Prediction of Respiratory Motion for Radiotherapy Applications

Textbook , 2022 , 49 Pages

Medicine - Radiology, Nuclear Medicine

Respiratory motion exhibits non-linear and non-stationary behavior in nature and this has been a great hindrance to the accurate prediction of tumor in motion adaptive radiotherapy. Accurate prediction of respiratory motion and subsequent tracking of tumor has been a challenge due to its irregularities and intra-trace variabilities. In order to overcome this issue, prediction models can be trained by using neural networks. In this book, we explore the usage of random vector function link (RVFL) based neural networks to train the model in a very efficient way to achieve high accuracy in respiratory motion prediction. In RVFL, the direct link from input features to output layer acts as regularization to prevent the network from overfitting. Further, the non-iterative nature of RVFL due to closed form solution makes it computationally fast. The method is validated on a bench mark respiration dataset.

Contents

List of Tables

List of Figures

ABSTRACT

1 Introduction
1.1 Respiratory motion
1.2 Types of treatment methods
1.3 Existing methods for respiratory motion prediction
1.4 Random Vector Functional Link and Empirical Mode Decompo­sition based Random Vector Functional Link
1.5 Organization

2 Cancer Disease and Dataset Description and Pre-Processing
2.1 Cancer statistics
2.2 Respiratory motion database
2.2.1 Data acquisition
2.2.2 Data processing
2.2.3 Data down-sampling
2.2.4 Data normalization and edge artifacts removal

3 Modelling of Respiratory Motion with Random Vector Functional Link based Neural Networks
3.1 Introduction
3.2 Methodology
3.2.1 Artificial Neural Networks
3.2.2 Single Layer Feedforward Neural Networks
3.2.3 Random Vector Functional Link
3.2.4 Extreme Learning Machine
3.2.5 Performance measures
3.3 Results
3.3.1 Parameter selection
3.3.2 Simulation results
3.3.3 Comparison between RVFL and ELM

4 Modelling of Respiratory Motion with Empirical Mode Decomposition based Random Vector Functional Link
4.1 Introduction
4.2 Methodology
4.2.1 Empirical Mode Decomposition
4.2.2 Hybrid model EMD-RVFL
4.2.3 Performance measures
4.3 Results
4.3.1 Parameter selection
4.3.2 Simulation results

5 Conclusion and Future Work

References

Dedicated to our families for all the love and support!

Preface

Respiratory motion exhibits non-linear and non-stationary behavior in nature and this has been a great hindrance to the accurate prediction of tumor in motion adaptive radiotherapy. Accurate prediction of respiratory motion and subsequent tracking of tumor has been a challenge due to its irregularities and intra-trace variabilities. In order to overcome this issue, prediction models can be trained by using neural networks. In this book, we explore the usage of random vector function link (RVFL) based neural networks to train the model in a very efficient way to achieve high accuracy in respiratory motion prediction. In RVFL, the direct link from input features to output layer acts as regularization to prevent the network from overfitting. Further, the non-iterative nature of RVFL due to closed form solution makes it computationally fast. The method is validated on a bench mark respiration dataset.

Asad Rasheed

Dr. Kalyana C. Veluvolu

Both authors are with the School of Electronics Engineering, Kyungpook National University, South Korea

List of Tables

1 Variance of the respiratory motion trace as shown in Figure 3a

2 Training and Testing Average RMSE of 304 respiratory motion traces during different activation functions of RVFL model at pre­diction length 576 ms

3 Parameters selection

4 Training and Testing average RMSE of 304 respiratory motion traces of RVFL model for 192 ms, 384 ms and 576 ms

5 Training and Testing average RMSE of 304 respiratory motion traces of ELM model for 192 ms, 384 ms and 576 ms

6 Statistical comparison of EMD-RVFL and RVFL in terms of RMSE of trace-65

List of Figures

1 Work flow for respiratory motion prediction with RVFL

2 Block diagram of the EMD based RVFL neural networks

3 Sample trajectory of the respiratory motion

4 An overview of data pre-processing

5 The structure of RVFL neural network

6 Workflow for the respiratory motion prediction with RVFL neural network

7 The basic structure of ELM

8 Average RMSE of RVFL on 304 traces with respect to the differ­ent number of hidden neurons at 192 ms

9 Average RMSE of RVFL on 304 traces with respect to the differ­ent number of hidden neurons at 384 ms

10 Average RMSE of RVFL on 304 traces with respect to the differ­ent number of hidden neurons at 576 ms

11 Performance of RVFL model during different sizes of sliding win­

dow versus average RMSE of 304 respiratory motion traces at prediction length 576 ms

