TY - JOUR
AU - Luis Calvo-Rolle, José
AB - Abstract Automatic control of physiological variables is one of the most active areas in biomedical engineering. This paper is centered in the prediction of the analgesic variables evolution in patients undergoing surgery. The proposal is based on the use of hybrid intelligent modelling methods. The study considers the Analgesia Nociception Index (ANI) to assess the pain in the patient and remifentanil as intravenous analgesic. The model proposed is able to make a one-step-ahead prediction of the remifentanil dose corresponding to the current state of the patient. The input information is the previous remifentanil dose, the ANI variable and the electromyogram signal. Modelling techniques used are Artificial Neural Networks and Support Vector machines for Regression combined with clustering methods. Both training and validation were done with a real dataset from different patients. Results obtained show the potential of this methodology to calculate the drug dose corresponding to a given analgesic state of the patient. 1 Introduction Automation in the field of medicine has undergone significant progress in the recent years. In particular, in the automatic control of physiological variables there are different areas in which important advances have been made (diabetes, cardiovascular variables, etc.). Among them, many studies can be found in the area of anesthesia control [15, 43]. It has been demonstrated that the use of automatic control in the anesthesia field offers better performance than manual administration. Thus, automatic systems improve the target deviation errors, avoid overdoses and awakening episodes and free the clinician too from repetitive tasks. In the control of the anesthetic process, there are three main variables to take in consideration: hypnosis (loss of consciousness), analgesia (pain) and neuromuscular blockade (muscular relaxation). In the past years, some proposals have been presented to guide the drug infusion according to the real needs of the patient [10, 40, 42, 47]. The main advances have been focused on the hypnosis control. Many different strategies ranging from Proportional Integral Derivative control to intelligent techniques have been proposed. However, further research is required to propose reliable strategies to deal with the control of analgesia. The main problem relies on the absence of a feedback variable capable of quantifying the analgesic state of patients during surgery. Different variables and monitors have been proposed as measures, which could be correlated to the analgesic state of patients [6, 17, 18]. The monitors use different variables to evaluate the pain like the pupil diameter, the skin conductance, the Electroencephalographic signal, the respiratory frequency or the electrocardiogram signal. Nevertheless, the reliability of these monitors has not been widely studied. Among the different alternatives, the Analgesia Nociception Index (ANI) developed by Mdoloris Medical Systems, has shown good results in clinical practice. The ANI monitor is a non-invasive system that computes an index obtained from the autonomic nervous system through the ElectroCardioGram. This index ranges from |$0$| to |$100$| in order to quantify the parasympathetic activity in patients undergoing surgery. A value between the range of 50 and 70 is supposed to ensure an adequate analgesia. Values under 50 involves the possibility of future hemodynamic reactions, while values over 70 indicates the possibility to decrease the opioids administration without any risk. When dealing with the design of a controller for the infusion automation in analgesia, there are three main stages. The first one is the availability of an index that correlates well with the variable of interest. The second stage concerns with the modelling of the process. It is necessary to have a reliable prediction of the variable response (ANI) to the drug infusion. The last challenge is the design of controller. In our case, the hypothesis is that the ANI has a good correlation with the analgesia level [14, 29, 37]. Concerning modelling, most of the approaches are based on the following: physiological models, autoregressive models and models based on