Hong S-M

Nazarpour K

Tatinati S

Veluvolu KC

\ua9 2014 IEEE. In this paper, we introduce a hybrid method for prediction of respiratory motion to overcome the inherent delay in robotic radiosurgery while treating lung tumors. The hybrid method adopts least squares support vector machine (LS-SVM) based ensemble learning approach to exploit the relative advantages of the individual methods local circular motion (LCM) with extended Kalman filter (EKF) and autoregressive moving average (ARMA) model with fading memory Kalman filter (FMKF). The efficiency the proposed hybrid approach was assessed with the real respiratory motion traces of 31 patients while treating with CyberKnife&lt;sup&gt;TM&lt;/sup&gt;. Results show that the proposed hybrid method improves the prediction accuracy by approximately 10% for prediction horizons of 460 ms compared to the existing methods

Newcastle University E-Prints

                Newcastle University ePrints - eprint.ncl.ac.uk  Tatinati S, Veluvolu KC, Hong S-M, Nazarpour K. Real-time prediction of respiratory motion traces for radiotherapy with ensemble learning. In: 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC 2014). 2014, Chicago, IL, USA: IEEE. Copyright: © 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. DOI link to article: https://doi.org/10.1109/EMBC.2014.6944551  Date deposited:   31/01/2018 Real-Time Prediction of Respiratory Motion Traces For Radiotherapywith Ensemble learningSivanagaraja Tatinati, Student Member, IEEE, Kalyana C. Veluvolu, Senior Member, IEEE, Sun-Mog Hong,and Kianoush Nazarpour, Senior Member, IEEEAbstract— In this paper, we introduce a hybrid method forprediction of respiratory motion to overcome the inherent delayin robotic radiosurgery while treating lung tumors. The hybridmethod adopts least squares support vector machine (LS-SVM) based ensemble learning approach to exploit the relativeadvantages of the individual methods local circular motion(LCM) with extended Kalman filter (EKF) and autoregressivemoving average (ARMA) model with fading memory Kalmanfilter (FMKF). The efficiency the proposed hybrid approachwas assessed with the real respiratory motion traces of 31patients while treating with CyberKnifeTM . Results show thatthe proposed hybrid method improves the prediction accuracyby approximately 10% for prediction horizons of 460 mscompared to the existing methods.I. INTRODUCTIONStereotactic body radiotherapy (SBRT) aims to deliverablative radiation dose to the targeted tumor tissues withminimal exposure to the surrounding normal tissues by track-ing the real-time movement of tumor tissues [1]. To upholdthe targeted tumor location details, several techniques havebeen developed in the recent past [1]–[3]. The commerciallyavailable robotic devices such as CyberKnife and VERO,employ the correlation technique developed in [2] to attainthe real-time movement of tumor. The technique proved thatthe movement of external body recorded with motion captureequipment can be a good estimator for the tumor movement[1]. Nevertheless, current commercial systems require com-pensation for the inevitable delay of 120ms - 400ms (varieswith devices [2]) between the actual movement of tumorand the movement obtained from the correlation model. Themajor sources of delay are inherent mechanical limitation,image acquisition and processing time. To overcome the de-lay, this study focuses on enhancing the real-time respiratorymotion prediction technique which is predominant in tumormovement.In recent past, several techniques have been proposed forpredicting the respiratory motion [1]–[5]. Few techniquesare: local circular motion (LCM) with extended Kalman filter(EKF) [4], Kernel density estimator (KDE) [3] and supportvector regression (SVRpred) [5]. A comparative analysis forThis work is supported by the Basic Science Research Program, NationalResearch Foundation of Korea (NRF), Ministry of Education, Science andTechnology (Grant No. 2011-0023999).S. Tatinati, K. C. Veluvolu, and S. M. Hong are with the School of Elec-tronics Engineering, College of IT Engineering, Kyungpook National Uni-versity, Daegu, South Korea 702-701. E-mails:{tatinati,veluvolu,smhong}@ee.knu.ac.kr.K. Nazarpour is with the School of Electrical and Electronic Engineeringand with the Institute of Neuroscience, Newcastle University, Newcastle-upon-Tyne NE1 7RU, UK. E-mail: Kianoush.Nazarpour@newcastle.ac.ukmost of the prediction techniques can be found in [2], [4].Of all the methods, LCM-EKF exhibited better estimationcapabilities with less computational complexity [4]. Despite,the performance of LCM-EKF prone to large predictionlengths (say approx. 