12 RVFL Training and Testing of segment of trace-65 at prediction length 192 ms

13 RVFL Training and Testing errors of segment of trace-65 at pre­diction length 192 ms

14 RVFL Training and Testing of segment of trace-65 at prediction length 384 ms

15 RVFL Training and Testing of segment of trace-65 at prediction length 384 ms

16 RVFL Training and Testing of segment of trace-65 at prediction length 576 ms

17 RVFL Training and Testing of segment of trace-65 at prediction length 576 ms

18 RVFL Training and Testing RMSE of 304 traces at different lengths of192ms,384ms,and576ms

19 Comparison between RVFL and ELM at prediction length of 192 msat5.2Hz

20 Comparison between RVFL and ELM errors at prediction length of192msat5.2Hz

21 Comparison between model performance of RVFL and ELM at prediction length of 192 ms

22 Comparison between model performance of RVFL and ELM at prediction length of 384 ms

23 Comparison between model performance of RVFL and ELM at prediction length of 576 ms

24 Structure of EMD-RVFL

25 RVFL Prediction of trace-65 at prediction length of 576 ms

26 EMD-RVFL Prediction of trace-65 at prediction length of 576 ms

1 Introduction

Biomedical signals depict the action capabilities of the tissues of human being. These biomedical signals contain the spatial and temporal information of the hu­man body activities. Like electrocardiogram (ECG), electroencephalogram (EEG), tremor, respiratory motion signals etc., are the examples of biomedical signals. Through these physiological signals, modern science becomes able to predict the different human body diseases. A tremendous progress has been made in the field of the biomedical signal processing including the prediction and classification of these kind of signals.

1.1 Respiratory motion

Respiratory motion is one of the biomedical signals that has been used in the treatment and diagnosis of various diseases that affects the abdomen, lungs and other areas of the body as well. The word respiration refers to the phenomenon of the gas exchange between the human body and surrounding environment. It is also known as the physiological process. Cellular respiratory system describes the metabolic process which happens due to the reaction between the oxygen and glu­cose that results into the energy. Respiratory process usually happens inside the lungs. However, other human body organs are also involved in the gas exchange process like nose, throat and trachea. Although lung is the elastic organ but still it cannot be moved itself. Respiratory motion causes the involuntary motion. Di­aphragm is an essential part of the respiratory muscle that is spanned along the transversal plane and split the abdominal and chest. Due to the inhaling, the di­aphragm get contracted which results in the displacement towards the abdomen. The other important part of the respiratory muscle is intercostal muscle. During the inspiration, the intercostal muscles move towards the superior and anterior sides of the ribs.

1.2 Types of treatment methods

The normal breathing ranges from 500 [1] to 800 ml [2]. In general, the breathing depend upon the height, gender and age of the subjects. The normal respiratory motion frequency of the normal is 0.25 Hz [1]. However, it changes between 0.1 and 0.5 Hz [3]. Radiotherapy is the oncological treatment method such as surgery or chemotherapy. The main idea behind the radiotherapy is to track the tumor cells in human body and break it down. There are few conventional methods listed below which have been used to solve the problem of tumor diagnosis:

1. Increase of the target area
2. Respiratory gating
3. Breath-hold techniques
4. Forced shallow-breathing
5. Adaptive motion compensation