artificial intelligence techniques. The contribution of this paper is related to the third stage, as the objective is to model how the clinician operates to decide the drug infusion using artificial intelligence techniques. A recent study in this field [35] used intelligent techniques with the aim of predicting the ANI in patients undergoing general anesthesia. The drug considered was intravenous remifentanil. The resulting model provides the evolution of ANI in terms of the remifentanil drug dose, the Electromyogram (EMG) and the previous values of ANI. Similarly, another work [12] predicts the EMG and BIS (BISpectral index). However, the present work is focused on the inverse problem and, in this case, the correct remifentanil infusion rate is predicted for the next five seconds from the previous values of ANI, EMG and remifentanil. Other existing techniques study similar problems but the procedure implies a more complex design. Thus, in [26], fuzzy algorithms are used in the drug supply decision-making process to decide when to increase or decrease the drug dose. The proposed predictive model can be obtained considering different regression methods. The most commonly used methods are based on Multiple Regression Analysis (MRA) techniques. In [4, 5, 19, 23, 24, 30], MRA techniques are used to address problems in applications of different fields. In some cases, the nature of the system to model can lead to wrong performance [5, 8, 33, 39, 41, 52], and for this reason, Soft Computing techniques are employed [2, 9, 11, 16, 31, 44, 51]. Their use improves significantly the performance of the predictive model [3, 21, 22, 25, 32, 46, 50]. In this work, Artificial Neural Networks (ANNs) and Support Vector Regression (SVR) will be employed to develop a model to predict the remifentanil infusion rate using the ANI and EMG signals [34]. The model is derived using real data from patients undergoing surgery at the Hospital Universitario de Canarias (HUC). The performance of the model will be evaluated using the Mean Squared Error (MSE). This paper is organized following the next structure. After this section, a brief case of study is presented. Then, the model approach and the used techniques used to obtain the model are shown. The results section shows the best configuration achieved by the proposed hybrid model. Finally, the conclusions and future works are presented. 2 Case of study The proposed model tries to describe the clinician behaviour when infusing analgesics during the anesthetic process. The model will be evaluated using real data from patients undergoing general anesthesia. As a first approach, a one-step-ahead prediction was considered. For this, fifteen adult patients under scheduled cholecystectomy surgery at the HUC were enrolled in the study. All patients received information about the data collection process and the written informed consent was signed before the surgeries. Demographic data (age, gender, size, body bass index and ASA classification) as well as individual relevant clinical information were previously registered by the clinicians. A Total Intravenous Anesthesia based on propofol (hypnotic) and remifentanil (analgesic) was proposed for the fifteen cases during both induction and maintenance phases. Two Graseby 3500 infusion pumps limited to a maximum rate of |$1200\;ml/h$| were used in this study. To measure the hypnotic level, the BIS monitor based on the electroencephalographic activity was used. BIS monitor also included information about EMG activity. For the manual control of analgesia, remifentanil infusion rate was updated according to standard clinical practice criteria (heart rate and blood pressure), anticipation to surgical stimuli and hemodynamic events. For the induction, intravenous remifentanil was supplied at |$0.2\;\mu g/kg/min$| during seven minutes. Then, intravenous propofol (⁠|$1\%$|⁠) |$1.5\;mg/kg$| at maximum rate was supplied. The maintenance phase began once the appropriate hypnotic level was reached during the induction. During the maintenance phase, a BIS value between 40 and 60 was aimed, with a BIS target of |$50$|⁠. As a result, the anaesthesiologist adapted the propofol infusion rate manually according to the current hypnotic