RAPID developments in image-guided radiation therapy offer. Irregular Breathing Classification From Multiple Patient Datasets Using Neural Networks

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1 IEEE TRANSACTIONS ON INFORMATION TECHNOLOGY IN BIOMEDICINE, VOL. 16, NO. 6, NOVEMBER Irregular Breathing Classification Fro Multiple Patient Datasets Using Neural Networks Suk Jin Lee, Student Meber, IEEE, YuichiMotai, Meber, IEEE, Elisabeth Weiss, and Shuei S. Sun Abstract Coplicated breathing behaviors including uncertain and irregular patterns can affect the accuracy of predicting respiratory otion for precise radiation dose delivery. So far investigations on irregular breathing patterns have been liited to respiratory onitoring of only extree inspiration and expiration. Using breathing traces acquired on a Cyberknife treatent facility, we retrospectively categorized breathing data into several classes based on the extracted feature etrics derived fro breathing data of ultiple patients. The novelty of this paper is that the classifier using neural networks can provide clinical erit for the statistical quantitative odeling of irregular breathing otion based on a regular ratio representing how any regular/irregular patterns exist within an observation period. We propose a new approach to detect irregular breathing patterns using neural networks, where the reconstruction error can be used to build the distribution odel for each breathing class. The proposed irregular breathing classification used a regular ratio to decide whether or not the current breathing patterns were regular. The sensitivity, specificity, and receiver operating characteristiccurve of the proposed irregular breathing pattern detector was analyzed. The experiental results of 448 patients breathing patterns validated the proposed irregular breathing classifier. Index Ters Abnoral detection, breathing classification, irregular respiration, neural networks, receiver operating characteristic. I. INTRODUCTION RAPID developents in iage-guided radiation therapy offer the potential of precise radiation dose delivery to ost patients with early or advanced lung tuors [1] [6]. While early stage lung tuors are treated with stereotactic ethods, locally advanced lung tuors are treated with highly conforal radiotherapy, such as intensity odulated radiotherapy (IMRT) [2]. Both techniques are usually planned based on 4-D coputed toography [1]. Thus, the prediction of individual breathing cycle irregularities is likely to becoe very deanding since Manuscript received January 25, 2012; revised May 20, 2012 and July 27, 2012; accepted August 15, Date of publication August 21, 2012; date of current version Noveber 16, This work was supported in part by the dean s office of the School of Engineering at Virginia Coonwealth University, and by National Science Foundation under Grant ECCS S. J. Lee and Y. Motai are with the Departent of Electrical and Coputer Engineering, Virginia Coonwealth University, Richond, VA USA (e-ail: leesj9@yail.vcu.edu; yotai@vcu.edu). E. Weiss is with the Departent of Radiation Oncology, Virginia Coonwealth University, Richond, VA USA (e-ail: eweiss@cvh-vcu.edu). S. S. Sun is with the Departent of Biostatistics, Virginia Coonwealth University, Richond, VA USA (e-ail: ssun@vcu.edu). Color versions of one or ore of the figures in this paper are available online at Digital Object Identifier /TITB tight safety argins will be used. Safety argins are defined based on the initial planning scan that also analyzes the average extent of breathing otion, but not the individual breathing cycle. In the presence of larger respiratory excursions, treatent can be triggered by respiration otion in such a way that radiation beas are only on when respiration is within predefined aplitude or phase [7]. Since argins are saller with ore conforal therapies, breathing irregularities ight becoe ore iportant unless there is a syste in place that can stop the bea in the presence of breathing irregularities. Real-tie tuor-tracking, where the prediction of irregularities really becoes relevant [8], has yet to be clinically established. The proposed ethodology for irregular breathing classification can ipact the dose calculation for patient treatents [9], [10]. The highly irregularly breathing patient ay be expected to have a uch bigger internal target volue (ITV) than a regular one, where ITV contains the acroscopic cancer and an internal argin to take into account the variations due to organ otions [9]. Thus, the detection of irregular breathing otion before and during the external bea radiotherapy is desired for iniizing the safety argin [10]. Only a few clinical studies, however, have shown a deteriorated outcoe with increased irregularity of breathing patterns [1], [8], [10], probably due to the lack of technical developent in this topic. Other reasons confounding the clinical effect of irregular otion such as variations in target volues or positioning uncertainties also influence the classification outcoes [8] [11]. The newly proposed statistical classification ay provide clinically significant contributions to iniize the safety argin during external bea radiotherapy based on the breathing regularity classification for the individual patient. An expected usage of the irregularity detection is to adapt the argin value, i.e., the patients classified with regular breathing patterns would be treated with tight argins to iniize the target volue. For patients classified with irregular breathing patterns, safety argins ay need to be adjusted based on the irregularity to cope with baseline shifts or highly fluctuating aplitudes that are not covered by standard safety argins [9], [10]. There exists a wide range of diverse respiration patterns in huan subjects [9] [15]. However, the decision boundary to distinguish the irregular patterns fro diverse respirations is not clear yet [11], [16]. For exaple, soe studies defined only two (characteristic and uncharacteristic [10]) or three (sall, iddle, and large [9]) types of irregular breathing otions based on the breathing aplitude to access the target dosietry [9], [10]. Our purpose is to classify irregular patterns, given syptos that fit into neither the regular pattern nor the regular copression pattern categorizations [17]. Respiratory patterns can be /$ IEEE

