Classification of Hemorrhage Using Priori Information of Electrode Arrangement With Electrical Impedance Tomography

Electrical impedance tomography is an emerging technique for brain disease detection. Generally, it requires that electrodes should be equidistantly placed around the detected region. However, this may be not possible for some patients who are undergoing post-surgical monitoring. Aiming at this problem, four kinds of non-uniform electrode arrangements are developed. To accurately detect the location of intracranial hemorrhage, a novel classification method based on a priori information of electrode arrangement is also proposed in this paper. According to the electrode arrangement information, the weight which corresponds to different kinds of electrode arrangement is separately determined during the training process. The proposed method is quantitatively evaluated with basic test dataset, test datasets under noise interruption, test datasets in the case of large contact impedance, test datasets with conductivity variation in different layers, and test datasets when considering modeling error and double inclusions. Comparisons with general classification methods are also conducted. The results show that the proposed method with residual network incorporated outperforms the classification methods of fully connected neural network and residual network. For all the test datasets, the results show that the accuracy is higher than 0.9 and the specificity reaches as high as 1 when the proposed method incorporating residual network is used.


I. INTRODUCTION
Intracranial hemorrhage is a common disease which is usually caused by the rupture of a blood vessel in the brain [1], [2]. Due to its high risk of mortality and disability, it is particularly meaningful to detect hemorrhage rapidly and accurately. Currently, computed tomography (CT) and magnetic resonance imaging (MRI) are standard methods for detecting intracranial hemorrhage [3], [4], [5], [6]. However, CT is radioactive while MRI is time-consuming, and neither of them is suitable for bedside monitoring. Comparatively, electrical impedance tomography (EIT) is a safe, low cost, reliable and fast method that has been successfully applied The associate editor coordinating the review of this manuscript and approving it for publication was Manuel Rosa-Zurera.
in various fields of medical imaging [7], [8], [9], [10]. In the brain imaging, conductivity variation caused by hemorrhage can be also recovered by EIT [11], [12], [13]. It is known that conductivity distribution in the measured region can be reconstructed by processing voltage measurement with EIT imaging methods. Based on the reconstructed images, location of the disease can be identified. Among these methods, regularization methods and iterative methods are very popular for image reconstruction [14], [15], [16]. In recent years, Bayesian learning based reconstruction methods have been presented [17], [18], [19]. With a structural prior incorporated, the computational complexity of the inverse problem is reduced and the accuracy of the reconstructed image is improved. However, such sensitivity-based methods are greatly influenced by various factors such as electrode VOLUME 11, 2023 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ arrangement and boundary shape [20]. Consequently, sensitivity based image reconstruction methods may be not very accurate leading to the fact that location of disease identified by reconstructed images is not very reliable in the clinical applications.
To cope with the problem, various machine learning-based approaches have been proposed for intracranial disease detection. These approaches are implemented by directly processing EIT measurement data. In [21], the effectiveness of the support vector machine method for brain hemorrhage classification is conducted. The performance of the method is validated under the influence of noise, lesion size, lesion location, electrode positioning and anatomy. In [22], a hybrid virtual edge approach is introduced for stroke classification. The performance of the network respectively trained with the hybrid virtual edge data and the original EIT data is tested. It is found that the neural network using the virtual hybrid edge data shows better performance. It should be remarked that the effect of the skull is not considered when detecting hemorrhage with support vector machine method. In the stroke classification with neural networks mentioned above, a simple circular region is used to simulate the head. Meantime, all the above methods require the electrodes to be placed evenly around the head. Such an arrangement of electrodes may be not possible for EIT monitoring of patients who have undergone intracranial surgery. To solve this problem, four kinds of different electrode configurations are introduced in this study and the classification of hemorrhage under such arrangements of electrodes is investigated. The proposed method is oriented to post-surgical monitoring of patients and the goal is to locate new bleeding or increase of bleeding. A two-dimensional head model which is comprised of scalp, skull and parenchyma is established. Unlike conventional methods which use a generalized weight matrix, a novel classification method using a priori information of electrode arrangement is proposed for accurate hemorrhage detection. The performance of the proposed method is validated by basic test dataset, noisy datasets, dataset under large contact impedance, datasets with conductivity variation in different layers of the head model, datasets in the case of modeling error and datasets considering double inclusions. Also, comparisons are made with the results obtained by fully connected neural network and residual network.
This article is organized as follows. Section II describes the modeling of EIT measurement. In Section III, the method for classification of hemorrhage based on a priori information of electrode arrangement is proposed. Also, comparison methods are briefly introduced. The performance of the proposed method is evaluated by several typical cases in Section IV. In Section V, concluding remarks are drawn.

