Respiratory motion prediction by using the adaptive neuro fuzzy inference system (ANFIS)

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1 INSTITUTE OF PHYSICS PUBLISHING Phys. Med. Biol. 50 (2005) PHYSICS IN MEDICINE AND BIOLOGY doi: / /50/19/020 Respiratory motion prediction by using the adaptive neuro fuzzy inference system (ANFIS) Manish Kakar 1, Håkan Nyström 4, Lasse Rye Aarup 4, Trine Jakobi Nøttrup 4 and Dag Rune Olsen 1,2,3 1 Department of Radiation Biology, Norwegian Radium Hospital, Montebello, 0310 Oslo, Norway 2 Department of Medical Physics and Technology, Norwegian Radium Hospital, Oslo, Norway 3 Department of Physics, University of Oslo, Norway 4 Department of Radiation Oncology, The Finsen Centre, Rigshospitalet, Copenhagen, Denmark mkakar@labmed.uio.no Received 28 April 2005, in final form 24 June 2005 Published 21 September 2005 Online at stacks.iop.org/pmb/50/4721 Abstract The quality of radiation therapy delivered for treating cancer patients is related to set-up errors and organ motion. Due to the margins needed to ensure adequate target coverage, many breast cancer patients have been shown to develop late side effects such as pneumonitis and cardiac damage. Breathingadapted radiation therapy offers the potential for precise radiation dose delivery to a moving target and thereby reduces the side effects substantially. However, the basic requirement for breathing-adapted radiation therapy is to track and predict the target as precisely as possible. Recent studies have addressed the problem of organ motion prediction by using different methods including artificial neural network and model based approaches. In this study, we propose to use a hybrid intelligent system called ANFIS (the adaptive neuro fuzzy inference system) for predicting respiratory motion in breast cancer patients. In ANFIS, we combine both the learning capabilities of a neural network and reasoning capabilities of fuzzy logic in order to give enhanced prediction capabilities, as compared to using a single methodology alone. After training ANFIS and checking for prediction accuracy on 11 breast cancer patients, it was found that the RMSE (root-mean-square error) can be reduced to submillimetre accuracy over a period of 20 s provided the patient is assisted with coaching. The average RMSE for the un-coached patients was 35% of the respiratory amplitude and for the coached patients 6% of the respiratory amplitude /05/ $ IOP Publishing Ltd Printed in the UK 4721

2 4722 M Kakar et al 1. Introduction The success of radiotherapy (RT) is dependent on a combination of good target coverage and at the same time a low dose to the normal tissue surrounding the target. The size of the necessary margins, and hence the risk for complications, can be reduced if the set-up uncertainties and the internal organ motion, such as those caused by breathing motion, are minimized. In the case of breast cancer patients treated after breast conserving surgery, the irradiation of healthy tissue, in particular lung and heart, has been reported to increase the risk for severe late toxicity (Gagliardi et al 1998, 2000). Breathing-adapted RT has been introduced as a way to reduce toxicity, for example, by margin reduction or by increasing the distance to organs at risk. Breathing-adapted RT can be facilitated either as gating, where the beam is turned on only in a pre-defined discrete phase of the breathing cycle, or as tracking, where the beam is moving synchronously with the movements of the target. In both cases, there is a need to predict the motion of the target and if breathing-adapted RT is to be used in conjunction with more advanced treatment techniques, such as IMRT, it might be necessary to predict the target position over several breathing cycles. Recent studies on respiratory tumor motion prediction have addressed the problem of organ prediction (Sharp et al 2004, Vedam et al 2004) and have shown that by using prediction, lower RMSE values are obtained as compared to not predicting at all. However, an improvement in prediction error (RMSE) is still required in order to maximize gains in accuracy. In this study, we propose a hybrid intelligent approach (ANFIS) for predicting breathing motion for real-time radiation therapy applications. In a hybrid intelligent system like ANFIS, we not only combine the learning capabilities of a neural network but also incorporate reasoning by using fuzzy inference, thereby enhancing the capability of the system for prediction. Previous studies have shown that ANFIS is a better predictor for a chaotic time series as compared to using a single technique like an artificial neural network alone (Jang et al 1997). In addition, it is more susceptible to chaotic motion and signal deficiencies seen in the sampled motion data, and thereby a better compensator for patient coughing and erratic movements. 2. Method We combine the ability of a neural network (NN) to learn with fuzzy logic (FL) to reason in order to form a hybrid intelligent system called ANFIS (adaptive neuro fuzzy inference system). The goal of ANFIS is to find a model or mapping that will correctly associate the inputs (initial values) with the target (predicted values). The fuzzy inference system (FIS) is a knowledge representation where each fuzzy rule describes a local behaviour of the system. The network structure that implements FIS and employs hybrid-learning rules to train is called ANFIS (Loukas 2001) ANFIS Let X be a space of objects and x be a generic element of X. A classical set A X is defined as a collection of elements or objects x X such that each x can either belong or not belong to the set A. By defining a characteristic function for each element x in X, we can represent a classical set A by a set of ordered pairs (x, 0)or(x, 1) which indicates x / A or x A, respectively. On the other hand, a fuzzy set expresses the degree to which an element belongs to a set. Hence the characteristic function of a fuzzy set is allowed to have values between 0