2 1254 IEEE TRANSACTIONS ON INFORMATION TECHNOLOGY IN BIOMEDICINE, VOL. 16, NO. 6, NOVEMBER 2012 classified as noral or abnoral patterns [16]. The key point of the classification as noral or abnoral breathing patterns is how to extract the doinant feature fro the original breathing datasets [18] [24]. For exaple, Lu et al. calculated a oving average curve using a fast Fourier transfor to detect respiration aplitudes [16]. Soe studies showed that the flow volue curve with neural networks can be used for the classification of noral and abnoral respiratory patterns [13], [14]. However, spiroetry data are not coonly used for abnoral breathing detection during iage-guided radiation therapy [13]. To detect irregular breathing, we present a ethod that retrospectively classifies breathing patterns using ultiple patientsbreathing data originating fro a Cyberknife treatent facility [25]. There is no iplicit assuption ade for the future breathing patterns at the tie of treatent. The ultiple patients-breathing data contain various breathing patterns. For the analysis of breathing patterns, we extracted breathing features, e.g., vector-oriented feature [22], [23], aplitude of breathing cycle [16], [26], and breathing frequency [11], etc., fro the original dataset, and then classified the whole breathing data into classes based on the extracted breathing features. To detect irregular breathing, we introduce the reconstruction error using neural networks as the adaptive training value for anoaly patterns in a class. The contribution of this paper is threefold. First, we propose a new approach to detect abnoral breathing patterns with ultiple patients breathing data that better reflect tuor otion in a way needed for radiotherapy than the spiroetry. Second, the proposed new ethod achieves the best irregular classification perforance by adopting expectation- axiization (EM) based on the Gaussian Mixture odel with the usable feature cobination fro the given feature extraction etrics. Third, we can provide clinical erits with prediction for irregular breathing patterns, such as to validate classification accuracy between regular and irregular breathing patterns fro receiver operating characteristic (ROC) curve analysis, and to extract a reliable easureent for the degree of irregularity. This paper is organized as follows. In Section II, the theoretical background for the irregular breathing detection is discussed briefly. In Section III, the proposed irregular breathing detection algorith is described in detail with the feature extraction ethod. The experiental results are presented in Section IV. A suary of the perforance of the proposed ethod and conclusion are presented in Section V. II. BACKGROUND Modeling and prediction of respiratory otion are of great interest in a variety of applications of edicine [27], [28] [31]. Variations of respiratory otions can be represented with statistical eans of the otion [29] which can be odeled with finite ixture odels for odeling coplex probability distribution functions [32]. This paper uses the EM algorith for learning the paraeters of the ixture odel [33], [34]. In addition, neural networks are widely used for breathing prediction and for classifying various applications because of the dynaic teporal behavior with their synaptic weights [4], [8], [17], [35], [36]. Therefore, we use neural networks to detect irregular breathing patterns fro feature vectors in given saples. A. EM Based on Gaussian Mixture Model A Gaussian ixture odel is a odel-based approach that deals with clustering probles in attepting to optiize the fit between the data and the odel. The joint probability density of the Gaussian ixture odel can be the weighted su of >1coponents φ(x μ, Σ ). Here φ is a general ultivariate Gaussian density function, expressed as follows [33]: [ exp 1 2 (x μ ) T ] 1 (x μ ) φ(x μ, Σ )= (1) (2π) d/2 Σ 1/2 where x is the d-diensional data vector, and μ and Σ are the ean vector and the covariance atrix of the th coponent, respectively. A variety of approaches to the proble of ixture decoposition have been proposed, any of which focus on axiu likelihood ethods such as the EM algorith [34]. An EM algorith is a ethod for finding axiu likelihood estiates of paraeters in a statistical odel. EM alternates between an expectation step, which coputes the expectation of the log likelihood using the current variable estiate, and a axiization step, which coputes paraeters axiizing the expected log likelihood collected fro the E-step. These estiated paraeters are used to select the distribution of variable in the next E-step [32]. The EM was applied due to the unsupervised nature of unlabeled datasets. B. Neural Network (NN) A neural network is a atheatical odel or coputational odel that is inspired by the functional aspects of biological neural networks [37]. A siple NN consists of an input layer, a hidden layer, and an output layer, interconnected by odifiable weights, which are represented by links between the layers. Our interest is to extend the use of such networks to pattern recognition, where network input vector x i denotes eleents of extracted breathing features fro the breathing dataset and interediate results generated by network outputs will be used for classification with discriinant criteria based on clustered degree. Each input vector x i is given to neurons of the input layer, and the output of each input eleent is ade equal to the corresponding eleent of the vector. The weighted su of its inputs is coputed by each hidden neuron j to produce its net activation (siply denoted as net j ). Each hidden neuron j gives a nonlinear function output of its net activation Φ( ), i.e., Φ(net j ) = Φ(Σ N x iw ji + w j0 ) in (2). The process of output neuron k is the sae as the hidden neuron. Each output neuron k calculates the weighted su of its net activation based on hidden neuron outputs Φ(net j ) as follows [38]: ( H N ) net k = w kj Φ x i w ji + w j0 + w k0 (2) j=1 where N and H denote neuron nubers of the input layer and hidden layer. The subscripts i, j, and k indicate eleents of the

