# Prediction of Blood Pressure after Induction of Anesthesia Using Deep Learning: A Feasibility Study
## 3 Results  
We set \(W=60\) and \(G=60\), which implies that we predict the blood pressure of three minutes later, given the observed vital signs for latest three minutes. Please note that we use the vital data only obtained between the induction of anesthesia and the beginning of operation; we do not employ any other information (e.g., age, sex, base blood pressures, ASA). The total number of transformed data is 26,887. Each dimension of the transformed data is normalized except for the timestep value. The normalization, of course, is done with only training data. We take 10-fold cross-validation and compute mean absolute error (MAE). We conduct three independent experiments: SBP prediction, MBP prediction, and DBP prediction. All experiments are performed using a computer with eight  
Figure 4: Structure of the proposed model. Central Processing Units (CPU) of i7-7700 3.6 GHz and two NVIDIA GeForce 1080 Ti. The proposed model is implemented with Python3 language with Google TensorFlow packages. The training recipe and parameter setting are as follows. The dimensions of RNN layers \(R_{1}\) and \(R_{2}\) are equally 15, and the dimensions of the fully connected (FC) layers \(F_{1}\) and \(F_{2}\) are 100 and 50, respectively. We applied the drop out [28] with a keep probability 0.1 to the RNN layers, and the decov [29] with a weight 0.1 to the FC layers. Both the drop out and the decov are known to have a regularization effect, which prevents from overfitting. In terms of the parameter initialization, the weight matrices of the FC layers are initialized using He initialization [30], and the biases are initialized as zero. The weight matrices of the RNN layers are initialized using Xavier initialization [31], and the initial bias value is one. We use Adam optimizer [32] with an initial learning rate 0.001 to train the model parameters, and the number of epochs is 60. For training phase, it computes a predicted blood pressure by feed-forward propagation; the RNN layers generate two vectors given a input, and the fully connected layers take the concatenation of the two vectors as an input and generate an output. It computes a cost (error) by comparing the predicted blood pressure and a true blood pressure, and all weights and bias values are updated via back propagation algorithm. For each epoch, the feed-forward and back propagation are conducted throughout all data with a mini-batch as a unit. In this paper, we set the size of mini-batch as 100. Table 3 summarizes the mean and standard deviation of the absolute errors obtained from the three predictions. Small mean and standard deviation mean that it predicts the blood pressure accurately. Among the three predictions, the DBP prediction is the most accurate while the SBP prediction exhibits the worst results. The Figures 5-7 depict histograms of errors, where horizontal axis represents error bins; for example, a bin [1; 2; 3] represents the range \(1\leq e<2\) where \(e\) indicates an error. The three figures seem to have a form of Gaussian distribution, and they generally follow the trend of the true blood pressures. For instance, in Figure 6, the peak of distribution is located around the interval [0-1], which implies that the predicted MBP values are mostly correct compared to the true MBP values. However, the shapes of three figures are a bit left skewed, so the overall mean is between 8.2 mmHg and 11.1 mmHg while the standard deviation is between 8.7 mmHg and 12.7 mmHg. Figure 8 shows Bland-Altman diagrams of the three blood pressures. The diagrams imply that errors tend to grow when the average of a predicted blood pressure and a true blood pressure is high. This can be interpreted that it is hard to correctly predict the true blood pressure when the average is abnormally high because such cases were barely seen in the data. Figure 5: Error histogram of SBP prediction, where horizontal axis represents error bins and vertical axis is the number of associated data.