1.3 Existing methods for respiratory motion prediction

Adaptive motion radiotherapy offers the ideal situations to mitigate the disadvan­tages of previously mentioned four methods. The idea behind the adaptive motion compensation is to track the tumor and throw the laser beam on it and to remove it. Motion adaptive radiotherapy plays an important role in the prediction of real time position of the thoracic and abdominal tumors. For the patients diagnosed with these tumors, motion adaptive radiotherapy has been a promising way for the cure. Sometimes, tumor motion induced by the respiratory motion mechanism exceeding 20 mm and significantly compromises the dose conformity in radiother­apy treatment [4], [5]. Motion adaptive radiotherapy tries to deliver the conformal dose precisely to the abdominal and thoracic regions where tumors are present with minimal exposure to the surrounding tissues by compensating the tumor mo­tion [5]-[8]. However, equipment which is used to track the tumors in real time like Cyberknife [9], there is an inherent latency up-to several milliseconds due to its limitation in data processing and mechanics. Eventually, this delay affects in targeting the beam to the target tumor [10]. To get rid of this latency, system’s known latency can be used to predict the future tumor motion [10]. Several predic­tion methods have been developed in the literature to solve this problem [8], [9], [11]-[14]. Usually the prediction methods have been divided into two categories: model-based and model-free. Model based methods are derived by using the math­ematical structures like least mean square (LMS) [11], wavelet-based multiscale regression (wLMS) [15], or local circular motion with extended Kalman filter (LCM-EKF) [14]. However, model-free based embody non-trivial relationships with the training data in order to interpret the testing data. For instance, artificial neural networks (ANN) [16], support vector regression (SVR) [17] can tackle the highly non-stationary and non-linear behavior of the respiratory motion at large prediction length. Artificial neural networks are very good to classify and predict the data having the highly non-linear behavior in nature especially for the biomed­ical data [8].

1.4 Random Vector Functional Link and Empirical Mode Decompo­sition based Random Vector Functional Link

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Figure 1: Work flow for respiratory motion prediction with RVFL

ANN can be categorized into two classes: feedforward neural networks (FNN), and recurrent neural networks (RNN). One of the common type of FNN is the single layer feedforward neural network (SLFN) and back propagation (BP) which can be used to train it. However, due to the slow training process and get stuck in local minima; these disadvantages restrict the BP to get the desired results. In the same time, when large amount of time is required to train the model using BP and high chance of getting stuck in local minima problem, randomization based neural network plays an important part to take the less time for training and provides precise and accurate solution [18]. Random vector function link (RVFL) which is classified as a semi-random realization of functional link neural networks [18], [19], where the direct link and closed form solution make it an attractive approach to solve the multistep ahead prediction problem. RVFL is the type of FNN, and it is the method which is based on the closed form solution. These methods are free from the gradient and derivative free iterative optimization based techniques [18]. RVFL is also known as universal approximator that can try to estimate most of the non-linearity of the signals [18]. The basic principle of the RVFL for respiratory motion prediction is given in the Figure 1.

In order to get more accuracy for the respiratory motion prediction as com­pared to the RVFL, we used the empirical mode decomposition (EMD) [20] method with RVFL which is known as the EMD-RVFL [21]. We trained the EMD based RVFL to get highest accuracy and to precisely track the motion of the tumor inside the body. In this method, the signal can be decomposed into several intrinsic mode functions (IMF) with their residue which represents the trend. EMD is basically empirical based approach that can be utilized to get the instantaneous frequency data from the highly non-linear and non-stationary signal. The system load con­sists of thousands of individual components which are highly non-stationary. As a result of EMD, IMF will be created that contains one extreme between zero cross­ing along with a mean value of zero. That is the reason why EMD is very effective for the multistep ahead prediction. The structure of EMD-RVFL has been drawn in Figure 2.

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Figure 2: Block diagram of the EMD based RVFL neural networks

1.5 Organization

The remaining chapters in the dissertation have been organized as follows:

In chapter 2, a brief introduction is given regarding the statistics of the can­cer and tumor disease as well as various steps are discussed to achieve the 304 respiratory motion traces from the Cyberknife treatment radiotherapy method.

Chapter 3 and 4 make the core part of this dissertation. In chapter 3, the mod­elling of the respiratory motion has been done with the random vector functional link (RVFL) based neural networks. In this chapter, we took the advantage of the direct link of the RVFL and we made the comparison between the RVFL and Extreme Learning Machine (ELM). In chapter 4, we applied the hybrid model Empirical Mode Decomposition (EMD) based RVFL termed as EMD-RVFL on the 304 respiratory motion traces to get the good accuracy as compared the RVFL.

Finally, chapter 5 concludes the dissertation by reviewing the limitations and accomplishments of this research, and gives the future scope of the research in other fields.

2 Cancer Disease and Dataset Description and Pre-Processing

2.1 Cancer statistics

The word cancer is derived from the Latin word which basically means crab. Can­cer consist of randomly or irregular shaped organ just like crab. The word cancer is specifically used to describe a new growth which has the ability to attack the sur­rounding tissues, gradually increase its attacking area which can eventually lead to the patient’s death if not treated well and regularly.

