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Ensembled neural networks for brain death prediction for patients with severe head injury
Biomedical Signal Processing and Control 6 (2011) 414–421
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Ensembled neural networks for brain death prediction for patients with severe head injury Maysam F. Abbod a , Kai-Yuan Cheng b , Xing-Ran Cui c , Sheng-Jean Huang d , Yin-Yi Han e , Jiann-Shing Shieh b,∗ a
Electronic and Computer Engineering, School of Engineering and Design, Brunel University, Uxbridge, UK Department of Mechanical Engineering, Yuan Ze University, Taiwan School of Information Engineering, Wuhan University of Technology, Wuhan, PR China d Department of Surgery, National Taiwan University Hospital, Taiwan e Department of Trauma, National Taiwan University Hospital, Taiwan b c
a r t i c l e
i n f o
Article history: Received 4 June 2010 Received in revised form 7 January 2011 Accepted 7 January 2011 Available online 3 February 2011 Keywords: Irreversible apnoeic coma (IAC) Ensembled neural networks (ENNs) Multi-layer perceptron (MLP) Brain death index (BDI)
a b s t r a c t The concept of organ donation has gradually been accepted by people in recent years so the judicial brain death determination process becomes very important. Clinically, patients with irreversible apnoeic coma (IAC) will be considered legally as brain death based on a judicial process, but this process can only be applied to people who had already signed the letter of consent to organ donation. The main idea behind the proposed model is to find out an easier way to diagnose the prognosis of patients with severe head injury, and offer the medical staffs more information to determine brain death. Therefore, the technique of ensembled neural networks (ENN) based on multi-layer perceptron (MLP) network has been applied to construct the prediction model of brain death index (BDI). Ten different signals were chosen to be the input data. Using these ten parameters, medical doctors depend on their experience to score the BDI hourly values. The BDI values from medical doctors become the training target of the ANN training process and the standard index of testing process. Moreover, in order to compare the differences between doctors’ and the network’s rankings for the input data, the ranking of order of precedence of each input signal is analyzed via sensitivity analysis. The results show that the 4 layers network with validation has better performance than 3 layers. For sensitivity analysis, most of the input variables’ ranking from trained model were similar to the ranking of the medical doctors except RR/RR(Set) this parameter and 4 other parameters (PS-R, PR-R, PS-L, and PR-L) are difficult to rank, even medical doctors cannot decide the ranking accurately. Using the best topology structure of MLP 10-10-5-1, the ensemble neural network could effectively predict the BDI with small errors (i.e. training error = 0.219087; validation error = 0.370485; testing error = 0.280515). In conclusion, this model can provide medical staffs a reference index to evaluate the status of IAC and brain death patients. However, more clinical data are still needed, perhaps to refine the weights of EANN, and certainly to see how widely the model is applicable. © 2011 Elsevier Ltd. All rights reserved.
1. Introduction The appearance of irreversible apnoeic coma (IAC) happens generally to a patient with severe head injury and subarachnoid hemorrhage. In an intensive care unit, a patient with irreversible apnoeic coma has a great risk of developing brainstem failure. The
∗ Corresponding author at: Department of Mechanical Engineering and Graduate School of Biotechnology and Bioengineering, Yuan Ze University, 135 Yuan-Tung Rd., Chung-Li, Taoyuan, 320, Taiwan. Tel.: +886 3 4638800x2470; fax: +886 3 455 8013. E-mail address: [email protected] (J.-S. Shieh). 1746-8094/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.bspc.2011.01.002
brainstem governs functions of heart and other physiological functions. If the condition of “brainstem failure” happens, the functions of heart beating and spontaneous breathing might be lost after a certain period of time. The patient’s life would be irremediable as his or her status passes the “irreversible point” of death. Thus, the IAC patients would be considered clinically as brain dead. The definition of brain death is not identical in many countries. In the USA, brain death is defined as irreversible and complete loss of entire brain function [1], while in the UK it becomes the brainstem failure. In Taiwan, the definition of brain death is the same as UK’s. Although the definition of brain death in many countries are not the same [2–4], most judicial process are still based on two examinations to diagnose the brainstem function, the “apnoea test”
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and “brainstem reflex test” [5]. The result of apnoea test can confirm the “irreversible point” that has occurred, but most the scholarly researches point out that an accurate time of the “irreversible point” cannot be verified. Recently, the review study of Nathan and Greer [6,7] assisted the clinician in understanding the concepts behind brain death, the proper technique for determination, and the areas of controversies that remain and debate. This symptom of IAC always accompanies the appearance of “sympathetic storm”, which is kind of hyperactive phenomenon occurring in the cardiovascular system and had already been verified by many experiments on animals [8–10]. This phenomenon resulted from the failure of sympathetic nerve to reflex the external impulse, which was caused by cerebral stem infarction. The symptoms of sympathetic storm always include the tachycardia and hypertension cause of the dramatic blood vessel constriction in IAC patients [11]. So far, the studies on sympathetic storm had only been carried out in organ donation and the experiments in laboratory, but no study has yet been done in sympathetic storm to the diagnosis of IAC patients. Recently, the concept of organ donation has gradually been accepted by people in Taiwan so the judicial brain death determination process becomes very important. However, this judicial process is only applied to people who had already signed the letter of consent to donate organs, and this standard procedure is very lengthy. In addition, when the doctor concludes that the patient might develop the IAC state, this patient still needs to be observed at least 12–72 h before testing the brain stem function [7,12]. Because of such a long process, it might miss the prime time of organ donation and palliative care for the patients. Therefore, we attempt to find out an alternative method, which can provide the medical staffs an easier way to evaluate the status of patients with severe head injury. Mathematical and statistical methods have been used in the past to develop models for prediction. The most commonly used methods include Bayesian network, logistic regression, and neural networks [13–18]. Particularly, artificial neural networks (ANNs) have been successfully used for surgical decisions on traumatic brain injury patients [19] and mortality prediction based on initial clinical data [20]. Based on previous studies by the authors [21], the input data come from many different physiological signals. Most variations of the physiological signals are due to the phenomenon of physiology changes in patients’ bodies. This phenomenon is so complicated and non-linear that almost cannot be simulated by any traditional mathematical models. In this study, the technique of ensembled neural networks (ENNs) based on multi-layer perceptron (MLP) network has been applied to construct the prediction model of brain death index (BDI). 2. Methods 2.1. Ensembled neural network (ENN) There are many different structure type of the ANN. One of common structure is multi-layer perceptron (MLP) network, and it is a feedforward type of the neural network [22]. The MLP network must be trained for its specific purpose using learning algorithms, i.e. back-propagation training. After the training phase, the MLP network can be used to generate the outputs. Ensembled neural network (ENN) is a learning paradigm, which can be seen as the collection of a finite number of neural networks trained for the same task and then combines the outputs of these networks [23]. The basic ensemble method is to find out the weights for each output that minimize the mean squared error (MSE) of the ensemble. This method can provide an improved accuracy over any individual output of the traditional neural network due to different initial weighting problems [24–26]. The advan-
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tage of this method is each individual artificial neural network is known to make errors but their combination using ensemble method minimizes the effect of these errors. It originates from Hansen and Salamon’s work [27], which shows that the generalization ability of a neural network system can be significantly improved through ensembling a number of neural networks. Two properties of ENN were discussed [28]: accuracy and diversity. One theory behind using ENN is that several less accurate networks that are diverse can be combined into a more-accurate ENN [29]. 2.2. Experimental procedure In order to procure the purpose of developing this diagnosis system of brain death index, a procedure to construct this model has been designed. First, some parameters must be selected to be the input data, and these parameters can represent the different conditions of the patients’ physiology status. In general, nurses always record patients’ vital signs for each hour in the intensive care unit, and medical doctors depend on their experience to observe and diagnose the variation of these physiological signals. So, these conventional signals sampled at 1 h rate from the nursing record become the input data for the ANN system. Ten different signals were chosen to be the input data which include the heart rate (HR), ratio value of respiration rate and respirator setting number (RR/RR (Set)), mean value of arterial blood pressure (MABP), body temperature (BT), pupil size of left and right eye (PS-L/R), pupil response of left and right eye (PR-L/R), Glasgow coma scale (GCS), and the motor response (MR). Particularly, the respiration rate of patient is affected by setting value of artificial ventilation machine for each patient. In order to normalize this parameter, we have divided it by the setting value of the machine. Although the signals are time-varying, we just use the average value of these signals per hour according to conventional measurements of these vital signs. Using these ten parameters, medical doctors depend on their experience to score the BDI hourly values. The BDI values from medical doctors become the training target of the ANN training process and the standard index of testing process. The flow chart of this procedure is shown in Fig. 1. All the data was assigned BDI value each hour by medical doctors. The 80% of these data will be for training, 10% will be for validation, and the last 10% will be for testing. The reason for this is the principle of ANN is to find the patterns in data during the process of learning. Since the data collected in this study is relatively small (i.e., the data of brain death are rare and difficult to collect), we have split it up into 80:10:10 for the training, validation, and testing rather into thirds. The learning process of the network is affected by different initial weighting. In order to reduce this unavoidable influence, an ENN configuration was chosen [27]. Using a random sequence of the training data to train the network can give better models than using the raw sequence. So, the first step of training process is to randomize the training data sequence. This step was repeated ten times and got ten different sequences of training data. Each sequence of training data could be used to train ten networks with different weight initialization. Therefore 100 networks were generated during the training phase. In each training epoch the validation data is used to test the network and prevent the network from over-fitting. After the training stage, the training data is used to test the accuracy of network output and find out the best one with the least value of mean square error (MSE) in each groups of network. This is selected to form the 10 best networks which will become the model of BDI diagnosis system. The final model output is the average of the outputs from these 10 members of the ensemble. A flow chart of this procedure is as shown in Fig. 2.