II. MODELING OF EIT MEASUREMENT
Considering the situation when electrodes cannot be uniformly arranged around the whole boundary of the head, four kinds of electrodes arrangement which consider left arrangement, right arrangement, down arrangement and top arrangement are designed as shown in Figure 1. The head is modeled by a simplified 2D model and sixteen electrodes have been used to monitor the hemorrhage. In order to place these electrodes, a two-dimensional transverse plane where the head circumference is largest has been selected. That is 1 cm above the eyebrow arch and 2 cm above the occipital tuberosity. The injection protocol of skip current injection and adjacent voltage measurement is applied. To establish the sensitive field, an alternating current is injected into a pair of electrodes with a skip of 8. Then voltage is measured from remaining adjacent electrode pairs. According to Maxwell equations, the established sensitive field can be described by [23] ∇ · (σ (x)∇φ(x)) = 0, x ∈ where σ denotes the conductivity which is related to spatial position x, represents the detected domain. Contact impedance exists between the electrode and the scalp. It is reported that complete electrode model (CEM) is the most approximate which describe the boundary conditions as [24], [25], [26]  where n is the outward unit normal to ∂ , L is the number of electrodes, z l is the contact impedance, I l and ψ l are respectively current and potential on the lth electrode e l . Due to the fact that the head boundary is irregular and the inner structure is complicated, it is challenging to solve (1) with the analytical method. Comparatively, finite element method (FEM) has been proved to be an effective method  which transforms continuous problem into discrete approximation [27], [28]. Based on FEM, sensitive field can be described by [29] Aθ = I where A denotes coefficient matrix, θ is electric potential vector and I represents current vector.

III. PROPOSED METHOD FOR CLASSIFICATION OF HEMORRHAGE A. ILLUSTRATION OF HEMORRHAGE LOCATION
Since the probability of cerebral hemorrhage varies in different lobes [30], the parenchyma region is divided into three sections ( 1, 2 and 3) in this work. These sections respectively correspond to frontal lobe, temporal/parietal lobe and occipital lobe. Figure 2 shows division of the parenchyma region and hemorrhage location in different sections. The red circular inclusion represents the hemorrhage. It is worth noting that measured voltage under different electrode arrangements is different. Fig. 3 gives comparisons of voltage under four electrode arrangements when the hemorrhage is located in 2. Considering the healthy case and according to the fact where the hemorrhage is located, there are thirteen cases. In the following study, how to classify location of the hemorrhage under four different electrode arrangements is studied.

B. COMPARISON NEURAL NETWORKS AND THE PROPOSED METHOD FOR CLASSIFICATION 1) GENERAL NEURAL NETWORKS FOR CLASSIFICATION
Fully connected neural network (FCNN) is a basic neural network which is known for its simple structure [31], [32]. By cascading multiple layers of neurons, input-to-output mapping is realized. In this work, the FCNN has a threelayer structure including an input layer, a hidden layer and an output layer. The flow chart of EIT data processing based on FCNN is depicted in Figure 4. Considering the injection protocol and the number of electrodes, the size of the input voltage data is 12 * 16. In order to match the input layer with the input data, a flatten layer is added before the input layer and the size of the voltage data is converted to 192 * 1.
Generally, the output of each layer is represented as where x is the input, y denotes the output of the layer, W is weight matrix, and b is a bias vector. In order to enhance the nonlinear mapping between the input and output, an activation function ReLU is added to the input layer and the hidden layer. Then (4) can be rewritten as The activation function of the output layer uses SoftMax which converts multiple inputs into an output vector with the sum of 1.  For the jth neuron, the output of the output layer S j is formulated as where e is the output of neuron and n is the number of neurons.
The output of the output layer can be used to represent the probability of classification. In this work, the serial number corresponding to the highest probability is selected as the classification result.
Residual network (RN) is a deep convolutional neural network that is introduced by Microsoft in 2015 [33]. It has shown its merits in the fields of image segmentation and recognition [34], [35], [36]. By stacking multiple convolutional layers, it is possible for the residual neural network to achieve deeper extraction of data features. Also, the problems of gradient loss and overfitting when the neural network is too deep can be reduced by jump connecting the output with the input after and before convolution. Figure 5 shows the residual network which is composed of multiple conv blocks. The arrow indicates the direction of data transfer. Different colors are used to represent different function blocks, and the data size processing after each function block is also marked. As shown in Figure 5, the data is fed to the global averaging pooling layer after processed by six residual blocks and the average of each filter can be obtained. Besides, the data can be stretched by global averaging pooling to match the subsequent fully connected layers.
The specific structural information of the residual block is shown in Figure 6. The number of layers in the residual block 1 is the same with that in the residual block 2. The difference is that convolutional layer 2 and convolutional layer 4 adopt a convolutional kernel with stride of 2 in the residual block 2. The remaining convolutional layers in both of the two blocks use a convolutional kernel with a stride of 1. The convolution layers are all using zero padding, so the size of the data passing through residual block 1 is kept. The size of the data passing through residual block 2 is compressed and the number of filters passing through residual block 2 is doubled to maintain the number of acquired feature values. The output of the first convolution layer can be rewritten as where a is the input matrix, W ′ is the weight matrix, b ′ is the bias.
In the output layer of FCNN and RN, the number of neurons n varies with the classification method. In this paper, two different classification methods are set: (1) under different electrode arrangements, the situation that hemorrhage occurs in the same section of the parenchyma region is assumed to be the same case. Thus, there are a total of four classification cases (including healthy data). That is, n is 4. For the two classification methods based on FCNN and RN, it is respectively denoted by FCNN-4 and RN-4. (2) The hemorrhage in the same section of the parenchyma region under different electrode arrangements is considered as different cases. There are thirteen classification cases. That is, n is 13. Similarly, such classification method is respectively denoted by FCNN-13 and RN-13 for the two general neural networks. It should be noted that voltage data under different electrode arrangements is simultaneously input to the general neural networks and a generalized weight is used for classification. This would lead to inaccurate classification results.