400ms) and subject-specific irregular-ities in breathing patterns. To overcome the limitations withLCM-EKF, in this paper, a hybrid method based on ensemblelearning technique is proposed for estimation of motiontraces. Ensemble learning is one of the successful techniquesto yield synergistic algorithms for time series prediction orclassification by aggregating individual methods (first-levelmethods) with a second-level algorithm.The proposed hybrid method exploits the relative advan-tages of individual methods LCM-EKF and another classicalmethod autoregressive moving average (ARMA) methodwith least-squares support vector machines (LS-SVM) asthe second-level algorithm. The proposed method is exper-imentally assessed with the motion traces obtained from31 patients while treating with CyberKnife. Results showthat the proposed hybrid method exhibits better predictionperformance compared to the existing methods.II. METHODS AND MATERIALSA. MethodsThroughout this article, s represents the respiratory motionand ŝ is the predicted trace. The prediction horizon isrepresented as k. ŝt+k denotes the k samples ahead predictedvalue at tth sample. For individual algorithms, the predictedvalues are represented with ŝLCMt+k and ŝARMAt+k .1) LCM-EKF: LCM-EKF characterizes the respiratorymotion as a local circular motion in a plane augmented withits axis and angular velocity as a part of the system state [4].The state-space representation of LCM model is givenwith:• state equation: x(t+ 1) = f(x(t)) + ν(t)• measurement equation: s(t) = Hx(t) + ω(t)where x(t) = [x(t) ẋ(t) ẏ(t) Ω(t)] represents positionand y(t) represents the auxiliary augmented axis. The stateevolution function isf(x(t)) =1sinΩ(t)TΩ(t)−1− cosΩ(t)TΩ(t)00 cosΩ(t)T − sinΩ(t)T 00 sinΩ(t)T cosΩ(t)T 00 0 0 1x(t),H = [1 0 0 0], ν(t) represents process noise withcovariance E[ν(t)ν(t)T ] = diag[q1T 3, q2T, q3T, q4T ]where q1, q2, q3, q4 characterize the possible changesin x(t), ẋ(t), ẏ(t), and Ω(t) respectively, T representssampling period and ω(t) represents measurement noise withvariance E[ω(t)ω(t)T ] = σ2ω.Multi-step prediction for k samples ahead, with LCM isgiven with (1):ŝ(t+ k|t) = x̂(t|t) +sin Ω̂(t|t)kTΩ̂(t|t)ˆ̇x(t|t)−1− cos Ω̂(t|t)kTΩ̂(t|t)ˆ̇y(t|t). (1)A first-order EKF was employed to update the LCMparameters iteratively. For more details about LCM-EKF,see [4].2) ARMA-FMKF: Multi-step prediction model forARMA is only possible under the assumption the signalcharacteristics do not change (stationary) in a givenprediction horizon. This assumption does not hold in ourcase since respiratory motion is non-stationary. In order toreduce the effect of prior measurements, fading memoryKalman filter (FMKF) was employed to update the statedynamics.The state-space model of the ARMA (p, q) is:Measurement equation: s(t) = wT (t) Φ(t) + ε(t) andState equation: w(t+ 1) = w(t) + η(t)where w = [−w1 · · · − wp − w1 · · · − wq]T represents theweights (regression coefficients), Φ(t) =[s(t−1) · · · s(t−p) e(t − 1) · · · e(t − q)]Trepresents delayed inputs,η(t) represents the state noise that was modeled as a zero-mean white-noise with covariance Q and ε(t) representsthe measurement noise that was modeled with a zero-meanwhite-noise with covariance R [6].The multi-step prediction model with ARMA-FMKF forh samples can be obtained as:ŝ(t+ k) = Φ̂(t+ k)T ŵ(t+ k) (2)where• ŵ(t+ k) = ŵ(t) (the weights vector remains constantfor t to (t+ k) samples)• Φ̂(t+ l) =[ŝ(t− l − 1) · · · ŝ(t− l − p)e(t− 1) · · · e(t− q)]T ;l = 1, 2, · · · , h. (the input vector Φ̂(t) is updatediteratively)The FMKF update equations are given by [6], [7]:ŵ(t+ 1) = ŵ(t) +K(t)(st − ΦT (t)ŵ(t))e(t) = s(t)− Φ(t)T ŵ(t)K(t) =P(t− 1)Φ(t)ΦT (t)P(t− 1)Φ(t) +RP(t) = λ((I−K(t)ΦT (t))P(t− 1)) +Qwhere e(t) is the prediction error; K(t) is the Kalman gainvector; P(t) is the error covariance matrix; λ is the forgettingfactor.3) The Proposed Hybrid Method (HM): The generalframework of the proposed hybrid method is illustrated inFig. 