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Fig. 1. Flow chart of the model establishing process. All the data was assigned the BDI value in each hour for medical doctors, and these BDI values became the target of network training process and the standard index of testing process.
2.3. Sensitivity analysis Sensitivity analysis is a critical step in network modeling process. It provides an idea of the model dynamics responses to variation of the input parameters. The purpose of sensitivity analysis is to study the behavior of a model, and to assess the importance of each independent variable with respect to the dependent variable of the model [30,31]. Broadly speaking, there are two common methods for the sensitivity analysis of the MLP network. The first one is to define the sensitivity as the partial derivative of the network’s output to input, and the second one is to calculate the variance of the network’s output error under some stochastic assumptions [32]. The testing steps of these two methods are as follows: for the partial derivative method: (1) find out the average for each group of input signals, and choose these averages to be the central number of the testing data. (2) Using these all average inputs to test the neural network, and measure the corresponding output. (3) Change single input data in each testing. In general,
it is always replaced by maximum to minimum. (4) If the changing ratio of the corresponding output for changing input is very large, it means this input data is very sensitivity and vice versa. For the variance method: (1) find out the average for each group of input signals firstly. (2) Change single group of inputs to the average in each testing, but other inputs are as usual, and then measure the mean-square error with the original and new output. (3) If the mean-square error of the change single group of inputs is very large, it means this input is very sensitivity and vice versa. For these two methods, the concept of the variance method is more intuitional than the partial derivative method, but the resolution of the variance method is insufficient for the variation of each input variable. In this work a modified variance method has been proposed which is based on the scale proportion. In this modified method the testing input signal is changed to mean value and the error of system output is calculated. The relationship between the error and the variable significance is directly proportional, however a single value (mean value) cannot represent the whole feature’s
Test Each Network ( by using raw training data )
Network 1
Random sampling
.......
Training Data ( 15 Cases )
Training
Input
Network 10 10 Best Network
ANN Model (Ensemble NN)
Network 1
Training
...
Training Data ( Sequence 10 )
...
Training Data ( Sequence 1 )
Testing Data ( 3 Cases )
Network 10
BDI Output
Validation Data ( 2 Cases ) To avoid the over-fitting of the Network Fig. 2. Flow chart of the ensemble neural network training process. The 80% of study cases became the training data, another 10% became the validation, and the other 10% became the testing data.
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weighting of the input signal, so each input variable is sequentially set from minimum value to maximum value, and the interval is 0.02, while other variables are kept constant. Medical doctors depend on their experience to observe the variation of the physiological signals and then decide the BDI value as the different signals have different weights in the BDI assessment process. In order to compare the differences between doctors’ and the network’s rankings for the input data, the ranking of order of precedence of each input signal is sought during the learning process of the neural network. Hence, the modified method for sensitivity analysis has been applied in this study. 3. Patients’ populations and data The main purpose of this research is to develop a method that can categorize the different patterns of brain-death patients. Data were collected from adult patients with severe head injury with different level of Glasgow coma scale (GCS). The GCS is the most widely used scoring system (i.e., between 3 and 15) used in quantifying level of consciousness following traumatic brain injury. It is easy to use and determine the eye opening response, the verbal response, and the motor response. The score represents the sum of the numeric scores of each of the categories. However, there are limitations to its use. Tracheal intubation and severe facial/eye swelling or damage make it impossible to test the verbal and eye responses. In these circumstances, the score is given as 1 with a modifier attached e.g. ‘E1c’ where ‘c’ = closed, or ‘V1t’ where t = tube. A composite might be ‘GCS 5tc’. This would mean, for example, eyes closed because of swelling = 1, intubated = 1, leaving a motor score of 3 for ‘abnormal flexion’. Another consideration of anesthetised patients, if the patient is in deep anesthesia for surgical operation in operating room, it is impossible to determine GCS. However, if the patient is in the ICU for light anesthesia (i.e., sedation) to prevent movement, GCS may be evaluated but with some bias. This study obtained the National Taiwan University Hospital (NTUH) research ethics committee approval and got informed consent from family of the patients. In general, the patients can be classified into three different coma levels. The first group of patients is about GCS value of 3 denoted as IAC patients; the second group with GCS values between 4 and 8 are seen as severe coma patients; the third group of GCS values between 9 and 15 are regarded as light coma patients. IAC patients include donors (organ donation) and others patients (i.e., GCS = 3) without going through the judicial process of brain death. All the experiment data are collected
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Table 2 Comparison results of the training error and testing error for different groups of networks without validation. In this table we can notice that the training error is far less than the testing error, and it is the feature of over-fitting. Group
Topology (MLP)
Training error
Testing error
3 Layers
10-5-1 10-10-1 10-20-1 10-25-1 10-30-1 10-10-5-1 10-15-5-1 10-20-5-1 10-25-5-1 10-30-5-1
0.006838 0.006596 0.011254 0.013292 0.012309 0.005214 0.007078 0.007005 0.006547 0.007924
0.343102 0.429319 0.360816 0.474516 0.409200 0.339669 0.336152 0.341595 0.351554 0.352473
4 Layers
from neurosurgical and traumatic intensive care unit of National Taiwan University Hospital. The experimental material for this study focused on the patients with severe head injury. The BDI value can represent the severity of the patients with severe head injury so the patients were classified into three groups. The first group is for score of one. Patients in this group lose their brain stem function completely so they do not have the spontaneous breathing and their sympathetic nerve cannot reflex the external impulse. This kind of patients can be seen clinically as brain death. The second group is for score BDI of two. In the second group, patients only lose the high cortical functions but their brainstem is still working so they can keep the basic vital function. This kind of patients can be seen as vegetative state [33–36]. The third group is for BDI score of three. These patients might have head injury, but their brain stem and cerebral cortex still functions. They can be determined with motor response score bigger than four points. Table 1 shows the patients’ basic information for 20 study cases. A total number of 20 patients (i.e. 15 male and 5 female) were chosen in this study. The whole length of all the cases is 670 data points for the 20 patients. Due to the small number of patients, 80% of the total data were selected as the training data, and the other 20% were the validation and testing data. 15 cases (514 data points) were selected for training, 2 cases (81 data points) for validation, and the last 3 cases (76 data points) for testing. The cases were randomly allocated to each category only once without the cross validation. However, the data points have been randomized for the training and validation data. After the data allotment, the design of the network structure is commissioned.