Cancer is becoming a major cause of death and the second most leading cause of death in strong economically developed countries [22]. In South Korea, cancer has been a major public heath issue since 1983 [22]. In 2016, more than 220,000 patients were diagnosed with cancer disease and one-fourth of them died due to the cancer disease [22]. The most common site that can be affected with the cancer is lung followed by the thyroid, breast, colon and stomach. Overall, these five types of cancer can be half of the burden of cancer in Korea. Most of the cancer patients die due to the lung cancer. Other developing countries like Germany, there were approximately 477,300 people diagnosed with the cancer in 2010. Within the same year, 218,258 were reported that were died due to the cancer. This is the major reason why cancer is becoming the second highest leading cause of the death after cardiovascular disease.

2.2 Respiratory motion database

The different prediction algorithms have been implemented on the large data set of the respiratory motion prediction. 304 respiratory motion traces has been recorded from 31 patients during the Cyberknife treatment at Georgetown University Hos­pital. In order to get the desire-able results, following steps are required for pre­processing on the dataset:

2.2.1 Data acquisition

The optical tracking system is typically used with the Cyberknife to record the respiratory motion traces from 31 patients during their medical treatment. Dubbed Synchrony Respiratory Motion Tracking System by Accuracy, Inc., which employ modified Flashpoint FP 5500 System, which is manufactured by Boulder Innova­tor, Inc., to record the position of optical fibres which transmit the red light. These optical fibers are placed on the abdomen and chest of the patient in such a way that the open ends of the fibres are at the right positions of respiratory motion with the largest amplitude. Three markers were set in 3D, which results into the three motion traces per patient during the fraction. There were some flaws in the mark­ers two and three of one fraction. The length of respiratory motion traces ranges from 80 to 158 minutes. The 304 traces were recorded at the sampling frequency of the 26 Hz.

2.2.2 Data processing

In order to avoid the overfitting problem and make the neural network training fast, the respiratory motion traces can be normalized between 0 and 1.

During the recording of the data sets, the data did not only capture the res­piratory motion but it also recorded the motion of the treatment coach whenever the patients felt a change in the alignment. This kind of behavior of traces can be seen in Fig. 3a [26]: where the couch movements prior to the longer period of the respiratory motion traces can be noticed. Only the data segment with the red rect­angle has been used for the algorithm evaluation. As respiratory motion occurs in

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(a) The main graph shows the x-coordinate of the trace. As it can be clearly seen in the respiratory motion (due to couch re-alignment). The data that used for the algorithm evaluation is marked with a red rectangle, which is above at the right corner.

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(b) PCA employed on the data segment that showed in green in Figure 3a trace

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(c) Zoomed data segment of the Figure 3b

Figure 3: Sample trajectory of the respiratory motion

the perpendicular direction to the chest wall, the data was reduced to its princi­ple axis. To avoid the curse of dimensionality, an external optical signal has been reduced to the principle component while taking care of the error that depends upon the type of algorithm. Figure 3b is showing the data segment which has been marked in green in Figure 3a after implementing the principle component analy­sis (PCA). There is a point to be noted that the PCA has been implemented on the respiratory motion traces to avoid the dimensionality curse.

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Figure 4: An overview of data pre-processing

Since the respiratory motion traces and chest are aligned in the prependicular direction, and the track­ing system of the Cyberknife can be mounted anywhere in room in such a way that the data from the chest of patient should be reasonable and relevant data. The variance of the trace in Figure 3a is showed in Table 1. Due to the signal drift, the variance can be seen in the X and Y coordinates, and it is mostly due to the motion caused by the patient.

Table 1: Variance of the respiratory motion trace as shown in Figure 3a

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2.2.3 Data down-sampling

Originally the respiratory motion traces are recorded at sampling frequency of 26 Hz. But in our own experiments, we down-sampled the data to 5.2 Hz to conform to kV/MV imaging rates [23]. The whole process can be seen in Figure 4.