1.RPM tracePrediction with Individual methodsLCM-EKFARMA-FMKFs^ LCMk+hs^ ARMAk+hsk Nonlinear EnsembleWith LS-SVMŝk+hHybrid MethodFinal Predictionf(.) - Nonlinear mappings^ LCMk+h s^ ARMAk+hf (         ,            )Fig. 1. Block diagram representation for the proposed hybrid methodThe prediction with the hybrid method can be given by:ŝt+h = f(ŝLCMt+k , ŝARMAt+k ) (3)where f(.) is a nonlinear function and determined offlineby using LS-SVM with N training data pairs, that is,{s(t), y(t)}Nt=1, where s(t) = [ŝLCMt+k ŝARMAt+k ] is input vectorand y(t) = s(t+k) as the corresponding output variable. Theregression model for LS-SVM is in the form:y = ωTϕ(s) + b (4)where ω is the weight vector and b is the bias. We optimizedthe estimation of f with LS-SVM:minω,b,eJ(ω, ξ) =12ωTω + CN∑t=1e2(k)subject to the constraints y(t) = ωTϕ(s(t)) + b+ e(t); t =1, 2, · · · , N ; where C is a regularization constant and e(t)is the estimation error.The final prediction model of hybrid method with LS-SVM isŝt+k = f(ŝLCMt+k , ŝARMAt+k )=∑Ni=1 αiK(s(i), s(t)) + b; t = N + 1, · · · , l.(5)where K(., .) represents the radial basis kernel function, αrepresents Lagrangian multipliers.B. CyberKnife Respiratory motion databaseThe respiratory motion database employed in this paperwas recorded during the radioactive therapy with CyberKnifeat Georgetown university hospital from 31 patients. Thedatabase contains 304 motion traces obtained from all sub-jects. The traces were recorded using optical tracking system,Synchrony respiratory motion tracking system by Accuracy,Inc. 3D motion traces are recorded from all the threemarkers placed on the patient. The principal componentsobtained with principal component analysis (PCA) from the3D motion traces of a marker are considered as the motiontrace of the corresponding marker [2]. Thereby, three tracesare acquired from three markers, namely m1, m2 and m3.The sampling frequency was 26 Hz. For more informationon the recording procedure and pre-processing of the motiontraces, see [2] and [8].1 2004006008000.1481216−50050100 C(a)σ2 % Accuracy1 2004006008000.1481216−200204060 C(b)σ2 1 2004006008000.1481216−50050 C(c)σ2 0102030405060Fig. 2. Optimal parameter selection for Subject #1C. Performance IndicesThe measures employed to quantify the prediction per-formance are prediction accuracy and relative MSE definedwithAccuracy =RMS(s)− RMS(e)RMS(s)× 100(6)Relative MSE(ŝh, s) =RMS(ŝh − s)RMS(s̆h − s)(7)where RMS(s) = (∑k=mk=1 s2k/m)0.5, m is the number ofsamples, sk is the input signal at instant k and the error e isthe mismatch between the actual and predicted signals. s̆hrepresents the signal s delayed by h samples.III. RESULTSA. Optimal Parameter SelectionFor adaptive prediction methods LCM-EKF and ARMA-FMKF, appropriate initialization of parameters is necessaryto obtain good performance. The parameters and initializa-tion for LCM-EKF are well documented [4]. For ARMA-FMKF model, Akakie information criterion (AIC) [9] iden-tified ARMA(16, 1) as the optimal order for the respira-tion motion traces employed in this study. The regressioncoefficients are zero initialized. The parameters and theinitialization for both the methods are provided in Table. I.TABLE IMETHODS & PARAMETERSMethod Model parameters and initial conditionsLCM-EKF [4] q1 = 0.2; q2 = 2−4; q3 = 2−3;R = 0.0001; P0 = 0.01× I;ARMA-AFKF p = 16 q = 1; R = 0.01; Q = 0.01× I;P0 = 0.01× I;The parameters that require careful selection to attainoptimal ensemble with LS-SVM are regularization constant(C), radial bias function (RBF) Kernel variance (σ2) andnumber of training sample (N ) [10]. We conducted extensivegrid search for these parameters to identify the optimalinitialization.To identify the appropriate N for all respiratory motiontraces in the database, we tested various values of N . Due toits semi-periodic characteristics with limited spectral range,we empirically identified that N = 1000. Larger valuesof N improves the prediction accuracy only marginally.Moreover, larger values of N will increase the computationalcomplexity considerably.To identify the appropriate initialization for C and σ2, anextensive grid search was conducted for wide range of values(0 < C < 1000 and 0.1 < σ2 < 20). Results obtained forSubject #1 are shown in Fig. 2. The plots represent obtainedaverage prediction accuracy for all traces of the subject. Theregion with highest prediction accuracy (white in color) isthe desired region to pick the optimal initialization for theparameters. The results obtained for Subject #1, shown inFig. 