Table 1 Basic information of 20 study cases (GCS: Glasgow Coma Scale). Case ID
Gender
Age
Symptom
GCS
Final status
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
M M M F M F M M F F M M M F F M M M M M
69 29 39 43 45 18 37 19 56 34 27 68 33 80 57 88 81 63 38 62
Brain death (IAC) Brain death (IAC) Brain death (IAC) Brain death (IAC) Brain death (for organ donation) Brain death (for organ donation) Brain death (clear sympathetic storm) Traumatic head injury Brain death (IAC) Brain death (clear sympathetic storm) Brain death (clear sympathetic storm) Traumatic head injury Traumatic head injury Traumatic head injury Traumatic head injury Traumatic head injury and Lung cancer Left temporal bone fracture Traumatic head injury Traumatic SDH Traumatic head injury
4–3 3 4–3 3 3 4–3 3 7–3 7–3 4–3 8–3 3 3 3 3 9–8 9–6 4–5 9–8 8
Death Death Death Death Death Death Death Death Death Death Death Death Death Death Death Live Death Live Live Live
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Table 3 Comparison results of the training error, validation error, and testing error for different groups of networks. In this table, the training error still less than the testing error, but the difference between these two values are closer than the results in Table 2. Group
Topology (MLP)
Training error
Validation error
Testing error
3 Layers
10-5-1 10-10-1 10-20-1 10-25-1 10-30-1 10-10-5-1 10-15-5-1 10-20-5-1 10-25-5-1 10-30-5-1
0.221703 0.215229 0.210132 0.195856 0.207520 0.219087 0.217394 0.227304 0.209862 0.207955
0.359643 0.374217 0.378147 0.391759 0.390181 0.370485 0.370312 0.365530 0.363851 0.378277
0.274120 0.287585 0.298169 0.326770 0.314620 0.280515 0.288638 0.287949 0.279805 0.307456
4 Layers
4. Results In order to find out the most suitable combination of the layer’s and neuron’s number for ensembled neural networks (ENNs) based on multi-layer perceptron (MLP) network, the number of hidden layer is fixed (single layer and double layers), then the network’s performance (RMSE) for different number of neurons is calculated. Hence, 100 networks have been trained, and the best 10 with least training error were chosen to build the BDI model. This whole process is the standard procedure for the model establishing. The first step of the whole procedure is to normalize the input data. The normalization procedure should be based on detecting the minimum and maximum in each input, and the normalizing scale is dependent on the activation function of the ANN input layer. When the “tan-sigmoid” is chosen the activation function the input data should be normalized to −1 to 1. However, if “log-sigmoid” is cho-
sen the activation function was chosen for each layer, the learning ratio (learning constant) of network is set as 0.01. The training target of each case is the normalized BDI value scored by the medical doctors. After finishing the data normalization, the second step is networks training. The concept of over-fitting in the training procedure is very important. This phenomenon happen to the network when the learning is performed for too long and the learner (network) adjusts to very specific random features of the training data. In the case of over-fitting, the performance of the training examples improves but the performance for the testing data becomes worse. In order to avoid over-fitting, the validation data is used to check the training performance so the training can be stopped when overfitting start to occur. Table 2 shows the prediction error without validation, and Table 3 represents the prediction error with validation. From the result, it is shown that the testing error of the model with validation is less than the error of model without validation.
Table 4 Ranking of input signals for different network structures. The numbers in each row represent the sensitivity of each input for one type of network structure. In this table, we class the structure of network as two groups, one group is for 3 layers and the other group is for 4 layers network. The abbreviations of each signal represent different kind of vital signs. Heart rate (HR), respiration rate (RR/RR(Set)), mean value of blood pressure (MABP), body temperature (BT), pupil size for left or right (PS-L/R), pupil response for left or right (PR-L/R), motor response (MR), Glasgow Coma Scale (GCS). This table is for the process of training without validation. ‘Ranking from Dr.’ is the result of sensitivity for each signal according to the experience of medical doctor. Group
Topology (MLP)
3 Layers
10-5-1 10-10-1 10-20-1 10-25-1 10-30-1 Ranking 10-10-5-1 4 Layers 10-15-5-1 10-20-5-1 10-25-5-1 10-30-5-1 Ranking Ranking from Dr.
HR
RR/RR(Set)
MABP
BT
PS-R
PR-R
PS-L
PR-L
MR
GCS
8 6 8 9 6 7 6 6 7 5 6 6 8
3 7 6 6 8 6 8 5 8 7 7 8 9
6 8 7 8 9 8 7 7 6 8 9 7 7
9 9 9 10 10 9 9 8 9 9 8 9 10
4 5 5 5 4 5 5 4 3 4 4 4
7 2 4 3 3 3 3 3 4 6 3 3
10 10 10 7 7 10 10 10 10 10 10 10
5 4 2 4 5 4 4 9 5 2 5 5
1 1 1 1 1 1 1 1 1 1 1 1 1
2 3 3 2 2 2 2 2 2 3 2 2 2
3–6
Table 5 Ranking of input signals for different network structures. Same annotation used for Table 4 but for training process with validation. Group 3 Layers
Topology (MLP)
10-5-1 10-10-1 10-20-1 10-25-1 10-30-1 Ranking 10-10-5-1 4 Layers 10-15-5-1 10-20-5-1 10-25-5-1 10-30-5-1 Ranking Ranking from Dr.
HR
RR/RR(Set)
MA BP
BT
PS-R
PR-R
PS-L
PR-L
MR
GCS
7 8 8 8 9 8 8 10 8 8 7 8 8
8 3 6 7 3 3 7 4 5 3 5 5 9
6 7 7 5 7 7 6 7 7 7 8 7 7
10 9 10 10 10 10 9 9 10 9 9 9 10
2 4 5 6 4 4 5 6 6 4 6 6
5 2 3 3 6 3 3 3 3 5 3 3
9 10 9 9 8 9 10 8 9 10 10 10
4 5 2 2 2 2 4 5 4 6 4 4
1 1 1 1 1 1 1 1 1 1 1 1 1
3 6 4 4 5 4 2 2 2 2 2 2 2
3–6
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Fig. 3. Sensitivity analysis of each input signal. In this figure, x axis represent the change input, and y axis represent the means square error of system output. The relationship between error and significance is direct proportion to the area below each curve, which can stand for the sensitivity of each input signal.
The next step in this procedure is the sensitivity analysis. The method used in this study to analyze the data sensitivity is the modified variance sensitivity analysis method. First the input data is divided into 50 intervals of the range from 0 to 1 (normalization scale), then the input is increased by one interval value each simulation time step, while the other input variables are kept the raw data. The error value is calculated in each time of the simulation so the area under the curve represents the ranking of order of precedence of each input can be composed of 51 data points of error value as shown in Fig. 3. Then the inputs are ranked accordingly for the five network structures as shown in Tables 4 and 5. Since it is based on five network structures, we can get ranking results according to ‘voting method’. The rank numbers of the last second row of each table were chosen according to the value that occurs most frequently among the 5 network structures. Also, for the 10 input variables in this study, their ranking of order of precedence by medical doctors can be seen as the expert determination index. The comparison between the last two rows (i.e., Ranking and Ranking from Dr.) of each table is the sum of absolute value of the differences between these two rows. However, we only account for 6 parameters (HR, RR/RR(Set), AMBP, BT, MR, and GCS) which medical doctors have accurate values and ignored the 4 parameters of PS-R, PR-R, PS-L, and PR-L which even medical doctors cannot decide very accurately. It has been shown that the 4 layers network has better performance than 3 layers, and has similarity to the doctors’ ranking. In the group of 4 layers networks, the topology structure of MLP 10-10-5-1 is the best performance network as shown in Table 3 with smaller testing error and Table 5 with smaller error of comparison with ranking from medical doctors. Using the best structure (i.e. MLP 10-10-5-1) 4 layer networks, the system performance of training data, validation data, and testing data are shown in Fig. 4. The testing result of the trained system showed acceptable accuracy; however some of the cases did not match the target index, especially in the transitional condition of BDI variation. The physiology change for patients is very complicated. In fact, it is almost impossible to simulate using some common vital signals. But in some particular situation, the patients’ vital signs might display the unique characteristics. These characteristics could become the key point of the determination for diagnosis process.