2) THE PROPOSED CLASSIFICATION METHOD
Different from general classification methods mentioned above, a novel classification method is proposed in this work as shown in Figure 7. As shown in Figure 7, the training set data is divided into four categories according to the electrode arrangement information. After training, four sets of weight information are obtained. Based on a priori information of the electrode arrangement, the corresponding weight is chosen for the neural network in the prediction. And then the classification result is finally obtained. According to the location of hemorrhage in the parenchyma region and considering the healthy condition, the number of classification is 4.
It is worth noting that the network structure under the four electrode arrangements is the same although the training process is divided into four types. For comparison, a fully connected neural network and a residual neural network are used in the proposed method for training and prediction.

3) LOSS FUNCTION AND OPTIMIZATION
Generally, binary cross-entropy is adopted as the loss function in classification [37]. The binary cross-entropy can be described as where H represents loss function, p represents the tag value and q represents the network output value. According to the previous section, the number of classification in this work can be divided into two cases, so that (8) can be extended to Once the loss function is obtained, the neural network is trained by back propagation using the adaptive moment estimation (Adam) algorithm [38]. The mathematical equation of Adam can be written as in which where m t and v t are respectively the first-order momentum and the second-order momentum with an initial value of 0, lr represents the learning rate, o is a minimal value (o = 10 −8 ), λ 1 and λ 2 are hyper-parameters which are 0.9 and 0.999 respectively, ∂H ∂W is the gradient of H with respect to W .

4) TRAINING AND TEST DATASETS
In the study, a two-dimensional three-layered head model which consists of scalp, skull and parenchyma has been established. Thus, subdural, epidural, subarachnoid hematomas are not considered in this work. Instead, hemorrhage in the parenchyma has been modeled and classification in different lobes is studied. A large amount of data is required to train the neural network.
where T i represents the length of the input vector and T o represents the length of the output vector. For the convolutional layer, the number of parameters CLP can be computed as VOLUME 11, 2023 where K represents the size of convolutional kernel, C i represents the channel number of the input and C o represents the channel number of the output. According to (11) and (12), the number of parameters required for the fully connected neural network and the residual network when n = 4 are 6899 and 697508, respectively. Similarly, the corresponding number of parameters when n = 13 are 7223 and 698669 separately.
In the simulation, the inclusion which simulates cerebral hemorrhage is randomly placed in the parenchymal layer of the head. Besides, the size is randomly set between 3 mm and 30 mm. All neural networks mentioned in this work are implemented by Python software installed on a computer with CPU of i7-7700 3.60 GHz and RAM of 16 GB. The Nvidia GTX 1660 GPU is used to accelerate the training process. Learning rate of the neural network is initially set to 10 −4 and slowly decreases to 10 −6 . The learning is performed for 200 epochs in batches of 64.
To validate the performance of different classification methods, multiple test datasets are established. Note that the testing sets are different from the training sets while the rule of dataset generation during testing is the same with that in the training. The test datasets are also obtained by Comsol and Matlab. During the study, the situation which may occur in the real-world measurement has been considered. Under representative situations such as noise distabance, contact impedance variation, conductivity change of different layers and modeling error, the performance of the proposed method will be comprehensively studied.
(1) Basic test dataset. A dataset different from the training set is generated.
(2) Test datasets with noise. Different noise conditions are considered to disturb the basic test dataset.
(3) Effect of contact impedance. The impact of contact impedance can not be ignored in the EIT measurements. A test dataset under large contact impedance is established.
(4) Variation of conductivity. In order to study the generalizability of the neural network, conductivity of each layer in the head model is set to change in the range of 80% to 120%.
(5) Test datasets in the case of modeling error. The modeling error caused by boundary variation is considered.
(6) Testing when considering double inclusions. Two inclusions with different sizes are used to simulate hemorrhage at different locations of the same lobe region.