state of the patient. Remifentanil rate changes were limited to |$0.05-0.1\;\mu g/kg/min$| according to the clinical protocol. Finally, the recovering phase started once the surgery had finished. The infusion of remifentanil as well as propofol was then stopped. During the surgeries, heart rate information and blood pressure changes were manually recorded every 5 minutes. On the other hand, BIS, ANI and EMG values were saved every 5 seconds in a laptop. For this purpose, a Matlab interface was previously developed. BIS and ANI monitors were connected via RS232 interfaces to the laptop. In addition, the anesthesiologist could annotate the information about both remifentanil and propofol infusion rates during the surgeries. This programme also included an alarm module in case of any failure during the data acquisition process. In practice, two anaesthesiologist were in charge of the process: one supplying the drugs according the protocol described above and another one for the supervision of the acquisition process. During the surgery, the first anesthesiologist could not have access to the information displayed by the ANI monitor to avoid conditioning their decisions. The main objective of this study was to compare the decisions made by the anaesthesiologist based on traditional clinical parameters to the information displayed by the ANI monitor to find any possible relationship between both criteria. As a result, it might demonstrate that the ANI level of patients undergoing anesthesia would vary not only depending on the concentration of remifentanil but also on the external disturbances registered from the EMG in this study. The studied problem could be represented as shown in Figure 1. Figure 1. Open in new tabDownload slide Case of study. Input/output representation. Figure 1. Open in new tabDownload slide Case of study. Input/output representation. 3 Model approach This main objective of this research consists of modeling the remifentanil infusion rate from the ANI and EMG signals. To achieve this goal, the model approach is presented in Figure 2. As shown in this figure, the initial dataset can be divided in different groups depending on the behaviour using a clustering algorithms. Then, for each created cluster, a new regression model is developed to predict the Remifentanil from the EMG and ANI signals as inputs. In addition to the clustering algorithm application, the possibility of obtaining a global model using the whole amount of dataset can be considered. Figure 2. Open in new tabDownload slide Model approach. Figure 2. Open in new tabDownload slide Model approach. According to Figure 2, the global model, ANI and EMG would be inputs and the remifentanil infusion rate the output. In case of dividing the dataset into different groups, a cluster selector block would select the right model depending on the operating point to be predicted. This block connects the selected models with the predicted output. The criteria to choose the cluster is based on the Euclidean distance between the input and the centroids of each cluster. After testing the configuration of the different algorithms, the best model is chosen. Regardless the use of hybrid model or global model, the modeling process followed is presented in Figure 3. To achieve general results of the obtained model, a K-fold cross-validation was performed. This cross-validation method consist of dividing the dataset for training and testing according to the Figure 3. Figure 3. Open in new tabDownload slide Modeling process. Figure 3. Open in new tabDownload slide Modeling process. To ensure the good performance of the K-fold cross-validation, the number of samples allowed on each cluster must be higher than a specific value, and in our case fifteen is set as a threshold. Also, the error obtained for each configuration is calculated taking into account all the dataset (Figure 3). 