Fig. 4. Testing results of training data (15 cases; 514 data points), validation data (3 cases; 81 data points) and testing data (1 case; 25 data points). (a) Shows the output performance and error for each training data. (b) Shows the output performance and error for each validation data. (c) Shows the output performance and error for this case.
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5. Conclusions and discussions In this study, it has been shown that the ENN is able to predict BDI for diagnosis system. In comparison with our previous preliminary study [21], we are doing more comprehensive works as described in the following. Firstly, we do the comparison with or without validation data as shown in Tables 2–5 to prove the need to have validation data to prevent the over-fitting problems in ENN. Secondly, we test in more details the number nodes of hidden layer as shown in Tables 2–5. The numbers of node for hidden layer are tested for 5, 10, 20, 25, and 30 in comparison with previous study, which were only tested for 5, 20, and 30. The numbers of node in the first hidden layer for 4 layers are also tested more details. These more tests gave us more confidence in concluding that 4 layers are better than 3 layers. Thirdly, for ranking analysis, we have done more investigation as shown in Tables 4 and 5 in comparison with previous study. The results show that most of the input variables’ ranking from trained model were similar to the ranking of the medical doctors except RR/RR(Set) this parameter and 4 other parameters (PS-R, PR-R, PS-L, and PR-L) are difficult to rank, even medical doctors cannot decide the ranking accurately. Hence, these ranking results are similar to expert’s experience which gave more confidence to say that the EANN model can achieve the good prediction results in comparison with medical doctors. However, more clinical data are still needed, perhaps to refine the weights of EANN, and certainly to see how widely the model is applicable. As describing in previous section, most of the input variables’ ranking from the trained model were similar to the ranking of the medical doctors but several parameters are still difficult to rank, even medical doctors cannot decide the ranking accurately. However, not all the input variables were similar because this phenomenon is due to the characteristic of signal variation not being regular as we think so that the variable weighting cannot totally match the expert’s ranking. Recently, there are several papers that investigate the relationship of electroencephalogram (EEG) and transcranial doppler (TCD) blood flow velocity with brain death. Beridze et al. [37] carried an investigation of the dominated EEG patterns in traumatic coma of different severity and elucidated their prognostic value for the outcome of disease within month. They found that delta EEG pattern is associated with deep coma state and predicts the poor functional outcome within month in severe traumatic coma patients. Also, de Freitas and Andre [38] found TCD is a sensitive, specific, and noninvasive technique to detect cerebral circulatory arrest in brain death by identifying specific pattern. However, it may lead to false-negative results in some cases if only considering one signal. Therefore, Vicenzini et al. [39] proposed not only to look at TCD but also to consider EEG pattern. Through the high technology and gradually reducing the cost of medical devices, more and more input variables can be included in brain death model. Fortunately, our EANN system has provided good platform for merging these important variables into the system. The determination of the appropriate number of hidden layers and the number of hidden nodes (NHNs) in each layer are one of the most critical tasks in ANN design. In fact, it has been shown that single-hidden-layer networks (i.e., 3 layers in this study) are not sufficient for stabilization, especially in discontinuous mapping, but the two-hidden-layer networks (i.e., 4 layers in this study) are adequate [40]. However, the neurons of a hidden layer are a fundamental question often raised in the application of ANN to real-world problems. Many of previous researchers used hidden layer neurons less than the neurons in the input layer [41,42]. Some researchers used hidden layer neurons 30% less than the number of neurons in the input layer [43]. In general, it is expected that the smallest suitable architecture, with hidden neurons at least less than that of the input layer, should avoid over-fitting and should most
likely achieve better generalization. A suitable NHN depends on many conditions, such as the number of inputs and outputs (NINP and NOUT), the amount of noise in the targets, the complexity of the function, regularization, etc. Although some rules for this problem were mentioned, the most popular method to get the optimal number of hidden neurons is trial and error. Recently, more researches on the dynamics of physiological systems have been conducted for understanding its mechanism using continuous ECG, blood pressure, EEG, TCD, and oximeter wave forms. However, conventional measurements of these vital signs are expressed in single measurement at one time (e.g., every 1 h). Such measurement is hard to express the dynamic changes in physiological systems. Also, these time series of signal measured from physiologic systems are always non-linear and non-stationary. Thus, there are many innovative algorithms of data analysis for nonlinear and non-stationary signal applied for physiologic signal analysis [44–47]. Hence, to figure out the relationship between these continuous wave forms signals, which is possible to analyze their dynamic changes every instantaneous time, and brain death, a combination of many innovative algorithms of data analysis for nonlinear and non-stationary signals and artificial neural networks will be made in the near future. The predicted BDI is not an integer value, which can provide more valuable information about transitions between states. In practice, medical doctors have to classify the patients into three states. They cannot classify a patient into a 0.5 level. However, some patients can be between two states. Besides, it may be argued that the data in this study is not large. According to the statistics, there are 20 cases of brain death in NTUH each year and many patients’ family refused to give consent for study, thus the data for this study is rare and precious. Therefore, due to the small data size, the results of this study are still preliminary and when more data can be collected and classified into more states, then the prediction results will be more accurate. Acknowledgement The authors wish to thank the National Science Council (NSC) of Taiwan (Grant number NSC96-2221-E-002-306-E) for supporting this research. References [1] G.A. Van Norman, A matter of life and death: what every anesthesiologist should know about the medical, legal, and ethical aspects of declaring brain death, Anesthesiology 91 (1999) 275–287. [2] N Zamperetti, R. Bellomo, C.A. Defanti, Irreversible apnoeic coma 35 years later towards a more rigorous definition of brain death, Intensive Care Med. 30 (2004) 1715–1722. [3] E.F. Wijdicks, Brain death worldwide: accepted fact but no global consensus in diagnostic criteria, Neurology 58 (2002) 20–25. [4] C.D. Reimers, The definition and determination of brain death, Bailliere’s Clin. Anaesthesiol. 13 (1999) 211–225. [5] E.F. Wijdicks, The diagnosis of brain death, N. Engl. J. Med. 344 (2001) 1215–1221. [6] S. Nathan, D.M. Greer, Brain death, Semin. Anesthesia Perioperative Med. Pain 25 (2006) 225–231. [7] M.K. Heran, N.S. Heran, S.D. Shemine, A review of ancillary tests in evaluating brain death, Can. J. Neurol. Sci. 35 (2008) 409–419. [8] B. Shivalkar, L.J. Van, W. Wieland, Variable effects of explosive or gradual increase of intracranial pressure on myocardial structure and function, Circulation 87 (1993) 230–239. [9] D.J. Powner, A. Hendricj, A. Nyhuis, Changes in serum catecholamine levels in patients who are brain dead, J. Heart Lung Transplant. 11 (1992) 1046– 1053. [10] M. Smith, Physiologic changes during brain stem death-lessons for management of the organ donor, J. Heart Lung Transplant. 23 (2004) 217–222. [11] C.L. Chai, Y.K. Tu, S.J. Huang, Can cerebral hypoperfusion after sympathetic storm be used to diagnose brain death? A retrospective survey in traumatic brain injury patients, J. Trauma 64 (2008) 688–697. [12] Task Force Report, Guidelines for the determination of brain death in children. American Academy of Paediatric, Paediatric, 80 (1987) 298–300.