3 LEE et al.: IRREGULAR BREATHING CLASSIFICATION FROM MULTIPLE PATIENT DATASETS USING NEURAL NETWORKS 1255 TABLE I FEATURE EXTRACTION METRICS INCLUDING THE FORMULA AND NOTATION Fig. 1. Irregular breathing pattern detection with the proposed algorith. input, hidden, and output layers, respectively. Here, the subscript 0 represents the bias weight with the unit input vector (x 0 = 1). We denote the weight vectors w ji as the input-to-hidden layer weights at the hidden neuron j and w kj as the hidden-tooutput layer weights at the output neuron k. Each output neuron k calculates the nonlinear function output of its net activation Φ(net k ) to give a unit for the pattern recognition. III. PROPOSED IRREGULAR BREATHING CLASSIFIER As shown in Fig. 1, we first extract the breathing feature vector fro the given patient datasets in Section III-A. The extracted feature vector can be classified with the respiratory pattern based on EM in Section III-B. Here, we assue that each class describes a regular pattern. In Section III-C, we will calculate a reconstruction error for each class using a neural network. Finally, in Section III-D, we show how to detect the irregular breathing pattern based on the reconstruction error. The proposed process flow is to first find out the feasible feature vector for the efficient classification of breathing patterns based on the discriinant criterion [38] while assuing that each class describes a regular pattern, and then to select the classes of the breathing patterns using the feature vector based on the EM algorith. A. Feature Extraction fro Breathing Analysis Feature extraction is a preprocessing step for classification by extracting the ost relevant data inforation fro the raw data [22]. In this study, we extract the breathing feature fro patient breathing datasets for the classification of breathing patterns. The typical vector-oriented feature extraction including principal coponent analysis (PCA) and ultiple linear regressions (MLR) have been widely used [22], [23]. Murphy et al.showed that autocorrelation coefficient and delay tie can represent breathing signal features [8]. Each breathing signal ay be sinusoidal variables [26] so that each breathing pattern can have quantitative diversity of acceleration, velocity, and standard deviation based on breathing signal aplitudes [16]. Breathing frequency also represents breathing features [11]. Table I shows the feature extraction etrics for the breathing pattern classification. We create Table I based on previous entities for breathing features, so that the table can be variable. The feature extraction etrics can be derived fro ultiple patient datasets with the corresponding forula. To establish feature etrics for breathing pattern classification, we define the candidate feature cobination vector x fro the cobination of feature extraction etrics in Table I. We defined 10 feature extraction etrics in Table I. The objective of this section is to find out the estiated feature etrics ˆx) fro the candidate feature cobination vector ( x) using discriinant criterion based on clustered degree. We can define the candidate feature cobination vector as x =(x 1,..., x z ), where variable z is the eleent nuber of feature cobination vector, and each eleent corresponds to each of the feature extraction etrics depicted in Table I. For exaple, let us define the nuber of feature cobination vectors as three (z = 3), where the feature cobination vector can be x = (BRF, PCA, STD) with three out of 10 feature etrics. The total nuber of feature cobination vectors using feature extraction etrics can be the suation of the cobination function C(10,z) as regards to z objects (z = 2,..., 10), where the cobination function C(10, z) is the nuber of ways of choosing z objects fro ten feature etrics. For the interediate step, we ay select which features to use for breathing pattern classification with the feature cobination vectors, i.e., the estiated feature etrics (ˆx). For the efficient and accurate classification of breathing patterns, selection of relevant features is iportant [24]. In this study, the discriinant criterion based on clustered degree can be used to select the estiated feature etrics, i.e., objective function J( ) using within-class scatter

4 1256 IEEE TRANSACTIONS ON INFORMATION TECHNOLOGY IN BIOMEDICINE, VOL. 16, NO. 6, NOVEMBER 2012 (S W ) and between-class scatter (S B ) [38], [39]. Here we define the S W as follows: S W = 1 z G n i S i, S i = ( x ij u i ) 2, u i = 1 n i n i j=1 j=1 (3) where z is the eleent nuber of a feature cobination vector in S W,G is the total nuber of class in the given datasets, S i is the su of squares of vectors within i-th class, and n i is the data nuber of the feature cobination vector in the i-th class. We define the S B as follows: G S B = n i (u i u) 2, u = 1 n x i (4) n where n is the total data nuber of the feature cobination vector. The objective function J to select the optial feature cobination vector can be written as follows: ( ) SW J(ˆx) = arg in (5) x S B where ˆx can be the estiated feature vector for the rest of the odules for breathing patterns classification. As shown in Section IV-A, three channel breathing datasets with a sapling frequency of 26 Hz are used to evaluate the perforance of the proposed irregular breathing classifier. Here, each channel akes a record continuously in three diensions for 448 patient datasets. The breathing recording tie for each patient is distributed fro 18 in to 