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Respiratory motion induces the limit in delivery accuracy due to the lack of the consideration of the anatomy motion in the treatment planning. Therefore, image-guided radiation therapy (IGRT) system plays an essential role in respiratory motion management and real-time tumor tracking in external beam radiation therapy. The objective of this research is the prediction of dynamic time-series images considering the motion and the deformation of the tumor and to compensate the delay that occurs between the motion of the tumor and the beam delivery. For this, we propose a prediction algorithm for dynamic time-series images. Prediction is performed using principal component analysis (PCA) and multi-channel singular spectral analysis (MSSA). Using PCA, the motion can be denoted as a vector function and it can be estimated by its principal component which is the linear combination of eigen vectors corresponding to the largest eigen values. Time-series set of 320-detector-row CT images from lung cancer patient and kilovolt (kV) fluoroscopic images from a moving phantom were used for the evaluation of the algorithm, and both image sets were successfully predicted by the proposed algorithm. The accuracy of prediction was quite high, more than 0.999 for CT images, whereas 0.995 for kV fluoroscopic images in cross-correlation coefficient value. This algorithm for image prediction makes it possible to predict the tumor images over the next breathing period with significant accuracy.

Respiratory motion management has been a major challenge in radiation therapy especially for lung cancer with the large amplitude of motion in lungs being clinically significant [

Even with the real-time monitoring, there exists a time delay between the beam irradiation and the motion of the target. This is mainly because the adaptive response of a radiotherapy system to a tumor position signal cannot occur instantaneously. Hence the beam cannot follow the target accurately [

Principal component analysis (PCA) or eigen value analysis is a data feature extraction and data representation technique widely used in data analysis and compression [

First, we examined with a four-dimensional CT (4DCT) image set. The CT image is convenient for the assessment of dynamic image prediction including the information of tumor deformation, but is not suitable for the real-time prediction because it is currently impossible to acquire the 4DCT images during treatment. Therefore, second, we examined with a kilovolt (kV) fluoroscopic image set, which can be handled in real time.

For the preliminary study of the image prediction, we employed a 4DCT image set obtained by AcquilionOne^{TM} 320-detector-row CT device (Toshiba). An example of coronal slice used as input image is shown in

For the image prediction, we evaluated the accuracy in the limited view of 4DCT slice referred as large view

4DCT and its region of interest (ROI) i.e. only the tumor and its surrounding area. The pixel size of the large view 4DCT was 140 ´ 300 whereas for the ROI, it was 60 ´ 52.

As second set of input images, kV fluoroscopic images from a linearly driven motion stage phantom were acquired. The phantom and the example of dynamic fluoroscopic images used in this study are illustrated in

The figure shows a mock tumor marked in red solid circle and the marker marked in blue dotted circle. We attempted two cases for the prediction of kV fluoroscopic images; the ROI from the image shown in

The algorithm for dynamic image prediction system is divided into three main steps as explained below.

A set of input images with pixel size

where n is the total number of input images for the training set. Next we calculate the auto-correlation matrix as shown in the Equation (2),

where T refers to transpose. Eigen analysis is then performed on Y resulting,

where V is the eigen vectors and

Multiplying X on both sides, we get,

and this leads to,

Equation (6) shows that the dimension of meaningful eigen vectors can only be considered instead of con- sidering the whole matrix. This is real with the very high correlation of consecutive frames in the time series images. The most dominant characteristics of the image are centralized on the highest eigen vector. Hence, in the equation, we setup the number of principal components as number i which denotes the number of dominant eigen vectors. The p eigen vectors

where

The coefficients calculated from PCA can be used for the prediction of future coefficient estimated by MSSA, which is an extended version to multi-dimensions from singular spectral analysis useful for analyzing non-linear time series [

where arbitrary parameter M is known as the embedded dimension, l is one dimension in L dimensions and N is the number of coefficients using one prediction and

This Equation (10) can further be denoted as Equation (11),

Auto-correlation matrix is defined with the above trajectory matrix and its transpose as,

where,

Eigen analysis is performed as in 2. We choose r (arbitrary number) largest eigen values and corresponding eigen vectors shown as,

Using MSSA, we can predict the future data using this E from the equation for principal components of previous time series data. Actually, we create

This denotes that

where

According to Equation (14) and Equation (15) we can evaluate P as,

We can obtain the L unknown future data by solving the condition and setting back the centering values,

Once the coefficients are predicted, the predicted image can be reformed as an image by multiplying the pre- dicted coefficients and the principal component images. Principal component images are already obtained in Section 2.2.1 by arranging the eigen vectors to two dimensional martrices. The three principal component images in case of whole 4DCT images are illustrated in

In order to quantify the accuracy of the prediction algorithm the cross correlation coefficient was employed to

analyze the similarity between the original and the predicted images. In this study, the cross correlation coefficient was evaluated between the 10 sets of testing images and the predicted images in all the cases of image prediction (large view 4DCT prediction, ROI 4DCT prediction, markerless kV images and with marker kV images).