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Contents lists available at ScienceDirect
Biomedical Signal Processing and Control journal homepage: www.elsevier.com/locate/bspc
Ensembled neural networks for brain death prediction for patients with severe head injury Maysam F. Abbod a , Kai-Yuan Cheng b , Xing-Ran Cui c , Sheng-Jean Huang d , Yin-Yi Han e , Jiann-Shing Shieh b,∗ a
Electronic and Computer Engineering, School of Engineering and Design, Brunel University, Uxbridge, UK Department of Mechanical Engineering, Yuan Ze University, Taiwan School of Information Engineering, Wuhan University of Technology, Wuhan, PR China d Department of Surgery, National Taiwan University Hospital, Taiwan e Department of Trauma, National Taiwan University Hospital, Taiwan b c
a r t i c l e
i n f o
Article history: Received 4 June 2010 Received in revised form 7 January 2011 Accepted 7 January 2011 Available online 3 February 2011 Keywords: Irreversible apnoeic coma (IAC) Ensembled neural networks (ENNs) Multi-layer perceptron (MLP) Brain death index (BDI)
a b s t r a c t The concept of organ donation has gradually been accepted by people in recent years so the judicial brain death determination process becomes very important. Clinically, patients with irreversible apnoeic coma (IAC) will be considered legally as brain death based on a judicial process, but this process can only be applied to people who had already signed the letter of consent to organ donation. The main idea behind the proposed model is to find out an easier way to diagnose the prognosis of patients with severe head injury, and offer the medical staffs more information to determine brain death. Therefore, the technique of ensembled neural networks (ENN) based on multi-layer perceptron (MLP) network has been applied to construct the prediction model of brain death index (BDI). Ten different signals were chosen to be the input data. Using these ten parameters, medical doctors depend on their experience to score the BDI hourly values. The BDI values from medical doctors become the training target of the ANN training process and the standard index of testing process. Moreover, in order to compare the differences between doctors’ and the network’s rankings for the input data, the ranking of order of precedence of each input signal is analyzed via sensitivity analysis. The results show that the 4 layers network with validation has better performance than 3 layers. For sensitivity analysis, most of the input variables’ ranking from trained model were similar to the ranking of the medical doctors except RR/RR(Set) this parameter and 4 other parameters (PS-R, PR-R, PS-L, and PR-L) are difficult to rank, even medical doctors cannot decide the ranking accurately. Using the best topology structure of MLP 10-10-5-1, the ensemble neural network could effectively predict the BDI with small errors (i.e. training error = 0.219087; validation error = 0.370485; testing error = 0.280515). In conclusion, this model can provide medical staffs a reference index to evaluate the status of IAC and brain death patients. However, more clinical data are still needed, perhaps to refine the weights of EANN, and certainly to see how widely the model is applicable. © 2011 Elsevier Ltd. All rights reserved.
1. Introduction The appearance of irreversible apnoeic coma (IAC) happens generally to a patient with severe head injury and subarachnoid hemorrhage. In an intensive care unit, a patient with irreversible apnoeic coma has a great risk of developing brainstem failure. The
∗ Corresponding author at: Department of Mechanical Engineering and Graduate School of Biotechnology and Bioengineering, Yuan Ze University, 135 Yuan-Tung Rd., Chung-Li, Taoyuan, 320, Taiwan. Tel.: +886 3 4638800x2470; fax: +886 3 455 8013. E-mail address: [email protected] (J.-S. Shieh). 1746-8094/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.bspc.2011.01.002
brainstem governs functions of heart and other physiological functions. If the condition of “brainstem failure” happens, the functions of heart beating and spontaneous breathing might be lost after a certain period of time. The patient’s life would be irremediable as his or her status passes the “irreversible point” of death. Thus, the IAC patients would be considered clinically as brain dead. The definition of brain death is not identical in many countries. In the USA, brain death is defined as irreversible and complete loss of entire brain function [1], while in the UK it becomes the brainstem failure. In Taiwan, the definition of brain death is the same as UK’s. Although the definition of brain death in many countries are not the same [2–4], most judicial process are still based on two examinations to diagnose the brainstem function, the “apnoea test”
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and “brainstem reflex test” [5]. The result of apnoea test can confirm the “irreversible point” that has occurred, but most the scholarly researches point out that an accurate time of the “irreversible point” cannot be verified. Recently, the review study of Nathan and Greer [6,7] assisted the clinician in understanding the concepts behind brain death, the proper technique for determination, and the areas of controversies that remain and debate. This symptom of IAC always accompanies the appearance of “sympathetic storm”, which is kind of hyperactive phenomenon occurring in the cardiovascular system and had already been verified by many experiments on animals [8–10]. This phenomenon resulted from the failure of sympathetic nerve to reflex the external impulse, which was caused by cerebral stem infarction. The symptoms of sympathetic storm always include the tachycardia and hypertension cause of the dramatic blood vessel constriction in IAC patients [11]. So far, the studies on sympathetic storm had only been carried out in organ donation and the experiments in laboratory, but no study has yet been done in sympathetic storm to the diagnosis of IAC patients. Recently, the concept of organ donation has gradually been accepted by people in Taiwan so the judicial brain death determination process becomes very important. However, this judicial process is only applied to people who had already signed the letter of consent to donate organs, and this standard procedure is very lengthy. In addition, when the doctor concludes that the patient might develop the IAC state, this patient still needs to be observed at least 12–72 h before testing the brain stem function [7,12]. Because of such a long process, it might miss the prime time of organ donation and palliative care for the patients. Therefore, we attempt to find out an alternative method, which can provide the medical staffs an easier way to evaluate the status of patients with severe head injury. Mathematical and statistical methods have been used in the past to develop models for prediction. The most commonly used methods include Bayesian network, logistic regression, and neural networks [13–18]. Particularly, artificial neural networks (ANNs) have been successfully used for surgical decisions on traumatic brain injury patients [19] and mortality prediction based on initial clinical data [20]. Based on previous studies by the authors [21], the input data come from many different physiological signals. Most variations of the physiological signals are due to the phenomenon of physiology changes in patients’ bodies. This phenomenon is so complicated and non-linear that almost cannot be simulated by any traditional mathematical models. In this study, the technique of ensembled neural networks (ENNs) based on multi-layer perceptron (MLP) network has been applied to construct the prediction model of brain death index (BDI). 2. Methods 2.1. Ensembled neural network (ENN) There are many different structure type of the ANN. One of common structure is multi-layer perceptron (MLP) network, and it is a feedforward type of the neural network [22]. The MLP network must be trained for its specific purpose using learning algorithms, i.e. back-propagation training. After the training phase, the MLP network can be used to generate the outputs. Ensembled neural network (ENN) is a learning paradigm, which can be seen as the collection of a finite number of neural networks trained for the same task and then combines the outputs of these networks [23]. The basic ensemble method is to find out the weights for each output that minimize the mean squared error (MSE) of the ensemble. This method can provide an improved accuracy over any individual output of the traditional neural network due to different initial weighting problems [24–26]. The advan-
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tage of this method is each individual artificial neural network is known to make errors but their combination using ensemble method minimizes the effect of these errors. It originates from Hansen and Salamon’s work [27], which shows that the generalization ability of a neural network system can be significantly improved through ensembling a number of neural networks. Two properties of ENN were discussed [28]: accuracy and diversity. One theory behind using ENN is that several less accurate networks that are diverse can be combined into a more-accurate ENN [29]. 2.2. Experimental procedure In order to procure the purpose of developing this diagnosis system of brain death index, a procedure to construct this model has been designed. First, some parameters must be selected to be the input data, and these parameters can represent the different conditions of the patients’ physiology status. In general, nurses always record patients’ vital signs for each hour in the intensive care unit, and medical doctors depend on their experience to observe and diagnose the variation of these physiological signals. So, these conventional signals sampled at 1 h rate from the nursing record become the input data for the ANN system. Ten different signals were chosen to be the input data which include the heart rate (HR), ratio value of respiration rate and respirator setting number (RR/RR (Set)), mean value of arterial blood pressure (MABP), body temperature (BT), pupil size of left and right eye (PS-L/R), pupil response of left and right eye (PR-L/R), Glasgow coma scale (GCS), and the motor response (MR). Particularly, the respiration rate of patient is affected by setting value of artificial ventilation machine for each patient. In order to normalize this parameter, we have divided it by the setting value of the machine. Although the signals are time-varying, we just use the average value of these signals per hour according to conventional measurements of these vital signs. Using these ten parameters, medical doctors depend on their experience to score the BDI hourly values. The BDI values from medical doctors become the training target of the ANN training process and the standard index of testing process. The flow chart of this procedure is shown in Fig. 1. All the data was assigned BDI value each hour by medical doctors. The 80% of these data will be for training, 10% will be for validation, and the last 10% will be for testing. The reason for this is the principle of ANN is to find the patterns in data during the process of learning. Since the data collected in this study is relatively small (i.e., the data of brain death are rare and difficult to collect), we have split it up into 80:10:10 for the training, validation, and testing rather into thirds. The learning process of the network is affected by different initial weighting. In order to reduce this unavoidable influence, an ENN configuration was chosen [27]. Using a random sequence of the training data to train the network can give better models than using the raw sequence. So, the first step of training process is to randomize the training data sequence. This step was repeated ten times and got ten different sequences of training data. Each sequence of training data could be used to train ten networks with different weight initialization. Therefore 100 networks were generated during the training phase. In each training epoch the validation data is used to test the network and prevent the network from over-fitting. After the training stage, the training data is used to test the accuracy of network output and find out the best one with the least value of mean square error (MSE) in each groups of network. This is selected to form the 10 best networks which will become the model of BDI diagnosis system. The final model output is the average of the outputs from these 10 members of the ensemble. A flow chart of this procedure is as shown in Fig. 2.