2.7 h, with 80 in as the average tie at the Georgetown University CyberKnife treatent facility. B. Clustering of Respiratory Patterns Based on EM This section is aied at finding the optial nuber of clustering of respiratory patterns in the given datasets. We assue that the total 448 patients breathing patterns can be categorized into several classes M, where each class is optiized with the finite ixture odel. We increase the M (fro 2 to 8 in Section IV-C) coponents to optiize the Gaussian ixture odel using the EM algorith. After extracting the estiated feature vector ˆx for the breathing feature, we can odel the joint probability density that consists of the ixture of Gaussians φ(ˆx μ, Σ ) for the breathing feature as follows [32], [33]: ( M p(ˆx, Θ) = α φ ˆx μ, ) M, α 0, α =1 =1 =1 (6) where ˆx is the d-diensional feature vector, α is the prior probability, μ is the ean vector, Σ is the covariance atrix of the th coponent data, and the paraeter Θ {α,μ, Σ } M =1 is a set of finite ixture odel paraeter vectors. For the solution of the joint distribution p(ˆx, Θ), we assue that the training feature vector sets ˆx k are independent and identically distributed, and our purpose of this section is to estiate the paraeters {α, μ, Σ } of the M coponents x ij that axiize the log-likelihood function as follows [33], [34]: L(M) = log p(ˆx k, Θ) (7) k=1 where M and K are the total cluster nuber and the total nuber of patient datasets, respectively. Given an initial estiation {α 0,μ 0, Σ 0 }, E-step in the EM algorith calculates the posterior probability p( ˆx k ) as follows: / (t) M (t) p( ˆx k )=α (t) ˆx k μ (t) α (t) ˆx k μ (t) φ, and then M-step is as follows: α (t+1) = 1 K p( ˆx k ) k=1 K μ (t+1) k=1 = p( ˆx k )ˆx k K k=1 p( ˆx k ) (t+1) = 1 α K k=1 [ p( ˆx k ) =1 = 1 α K φ p( ˆx k )ˆx k k=1 (ˆx k μ (t+1) k, (8) )(ˆx k μ (t+1) k ) T]. (9) With (8) in the E-step, we can estiate the tth posterior probability p( ˆx k ). Based on this estiate result, the prior probability α, the ean μ, and the covariance Σ in the (t+1)th iteration can be calculated using (9) in the M-step. Based on clustering of respiratory patterns, we can ake a class for each breathing feature with the corresponding feature vector ˆx of class. With the classified feature cobination vector (ˆx ), we can get the reconstruction error for the preliinary step to detect the irregular breathing pattern. For the quantitative analysis of the cluster odels, we use two criteria for odel selection, i.e., Akaike inforation criterion (AIC) and Bayesian inforation criterion (BIC), aong a class of paraetric odels with different cluster nubers [40]. Both criteria easure the relative goodness of fit of a statistical odel. In general, the AIC and BIC are defined as follows: AIC = 2 k 2ln(L), BIC= 2 lnl + kln(n), where n is the nuber of patient datasets, k is the nuber of paraeters to be estiated, and L is the axiized log-likelihood function for the estiated odel that can be derived fro (7). C. Reconstruction Error for Each Cluster Using NN Using the classification based on EM, we can get M classes of respiratory patterns, as shown in Fig. 1. With the classified feature vectors ˆx, we can reconstruct the corresponding feature vectors o with the neural networks in Fig. 2 and get the following output value: ( H N ) o =Φ w kj Φ ˆx i w ji + w j0 + w k0 (10) j=1 where Φ is the nonlinear activation function, and N and H denote the total neuron nuber of input and hidden layers,

5 LEE et al.: IRREGULAR BREATHING CLASSIFICATION FROM MULTIPLE PATIENT DATASETS USING NEURAL NETWORKS 1257 Fig. 2. Reconstruction error to detect the irregular pattern using NN. Fig. 3. Detection of regular/irregular patterns using the threshold value ξ. respectively. The neural weights w are deterined by training saples of ultiple patient datasets for each class M. Then, the neural networks using a ultilayer perceptron for each class in Fig. 2 calculate the reconstruction error δ for each feature vector ˆx i as follows [17]: δ i = 1 F F f =1 (ˆx if o ) 2 if (11) where i is the nuber of patient datasets in a class, and f is the nuber of features. After calculating the reconstruction error δ for each feature vector in Fig. 2, δ can be used to detect the irregular breathing pattern in the next section. D. Detection of Irregularity Based on Reconstruction Error For the irregular breathing detection, we introduce the reconstruction error δ, which can be used as the adaptive training value for anoaly pattern in a class. With the reconstruction error δ, we can construct the distribution odel for each cluster. That eans the patient data with sall reconstruction error can have a uch higher probability of becoing regular than the patient data with any reconstruction errors in our approach. For class, the probability β, class eans ν, and covariance Σ can be deterined as follows: β = 1 K ν = I( ˆx i ) (12) Σ = 1 β K K I( ˆx i)δ i K I( ˆx i) = 1 β K I( ˆx i )δi (13) I( ˆx i ) [ (ˆx i M )(ˆx i M ) T ] (14) where I( ˆx i )=1, if ˆx i is classified into class ; otherwise, I( ˆx i )=0, M is the ean value of the classified feature vectors (ˆx ) in class, and K is the total nuber of the patient datasets. To decide the reference value to detect the irregular breathing pattern, we cobine the class eans (13) and the covariance (14) with the probability (12) for each class as follows: ν = 1 M M β ν, =1 = 1 M M β. (15) =1 With (15), we can ake the threshold value ξ to detect the irregular breathing pattern in (16), as follows: ξ = (ν ν) Σ (16) L where L is the total nuber of breathing data in class. For each patient i in class, we define P as a subset of the patient whose score δi is within the threshold value ξ in class, and 1 P as a subset of the patient whose score δi is greater than the threshold value ξ in class, as shown in Fig. 3. The digit 1 represents the entire patient set for class in Fig. 3. With Fig. 3, we can detect the irregular breathing patterns in the given class with the threshold