IV. RESULTS AND DISCUSSION
In this work, a new data-based classification method is presented. Unlike traditional image-based classification methods, it has been pointed out that the hemorrhage will be classified by directly processing voltage data in the proposed method. Thus, reconstruction in terms of true location and estimated location of hemorrhage are not provided. To evaluate the classification performance of different methods, three evaluation metrics which have been commonly used in the field of classification are introduced. With the three evalua- tion metrics, not only the hemorrhage but also the lobe where hemorrhage occurs can be classified and identified.
(1) Sensitivity. Sensitivity denotes whether the location of hemorrhage is correctly classified. It is calculated as the ratio of the number of correctly classified hemorrhage data to that of total hemorrhage data.
(2) Specificity. Specificity represents the ability to accurately distinguish hemorrhage and healthy data. It is calculated as ratio of the number of correctly classified data types (hemorrhage or healthy) to the total number of data.
(3) Accuracy. Accuracy is an important evaluation metric which estimates how the method performs in the classification. It represents the percentage of data that is correctly classified (including the location and the type) among all data.
It is worth noting that sensitivity is used to evaluate whether the neural network can correctly classify the hemorrhage position. Specificity represents the ability of the neural network to correctly classify healthy and hemorrhage data. It is expected that the specificity is kept at 1. The accuracy evaluates the overall correctness of the classification method. The closer the accuracy value is to 1, the better the performance of classification method is.

A. BASIC TEST DATASET
The basic test dataset includes 2000 sets of hemorrhage data at different locations and 500 healthy data. According to the difference of the neural network in the proposed method, the classification method developed in this work is respectively denoted by P-FCNN and P-RN. The performance of the proposed method is compared with the results obtained by FCNN-4, FCNN-13, RN-4 and RN-13 as shown in Figure 8.
It is observed from Figure 8 that P-FCCN shows the worst performance in the classification among the methods. Except P-FCNN, the specificity of other classification methods is kept at 1 which suggests that hemorrhage and healthy data can be accurately distinguished by these methods. For the two FCNN-based classification methods, FCNN-13 shows better performance. In terms of sensitivity and accuracy, the performance of the FCNN-4 and FCNN-13 is not as well as the RN-4 and RN-13. For the proposed P-RN method, its performance in the classification is comparable with the RNbased methods.

B. TEST DATASETS WITH NOISE
Noise is unavoidable during EIT measurement and has an impact on the boundary measurement. Consequently, the classification result would be affected. As a result of this, we have tested the performance of the proposed method to the interruption of noise. Generally, Gaussian noise has been considered in the EIT study [40]. By adding Gaussian white noise to the basic dataset, the signal to noise ratio (SNR) is calculated by SNR ≜ 10 log 10 ∥ U ∥ 2 2 ∥e∥ 2 2 .
where U represents boundary voltage difference, e represents Gaussian noise with mean value of 0 and variance of 1.
Under the impact of noise with SNRs of 60 dB, 40 dB and 20 dB, the performance of different classification methods is respectively studied, as shown in Figure 9. With the decrease of SNR value, it can be seen that the performance of all classification methods deteriorates in terms of sensitivity and accuracy. Under the high SNR of 60 dB, there is almost no effect on the classification result. Among these methods, the proposed P-RN method is more advantageous under low SNR values especially when a strong noise is added. Aside from P-FCNN method, the specificity of other classification methods remained at 1. With a priori information of the electrode arrangement, it can be found that the proposed P-RN method outperforms other five methods in terms of noise immunity.