3.1 Dataset obtaining and description The dataset used on this research consist on the recorded values of EMG and ANI signals and Remifentanil infusion rate from fifteen different patients undergoing general anesthesia. The signals were registered with a 5-second sample rate. To avoid modeling with wrong data, the dataset was initially pre-processed using a low-pass filter to avoid undesirable noise in the three monitored signals. Taking into account that only the maintenance phase was modeled, the induction and recovery phases were discarded on this research. After the pre-processing, and considering only the maintenance phase, the dataset has |$17064$| samples, and after discarding two patient to use as validation data, the samples to train the model were |$16750$|⁠. 3.2 Used techniques In this section, a description of the different regression techniques combined with clustering algorithms is made. As explained at the beginning of this section, the first step followed to obtain the hybrid model consists on applying clustering algorithm, in this case K-means, to group the data in different clusters. Then, three regression techniques are applied to model each group, and the best model for each cluster is determined. The criteria to evaluate the performance of each regression technique is based on K-fold cross-validation and the MSE [28] (equation 1). $$\begin{align}& MSE = \frac{1}{n} \sum_{i=1}^{n} (y_{i_{predicted}} - y_{i_{real}})^{2} \end{align}$$(1) 3.2.1 Data clustering - The K-means algorithm Clustering algorithms are commonly applied to perform a data grouping depending on the similarity of the samples [36, 45, 48, 49]. To do so, the K-means algorithm separates the initial unlabeled data into different clusters, so that, all the data contained in a cluster present similarity [36]. The K-means distributes the data into groups minimizing the error function shown in Equation 2, where |$x$| is the new input vector and |$c_{k}$| the centroid of the cluster |$k$|⁠. $$\begin{align}& e=\sum_{k=1}^{K}\sum_{x\epsilon Q_{k}}\left \|x-c_{k} \right \|^{2} \end{align}$$(2) The algorithm starts the clustering process from |$K$| initial centroids. The most critical choice is the value of |$K$|⁠, since it needs a prior knowledge of the number of clusters of the data. In terms of computational cost, this algorithm is effective and works properly, if the data are close to its cluster, and if the clusters are hyperspherical and well-separated in the hyperspace. 3.2.2 ANN. Multi-Layer Perceptron (MLP) The MLP is the most commonly used feedforward ANN [55, 57] due to different features, like its simple configuration as well as its robustness. In spite of this features, a good selection of the ANN configuration plays a key role in the task of obtaining good results. The MLP is designed with three different parts: one input layer, one output layer and one or more hidden layers. The neuron of each layer has an specific activation function that can be configured as step, linear, log-sigmoid or tan-sigmoid. In a typical configuration, the neurons activation function of the same layer are the same. 3.2.3 SVR, Least Square Support Vector Regression (LS-SVR) The well known SVR algorithm is based on the Support Vector Machines (SVM) algorithm used for classification. The objective of SVR consists on mapping the dataset into a high-dimensional feature space |$F$| using a nonlinear plotting. After the mapping, linear regression is performed in the |$F$| space [54]. It is called LS-SVM to the Least Square algorithm of SVM. The estimated solution is calculated by solving a linear equations system, giving a performance generalization compared to SVM [7, 9, 20]. When the LS-SVM algorithm is applied to regression, it is known as LS-SVR [13, 38]. In LS-SVR, a classical squared loss function replaces an insensitive loss function. This squared loss function makes the Lagrangian by solving a linear Karush–Kuhn–Tucker. 3.2.4 Polynomial regression A polynomial regression model [27, 56, 58] can be defined as the linear sum of basis functions. The number of inputs and the polynomial degree have direct influence on the quantity of basis functions. When the polynomial degree is |$1$|⁠, the linear sum is defined as shown in Equation 3. If the degree has a higher value, the regression model becomes more complex. Equation 4 shows the regression model of a second-degree polynomial. $$\begin{align}& F(x)=p_0+p_1x_1+p_2x_2 \end{align}$$(3) $$\begin{align}& F(x)=p_0+p_1x_1+p_2x_2+p_3x_1x_2+p_4x_1^2+p_5x_2^2 \end{align}$$(4) 4 Results The created hybrid model created obtains