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Fig. 1. Flow chart of the model establishing process. All the data was assigned the BDI value in each hour for medical doctors, and these BDI values became the target of network training process and the standard index of testing process.
2.3. Sensitivity analysis Sensitivity analysis is a critical step in network modeling process. It provides an idea of the model dynamics responses to variation of the input parameters. The purpose of sensitivity analysis is to study the behavior of a model, and to assess the importance of each independent variable with respect to the dependent variable of the model [30,31]. Broadly speaking, there are two common methods for the sensitivity analysis of the MLP network. The first one is to define the sensitivity as the partial derivative of the network’s output to input, and the second one is to calculate the variance of the network’s output error under some stochastic assumptions [32]. The testing steps of these two methods are as follows: for the partial derivative method: (1) find out the average for each group of input signals, and choose these averages to be the central number of the testing data. (2) Using these all average inputs to test the neural network, and measure the corresponding output. (3) Change single input data in each testing. In general,
it is always replaced by maximum to minimum. (4) If the changing ratio of the corresponding output for changing input is very large, it means this input data is very sensitivity and vice versa. For the variance method: (1) find out the average for each group of input signals firstly. (2) Change single group of inputs to the average in each testing, but other inputs are as usual, and then measure the mean-square error with the original and new output. (3) If the mean-square error of the change single group of inputs is very large, it means this input is very sensitivity and vice versa. For these two methods, the concept of the variance method is more intuitional than the partial derivative method, but the resolution of the variance method is insufficient for the variation of each input variable. In this work a modified variance method has been proposed which is based on the scale proportion. In this modified method the testing input signal is changed to mean value and the error of system output is calculated. The relationship between the error and the variable significance is directly proportional, however a single value (mean value) cannot represent the whole feature’s
Test Each Network ( by using raw training data )
Network 1
Random sampling
.......
Training Data ( 15 Cases )
Training
Input
Network 10 10 Best Network
ANN Model (Ensemble NN)
Network 1
Training
...
Training Data ( Sequence 10 )
...
Training Data ( Sequence 1 )
Testing Data ( 3 Cases )
Network 10
BDI Output
Validation Data ( 2 Cases ) To avoid the over-fitting of the Network Fig. 2. Flow chart of the ensemble neural network training process. The 80% of study cases became the training data, another 10% became the validation, and the other 10% became the testing data.
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weighting of the input signal, so each input variable is sequentially set from minimum value to maximum value, and the interval is 0.02, while other variables are kept constant. Medical doctors depend on their experience to observe the variation of the physiological signals and then decide the BDI value as the different signals have different weights in the BDI assessment process. In order to compare the differences between doctors’ and the network’s rankings for the input data, the ranking of order of precedence of each input signal is sought during the learning process of the neural network. Hence, the modified method for sensitivity analysis has been applied in this study. 3. Patients’ populations and data The main purpose of this research is to develop a method that can categorize the different patterns of brain-death patients. Data were collected from adult patients with severe head injury with different level of Glasgow coma scale (GCS). The GCS is the most widely used scoring system (i.e., between 3 and 15) used in quantifying level of consciousness following traumatic brain injury. It is easy to use and determine the eye opening response, the verbal response, and the motor response. The score represents the sum of the numeric scores of each of the categories. However, there are limitations to its use. Tracheal intubation and severe facial/eye swelling or damage make it impossible to test the verbal and eye responses. In these circumstances, the score is given as 1 with a modifier attached e.g. ‘E1c’ where ‘c’ = closed, or ‘V1t’ where t = tube. A composite might be ‘GCS 5tc’. This would mean, for example, eyes closed because of swelling = 1, intubated = 1, leaving a motor score of 3 for ‘abnormal flexion’. Another consideration of anesthetised patients, if the patient is in deep anesthesia for surgical operation in operating room, it is impossible to determine GCS. However, if the patient is in the ICU for light anesthesia (i.e., sedation) to prevent movement, GCS may be evaluated but with some bias. This study obtained the National Taiwan University Hospital (NTUH) research ethics committee approval and got informed consent from family of the patients. In general, the patients can be classified into three different coma levels. The first group of patients is about GCS value of 3 denoted as IAC patients; the second group with GCS values between 4 and 8 are seen as severe coma patients; the third group of GCS values between 9 and 15 are regarded as light coma patients. IAC patients include donors (organ donation) and others patients (i.e., GCS = 3) without going through the judicial process of brain death. All the experiment data are collected
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Table 2 Comparison results of the training error and testing error for different groups of networks without validation. In this table we can notice that the training error is far less than the testing error, and it is the feature of over-fitting. Group
Topology (MLP)
Training error
Testing error
3 Layers
10-5-1 10-10-1 10-20-1 10-25-1 10-30-1 10-10-5-1 10-15-5-1 10-20-5-1 10-25-5-1 10-30-5-1
0.006838 0.006596 0.011254 0.013292 0.012309 0.005214 0.007078 0.007005 0.006547 0.007924
0.343102 0.429319 0.360816 0.474516 0.409200 0.339669 0.336152 0.341595 0.351554 0.352473
4 Layers
from neurosurgical and traumatic intensive care unit of National Taiwan University Hospital. The experimental material for this study focused on the patients with severe head injury. The BDI value can represent the severity of the patients with severe head injury so the patients were classified into three groups. The first group is for score of one. Patients in this group lose their brain stem function completely so they do not have the spontaneous breathing and their sympathetic nerve cannot reflex the external impulse. This kind of patients can be seen clinically as brain death. The second group is for score BDI of two. In the second group, patients only lose the high cortical functions but their brainstem is still working so they can keep the basic vital function. This kind of patients can be seen as vegetative state [33–36]. The third group is for BDI score of three. These patients might have head injury, but their brain stem and cerebral cortex still functions. They can be determined with motor response score bigger than four points. Table 1 shows the patients’ basic information for 20 study cases. A total number of 20 patients (i.e. 15 male and 5 female) were chosen in this study. The whole length of all the cases is 670 data points for the 20 patients. Due to the small number of patients, 80% of the total data were selected as the training data, and the other 20% were the validation and testing data. 15 cases (514 data points) were selected for training, 2 cases (81 data points) for validation, and the last 3 cases (76 data points) for testing. The cases were randomly allocated to each category only once without the cross validation. However, the data points have been randomized for the training and validation data. After the data allotment, the design of the network structure is commissioned.