value ξ. Accordingly, all the saples within the threshold value highlighted with yellow in Fig. 3 can be the regular respiratory patterns, whereas the other saples highlighted with gray in Fig. 3 can becoe the irregular respiratory patterns. Fig. 3 shows that the threshold value ξ depicted by dotted lines can divide the regular respiratory patterns P fro the irregular respiratory patterns (1 P ) for each class.asshown in Fig. 3, we can suarize the process of the regular/irregular breathing detection, and denote the regular respiratory patterns highlighted with yellow as M =1(P ) and the irregular respiratory patterns highlighted with gray as M =1(1 P ). We will use these notations for the predicted regular/irregular patterns in the following section. E. Evaluation Method for Irregular Classifier We apply standard sensitivity and specificity criteria as statistical easures of the perforance of a binary classification test for irregularity detection. The classifier result ay be positive, indicating an irregular breathing pattern as the presence of an anoaly. On the other hand, the classifier result ay be negative, indicating a regular breathing pattern as the absence of the anoaly. Sensitivity is defined as the probability that the classifier result indicates a respiratory pattern has the anoaly when in fact they do have the anoaly. Specificity is defined as

6 1258 IEEE TRANSACTIONS ON INFORMATION TECHNOLOGY IN BIOMEDICINE, VOL. 16, NO. 6, NOVEMBER 2012 Fig. 4. True positive range R TP versus true negative range R TN. This figure shows how to decide R TP or R TN of patient i (DB17). In this exaple, the breathing cycle BC i, the period of observation T i, and the su of ψ i (Σ j ψ ij ) are given by the nubers of 4.69, , and 26, respectively. Accordingly, we can calculate the ratio γ i of the true negative range Ri TN to the period of observation T i, i.e., That eans 75% of the breathing patterns during the observation period show regular breathing patterns in the given saple. the probability that the classifier result indicates a respiratory pattern does not have the anoaly when in fact they are anoaly free [41]. For the sensitivity and specificity, we can use Fig. 3 as the hypothesized class, i.e., the predicted regular and irregular patterns, as follows: M M FN + TN = P, TP + FP = (1 P ). (17) =1 =1 The proposed classifier should have high sensitivity and high specificity. The given patient data show that the breathing data can be ixed up with the regular and irregular breathing patterns in Fig. 4. There are as yet no gold standard ways of labeling regular or irregular breathing signals. Lu et al. showed, in a clinical way, that the oving average value can be used to detect irregular patterns where inspiration or expiration was considered irregular if its aplitude was saller than 20% of the average aplitude [16]. In this study, for the evaluation of the proposed classifier of abnorality, we define all the breathing patterns that are saller than half the size of the average breathing aplitude as irregular patterns, shown with dotted lines in Fig. 4. During the period of observation T, we noticed soe irregular breathing patterns. Let us define BC i as the breathing cycle range for the patient i as shown in Table I and ψ i as the nuber of irregular breathing pattern regions between a axiu (peak) and a iniu (valley). For the patient i, we define the true positive/negative ranges (R TP i /R TN i ) and the regular ratio γ i as follows: ψ ij, Ri TP = BC i γ i = RTN i 2 T j j i (18) where the ratio γ i is variable fro 0 to 1. For the seisupervised Ri TN =T i BC i 2 ψ ij, learning of the TP and TN in the given patient datasets, we used the ratio γ i of the true negative range Ri TN to the period of observation T i in (18). Let us denote Ψ th as the regular threshold to decide whether the patient dataset is regular or not. For patient i, we would like to decide a TP or TN based on values with the TABLE II CHARACTERISTICS OF THE BREATHING DATASETS ratio γ i and the regular threshold Ψ th, i.e., if the ratio γ i of patient i is greater than that of the regular threshold Ψ th,the patient is true negative, otherwise γ i Ψ th true positive. We should notice also that the regular threshold can be variable fro 0 to 1. Accordingly, we will show the perforance of sensitivity and specificity with respect to the variable regular threshold in Section IV-E. IV. EXPERIMENTAL RESULTS A. Breathing Motion Data Table II shows the characteristics of the breathing datasets. The iniu and the axiu recording ties are 18 and 166 in, respectively. To extract the feature extraction etrics in Table I, therefore, we randoly selected 18-in saples fro the whole recording tie for each breathing dataset because the iniu breathing recording tie is 18 in. That eans we use saples to get the feature extraction etrics for each breathing dataset. Every dataset for each patient is analyzed to predict the irregular breathing patterns. That eans we inspect all the datasets to detect the irregular pattern ψ i within the entire recording tie. The detected irregular patterns can be used to calculate the true positive/negative ranges (Ri TP /Ri TN ) and the ratio γ i for the patients. B. Selection of the Estiated Feature Metrics ˆx The objective of this section is to find out the estiated feature etrics ˆx fro the candidate feature cobination vector x using