the remifentanil infusion rate taking into account the current and the two previous values of EMG, remifentanil and ANI. The previous values use incorporates the dynamics of the system into the model. Some different regression techniques performance were analyzed, and the best technique selection was done using a 10 K-fold cross-validation, ensuring a real measure of the errors. The ANN algorithm was trained using different configurations: the number of neurons of the unique hidden layer was tested from 1 to 15. Tan-sigmoid is used as activation function for the hidden layer neurons, while the output layer neuron has a linear activation function. To train of each ANN configuration, the Levenberg–Marquardt optimization algorithm was used. Moreover, to finish the training phase, gradient descent was used base on the MSE. The LS-SVR algorithm was trained with the KULeuven-ESAT-SCD auto-tuning algorithm implemented with the Matlab toolbox [1, 53]. The regression type was set to ‘Function Estimation’ and the model kernel was configured as Radial Basis Function. The cost criterion is ‘leaveoneoutlssvm’, the performance function is ‘mse’ and the optimization function is set as ‘simplex’. The polynomial regression algorithm is test only with first and second degree. 4.1 Clustering results As the first step, the data was divided into different clusters using the K-means algorithm, as was explained previously. It was created nine hybrid systems, between 2 and 9 clusters, as the optimal number of groups were previously unknown. The initial centroids are set to random values, and the training was repeated 20 times to ensure the best divisions of the data. Table 1 shows the different number of samples in each cluster and also in the global model (first column in the table). Table 1. Number of samples in each created cluster. . Global . Hybrid model (local models) . . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . Cl-1 16750 7566 4367 1084 1069 661 272 522 273 273 Cl-2 9184 5683 4184 3205 944 648 568 521 518 Cl-3 6700 5313 3263 2825 934 575 564 562 Cl-4 6169 4372 3220 2919 2284 571 567 Cl-5 4841 4264 3009 2323 2229 1811 Cl-6 4836 4349 3087 2389 1924 Cl-7 4619 3564 3087 2260 Cl-8 3827 3456 2675 Cl-9 3660 3042 Cl-10 3118 . Global . Hybrid model (local models) . . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . Cl-1 16750 7566 4367 1084 1069 661 272 522 273 273 Cl-2 9184 5683 4184 3205 944 648 568 521 518 Cl-3 6700 5313 3263 2825 934 575 564 562 Cl-4 6169 4372 3220 2919 2284 571 567 Cl-5 4841 4264 3009 2323 2229 1811 Cl-6 4836 4349 3087 2389 1924 Cl-7 4619 3564 3087 2260 Cl-8 3827 3456 2675 Cl-9 3660 3042 Cl-10 3118 Open in new tab Table 1. Number of samples in each created cluster. . Global . Hybrid model (local models) . . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . Cl-1 16750 7566 4367 1084 1069 661 272 522 273 273 Cl-2 9184 5683 4184 3205 944 648 568 521 518 Cl-3 6700 5313 3263 2825 934 575 564 562 Cl-4 6169 4372 3220 2919 2284 571 567 Cl-5 4841 4264 3009 2323 2229 1811 Cl-6 4836 4349 3087 2389 1924 Cl-7 4619 3564 3087 2260 Cl-8 3827 3456 2675 Cl-9 3660 3042 Cl-10 3118 . Global . Hybrid model (local models) . . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . Cl-1 16750 7566 4367 1084 1069 661 272 522 273 273 Cl-2 9184 5683 4184 3205 944 648 568 521 518 Cl-3 6700 5313 3263 2825 934 575 564 562 Cl-4 6169 4372 3220 2919 2284 571 567 Cl-5 4841 4264 3009 2323 2229 1811 Cl-6 4836 4349 3087 2389 1924 Cl-7 4619 3564 3087 2260 Cl-8 3827 3456 2675 Cl-9 3660 3042 Cl-10 3118 Open in new tab Table 2. Configuration for each individual hybrid model. . Global . Hybrid model (local models) . . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . Cl-1 ANN13 ANN13 ANN11 ANN15 ANN12 ANN14 ANN14 ANN15 ANN13 ANN13 Cl-2 ANN11 ANN15 ANN14 ANN15 ANN12 ANN13 ANN11 ANN13 ANN14 Cl-3 ANN12 ANN14 ANN13 ANN14 ANN11 ANN15 ANN11 ANN11 Cl-4 ANN11 ANN13 ANN11 ANN11 ANN11 ANN12 ANN15 Cl-5 ANN13 ANN15 ANN11 ANN11 ANN12 ANN12 Cl-6 ANN13 ANN11 ANN15 ANN12 ANN12 Cl-7 ANN12 ANN12 ANN13 ANN12 Cl-8 ANN11 ANN12 ANN13 Cl-9 ANN13 ANN13 Cl-10 ANN13 . Global . Hybrid model (local models) . . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . Cl-1 ANN13 ANN13 ANN11 ANN15 ANN12 ANN14 ANN14 ANN15 ANN13 ANN13 Cl-2 ANN11 ANN15 ANN14 ANN15 ANN12 ANN13 ANN11 ANN13 ANN14 Cl-3 ANN12 ANN14 ANN13 ANN14 ANN11 ANN15 ANN11 ANN11 Cl-4 ANN11 ANN13 ANN11 ANN11 ANN11 ANN12 ANN15 Cl-5 ANN13 ANN15 ANN11 ANN11 ANN12 ANN12 Cl-6 ANN13 ANN11 ANN15 ANN12 ANN12 Cl-7 ANN12 ANN12 ANN13 ANN12 Cl-8 ANN11 ANN12 ANN13 Cl-9 ANN13 ANN13 Cl-10 ANN13 Open in new tab Table 2. Configuration for each individual hybrid model. . Global . Hybrid model (local models) . . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . Cl-1 ANN13 ANN13 ANN11 ANN15 ANN12 ANN14 ANN14 ANN15 ANN13 ANN13 Cl-2 ANN11 ANN15 ANN14 ANN15 ANN12 ANN13 ANN11 ANN13 ANN14 Cl-3 ANN12 ANN14 ANN13 ANN14 ANN11 ANN15 ANN11 ANN11 Cl-4 ANN11 ANN13 ANN11 ANN11 ANN11 ANN12 ANN15 Cl-5 ANN13 ANN15 ANN11 ANN11 ANN12 ANN12 Cl-6 ANN13 ANN11 ANN15 ANN12 ANN12 Cl-7 ANN12 ANN12 ANN13 ANN12 Cl-8 ANN11 ANN12 ANN13 Cl-9 ANN13 ANN13 Cl-10 ANN13 . Global . Hybrid model (local models) . . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . Cl-1 ANN13 ANN13 ANN11 ANN15 ANN12 ANN14 ANN14 ANN15 ANN13 ANN13 Cl-2 ANN11 ANN15 ANN14 ANN15 ANN12 ANN13 ANN11 ANN13 ANN14 Cl-3 ANN12 ANN14 ANN13 ANN14 ANN11 ANN15 ANN11 ANN11 Cl-4 ANN11 ANN13 ANN11 ANN11 ANN11 ANN12 ANN15 Cl-5 ANN13 ANN15 ANN11 ANN11 ANN12 ANN12 Cl-6 ANN13 ANN11 ANN15 ANN12 ANN12 Cl-7 ANN12 ANN12 ANN13 ANN12 Cl-8 ANN11 ANN12 ANN13 Cl-9 ANN13 ANN13 Cl-10 ANN13 Open in new tab 4.2 Modelling results The best configuration for each cluster is shown in Table 2, and Table 3 shows the MSE error measures. Table 3. Mean square error for each individual hybrid model. . Global . Hybrid model (local models) . . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . Cl-1 0.0043 0.0037 0.0004 0.0536 0.0734 0.0013 0.0000 0.0023 0.0000 0.0000 Cl-2 0.0014 0.0139 0.0006 0.0003 0.0055 0.0011 0.0001 0.0056 0.0021 Cl-3 0.0001 0.0009 0.0005 0.0004 0.0049 0.0273 0.0012 0.0003 Cl-4 0.0003 0.0005 0.0002 0.0001 0.0004 0.1487 0.0254 Cl-5 0.0032 0.0025 0.0171 0.0025 0.0073 0.0057 Cl-6 0.0033 0.0009 0.0082 0.0007 0.0010 Cl-7 0.0016 0.0023 0.0008 0.0051 Cl-8 0.0019 0.0026 0.0065 Cl-9 0.0056 0.0015 Cl-10 0.0053 . Global . Hybrid model (local models) . . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . Cl-1 0.0043 0.0037 0.0004 0.0536 0.0734 0.0013 0.0000 0.0023 0.0000 0.0000 Cl-2 0.0014 0.0139 0.0006 0.0003 0.0055 0.0011 0.0001 0.0056 0.0021 Cl-3 0.0001 0.0009 0.0005 0.0004 0.0049 0.0273 0.0012 0.0003 Cl-4 0.0003 0.0005 0.0002 0.0001 0.0004 0.1487 0.0254 Cl-5 0.0032 0.0025 0.0171 0.0025 0.0073 0.0057 Cl-6 0.0033 0.0009 0.0082 0.0007 0.0010 Cl-7 0.0016 0.0023 0.0008 0.0051 Cl-8 0.0019 0.0026 0.0065 Cl-9 0.0056 0.0015 Cl-10 0.0053 Open in new tab Table 3. Mean square error for each individual hybrid model. . Global . Hybrid model (local models) . . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . Cl-1 0.0043 0.0037 0.0004 0.0536 0.0734 0.0013 0.0000 0.0023 0.0000 0.0000 Cl-2 0.0014 0.0139 0.0006 0.0003 0.0055 0.0011 0.0001 0.0056 0.0021 Cl-3 0.0001 0.0009 0.0005 0.0004 0.0049 0.0273 0.0012 0.0003 Cl-4 0.0003 0.0005 0.0002 0.0001 0.0004 0.1487 0.0254 Cl-5 0.0032 0.0025 0.0171 0.0025 0.0073 0.0057 Cl-6 0.0033 0.0009 0.0082 0.0007 0.0010 Cl-7 0.0016 0.0023 0.0008 0.0051 Cl-8 0.0019 0.0026 0.0065 Cl-9 0.0056 0.0015 Cl-10 0.0053 . Global . Hybrid model (local models) . . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . Cl-1 0.0043 0.0037 0.0004 0.0536 0.0734 0.0013 0.0000 0.0023 0.0000 0.0000 Cl-2 0.0014 0.0139 0.0006 0.0003 0.0055 0.0011 0.0001 0.0056 0.0021 Cl-3 0.0001 0.0009 0.0005 0.0004 0.0049 0.0273 0.0012 0.0003 Cl-4 0.0003 0.0005 0.0002 0.0001 0.0004 0.1487 0.0254 Cl-5 0.0032 0.0025 0.0171 0.0025 0.0073 0.0057 Cl-6 0.0033 0.0009 0.0082 0.0007 0.0010 Cl-7 0.0016 0.0023 0.0008 0.0051 Cl-8 0.0019 0.0026 0.0065 Cl-9 0.0056 0.0015 Cl-10 0.0053 Open in new tab Taking into account the number of samples in each cluster, it is possible to calculate a pondered error for the hybrids models, as shows the Table 4. According to these results tables, the best performance of the model is achieved with a hybrid model with six clusters. Table 4. Mean squared error for each model. . Global . Hybrid model (local models) . . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . MSE 0.0043 0.0024 0.0049 0.0040 0.0059 0.0021 0.0041 0.0038 0.0082 0.0047 . Global . Hybrid model (local models) . . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . MSE 0.0043 0.0024 0.0049 0.0040 0.0059 0.0021 0.0041 0.0038 0.0082 0.0047 Open in new tab Table 4. Mean squared error for each model. . Global . Hybrid model (local models) . . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . MSE 0.0043 0.0024 0.0049 0.0040 0.0059 0.0021 0.0041 0.0038 0.0082 0.0047 . Global . Hybrid model (local models) . . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . MSE 0.0043 0.0024 0.0049 0.0040 0.0059 0.0021 0.0041 0.0038 0.0082 0.0047 Open in new tab 4.3 Validation procedure To validate this model, the signals acquired of two patients are used. These data was not included in the training data with the aim of presenting a real response. The error measures from the validation data are shown in Table 5 and the signals in Figures 4 and 5. In these validation figures, the continuous blue line is the real signal, and the model output is the dashed green one. Table 5 Performance values for the validation tests . MSE . NMSE . MAE . Validation test 1 0.0721 0.9732 0.0227 Validation test 2 0.0070 0.3726 0.0149 . MSE . NMSE . MAE . Validation test 1 0.0721 0.9732 0.0227 Validation test 2 0.0070 0.3726 0.0149 Open in new tab Table 5 Performance values for the validation tests . MSE . NMSE . MAE . Validation test 1 0.0721 0.9732 0.0227 Validation test 2 0.0070 0.3726 0.0149 . MSE . NMSE . MAE . Validation test 1 0.0721 0.9732 0.0227 Validation test 2 0.0070 0.3726 0.0149 Open in new tab Figure 4. Open in new tabDownload slide Validation test 1 Figure 4. Open in new tabDownload slide Validation test 1 Figure 5. Open in new tabDownload slide Validation test 2 Figure 5. Open in new tabDownload slide Validation test 2 5 Conclusions and future works A hybrid intelligent model to predict the analgesic drug dose for patients undergoing surgery was presented. Training and validation of results was done using real data from patients undergoing general anesthesia. Results obtained were highly satisfactory in training and validation phase. The model presented is limited to a one-step-ahead prediction, but the resulting errors suggest that this methodology could be helpful for the design of a closed-loop control system for analgesia. Another potential application of the model presented is related to fault-detection in the process. This could be an important tool to improve safety for the patient during surgery. The hybrid nature of the model arise as a consequence of the clustering processing. The final hybrid model consisted of 6 cluster. The best regression algorithm was obtained using ANNs with different number of neurons in the hidden layer, and the mean absolute error in the validation data have values under 0.025. Future work in this area will be oriented to the development of intelligent decision system for helping the clinicians during the surgery. And, in a second stage, the design of an automatic closed-loop control system using these models is also an open research line. These new systems could improve the control of different variables during surgeries such as BIS (hypnotic) or ANI (analgesia); it is important to remark that the medical field is one with very few automatic closed-loop control systems. Acknowledgements This research is partially supported through the ‘Fundación Canaria de Investigación Sanitaria’ (FUNCANIS) [ref: PIFUN23/18]. Jose M. Gonzalez-Cava’s research was supported by the Spanish Ministry of Education, Culture and Sport (www.mecd.gob.es), under the ‘Formación de Profesorado’ grant FPU15/03347. References [1] A. K. Suykens Johan Least Squares Support Vector Machines . World Scientific , 2002 . Google Scholar Crossref Search ADS Google Preview WorldCat COPAC [2] H. A. Moretón , J. L. C. Rolle, I. García and A. A. Alvarez. 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TI - Hybrid Intelligent Model to Predict the Remifentanil Infusion Rate in Patients Under General Anesthesia
JO - Logic Journal of the IGPL
DO - 10.1093/jigpal/jzaa046
DA - 2020-09-11
UR - https://www.deepdyve.com/lp/oxford-university-press/hybrid-intelligent-model-to-predict-the-remifentanil-infusion-rate-in-2g06g0D853
SP - 1
EP - 1
VL - Advance Article
IS - 
DP - DeepDyve
ER -