3 Respiratory motion prediction by using the adaptive neuro fuzzy inference system 4723 Figure 1. An illustration of the reasoning mechanism for a Sugeno-type model and the corresponding ANFIS architecture. and 1, which denotes the degree of membership of an element in a given set. So a fuzzy set A in X is defined as a set of ordered pairs: A ={(x, µ A (x)) x X}. (1) Here µ A (x) is called the membership function (MF) for the fuzzy set A. The MF maps each element of X to a membership grade (or a value) between 0 and 1. Usually X is referred to as the universe of discourse or simply the universe. The most widely used MF is the generalized bell MF (or the bell MF), which is specified by three parameters {a,b,c} and defined as (Loukas 2001, Jang and Chuen-Tsai 1995) 1 bell(x; a, b, c) = 1+. (2) x c 2b a Parameter b is usually positive. A desired bell MF can be obtained by a proper selection of the parameter set {a,b,c}. During the learning phase of ANFIS, these parameters are changing continuously in order to minimize the error function between the target output values and the calculated ones (Lee 1990a, 1990b). The proposed neuro fuzzy model of ANFIS is a multilayer neural network-based fuzzy system. Its topology is shown in figure 1, and the system has a total of five layers. In this connected structure, the input and output nodes represent the training values and the predicted values, respectively, and in the hidden layers, there are nodes functioning as membership

4 4724 M Kakar et al Table 1. Forward and backward pass for ANFIS. Forward pass Backward pass Premise parameters Fixed Gradient descent Consequent parameters Least-squares estimator Fixed Signals Node outputs Error signals functions (MFs) and rules. This architecture has the benefit that it eliminates the disadvantage of a normal feed forward multilayer network, where it is difficult for an observer to understand or modify the network. For simplicity, we assume that the examined fuzzy inference system has two inputs x and y and one output. For a first-order Sugeno fuzzy model (Loukas 2001), a common rule set with two fuzzy if then rules is defined as Rule 1: If x is A 1 and y is B 1, then f 1 = p 1 x + q 1 y + r 1, Rule 2: If x is A 2 and y is B 2, then f 2 = p 2 x + q 2 y + r 2. As seen from figure 1, different layers of ANFIS have different nodes. Each node in a layer is either fixed or adaptive (Jang 1993). Different layers with their associated nodes are described below: Layer 1. Every node I in this layer is an adaptive node. Parameters in this layer are called premise parameters. Layer 2. Every node in this layer is a fixed node labelled, whose output is the product of all the incoming signals. Each node output represents the firing strength of a rule. Layer 3. Every node in this layer is a fixed node labelled N. Theith node calculates the ratio of the ith rules firing strength. Thus the outputs of this layer are called normalized firing strengths. Layer 4. Every node i in this layer is an adaptive node. Parameters in this layer are referred to as consequent parameters. Layer 5. The single node in this layer is a fixed node labelled, which computes the overall output as the summation of all incoming signals. The learning algorithm for ANFIS is a hybrid algorithm, which is a combination of gradient descent and the least-squares method. More specifically, in the forward pass of the hybrid learning algorithm, node outputs go forward until layer 4 and the consequent parameters are identified by the least-squares method (Jang 1993). In the backward pass, the error signals propagate backwards and the premise parameters are updated by gradient descent. Table 1 summarizes the activities in each pass. The consequent parameters are optimized under the condition that the premise parameters are fixed. The main benefit of the hybrid approach is that it converges much faster since it reduces the search space dimensions of the original pure backpropagation method used in neural networks. The overall output can be expressed as a linear combination of the consequent parameters. The error measure to train the above-mentioned ANFIS is defined as (Loukas 2001) E = n k=1 (f k ˆ f k ) 2 (3) where f k and ˆ f k are the kth desired and estimated output, respectively, and n is the total number of pairs (inputs outputs) of data in the training set.