In 4DCT images, a few principal components were enough to represent the original feature of lung motion and deformation; ^{nd} step for the next ten steps. The predicted coefficient values are in agreement with the original ones. The evaluated image correlation was 0.9998 ± 0.0001 for large-view 4DCT, and 0.9992 ± 0.0002 for ROI 4DCT (

In contrast to 4DCT images, first twenty principal components had to be collected for the precise image prediction in kV fluoroscopic images.

The programming environment was MATLAB 2013A. The calculation time was less than 0.6 sec in all cases by using IntelCore^{TM} 2 Duo CPU P880 @ 2.66 GHz 4.00 GB RAM. For time improvement and comparison, calculation time is analysed using CPU Intel Xeon: E 31225 @ 3.10 GHz RAM: 4:00 GB which led to the improvement of the time by 3 times. The calculation time for each case is illustrated in

This study aims in the development of the prediction algorithm for the possible implementation in image guided lung cancer radiation therapy. To our best knowledge this is the first study which explores the possibility of dynamic tumor tracking with prediction based upon the images. The need of consideration of tumor deformation has been reported using active shape models [

It should be noted that the parameter optimization plays a major role in this algorithm. In case of 4DCT

Input Image | Cross Corr | Calc Time |
---|---|---|

Large view 4DCT | 0.9998 ± 0.0001 | 0.60 sec |

ROI 4DCT | 0.9992 ± 0.0002 | 0.12 sec |

kV (with marker) | 0.9984 ± 0.0017 | 0.53 sec |

kV (without marker) | 0.9957 ± 0.0030 | 0.28 sec |

images, three eigen vectors were enough to predict and reform. Further increase in the number of eign vectors did not have noticeable effects on the results. The reshaped eigen vectors (the principal component images) shown in

Our input kV fluoroscopic images include both tumor and the marker. We have shown the prediction result including the marker (tumor and marker) and without the marker (only tumor). In both cases there is no much change in the correlation coefficient but there is significant reduction in time due to the reduction of the image size (smaller ROI) hence this method eliminates the use of considering markers. It can also be seen from the result in

In order to evaluate the accuracy of this algorithm the cross correlation has been calculated. This study is focused mainly upon the ability of tumor tracking with prediction with maximum accuracy and acceptable computing time rather than the computing time alone. This is because of the recent papers reporting the increasing computational power and the possible acceleration using a GPU-based computer [

Since this dynamic tracking method is still in its preliminary stage we plan to test the accuracy of our algorithm in the kV projection images from the patients. In that case we can consider the deformation of the tumor and some real breathing pattern as in case of our 4DCT images in Section 2.1. Some artifacts and other physical effects are expected which will degrade the quality of image in the patient data. Some pre-processing such as noise removal or image enhancement might be necessary in those cases. We also need to evaluate this algorithm for the projection images in case of the treatment with rotating gantry such as a volumetric modulated arc therapy.

We have developed an algorithm using PCA and MSSA for the prediction of dynamic images of lung tumor during radiation therapy. We have used two different input images (4DCT and kV fluoroscopic images) for the validation of this algorithm. In kV images, we have also shown that including the marker shows no significant change in the prediction accuracy, while the calculation time is significantly reduced. The present result indicated that images were predicted with significant accuracy (more than 99% using correlation coefficient in each case). By using a high performance computer, the calculation time has been improved. Further improvements will be made by the application of the existing algorithm in the patient images acquired during treatment and doing the quantitative analysis for the reduction of target volume which is the ultimate goal of this research.

This research was partially supported by New Eenergy and Industrial Technology Development Organization (NEDO).

Ritu BhusalChhatkuli,KazuyukiDemachi,NaokiMiyamoto,MitsuruUesaka,AkihiroHaga, (2015) Dynamic Image Prediction Using Principal Component and Multi-Channel Singular Spectral Analysis: A Feasibility Study. Open Journal of Medical Imaging,05,133-142. doi: 10.4236/ojmi.2015.53017