During radiotherapy treatment for thoracic and abdomen cancers, for example, lung cancers, respiratory motion moves the target tumor and thus badly affects the accuracy of radiation dose delivery into the target. A real-time image-guided technique can be used to monitor such lung tumor motion for accurate dose delivery, but the system latency up to several hundred milliseconds for repositioning the radiation beam also affects the accuracy. In order to compensate the latency, neural network prediction technique with real-time retraining can be used. We have investigated real-time prediction of 3D time series of lung tumor motion on a classical linear model, perceptron model, and on a class of higher-order neural network model that has more attractive attributes regarding its optimization convergence and computational efficiency. The implemented static feed-forward neural architectures are compared when using gradient descent adaptation and primarily the Levenberg-Marquardt batch algorithm as the ones of the most common and most comprehensible learning algorithms. The proposed technique resulted in fast real-time retraining, so the total computational time on a PC platform was equal to or even less than the real treatment time. For one-second prediction horizon, the proposed techniques achieved accuracy less than one millimeter of 3D mean absolute error in one hundred seconds of total treatment time.

Department of Instrumentation and Control Engineering Faculty of Mechanical Engineering Czech Technical University Prague 16607 Prague Czech Republic

Department of Radiological Imaging and Informatics Graduate School of Medicine Tohoku University Sendai 980 8575 Japan

Division on Advanced Information Technology Yoshizawa Laboratory Tohoku University Sendai 980 8578 Japan

See more in PubMed

Hoisak J. D. P., Sixel K. E., Tirona R., Cheung P. C. F., Pignol J.-P. Prediction of lung tumour position based on spirometry and on abdominal displacement: accuracy and reproducibility. Radiotherapy & Oncology. 2006;78(3):339–346. doi: 10.1016/j.radonc.2006.01.008. PubMed DOI

Sharp G. C., Jiang S. B., Shimizu S., Shirato H. Prediction of respiratory tumour motion for real-time image-guided radiotherapy. Physics in Medicine and Biology. 2004;49(3):425–440. doi: 10.1088/0031-9155/49/3/006. PubMed DOI

Ma L., Herrmann C., Schilling K. Modeling and prediction of lung tumor motion for robotic assisted radiotherapy. Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS ’07); November 2007; San Diego, Calif, USA. pp. 189–194. DOI

Li X. A., Keall P. J., Orton C. G. Respiratory gating for radiation therapy is not ready for prime time. Medical Physics. 2007;34(3)86787 PubMed

Isaksson M., Jalden J., Murphy M. J. On using an adaptive neural network to predict lung tumor motion during respiration for radiotherapy applications. Medical Physics. 2005;32(12):3801–3809. doi: 10.1118/1.2134958. PubMed DOI

Demachi K., Zhu H., Ishikawa M., Shirato H. Predictive Simulation of tumor movement for chasing radiotherapy. Journal of the Japan Society of Applied Electromagnetics and Mechanics. 2009;17:222–226.

Yan H., Yin F.-F., Zhu G.-P., Ajlouni M., Kim J. H. Adaptive prediction of internal target motion using external marker motion: a technical study. Physics in Medicine and Biology. 2006;51(1):31–44. doi: 10.1088/0031-9155/51/1/003. PubMed DOI

Ruan D. Kernel density estimation-based real-time prediction for respiratory motion. Physics in Medicine and Biology. 2010;55(5):1311–1326. doi: 10.1088/0031-9155/55/5/004. PubMed DOI

Ruan D. Prospective detection of large prediction errors: a hypothesis testing approach. Physics in Medicine and Biology. 2010;55(13):3885–3904. doi: 10.1088/0031-9155/55/13/021. PubMed DOI

Murphy M. J., Dieterich S. Comparative performance of linear and nonlinear neural networks to predict irregular breathing. Physics in Medicine and Biology. 2006;51:5903–5914. doi: 10.1088/0031-9155/51/22/012. PubMed DOI

Buzurovic I., Podder T. K., Huang K., Yu Y. Tumor motion prediction and tracking in adaptive radiotherapy. Proceedings of the IEEE International Conference on Bioinformatics and Bioengineering (BIBE ’10); June 2010; Philadelphia, Pa, USA. pp. 273–278. DOI

Benchetrit G. Breathing pattern in humans: diversity and individuality. Respiration Physiology. 2000;122(2-3):123–129. doi: 10.1016/S0034-5687(00)00154-7. PubMed DOI

Dieterich S., Tang J., Rodgers J., Cleary K. Sking respiratory motion tracking for stereotactic radiosurgery using the CyberKnife. International Congress Series. 2003;1256:130–136. doi: 10.1016/S0531-5131(03)00477-1. DOI

Sahih A., Haas O. C. L., Goodband J. H., Putra D., Mills J. A., Burnham K. J. Respiratory motion prediction for adaptive radiotherapy. Proceedings of the DVD-ROM IAR & ACD Conference; 2006; Nancy, France.