2.2.4 Data normalization and edge artifacts removal

By normalizing all the data to a standard scale, we allow the network to quickly learn and converge to the optimal parameters for each input node. Moreover, by normalizing the data between 0 and 1 (min and max normalization), we are assist­ing the computer to avoid losing the accuracy when performing with the large or very small numbers. Moreover, few samples are trimmed from the beginning and ending of each respiratory motion trace due to couch motion of patients.

3 Modelling of Respiratory Motion with Random Vector Functional Link based Neural Networks

This chapter will illustrate simple and robust random vector functional link (RVFL) method for the multistep ahead prediction for the respiratory motion traces.

3.1 Introduction

The radiotherapy application based machines like stereo-tactic body radiation therapy (SBRT) aims to get the high precision in provision of conformal dose to the clinical target volume (CTV) by reducing the beam exposure to the sur­rounding tissues [24]. Involuntary motion is induced due to the existence of the respiratory motion in the thorax and abdomen sides, particularly at breast, pan­creas, liver and lung ranges from 20 mm to 50 mm [10]. This involuntary motion will affect the precision of delivering of dose to the targeted place as well as the accuracy of the radiotherapy. Motion adaptive methods try to mitigate the causes that will affect the precision of the radiotherapy in the presence of involuntary motion in real time [25]. Cyberknife which is commercially available radiother­apy instrument has to face the latency of 50 ms to 500 ms due to the inherent data processing and mechanical limitations. To mitigate this delay, prediction of the tumor is required equivalent to the delay horizon of the Cyberknife [9].

Several prediction algorithms have been published in the literature to predict the respiratory motion for multistep ahead [8], [9], [12], [13]. There are two types of modelling: model based and learning based methods. Compared to the model based methods [9], [14], [15], the learning based methods, for instance, artificial neural networks (ANN) [16], [26] could give the better stability and adaptibility to predict the respiratory motion traces for multi-step ahead.

3.2 Methodology

In this section, first we provide the brief explanation of the artificial neural net­works, its types and finally will give the detailed explanation of the random vector functional link for multi-step ahead prediction of traces.

3.2.1 Artificial Neural Networks

Artificial neural networks (ANN) simply known as neural networks is inspired by the biological neural networks. ANN is composed of collection of the artificial nodes which are called as the neurons. Like in synapses in the brain, each con­nection serves the role of transmitting the information between different neurons. Artificial neural network (ANN) has been very popular for the solving the classi­fication and regression problem. Especially the ANN draws a huge attention due to solving the regression problems of biomedical data set which is having a lot of non-stationarity and non-linearity [8]. ANN has been classified into two main categories according to the connection of the network structure: recurrent neu­ral networks (RNN) and feedforward neural networks (FNN). In this thesis, we focused on the feedforward neural networks (FNN) method for multistep ahead prediction of the respiratory motion traces. Single layer feedforward neural net­work (SLFN) is the most common and simplest example of the FNN. Traditional methods like Backpropagation can be employed to train the SLFN. However, there are some disadvantages of employing the BP to train the SLFN. The first disad­vantage is that it usually takes long duration to train the network and second one is getting stuck in minima as its major drawback. Meanwhile, in a situation where training takes longer period of time and there is higher chance of getting trapped in local minima, randomization based neural networks has been a better choice [18] . Random vector functional link (RVFL) neural network is categorized as a semi-random realization of functional link neural networks where the direct link as well as the closed form solution features make it an attractive approach for the prediction problem. In this thesis, we employed RVFL to predict the respiratory motion for longer prediction horizons on respiratory motion data set containing 304 traces from 31 subjects.

3.2.2 Single Layer Feedforward Neural Networks

Single layer feedforward neural network is a form of Artificial neural networks (ANN) which consists of an input layer, a hidden layer of neurons with non­linear activation function, and an output layer. In our architecture, the SLFN is constructed with adjacent layers containing adjustable weight, making them more robust in activation. The interconnection of neurons within the same layer were avoided aligning with the traditional approach of SLFN architecture. Output from each hidden node was calculated using the following equation [21]:

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where f (.) is representing non-linear activation function; n represents number of input features; x i is the input to the hidden neuron j; w ij is the weight of con­nection between the input node i and hidden neuron j of the hidden layer; and b i represents the bias to the neurons at the hidden layer.