Table 1 Basic information of 20 study cases (GCS: Glasgow Coma Scale). Case ID
Gender
Age
Symptom
GCS
Final status
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
M M M F M F M M F F M M M F F M M M M M
69 29 39 43 45 18 37 19 56 34 27 68 33 80 57 88 81 63 38 62
Brain death (IAC) Brain death (IAC) Brain death (IAC) Brain death (IAC) Brain death (for organ donation) Brain death (for organ donation) Brain death (clear sympathetic storm) Traumatic head injury Brain death (IAC) Brain death (clear sympathetic storm) Brain death (clear sympathetic storm) Traumatic head injury Traumatic head injury Traumatic head injury Traumatic head injury Traumatic head injury and Lung cancer Left temporal bone fracture Traumatic head injury Traumatic SDH Traumatic head injury
4–3 3 4–3 3 3 4–3 3 7–3 7–3 4–3 8–3 3 3 3 3 9–8 9–6 4–5 9–8 8
Death Death Death Death Death Death Death Death Death Death Death Death Death Death Death Live Death Live Live Live
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Table 3 Comparison results of the training error, validation error, and testing error for different groups of networks. In this table, the training error still less than the testing error, but the difference between these two values are closer than the results in Table 2. Group
Topology (MLP)
Training error
Validation error
Testing error
3 Layers
10-5-1 10-10-1 10-20-1 10-25-1 10-30-1 10-10-5-1 10-15-5-1 10-20-5-1 10-25-5-1 10-30-5-1
0.221703 0.215229 0.210132 0.195856 0.207520 0.219087 0.217394 0.227304 0.209862 0.207955
0.359643 0.374217 0.378147 0.391759 0.390181 0.370485 0.370312 0.365530 0.363851 0.378277
0.274120 0.287585 0.298169 0.326770 0.314620 0.280515 0.288638 0.287949 0.279805 0.307456
4 Layers
4. Results In order to find out the most suitable combination of the layer’s and neuron’s number for ensembled neural networks (ENNs) based on multi-layer perceptron (MLP) network, the number of hidden layer is fixed (single layer and double layers), then the network’s performance (RMSE) for different number of neurons is calculated. Hence, 100 networks have been trained, and the best 10 with least training error were chosen to build the BDI model. This whole process is the standard procedure for the model establishing. The first step of the whole procedure is to normalize the input data. The normalization procedure should be based on detecting the minimum and maximum in each input, and the normalizing scale is dependent on the activation function of the ANN input layer. When the “tan-sigmoid” is chosen the activation function the input data should be normalized to −1 to 1. However, if “log-sigmoid” is cho-
sen the activation function was chosen for each layer, the learning ratio (learning constant) of network is set as 0.01. The training target of each case is the normalized BDI value scored by the medical doctors. After finishing the data normalization, the second step is networks training. The concept of over-fitting in the training procedure is very important. This phenomenon happen to the network when the learning is performed for too long and the learner (network) adjusts to very specific random features of the training data. In the case of over-fitting, the performance of the training examples improves but the performance for the testing data becomes worse. In order to avoid over-fitting, the validation data is used to check the training performance so the training can be stopped when overfitting start to occur. Table 2 shows the prediction error without validation, and Table 3 represents the prediction error with validation. From the result, it is shown that the testing error of the model with validation is less than the error of model without validation.
Table 4 Ranking of input signals for different network structures. The numbers in each row represent the sensitivity of each input for one type of network structure. In this table, we class the structure of network as two groups, one group is for 3 layers and the other group is for 4 layers network. The abbreviations of each signal represent different kind of vital signs. Heart rate (HR), respiration rate (RR/RR(Set)), mean value of blood pressure (MABP), body temperature (BT), pupil size for left or right (PS-L/R), pupil response for left or right (PR-L/R), motor response (MR), Glasgow Coma Scale (GCS). This table is for the process of training without validation. ‘Ranking from Dr.’ is the result of sensitivity for each signal according to the experience of medical doctor. Group
Topology (MLP)
3 Layers
10-5-1 10-10-1 10-20-1 10-25-1 10-30-1 Ranking 10-10-5-1 4 Layers 10-15-5-1 10-20-5-1 10-25-5-1 10-30-5-1 Ranking Ranking from Dr.
HR
RR/RR(Set)
MABP
BT
PS-R
PR-R
PS-L
PR-L
MR
GCS
8 6 8 9 6 7 6 6 7 5 6 6 8
3 7 6 6 8 6 8 5 8 7 7 8 9
6 8 7 8 9 8 7 7 6 8 9 7 7
9 9 9 10 10 9 9 8 9 9 8 9 10
4 5 5 5 4 5 5 4 3 4 4 4
7 2 4 3 3 3 3 3 4 6 3 3
10 10 10 7 7 10 10 10 10 10 10 10
5 4 2 4 5 4 4 9 5 2 5 5
1 1 1 1 1 1 1 1 1 1 1 1 1
2 3 3 2 2 2 2 2 2 3 2 2 2
3–6
Table 5 Ranking of input signals for different network structures. Same annotation used for Table 4 but for training process with validation. Group 3 Layers
Topology (MLP)
10-5-1 10-10-1 10-20-1 10-25-1 10-30-1 Ranking 10-10-5-1 4 Layers 10-15-5-1 10-20-5-1 10-25-5-1 10-30-5-1 Ranking Ranking from Dr.
HR
RR/RR(Set)
MA BP
BT
PS-R
PR-R
PS-L
PR-L
MR
GCS
7 8 8 8 9 8 8 10 8 8 7 8 8
8 3 6 7 3 3 7 4 5 3 5 5 9
6 7 7 5 7 7 6 7 7 7 8 7 7
10 9 10 10 10 10 9 9 10 9 9 9 10
2 4 5 6 4 4 5 6 6 4 6 6
5 2 3 3 6 3 3 3 3 5 3 3
9 10 9 9 8 9 10 8 9 10 10 10
4 5 2 2 2 2 4 5 4 6 4 4
1 1 1 1 1 1 1 1 1 1 1 1 1
3 6 4 4 5 4 2 2 2 2 2 2 2
3–6
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Fig. 3. Sensitivity analysis of each input signal. In this figure, x axis represent the change input, and y axis represent the means square error of system output. The relationship between error and significance is direct proportion to the area below each curve, which can stand for the sensitivity of each input signal.
The next step in this procedure is the sensitivity analysis. The method used in this study to analyze the data sensitivity is the modified variance sensitivity analysis method. First the input data is divided into 50 intervals of the range from 0 to 1 (normalization scale), then the input is increased by one interval value each simulation time step, while the other input variables are kept the raw data. The error value is calculated in each time of the simulation so the area under the curve represents the ranking of order of precedence of each input can be composed of 51 data points of error value as shown in Fig. 3. Then the inputs are ranked accordingly for the five network structures as shown in Tables 4 and 5. Since it is based on five network structures, we can get ranking results according to ‘voting method’. The rank numbers of the last second row of each table were chosen according to the value that occurs most frequently among the 5 network structures. Also, for the 10 input variables in this study, their ranking of order of precedence by medical doctors can be seen as the expert determination index. The comparison between the last two rows (i.e., Ranking and Ranking from Dr.) of each table is the sum of absolute value of the differences between these two rows. However, we only account for 6 parameters (HR, RR/RR(Set), AMBP, BT, MR, and GCS) which medical doctors have accurate values and ignored the 4 parameters of PS-R, PR-R, PS-L, and PR-L which even medical doctors cannot decide very accurately. It has been shown that the 4 layers network has better performance than 3 layers, and has similarity to the doctors’ ranking. In the group of 4 layers networks, the topology structure of MLP 10-10-5-1 is the best performance network as shown in Table 3 with smaller testing error and Table 5 with smaller error of comparison with ranking from medical doctors. Using the best structure (i.e. MLP 10-10-5-1) 4 layer networks, the system performance of training data, validation data, and testing data are shown in Fig. 4. The testing result of the trained system showed acceptable accuracy; however some of the cases did not match the target index, especially in the transitional condition of BDI variation. The physiology change for patients is very complicated. In fact, it is almost impossible to simulate using some common vital signals. But in some particular situation, the patients’ vital signs might display the unique characteristics. These characteristics could become the key point of the determination for diagnosis process.