7 LEE et al.: IRREGULAR BREATHING CLASSIFICATION FROM MULTIPLE PATIENT DATASETS USING NEURAL NETWORKS 1259 Fig. 5. Objective functions with respect to the feature etrics nuber to select the estiated feature etrics ˆx. Fig. 6. Quantitative odel analysis for the selection of cluster nuber. discriinant criteria based on clustered degree. Fig. 5 shows all the results of the objective function J with respect to the feature etrics nuber. That eans each colun in Fig. 5 represents the nuber of feature extraction etrics in Table I. The red spot shows the objective function J( ) for each feature cobination vector, whereas the black and the blue spots represent the averaged objective function and the standard deviation of the objective function with respect to the feature etrics nuber. We notice that two feature cobination vector can have a inial feature cobination vector. Even though z = 9 has the iniu standard deviation, a iniu objective function J of z = 9 is uch bigger than those in z = 3, 4, 5, and 6 shown in Fig. 5. The interesting result is that the cobinations of BRF, PCA, MLR, and STD have iniu objective functions in z = 3 and 4. Therefore, we would like to use these four feature extraction etrics, i.e., BRF, PCA, MLR, and STD as the estiated feature vector ˆx for the rest of odules for breathing patterns classification. Fig. 7. Frequency distribution of breathing cycle BC i for the breathing datasets. The breathing cycles are variable fro 2.9 s/cycle to 5.94 s/cycle, with 3.91 s/cycle as the average tie. C. Clustering of Respiratory Patterns Based on EM In this section, the breathing patterns will be arranged into groups with the estiated feature vector ˆxfor the analysis of breathing patterns. In Fig. 6, we can notice that both criteria have selected the identical clustering nuber; M = 5. Therefore, we can arrange the whole pattern datasets into five different clusters of breathing patterns based on the siulation results. D. Breathing Pattern Analysis to Detect Irregular Pattern Before predicting irregular breathing, we analyze the breathing pattern to extract the ratio γ i with the true positive and true negative ranges for each patient. For the breathing cycle BC i, we search the breathing curves to detect the local axia and inia. After detecting the first extrea, we set up the searching range for the next extrea as s [11]. Accordingly, we can detect the next extrea within half a breathing cycle because one breathing cycle is around 4 s [16]. The BC i is the ean value of the consecutive axia or inia. Fig. 7 shows Fig. 8. Frequency distribution of ratio γ i.hereγ i is the ratio of the true negative range Ri TN to the period of observation T i ; thus, it is diensionless. The ratio γ i for each breathing dataset is distributed fro 0.02 to 1 with 0.92 as the average ratio value. the frequency distribution of BC i for the breathing datasets. The breathing cycles are distributed with a iniu of 2.9 s/cycle and a axiu of 5.94 s/cycle. The average breathing cycle of the breathing datasets is 3.91 s/cycle. Fig. 8 shows the frequency distribution of the ratio γ i.here γ i is the ratio of the true negative range Ri TN to the period of

8 1260 IEEE TRANSACTIONS ON INFORMATION TECHNOLOGY IN BIOMEDICINE, VOL. 16, NO. 6, NOVEMBER 2012 Fig. 9. Representing regular breathing patterns: (a) patient nuber 1 with the ratio γ 1 = 0.98, and (b) patient nuber 177 with the ratio γ 177 = Fig. 10. Representing gray-level breathing patterns: (a) patient nuber 162 with the ratio γ 162 = 0.87, and (b) patient nuber 413 with the ratio γ 413 = observation T i ; thus, it is diensionless. The ratio γ i for each breathing dataset is distributed fro 0.02 to 1 with 0.92 as the average ratio value. In Fig. 8, we can see that the frequency nuber of the regular breathing patterns is uch higher than that of the irregular breathing patterns in the given datasets. But we can also see that it is not a siple binary classification to decide which breathing patterns are regular or irregular because the frequency distribution of the ratio is analog. We define the vague breathing patterns with the ratio as the graylevel breathing pattern. We have shown the regular/irregular gray-level breathing patterns aong the entire dataset in the following figures. Fig. 9 shows regular breathing patterns in the given datasets. There exist several irregular points depicted with green spots. But ost of breathing cycles have the regular patterns of breathing curve. Note that the regular breathing patterns have a higher ratio γ i in coparison to the irregular breathing patterns. Fig. 10 shows gray-level breathing patterns in the given datasets. Even though the gray-level breathing patterns show soe consecutive irregular points, the overall breathing patterns are alost identical as shown in Fig. 10. Fig. 11 shows irregular breathing patterns in the given datasets. Note that the breathing pattern in Fig. 11(b) with a very low ratio (γ 317 = 0.51) is void of regular patterns and that there exists a ass of irregular breathing points in Fig. 11. E. Classifier Perforance An ROC curve is used to evaluate irregular breathing patterns with true positive rates versus regular breathing patterns with false positive rates. For the concrete analysis of the given breathing datasets, we would like to show an ROC curve with respect to different regular thresholds. In addition, we will change the discriination threshold by the period of observation T i to validate the perforance of the proposed binary classifier syste. To predict the irregular breathing patterns fro the patient datasets, we ay evaluate the classification perforance by showing the following two ROC analyses: In the first ROC, we ay increase the threshold value ξ defined in (16) in Section III-D fro 0.1 to By changing the observation period T i to 900, 300, and 100 s, the syste ay include the irregular breathing patterns extracted