Our input matrix constructed from the respective respiratory motion traces with the use of sliding window of fixed length were fed into the SLFN so that on activation within the hidden layer, the final output of SLFN is computed as

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Figure 5: The structure of RVFL neural network

follows:

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where g (.) is the non-linear activation function; h represents number of hidden layer neurons; v j is the output of the hidden layer neuron j; w jo is the weight of connection between hidden layer neuron j and output node and b j is the bias of the neurons at the output layer. The weights in SLFN (w ij and w jo) are optimized by back propagation (BP) method.

3.2.3 Random Vector Functional Link

RVFL network being a randomized form of FNN, a direct link is established be­tween input and output neurons and this approach helps to avoid overfitting issues. In our implementation of RVFL architecture, we adopted the use of least square estimation in a closed form and fixed random weights and biases between input and hidden layers.

The basic architecture of RVFL is as shown in Figure 5. Our RVFL design is such that the hidden layer weights W h follow the uniform distribution whose values are present in a given interval [-S, +S], where S is the scaling factor deter­mined during parameter tuning phase of the experimentation process. Therefore, we compute hidden features H with the use of the activation function f given in equation:

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where X is the training data. There are various optimizers that can be em­ployed to calculate or train the output weights. But in random vector functional link (RVFL), two methods are very common which can be deployed to get the ac­curate results. Those methods are Moore Penrose Pseudo inverse and regularized least square. Thus, the only weights that need to be optimised are the output layer weights W o. W o can be optimized through optimizer method as given in (4).

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Here, H concatenates the hidden features as well as input features X, which is followed by the definition of RVFL.

Applying W o and W h on the testing data X s, the predicted values can thus be calculated as:

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where Y s denotes predicted values and X s is the testing data.

The overall overview of the approach is given in Figure 6.

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Figure 6: Workflow for the respiratory motion prediction with RVFL neural net­work

3.2.4 Extreme Learning Machine

Extreme Learning Machine (ELM) [27] developed in 2004 and it can be consid­ered as the variant of RVFL. The main difference between the ELM and RVFL is the absence of the direct link as well as the bias term into the output layer. So in (4), H only represents the hidden features which is followed by the definition of ELM. The output weights of ELM can also be trained by using the aforementioned optimizers (Moore Penrose Psuedo Inverse). The basic structure of the ELM can be seen in Figure 7.

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Figure 7: The basic structure of ELM

3.2.5 Performance measures

For analyzing the performance of the proposed approach (RVFL), we employed root mean square error (RM SE) for different prediction lengths l.If y i (k) de­notes the actual value for a trace i at discrete time index k. Then y i (k + l) rep­resents the actual value at k + l for a trace i and y i (k + l) is representing its corresponding l steps ahead predicted value. Hence, the prediction error e i (k + 1) could be easily computed as:

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Therefore, the RMS prediction error (RMSE i) for a trace i can be computed as:

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where N i denotes the total number of samples in testing data of a trace i.

Further, we also computed the average RMS prediction error averaged across all traces for multiple steps ahead prediction as follows [28]:

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where N l denotes the total number of traces.

By using this performance metric, we compared the accuracy of the RVFL and ELM.

3.3 Results

In this section, we used RVFL for the prediction of respiratory motion. There­after, we explain the implementation of our approach on a data set consisting of 304 respiratory motion traces obtained from a total of 31 patients at Georgetown University Hospital during CyberKnife treatments. The prediction in this work is done for different prediction lengths. RVFL is basically randomized version of functional link neural network and its direct link is employed in this work to get high accuracy in prediction of respiratory motion. Later, we compared RVFL and ELM.

3.3.1 Parameter selection

For multistep ahead prediction of respiratory motion, we applied the exhaustive grid search. The optimal number of hidden neurons where we found the less aver­age RMSE error was at 64 i.e. 0.2275 at 192 ms prediction length which is showed in Figure 8. The same kind of behavior is observed with the prediction length of 384 ms and 576 ms and obtained the less average RMSEs of 304 traces at 64 hidden neurons which are showed in Figures 9 and 10 respectively.