Fig. 4. Testing results of training data (15 cases; 514 data points), validation data (3 cases; 81 data points) and testing data (1 case; 25 data points). (a) Shows the output performance and error for each training data. (b) Shows the output performance and error for each validation data. (c) Shows the output performance and error for this case.
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5. Conclusions and discussions In this study, it has been shown that the ENN is able to predict BDI for diagnosis system. In comparison with our previous preliminary study [21], we are doing more comprehensive works as described in the following. Firstly, we do the comparison with or without validation data as shown in Tables 2–5 to prove the need to have validation data to prevent the over-fitting problems in ENN. Secondly, we test in more details the number nodes of hidden layer as shown in Tables 2–5. The numbers of node for hidden layer are tested for 5, 10, 20, 25, and 30 in comparison with previous study, which were only tested for 5, 20, and 30. The numbers of node in the first hidden layer for 4 layers are also tested more details. These more tests gave us more confidence in concluding that 4 layers are better than 3 layers. Thirdly, for ranking analysis, we have done more investigation as shown in Tables 4 and 5 in comparison with previous study. The results show that most of the input variables’ ranking from trained model were similar to the ranking of the medical doctors except RR/RR(Set) this parameter and 4 other parameters (PS-R, PR-R, PS-L, and PR-L) are difficult to rank, even medical doctors cannot decide the ranking accurately. Hence, these ranking results are similar to expert’s experience which gave more confidence to say that the EANN model can achieve the good prediction results in comparison with medical doctors. However, more clinical data are still needed, perhaps to refine the weights of EANN, and certainly to see how widely the model is applicable. As describing in previous section, most of the input variables’ ranking from the trained model were similar to the ranking of the medical doctors but several parameters are still difficult to rank, even medical doctors cannot decide the ranking accurately. However, not all the input variables were similar because this phenomenon is due to the characteristic of signal variation not being regular as we think so that the variable weighting cannot totally match the expert’s ranking. Recently, there are several papers that investigate the relationship of electroencephalogram (EEG) and transcranial doppler (TCD) blood flow velocity with brain death. Beridze et al. [37] carried an investigation of the dominated EEG patterns in traumatic coma of different severity and elucidated their prognostic value for the outcome of disease within month. They found that delta EEG pattern is associated with deep coma state and predicts the poor functional outcome within month in severe traumatic coma patients. Also, de Freitas and Andre [38] found TCD is a sensitive, specific, and noninvasive technique to detect cerebral circulatory arrest in brain death by identifying specific pattern. However, it may lead to false-negative results in some cases if only considering one signal. Therefore, Vicenzini et al. [39] proposed not only to look at TCD but also to consider EEG pattern. Through the high technology and gradually reducing the cost of medical devices, more and more input variables can be included in brain death model. Fortunately, our EANN system has provided good platform for merging these important variables into the system. The determination of the appropriate number of hidden layers and the number of hidden nodes (NHNs) in each layer are one of the most critical tasks in ANN design. In fact, it has been shown that single-hidden-layer networks (i.e., 3 layers in this study) are not sufficient for stabilization, especially in discontinuous mapping, but the two-hidden-layer networks (i.e., 4 layers in this study) are adequate [40]. However, the neurons of a hidden layer are a fundamental question often raised in the application of ANN to real-world problems. Many of previous researchers used hidden layer neurons less than the neurons in the input layer [41,42]. Some researchers used hidden layer neurons 30% less than the number of neurons in the input layer [43]. In general, it is expected that the smallest suitable architecture, with hidden neurons at least less than that of the input layer, should avoid over-fitting and should most
likely achieve better generalization. A suitable NHN depends on many conditions, such as the number of inputs and outputs (NINP and NOUT), the amount of noise in the targets, the complexity of the function, regularization, etc. Although some rules for this problem were mentioned, the most popular method to get the optimal number of hidden neurons is trial and error. Recently, more researches on the dynamics of physiological systems have been conducted for understanding its mechanism using continuous ECG, blood pressure, EEG, TCD, and oximeter wave forms. However, conventional measurements of these vital signs are expressed in single measurement at one time (e.g., every 1 h). Such measurement is hard to express the dynamic changes in physiological systems. Also, these time series of signal measured from physiologic systems are always non-linear and non-stationary. Thus, there are many innovative algorithms of data analysis for nonlinear and non-stationary signal applied for physiologic signal analysis [44–47]. Hence, to figure out the relationship between these continuous wave forms signals, which is possible to analyze their dynamic changes every instantaneous time, and brain death, a combination of many innovative algorithms of data analysis for nonlinear and non-stationary signals and artificial neural networks will be made in the near future. The predicted BDI is not an integer value, which can provide more valuable information about transitions between states. In practice, medical doctors have to classify the patients into three states. They cannot classify a patient into a 0.5 level. However, some patients can be between two states. Besides, it may be argued that the data in this study is not large. According to the statistics, there are 20 cases of brain death in NTUH each year and many patients’ family refused to give consent for study, thus the data for this study is rare and precious. Therefore, due to the small data size, the results of this study are still preliminary and when more data can be collected and classified into more states, then the prediction results will be more accurate. Acknowledgement The authors wish to thank the National Science Council (NSC) of Taiwan (Grant number NSC96-2221-E-002-306-E) for supporting this research. References [1] G.A. Van Norman, A matter of life and death: what every anesthesiologist should know about the medical, legal, and ethical aspects of declaring brain death, Anesthesiology 91 (1999) 275–287. [2] N Zamperetti, R. Bellomo, C.A. Defanti, Irreversible apnoeic coma 35 years later towards a more rigorous definition of brain death, Intensive Care Med. 30 (2004) 1715–1722. [3] E.F. Wijdicks, Brain death worldwide: accepted fact but no global consensus in diagnostic criteria, Neurology 58 (2002) 20–25. [4] C.D. Reimers, The definition and determination of brain death, Bailliere’s Clin. Anaesthesiol. 13 (1999) 211–225. [5] E.F. Wijdicks, The diagnosis of brain death, N. Engl. J. Med. 344 (2001) 1215–1221. [6] S. Nathan, D.M. Greer, Brain death, Semin. Anesthesia Perioperative Med. Pain 25 (2006) 225–231. [7] M.K. Heran, N.S. Heran, S.D. Shemine, A review of ancillary tests in evaluating brain death, Can. J. Neurol. Sci. 35 (2008) 409–419. [8] B. Shivalkar, L.J. Van, W. Wieland, Variable effects of explosive or gradual increase of intracranial pressure on myocardial structure and function, Circulation 87 (1993) 230–239. [9] D.J. Powner, A. Hendricj, A. Nyhuis, Changes in serum catecholamine levels in patients who are brain dead, J. Heart Lung Transplant. 11 (1992) 1046– 1053. [10] M. Smith, Physiologic changes during brain stem death-lessons for management of the organ donor, J. Heart Lung Transplant. 23 (2004) 217–222. [11] C.L. Chai, Y.K. Tu, S.J. Huang, Can cerebral hypoperfusion after sympathetic storm be used to diagnose brain death? A retrospective survey in traumatic brain injury patients, J. Trauma 64 (2008) 688–697. [12] Task Force Report, Guidelines for the determination of brain death in children. American Academy of Paediatric, Paediatric, 80 (1987) 298–300.
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