9 LEE et al.: IRREGULAR BREATHING CLASSIFICATION FROM MULTIPLE PATIENT DATASETS USING NEURAL NETWORKS 1261 Fig. 11. Representing irregular breathing patterns: (a) patient nuber 125 with the ratio γ 125 = 0.63, and (b) patient nuber 317 with the ratio γ 317 = under the different paraeters of ξ. Specifically, depending on the observation period T i, we would like to adjust the threshold value ξ for the ROC evaluation of the proposed classifier. In the second ROC, we ay increase the regular threshold Ψ th so that the patient datasets with the ratio γ i of patient i ay be changed fro true negative to true positive. For the analysis based on the regular threshold, we extract the ratio γ i of patient i by changing the observation period T i of 900, 300, and 100 s. The regular threshold Ψ th can be variable fro 0.1 to 0.99, especially by changing the regular threshold Ψ th of 0.80, 0.85, and 0.90, defined in Section IV-A. Depending on the regular threshold Ψ th, the ROC is analyzed for the perforance of the proposed classifier. After we ake a class for each breathing pattern, and analyze breathing patterns to detect irregular patterns, the free paraeters of neural networks are deterined by the training saples of ultiple patient datasets for each class, where these saples are used as input with 10 iterations through the process of providing the network and updating the network s free paraeters. We evaluate the classification perforance whether the breathing patterns are irregular or regular to extract the true positive/negative ranges and the ratio as shown in Fig. 12. To decide the regular/irregular breathing pattern of the patient datasets, we have varied observation periods T i for feature extraction with 900, 300, and 100 s. Fig. 12 shows ROC graphs to evaluate how different observation periods affect the classification perforance. Here, we fixed the regular threshold Ψ th of 0.92 that is the ean value of the ratio γ i. In Fig. 12, we can see that the proposed classifier shows a better perforance with a long observation period T i.the ore observation periods we have, the better perforance we obtain in the proposed classifier. That eans the classifier can be iproved by extending the observation period for feature extraction. Fig. 13 shows ROC graphs of irregular detection with different regular thresholds Ψ th of 0.8, 0.85, and 0.9. In this figure, the ratio γ i of patients i are extracted with observation periods T i of 100, 300, and 900 s. Fig. 12. ROC graph of irregular detection with different observation period. The different regular thresholds Ψ th also affect the classifier perforance. The classifier perforance is slightly iproved by lowering the regular thresholds. The saller the regular threshold Ψ th, the better the classifier perforance. Here, we notice that the true positive rate for the proposed classifier is 97.83% when the false positive rate is 50% in Fig. 13(c). Based on the result of ROC graph in Fig. 13(c), we notice that the breathing cycles of any given patient with a length of at least 900 s can be classified reliably enough to adjust the safety argin prior to therapy in the proposed classification. For the overall analysis of the curve, we have shown the area under the ROC curve (AUC) in Fig. 14. The AUC value can be increased by lowering the regular threshold Ψ th. The axiu AUCs for observation period T i of 100, 300, and 900 s are 0.77, 0.92, and 0.93, respectively. Based on Fig. 14, Fig. 13(a) (c) picked 0.8, 0.85, and 0.9 for Ψ th. We show the coputational efficiency of the proposed ethod with CPU tie used to train the proposed classifier with the given saple sets and to classify the patient datasets for its applicability to practical scenarios. The following table shows

10 1262 IEEE TRANSACTIONS ON INFORMATION TECHNOLOGY IN BIOMEDICINE, VOL. 16, NO. 6, NOVEMBER 2012 Fig. 14. Area under the ROC curve. The axiu AUCs for the observation period T i of 100, 300, and 900 s are 0.77, 0.92, and 0.93, respectively. TABLE III CPU TIME USED FOR THE COMPUTATIONAL EFFICIENCY TABLE IV CLASSIFIER STUDIES OF IRREGULAR BREATHING DETECTION Fig. 13. ROC graph of irregular detection with different regular thresholds and observation period; (a) observation period T i = 100 s, (b) observation period T i = 300 s, and (c) observation period T i = 900 s. the CPU tie used for the training and classification tie of the proposed algorith for each class. As shown in Table III, the CPU tie used can be increased with regard to the nuber of patients. The average coputational tie for each class is 289 s per patient. Soe studies investigated the classification of regular/irregular breathing patterns for the detection of lung diseases with spiroetry [12] [15]. Irregular breathing patterns can also ipact on the dosietric treatent for lung tuors in stereotactic body radiotherapy [6], [9], [10]. However, there are few studies with the results on the classification of breathing irregularity in this area. The following table shows the classification perforance of irregular breathing detection using a variety of respiratory easureent datasets. Table IV shows the classification perforances of the irregular detection with other ethods and easureent datasets. The existing classifier studies deonstrated that spiroetry data using an ANN-based approach could provide a good perforance of breathing classification, i.e., TPR 92.6% [13] and 97.5% [14]. Our proposed ethod can also provide siilar or better perforance (TPR 97.8%) of breathing classification with an EM/ANN-based approach. Please note that the classification perforance of the proposed ethod is based on breathing otion datasets of ore than 400 patients. Sleep-disorder data showed a better perforance of 98% TP(TP+FP) [15]. However, sleep-disorder data are not applicable for breathing otion assessent of lung cancer treatent in patients with usually