After selecting the optimal number of the hidden neurons, then we also opted the optimal input size for sliding training window. As shown in Figure 11, 45 was

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Figure 8: Average RMSE of RVFL on 304 traces with respect to the different number of hidden neurons at 192 ms

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Figure 9: Average RMSE of RVFL on 304 traces with respect to the different number of hidden neurons at 384 ms

chosen as the optimal sliding window length of input features because of getting the less average RMSE of 304 traces. Then at the last with optimal hidden neurons and sliding window size, we also tried to find the optimal activation function and

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Figure 10: Average RMSE of RVFL on 304 traces with respect to the different number of hidden neurons at 576 ms

Table 2: Training and Testing Average RMSE of 304 respiratory motion traces during different activation functions of RVFL model at prediction length 576 ms

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their training and testing average RMSEs are listed in table 2. It shows that the signum is most fitted activation function to our data. So according to these optimal parameters are given in Table 3, we conducted our experiments using RVFL based models.

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Figure 11: Performance of RVFL model during different sizes of sliding window versus average RMSE of 304 respiratory motion traces at prediction length 576 ms

Table 3: Parameters selection

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3.3.2 Simulation results

In this section, the large database of 304 respiratory motion traces were used to evaluate the performance of the proposed RVFL model. The length of each trace was divided into training and testing data. The first 54 min were used for train­ing while remaining data were used for the testing. The RVFL model is trained for different prediction lengths to predict the respiratory motion. For instance, RVFL training and testing segment of trace-65 is given at prediction length 192 ms in Figure 12. The corresponding errors of the training and testing at the same prediction length can also be observed in Figure 13. Moreover, the RVFL neural network model was tested when prediction length was increased, and obviously, the accuracy would be decreased whenever the prediction length was increased. These results are shown in Figure 14, 15, 16, and 17.

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Figure 12: RVFL Training and Testing of segment of trace-65 at prediction length 192 ms

In Figure 18, the RMSE of each trace is also given for 192 ms, 382 ms, and 576 ms lookahead length.

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Figure 13: RVFL Training and Testing errors of segment of trace-65 at prediction length 192 ms

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Figure 14: RVFL Training and Testing of segment of trace-65 at prediction length 384 ms

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Figure 15: RVFL Training and Testing of segment of trace-65 at prediction length 384 ms

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Figure 16: RVFL Training and Testing of segment of trace-65 at prediction length 576 ms

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Figure 17: RVFL Training and Testing of segment of trace-65 at prediction length 576 ms

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Figure 18: RVFL Training and Testing RMSE of 304 traces at different lengths of 192 ms, 384 ms, and 576 ms

Table 4: Training and Testing average RMSE of 304 respiratory motion traces of RVFL model for 192 ms, 384 ms and 576 ms

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The average RMSE for training and testing of each prediction length for 304 traces are listed in Table 4.

3.3.3 Comparison between RVFL and ELM

In this section, we made the brief comparison between the RVFL and ELM. We have shown the difference between them by applying the algorithms on the 304 respiratory motion traces according to the same above selected parameters for different prediction lengths. In Figure 19, we showed the RVFL and ELM model output. Their errors have been plotted in Figure 20. Their individual RMSE of 304 traces for 192 ms, 384 ms and 576 ms are also given in Figures 21, 22 and 23 respectively.

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Figure 19: Comparison between RVFL and ELM at prediction length of 192 ms at 5.2 Hz

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Figure 20: Comparison between RVFL and ELM errors at prediction length of 192 ms at 5.2 Hz

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Figure 21: Comparison between model performance of RVFL and ELM at pre­diction length of 192 ms

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Figure 22: Comparison between model performance of RVFL and ELM at pre­diction length of 384 ms

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Figure 23: Comparison between model performance of RVFL and ELM at pre­diction length of 576 ms

Table 5: Training and Testing average RMSE of 304 respiratory motion traces of ELM model for 192 ms, 384 ms and 576 ms

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By comparing Table 4 and 5, the performance of the RVFL is quite better than the ELM. The main reason behind having the good accuracy of RVFL against ELM is the direct link. This link will concatenate the hidden features from the hidden nodes as well as the original input (sometimes it is known as reuse) to produce the better result. This link will save the entire RVFL network from the overfitting.

4 Modelling of Respiratory Motion with Empirical Mode Decomposition based Random Vector Functional Link

4.1 Introduction

In previous chapter, we only used the random vector functional link (RVFL) for the respiratory motion prediction. However, the accuracy of RVFL is not sufficient to get the desired results and mitigate the delay from the radiotherapy equipments. In order to resolve this issue, we took the help of hybrid model and tried to get the more accuracy in radiotherapy application. We used the empirical mode decom­position (EMD) based RVFL model which is combined known as EMD-RVFL.