C. TEST DATASET UNDER LARGE CONTACT IMPEDANCE
In the medical applications of EIT, contact impedance is an essential factor that cannot be ignored. Usually, conductive paste is applied between the electrode and the scalp for well injection of the current. Due to drying of conductive paste with time, contact impedance will gradually increase. In the above discussion, contact impedance is set to a small value which is about 10 −8 ·m. To validate the performance of the proposed method under large contact impedance, contact impedance is randomly set to vary around 0.01 ·m in the range of ± 0.001 ·m. The test dataset covers 600 sets of hemorrhage data and 200 sets of healthy data. Figure 10 compares the performance of different methods in the classification. In comparison to the results under small contact impedance, values of sensitivity and accuracy of FCNN-13, P-FCNN, RN-4 and RN-13 methods drops. However, the performance of FCNN-4 is almost the same with that under small contact impedance. Among all the classification methods, the proposed P-RN method shows the most excellent performance in the classification.

D. TEST DATASETS WHEN CONDUCTIVITY OF DIFFERENT LAYERS VARIES
For different patients, conductivity distribution of the head varies. During the training, conductivity distribution is set to be fixed. In order to study performance of the proposed method in the case of conductivity distribution variation, three test datasets when conductivity of the three layers respectively varies within a range of ±20% are established. Table 1 gives the range of conductivity variation in different layers.
The performance of different methods is compared in Figure 11. It can be seen that change of conductivity distribution significantly affects the classification result. The scalp layer has the largest impact due to its proximity to the electrodes while the parenchyma layer has the smallest impact. Overall, the proposed P-RN method performs better than other five classification methods. Its accuracy is higher than 90% no matter which layer has conductivity variation. In the remaining five methods, the RN-4 method shows accuracy around 90% only when conductivity of parenchyma layer varies.

E. TEST DATASETS IN THE CASE OF MODELING ERROR
During the training of the classification method, the head boundary is fixed and constant. However, boundary shape of the head is different for different patients. Therefore, the performance of different classification methods when there is a modeling error caused by head boundary variation should be evaluated. In the study, the head boundary is enlarged or reduced by 10%, respectively. Under each modeling variation, there are 100 cases of hemorrhage data and 25 cases of healthy data for every electrode configuration. Figure 12 shows the prediction results of different classification methods. It can be seen that modeling error caused by boundary variation has an impact on the classification results. Nevertheless, the proposed method is the most insensitive to the modeling error.

F. TEST DATASETS WHEN DOUBLE INCLUSIONS ARE CONSIDERED
In the above discussion, the performance of the proposed method has been estimated under various situations. Note that the hemorrhage has been simulated by one inclusion.   To further study the performance of different classification methods, classification of double inclusions is considered in this section. In the study, two inclusions with different sizes are placed at different locations of the same lobe region and voltage measurements are obtained as testing datasets. For each electrode configuration, 200 sets of hemorrhage data and 50 sets of healthy data are acquired. The performance of different classification methods is studied as shown in Figure 12. Since the training set does not contain data with two inclusions, the performance of all classification methods deteriorates. Only the accuracy of RN-4 and P-RN methods is around 90%. For other methods, the accuracy is lower than 80%. Considering the three evaluation metrics, it is seen that the proposed P-RN method still shows the best performance.
To show whether the classification result is correct when the proposed method is used, a validation test is conducted. Four groups of boundary measurements which separately correspond to healthy data and hemorrhage in different lobes are obtained from the head model equipped with left electrode arrangement. After processing with the proposed method, the classification result is shown in Table 2. It can be seen that the four groups of boundary measurements have been correctly classified with the proposed method.

V. CONCLUSION
In this paper, a new classification method using a priori information of electrode arrangement is proposed for hemorrhage disease detection. Unlike traditional classification methods which use a single weight for prediction, different weights are chosen in the proposed method according to the electrode arrangement information. This would improve classification accuracy under different kinds of electrode arrangements. In the study, an inclusion which simulates hemorrhage is respectively placed in three different sections of parenchyma layer under four electrode arrangements. To verify the reliability of the proposed method in the classification, six kinds of test datasets are used. Two general classification methods based on fully connected neural network and residual network are also presented for comparison. The results show that the overall performance of the RN-based classification method is better than that of the FCNN-based method. With either of the two networks combined in the proposed method, the corresponding performance of classification may be not definitely improved. The proposed method which incorporates FCNN is the worst. In the case of basic test dataset, the performance of the proposed method with RN incorporated is competitive with the two RN-based methods. However, the proposed method with RN incorporated is more robust to noise interruption, contact impedance variation and conductivity variation in different layers than the RN-based methods. In summary, the proposed P-RN method is more reliable when classifying a large amount of EIT voltage data under different electrode arrangements. The effectiveness of the proposed method will be further estimated by experimental results in the future study. Also, it should be remarked that it is also possible to combine other networks in the proposed method according to different requirements.