2, show a vast desirable region for m1 and m3 whereasm2 has a narrow such region. One can pick any set of valuesfor C and σ2 from the desired region and it will yield betterprediction of traces compared to the set of values selectedform the colored region. Similar analysis was conducted forthe rest 30 subjects in the database. The optimal initializationis identified individually from the grid search for each makerof every subject.B. Performance analysis for prediction horizon of 460msIn this analysis, results of the proposed hybrid approachare compared with the results obtained by employing theLCM-EKF and the ARMA-FMKF methods. The horizon wasselected considering the typical latencies involved in com-mercial robotic systems such as CyberKnife (approximately230ms), and multi-leaf collimators (approximately 460ms)[11]. Comparative performance analysis for all methods isperformed on the complete database for both predictionhorizons.Prediction performance obtained for all markers of asubject for a given method is similar. Thereby, to quantifythe performance, %Accuracy and relative RMSE for allmarkers and traces for a subject are averaged. The predictionaccuracies obtained with all methods for all 31 subjects areshown in Fig. 3. Results show that, the proposed hybridmethod provides better prediction accuracy and has lessrelative RMSE compared to both LCM-EKF and ARMA-FMKF for all subjects. Further, statistical analysis wasperformed over all the subjects and the results obtained areshown in Fig. 4. There was a significant main effect of thepredictor (F (2, 60) = 130.60, n = 31, p < 10−4). Post-0 5 10 15 20 25 30406080% Accuracy  LCM−EKF ARMA−FMKF HM0 5 10 15 20 25 30406080100SubjectsRelative RMSE  (a)(b)Fig. 3. Performance analysis of all methods in presence of 460ms delay for complete database (a) Prediction accuracyhoc pair-wise t-test showed that the proposed hybrid methodoutperformed both LCM-EKF (p < 10−4) and ARMA-FMKF (p < 10−4) methods. For completeness, we reportthat the performance of LCM-EKF was better than that ofARMA-FMKF (p < 10−4). From Fig. 4, it can be seenthat the mean value of prediction accuracy obtained with theproposed method over all subjects achieved an improvementof approximately 10% compared to both individual methodsLCM-EKF and ARMA-FMKF.LCM−EKF ARMA−FMKF HM304050607080% AccuracyLCM−EKF ARMA−FMKF HM406080100Relative RMSEFig. 4. Statistical analysis for prediction performance of all methods withprediction horizon as 460msTo further analyze the performance, the improvement inprediction accuracy for all traces is tabulated in Table.II. The number of traces with prediction accuracy in therange of 60 to 70% and 70 to 80% for hybrid methodare approximately three times compared to both individualmethods.TABLE IICOUNT OF TRACES REFLECTING SPREAD OF PREDICTION ACCURACIES -HORIZON: 460MSMethod %Accuracy< 50% 50 to 60% 60 to 70% 70 to 80%LCM-EKF 103 101 52 18ARMA-FMKF 144 100 48 12Hybrid Method 60 64 126 54IV. CONCLUSIONSTo enhance the prediction performance of respiratorymotion traces, a hybrid method which is an ensemble ofLCM-EKF and ARMA-FMKF with LS-SVM is proposed inthis paper. To evaluate the performance of proposed hybridmethod, analysis was conducted on the database collectedform 31 subjects with CyberKnife. The analysis was per-formed with prediction horizons 460 ms which is well in linewith the commercially available robotic radiotherapy devices.Results show that, the proposed hybrid method providesoverall improvement of approximately 10% in predictionaccuracy for both prediction horizons compared to LCM-EKF.REFERENCES[1] J. Wilbert, J. Meyer, K. Baier, M. Guckenberger, C. Herrmann, R. J.Hess, L. Ma, T. Mersebach, A. Richter, M. Roth, K. Schilling,and M. Flentje, “Tumor tracking and motion compensation withan adaptive tumor tracking system (ATTS): System description andprototype testing,” Medical Physics, vol. 35, pp. 3911–3921, 2008.[2] F. Ernst, R. Durichen, A. 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Xuemin, “Adaptive fading Kalmanfilter with an application,” Automatica, vol. 30, pp. 1333–1338, 1994.[8] “Respiratory motion database,” http://signals.rob.uni-luebeck.de.[9] H. Akaike, “A new look at the statistical model identification,” IEEETransactions on Automatic Control, vol. 19, pp. 716–723, 1974.[10] J. A. K. Suykens, T. Van Gestel, J. De Brabanter, B. De Moor, andJ. Vandewalle, Least Squares Support Vector Machines, Singapore, Ed.World scientific, 2002.[11] P. R. Poulsen, B. C. Cho, A. Sawant, D. Ruan, and P. J. Keall, “De-tailed analysis of latencies in image-based dynamic MLC tracking,”Medical Physics, vol. 37, pp. 4998–5005, 2010.

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Real-time prediction of respiratory motion traces for radiotherapy with ensemble learning

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Real-time prediction of respiratory motion traces for radiotherapy with ensemble learning

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