11 LEE et al.: IRREGULAR BREATHING CLASSIFICATION FROM MULTIPLE PATIENT DATASETS USING NEURAL NETWORKS 1263 coproised lung function; in addition, the breathing dataset was liited to sleep-disordered breathing data of 74 patients. Our proposed classification shows results of the classifier perforance of 97.83% TPR with 448 saples breathing otion data. That eans the proposed classifier can achieve acceptable results coparable to the classifier studies using the spiroetry data. The proposed ethod assues that the data used to build the classifier is representative enough of breathing patterns of other subjects in general. It also assues that the breathing pattern of a huan captured at soe point in tie before the treatent is indicative of its future breathing patterns. The proposed syste with this value is not intended to be used as real tie classification syste. The proposed ethodology is based on the three-coordinate breathing datasets for external bea radiation treatent. Typically, radiation treatent is delivered after a planning process in which X-ray iaging and advanced treatent planning are prepared. Spiroetry is not used for radiotherapy planning or delivery except for breath hold treatent to which otion prediction does not apply. Reasons for not using spiroetry ight be that it does not provide any directional data and that it ight be not tolerable in all lung cancer patients to continuously onitor respiration due to coproised lung function. The proposed ethod with breathing datasets ay provide clinical advantages to adjust the dose rate before and during the external bea radiotherapy for iniizing the safety argin. V. CONCLUSIONS In this paper, we have presented an irregular breathing classifier that is based on the regular ratio γ detected in ultiple patients datasets. Our new ethod has two ain contributions to classify irregular breathing patterns. The first contribution is to propose a new approach to detect abnoral breathing patterns with ultiple patients breathing data that better reflect tuor otion in a way needed for radiotherapy than spiroetry data. The second contribution is that the proposed new ethod achieves the best irregular classification perforance by adopting EM based on the Gaussian Mixture odel with the usable feature cobination fro the given feature extraction etrics. The proposed irregular breathing classification used a regular ratio to decide whether or not the current breathing patterns are regular. The particular ratio value ay be used to individually adjust the argin size for radiation treatent delivery. The patients classified with regular breathing patterns would be treated with tight argins to iniize projection span and thereby allow better noral tissue sparing. The patients classified with irregular breathing patterns ay have their safety argins adjusted based on the irregular patterns to cope with baseline shifts or highly fluctuating aplitudes that are not covered by population-based safety argins. The recorded breathing otions of 448 patients include regular and irregular patterns in our testbed. With the proposed ethod, the breathing patterns can be divided into regular/irregular breathing patterns based on the regular ratio γ of the true negative range to the period of observation. The experiental results validated that our proposed irregular breathing classifier can successfully detect irregular breathing patterns based on the ratio, and that the breathing cycles of any given patient with a iniu length of 900 s can be classified reliably enough to adjust the safety argin prior to therapy in the proposed classification. 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Stork, Pattern Classification. Hoboken, NJ: Wiley, [39] Z. Li, D. Lin, and X. Tang, Nonparaetric discriinant analysis for face recognition, IEEE Trans. Pattern Anal. Mach. Intell., vol. 31, no. 4, pp , Apr [40] K. P. Burnha and D. R. Anderson, Model selection and ulti-odel inference: a practical inforation-theoretic approach. New York: Springer-Verlag, [41] T. Fawcett, An introduction to ROC analysis, Pattern Recognit. Lett., vol. 27, no. 8, pp , Suk Jin Lee (S 11) received the B.Eng. degree in electronic engineering and the M.Eng. degree in teleatics engineering fro Pukyong National University, Busan, Korea, in 2003 and 2005, respectively, and the Ph.D. degree in electrical and coputer engineering fro Virginia Coonwealth University, Richond, VA, in In 2007, he worked as a visiting research scientist at GW Center for Networks Research, George Washington University, Washington, DC. His research interests include network protocols, neural network, target estiate, and classification. Yuichi Motai (M 01) received the B.Eng. degree in instruentation engineering fro Keio University, Tokyo, Japan, in 1991, the M.Eng. degree in applied systes science fro Kyoto University, Kyoto, Japan, in 1993, and the Ph.D. degree in electrical and coputer engineering fro Purdue University, West Lafayette, IN, in He is currently an Assistant Professor of electrical and coputer engineering in Virginia Coonwealth University, Richond, VA. His research interests include the broad area of sensory intelligence, particularly in edical iaging, pattern recognition, coputer vision, and sensory-based robotics. Elisabeth Weiss received the Graduate Degree fro the University of Würzburg, Gerany, in 1990 and received the doctorate degree in She copleted residency in radiation oncology at the University of Göttingen, Göttingen, Gerany, in 1997 after participating in various residency progras in Berne (Switzerland), Würzburg (Gerany), and Tübingen (Gerany). She received an Acadeic Teacher s degree fro the University of Goettingen in Gerany, in She is currently a Professor in the Departent of Radiation Oncology and a Research Physician in the Medical Physics Division, Virginia Coonwealth University (VCU), Richond, where she is also involved in the developent of iage-guided radiotherapy techniques and 4-D radiotherapy of lung cancer. Shuei S. Sun received the B.P.H. (Public Health) degree fro the College of Medicine, National Taiwan University, Taipei, Taiwan in 1976, the M.S. degree in applied atheatics and statistics fro the State University of New York, Cobleskill in 1980, and the Ph.D. degree in biostatistics fro the University of Pittsburgh, PA, in She is currently the Departent Chair and Professor in the Departent of Biostatistics, School of Medicine, Virginia Coonwealth University, Richond. Her research interests include the broad area of understanding the natural history of huan growth, body coposition, and risk factors for cardiovascular and related diseases in the huan lifespan, and to indirectly iprove the quality of life through health prootion and disease prevention.