5 Respiratory motion prediction by using the adaptive neuro fuzzy inference system Materials Data were obtained by monitoring respiratory motion for breast cancer patients referred for post-operative adjuvant radiotherapy at the Department of Radiation Oncology, The Finsen Centre, Rigshospitalet, Copenhagen, Denmark. All patients received respiratorygated radiotherapy (Korreman et al 2005). The target of radiation, for all of the patients, was the whole breast, the parasternal lymphnodes and the periclavicular lymphnodes. This implies that the target motion equals the motion of the chest wall. The monitoring system was the RPM-system TM provided by Varian Medical System Inc. The RPM TM system consists of a passive, infrared light-reflecting marker that is placed on the patient s chest wall. The anterior posterior (AP) motion of the marker is tracked by an infrared sensitive video camera and the input projected to a computer screen as a breathing curve (Kubo et al 2000). The data sampling frequency of the system is 25 Hz and the signal was recorded continuously with intervals where the patients were assisted with an audio-coaching signal (breath in/breath out) and intervals without coaching (free breathing). Prediction accuracies were evaluated for 11 patients with peak-to-peak motion greater than 6.95 mm. In order to combine the results from different patients, we computed RMSE for each patient and then averaged these to give the average RMSE in predicting respiratory motion. Simulations were carried on a 2.53 GHz Pentium Processor R with an MS Windows 2000 R operative system. ANFIS was trained with the help of Matlab R version 6.5, release 13. Matlab R was also used for RMSE and statistical calculations. 4. Results For each patient, the coached and the non-coached data were separated from the sampled points. For predicting with ANFIS, a two-dimensional matrix of dimensions (each row being referred to as an epoch) was constructed as shown in (4). Data points in each row were chosen to be 6 steps apart and each epoch contained 5 data points: x(t 118), x(t 112), x(t 106), x(t), x(t + 106) x(t 112), x(t 106), x(t), x(t + 106), x(t + 112) x(t 106), x(t), x(t + 106), x(t + 112), x(t + 118) (4)... ANFIS was trained with the first 500 epochs and the next 500 epochs were used for validation. RMSE from each of the validating 500 epochs was calculated and averaged to give the RMSE per patient. Averages of RMSE per patient were calculated for all 11 patients to give the average RMSE for predicting the position for coached and non-coached data in the AP direction. The number and type of parameters for training ANFIS are shown in table 2. Figure 2 shows plots of coached and non-coached data from a randomly chosen patient with ID = 492. One thousand points were extracted from the sampled data to construct the matrix described in (4). Figure 3 shows the RMSE error for both coached and un-coached patients in the AP direction for 11 patients. Table 3 gives the value of mean and standard deviation calculated from RMSE of 11 patients for both coached and non-coached data in the AP direction. The results show the average RMSE to be mm when the patient is coached, and mm when the patient is breathing freely (un-coached) over an interval of 20 s in the AP direction. This corresponds to an average RMSE for un-coached patients of 35% of the respiratory amplitude and for the coached patients of 6% of the respiratory amplitude.

6 4726 M Kakar et al Figure 2. A plot showing the training and validating data used for the patient with ID = 492 with and without coaching. In both cases, a total of 1000 points were used to train and validate prediction accuracies by ANFIS. Table 2. Different parameter types and their values used for training ANFIS. ANFIS parameter type Value MF type Bell function Number of MFs 16 Output MF Linear Number of Nodes 55 Number of linear parameters 80 Number of nonlinear parameters 24 Total number of parameters 104 Number of training data pairs 500 Number of checking data pairs 500 Number of fuzzy rules 16 Table 3. RMSE error for each patient was calculated by ANFIS with training and checking 500 epochs each. Table shows the mean and standard deviation taken from RMSE calculated for 11 patients. Average RMSE for Average RMSE error for Statistical parameters coached data (mm) non-coached data (mm) Mean Standard deviation

