown in Figure 4. Given the input \(i_{t}\) for \(r\)-th operation, the \(W\) vital vectors are sequentially injected to the RNN. Please note that our RNN has bidirectional and hierarchical structure. The bidirectional RNN consists of a forward RNN and a backward RNN, where the forward RNN and the backward RNN can capture forward patterns and backward patterns, \begin{table}
\begin{tabular}{c c} \hline \hline
**Item** & **Value** \\ \hline Sex ratio (female:male) & 57:45 \\ Age (mean \(\pm\) sd) & 52.11 \(\pm\) 13.13 years \\ Weight (mean \(\pm\) sd) & 67.66 \(\pm\) 12.96 kg \\ Height (mean \(\pm\) sd) & 162.42 \(\pm\) 9.51 cm \\ American Society of Anesthesiologist (ASA) physical status ratio (1:2:3) & 42:47:13 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistics of the collected data. Figure 3: Data preparation for the prediction of future blood pressure in real time. respectively. There might be sequential patterns of a forward direction and a backward direction, so we take the bidirectional RNN to incorporate such patterns. Meanwhile, both forward and backward RNN are hierarchical as they have two stacked layers. The first RNN layer may capture sequential correlations between different vital signs (e.g., a propofol rate and the heart-rate), and the second RNN layer catches high-level sequential correlations between the correlations found at the first layer. Thanks to the bidirectional and hierarchical structure, the RNN will memorize high-level sequential patterns in both directions. The forward RNN yields a \(R_{2}\)-dimensional summary vector \(h_{F}\), and the backward RNN also gives a \(R_{2}\)-dimensional summary \(h_{B}\). These two summary vectors are then concatenated and the supplementary input \(si_{t}\) comes into the vector, resulting in a \(2\times R_{2}+1\)-dimensional vector. The concatenated vector is passed to the fully connected layers that are supposed to find some correlations between the \(h_{F}\) and \(h_{B}\). For example, when the RNN layers may capture 'increasing trend of heart rates' and 'fluctuating ETCO2' patterns, the fully connected layers may find how positive or negative correlation they have.