Development of motion image prediction method using principal componentanalysis
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Ritu Bhusal Chhatkuli “, Kazuyuki Demachi““, Masaki Kawai', Hiroshi Sakakibara', Kazuma Kamiakastill under investigation. Tumor tracking with fiducial marker is invasive for the patients as there is always a risk of pneumothorax. And localizing tumor based on the surrogates requires a good correlation between the tumor and the surrogate [4].Hence the goal of this study is to predict the future motion image of the tumor in order to improve the image guided radiation therapy. (Fig1.)Introduction : Cancer related death in Japan is increasing yearly and lung cancer has the highest rate of occurrence among all other cancers. The standard treatment is surgery, radiation therapy, chemotherapy or the combination of both chemotherapy and radiation therapy. In modern day radiation therapy precision has been a major challenge, when it comes to a moving organ like lungs, the amplitude of motion can be clinically significant (~2-3cm)[1] so limiting the radiation to the target and sparing the surrounding healthy tissue is always a concern. In order to compensate the tumor motion, various strategies such as like radiation respiration gating, breath hold, beam tracking etc. have been investigated [2]. The breath hold technology is not widely accepted by the patients. Both respiratory gating and beam tracking requires a precise knowledge of tumor position. The advancing technology in image guidance has led to the more improved result for the patients in lung cancer radiation therapy. There are several methods to determine the position of the tumor during the treatment which includes direct fluoroscopic tumor tracking, using fiducial markers or interference of the tumor position from anatomic surrogates such as abdomen [1]. Direct tumor tracking isMaterial and Methods To develop the purposed algorithm time series X-ray images are used as an input. The input data are divided into training set of data and testing set of data.The procedure mainly consists of three parts.i). Principal component calculation using PCAFirst we have number of time series images. Each image is considered as vector In, where N is the number of images. We construct a matrix X for vector I where each row represents a displacement vector of a certain voxel in the lung. Performing a PCA gives the eigen value and eigen vector. We can express X(t) as a linear combination of the eigen vectors obtained from PCA [3]. Eigenvector with highest eigenvalue is the principal component of the matrix. Then the coefficient is calculated as shown in equation (1) below.X-ray detectorPatientIX-ray sourea; (t1,62,tzn......In)=XT(V1, V2 .........;) ......... d)still under investigation. Tumor tracking with fiducial marker is invasive for the patients as there is always a risk of pneumothorax. And localizing tumor based on the surrogates requires a good correlation between the tumor and the surrogate [4].Hence the goal of this study is to predict the future motion image of the tumor in order to improve the image guided radiation therapy. (Figl.)Material and Methods To develop the purposed algorithm time series X-ray images are used as an input. The input data are divided into training set of data and testing set of data.The procedure mainly consists of three parts.i). Principal component calculation using PCAFirst we have number of time series images. Each image is considered as vector In, where N is the number of images. We construct a matrix X for vector I where each row represents a displacement vector of a certain voxel in the lung. Performing a PCA gives the eigen value and eigen vector. We can express X(t) as a linear combination of the eigen vectors obtained from PCA [3]. Eigenvector with highest eigenvalue is the principal component of the matrix. Then the coefficient is calculated as shown in equation (1) below.a;(t?,t2,t3........n)=x““(V1, V2.........,:) .........0)441Here, a is the coefficient, i is the number of principal component, t represents the time, T is the transpose and N is the number of images.ii). Prediction using MSSAThe second part of our method is the prediction part using MSSA. The future coefficient is predicted using multiple channel singular spectral analysis by using the principal coefficient for the previous time series images. Equation (2) shows the future coefficient which are to be used for the reconstruction of future images.a; (tx+1≫t N+29tN+3...............(2)iii). Reconstruction using PCAAfter the prediction of the coefficients by MSSA which is the extension to the multiple dimension from SSA, singular spectral analysis [4]. We reconstruct the new future motion image as shown in equation (3) using the coefficient predicted by MSSA.Istn≫tN+19tN+2,6 N+3 ...............(3)....ai(t)Result and Discussion : Fig 2. shows that the future coefficients were successfully predicted with some minimum error. ai(t), az(t) and az(t) are the coefficients obtained from PCA and successfully predicted using MSSA. We were also able to reconstruct the image with considerable accuracy and time less than 50secs. In addition to the prediction the evaluation of predictability was performed. We50004000al(t)Original3000Predicted20001000az(t)az(t)-1000510 time(t)25az(t)az(t)5time (+)““-442used some input image sequences as testing images to verify the result. The quantitative analysis of the error is less than 3%.Conclusion : We have developed the prediction method using PCA and MSSA. The prediction time is less than 50secs which seems to be quite considerable. As a future task, the reduction of the error and improvement in calculation time for real time prediction needs to be done. We are also considering the sudden abdominal change detection and possibly its prediction for our future works.References : 1). L.I. Cervino et al. Diaphragm as an anatomic surrogate for lung tumor motion. Physics in Medicine and Biology, Volume: 54 Issue (2009) Pages: 3529-3541 2). Lei Ma et al. Modeling and prediction of lung tumor motion for robotic assisted radiotherapy. Proceedings of the EEE/RSJ international conference on intelligent robots and systems. (2007). 3). R. Li, X. Jia, J.H. Lewis, X. Gu, M. Folkerts, C. Men and S.B. Jiang. Real- time volumetric image reconstruction and 3D tumor localization based on a single x-ray projection image for lung cancer radiotherapy. American Association of Physicists in Medicine. 2010.11.18/1.3426002. 4). A Mizuguchi et al. Establish of the prediction system of chest skin motion with SSA method. International journal of applied electromagnetic and mechanics 2010:1529-1533“ “Development of motion image prediction method using principal componentanalysis “ “Ritu Bhusal Chhatkuli, Kazuyuki Demachi,Masaki Kawai,Hiroshi Sakakibara,Kazuma Kamiaka