7 Respiratory motion prediction by using the adaptive neuro fuzzy inference system 4727 Figure 3. RMSE for 11 patients with and without coaching. Mean processing time for ANFIS was found to be s for coached and 126 s for noncoached data. During this time, ANFIS calculated the parameters for learning and performed prediction and validation on an epoch-by-epoch basis. For a sampling rate of 25 Hz, the predicted interval of time is 20 s i.e., 500 points in advance. Looking at the figure 2 and patient with ID= 492, we can see that it corresponds to approximately 3 4 cycles of respiration data. 5. Discussion and conclusions In this study, ANFIS was trained without filtering the data for bad signals, lost signals or other signal procurement deficiencies. Therefore better accuracies can be expected if the signal is first filtered specially for the non-coached data as these have more fluctuations in the form of spikes and erratic patient movement. We have tested ANFIS on the raw data (i.e., without filtering) in order to see the prediction accuracies without filtering. In the future, a signal-filtering algorithm can also be incorporated with ANFIS to improve accuracies further. Clearly, there are many benefits of using ANFIS for prediction, including the following: (1) it is a general framework that combines two technologies, namely neural networks and fuzzy systems; (2) by using fuzzy techniques, both numerical and linguistic knowledge can be combined into a fuzzy rule base; (3) the combined fuzzy rule base represents the knowledge of the network structure so that structure learning techniques can easily be accomplished; (4) Fuzzy membership functions can be tuned optimally by using learning methods; (5) the architecture requirements are fewer and simpler compared to neural networks, which require extensive trails and errors for optimization of their architecture; and (6) ANFIS does not require extensive initializations through several random starts before training, as always happens in neural networks. Other advantages of the two-phase neuro fuzzy hybrid technique in the ANFIS model also include its nonlinear ability, its capacity for fast learning from numerical and linguistic knowledge, and its adaptation capability. In this work, the respiratory prediction algorithm was applied to a clinical situation where there is a very close correlation between the markers monitoring the breathing of the patient. In other situations, e.g. for lung patients or when the breathing is monitored by spirometry

8 4728 M Kakar et al or abdominal straps, the exact correlation between the breathing signal and the target motion must be explored. The need for breathing motion prediction is, however, still is an important issue. Respiratory motion prediction was repeated 5 times for the same patient. It was observed that the RMSE did not show major variations in the case when the patient was coached; however, fluctuations in RMSE were more evident in the case when the patient was uncoached. The patient was not suffering from a cough, upper way infection or pulmonary disease. Fluctuations in RMSE were seen to be related to a particular session for reasons yet unknown. It seems that ANFIS is more dependent on the stability of the breathing motion and is better suited for prediction on coached data. Another aspect for prediction is the real-time applicability, for which we have to consider time of acquisition, processing time of the algorithm and system latencies. Although ANFIS has many advantages it takes a longer time for processing data as compared to the prediction interval. In the future, we can look into a hardware-based implementation, in particular a DSPbased system, which can significantly enhance the processing time for real time applicability. Conclusively, results show that using a hybrid intelligent approach, in particular ANFIS, gives good prediction accuracies for respiratory motion prediction in breast cancer patients provided the patient is assisted with coaching. Acknowledgments We would like to extend our thanks to Olav Kaalhus and Bjørn Høvik for providing helpful suggestions. References Gagliardi G, Bjohle J, Lax I, Ottolenghi A, Eriksson F, Liedberg A, Lind P and Rutqvist L E 2000 Radiation pneumonitis after breast cancer irradiation: analysis of the complication probability using the relative seriality model Int. J. Radiat. Oncol. Biol. Phys Gagliardi G, Lax I, Soderstrom S, Gyenes G and Rutqvist L E 1998 Prediction of excess risk of long-term cardiac mortality after radiotherapy of stage I breast cancer Radiother. Oncol Jang J S R 1993 ANFIS: adaptive-network-based fuzzy inference system IEEE Trans. on Syst. Man Cybern Jang J S R and Chuen-Tsai S 1995 Neuro-fuzzy modeling and control Proc. IEEE Jang J S R, Sun C T and Mizutani E 1997 Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence (Upper Saddle River, NJ 07458: Prentice Hall) Korreman S S, Pedersen A P, Nøttrup T J, Specht L and Nyström H 2005 Breathing-adapted radiotherapy for breast cancer: comparison of free breathing gating with the breath-hold technique Radiother. Oncol. at press Kubo H D, Len P M, Minohara S and Mostafavi H 2000 Breathing-synchronized radiotherapy program at the University of California Davis Cancer Center Med. Phys Lee C C 1990a Fuzzy logic in control systems: fuzzy logic controller. I IEEE Trans. on Syst. Man Cybern Lee C C 1990b Fuzzy logic in control systems: fuzzy logic controller. II IEEE Trans. on Syst. Man Cybern Loukas Y L 2001 Adaptive neuro-fuzzy inference system: an instant and architecture-free predictor for improved QSAR studies J. Med. Chem Sharp G C, Jiang S B, Shimizu S and Shirato H 2004 Prediction of respiratory tumour motion for real-time imageguided radiotherapy Phys. Med. Biol Vedam S S, Keall P J, Docef A, Todor D A, Kini V R and Mohan R 2004 Predicting respiratory motion for four-dimensional radiotherapy Med. Phys