According to the experimental results [21], it is concluded that EMD based models perform better than using the single learning based models. EMD based models used for the various applications including the wind and monthly electric­ity load prediction. EMD also known as Hilbert -Huang transform (HHT), is a method to split the signal into several intrinsic mode functions (IMF) along with the residue. It is basically empirical based technique to get the instantaneous fre­quency information from the highly non-linear and non-stationary data. Therefore, we combined the EMD with RVFL to get the more accuracy.

4.2 Methodology

4.2.1 Empirical Mode Decomposition

Respiratory motion is highly time-varying and non-stationary signal which can be decomposed into various individual components. Thus, in this way, EMD can be very useful to split the signal into various IMF. An IMF is a function that has only one extreme between zero crossings, along with a mean value of zero. After applying EMD, respiratory motion trace is splitted into a set of IMF functions by using following equation:

Abbildung in dieser Leseprobe nicht enthalten

where c i is the i th IMF, r n is the remaining residue, and n is the number of functions which depend upon the original signal.

4.2.2 Hybrid model EMD-RVFL

Following are the steps that need to be implemented in the sequential order to build up the EMD-RVFL structure:

1. Apply the EMD on the traces to decompose the signals into various IMFs and residue.
2. Then make the input in form of the matrix from each IMF and feed it to the RVFL to get the trained models.
3. After that, combine all the outputs from each IMF and again apply the RVFL to train the model.
4. In the last step, apply the trained model (weights) on the testing data to evaluate the performance of the model.

The overall procedure of the above algorithm is given in Figure 24.

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Figure 24: Structure of EMD-RVFL

4.2.3 Performance measures

To evaluate the performance of the EMD-RVFL, we used the performance metric (RMSE), that has already been discussed in chapter 3.

4.3 Results

4.3.1 Parameter selection

We used the same optimal parameters for EMD-RVFL, that we previously found through our rigorous grid search for RVFL which is given in Table 3. Moreover, through different hit and trial approach, we found that with 2 IMF functions of EMD and hidden nodes of 500, where we are getting the better accuracy of EMD- RVFL as compared to the RVFL.

4.3.2 Simulation results

In this section, we used respiratory motion traces, to check the performance of EMD-RVFL for multisteps ahead prediction. Similarly, we used the first 54 min of the traces in training and kept remaining data to evaluate the performance of the model against RVFL.

For example, in Figure 25 and Figure 26 showed the comparison between EMD-RVFL and RVFL. In these figures, it can easily be noticed that EMD-RVFL tried to track the trace more precisely and accurately as compared to the RVFL.

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Figure 25: RVFL Prediction of trace-65 at prediction length of 576 ms

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Figure 26: EMD-RVFL Prediction of trace-65 at prediction length of 576 ms

Table 6: Statistical comparison of EMD-RVFL and RVFL in terms of RMSE of trace-65

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Based on this comparison given in Table 6, we can conclude that the accuracy of EMD-RVFL is better than RVFL.

5 Conclusion and Future Work

In this thesis, we implemented the Random vector functional link (RVFL) for the respiratory motion prediction. 304 respiratory motion traces were used to evalu­ate the prediction performance of the RVFL model. Our analysis with different combinations of activation functions and number of hidden nodes in RVFL iden­tified that the most fitted activation function for respiratory dataset is signum at 64 number of hidden neurons. We have observed from the RVFL performance that, optimal number of hidden neurons is necessary to avoid over-fitting. By compar­ing the results of both RVFL and ELM based on different prediction lengths, we found that the performance of RVFL is better than the ELM. In order to improve the robustness of the model for further steps ahead prediction of respiratory mo­tion, we trained the EMD-RVFL model. It showed the better accuracy as well as the robust tracking of the respiratory motion traces as compared to RVFL. In fu­ture, we will combine this learning based model with mathematical based model to develop the clinical applications to give the early prediction and detection of the various medical diseases.

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[...]

• Authors: Asad Rasheed (Author), Kalyana C. Veluvolu (Author)
• Publication Year: 2022
• Pages: 49
• Catalog Number: V1359064
• ISBN (PDF): 9783346880574
• ISBN (Book): 9783346880581
• Language: English
• Tags: prediction, respiratory, motion, radiotherapy, applications