Homma N., Sakai M., Endo H., Mitsuya M., Takai Y., Yoshizawa M. A new motion management method for lung tumor tracking radiation therapy. WSEAS Transactions on Systems. 2009;8(4):471–480.

Riaz N., Shanker P., Wiersma R., et al. Predicting respiratory tumor motion with multi-dimensional adaptive filters and support vector regression. Physics in Medicine and Biology. 2009;54(19):5735–5748. doi: 10.1088/0031-9155/54/19/005. PubMed DOI

Ichiji K., Homma N., Bukovsky I., Yoshizawa M. Intelligent sensing of biomedical signals: lung tumor motion prediction for accurate radiotherapy. Proceeding of the IEEE Merging Fields Of Computational Intelligence And Sensor Technology (CompSens ’11); April 2011; Paris, France. pp. 35–41. DOI

Murphy M. J. Using neural networks to predict breathing motion. Proceedings of the 7th International Conference on Machine Learning and Applications (ICMLA '08); December 2008; San Diego, Calif, USA. pp. 528–532. DOI

Kakar M., Nyström H., Aarup L. R., Nøttrup T. J., Olsen D. R. Respiratory motion prediction by using the adaptive neuro fuzzy inference system (ANFIS) Physics in Medicine and Biology. 2005;50(19):4721–4728. doi: 10.1088/0031-9155/50/19/020. PubMed DOI

Hornik K., Stinchcombe M., White H. Multilayer feedforward networks are universal approximators. Neural Networks. 1989;2(5):359–366. doi: 10.1016/0893-6080(89)90020-8. DOI

Gupta M. M., Liang J., Homma N. Static and Dynamic Neural Networks: From Fundamentals to Advanced Theory. New Jersey, NJ, USA: John Wiley & Sons; 2003.

Gupta M. M., Homma N., Hou Z.-G., Solo M. G., Bukovsky I. Higher order neural networks: fundamental theory and applications. In: Zhang M., editor. Artificial Higher Order Neural Networks for Computer Science and Engineering: Trends for Emerging Applications. IGI Global; 2010. pp. 397–422.

Gupta M., Bukovsky M., Homma I., Solo M. G. A., Hou Z.-G. Fundamentals of higher order neural networks for modeling and simulation. In: Zhang M., editor. Artificial Higher Order Neural Networks for Modeling and Simulation. chapter 6. IGI Global; 2012. pp. 103–133. DOI

Bukovsky I., Bila J., Gupta M. M., Hou Z.-G., Homma N. Foundation and classification of nonconventional neural units and paradigm of nonsynaptic neural interaction. In: Wang Y., editor. Discoveries and Breakthroughs in Cognitive Informatics and Natural Intelligence. Hershey, Pa, USA: University of Calgary, Calgary, Canada; IGI Publishing; 2009.

Bukovsky I., Bila J. Adaptive evaluation of complex dynamical systems using low-dimensional neural architectures. In: Zhang D., Wang Y., Kinsner W., editors. Advances in Cognitive Informatics and Cognitive Computing. Vol. 323. Springer; 2010. pp. 33–57. (Studies in Computational Intelligence). DOI

Ivakhnenko A. G. Polynomial theory of complex systems. IEEE Transactions on Systems, Man, and Cybernetics. 1971;1(4):364–378.

Nikolaev N. Y., Iba H. Learning polynomial feedforward neural networks by genetic programming and backpropagation. IEEE Transactions on Neural Networks. 2003;14(2):337–350. doi: 10.1109/TNN.2003.809405. PubMed DOI

Nikolaev N. Y., Iba H. Adaptive Learning of Polynomial Networks: Genetic Programming, Backpropagation and Bayesian Methods. Vol. 14. New York, NY, USA: Springer; 2006. (Genetic and Evolutionary Computation).

Shin Y., Ghosh J. The pi-sigma network: an efficient higher-order neural network for pattern classification and function approximation. Proceedings of the International Joint Conference on Neural Networks (IJCNN '91); July 1991; Seattle, Wash, USA. pp. 13–18.

Softky R. W., Kammen D. M. Correlations in high dimensional or asymmetric data sets: Hebbian neuronal processing. Neural Networks. 1991;4(3):337–347. doi: 10.1016/0893-6080(91)90070-L. DOI

Taylor J. G., Coombes S. Learning higher order correlations. Neural Networks. 1993;6(3):423–427. doi: 10.1016/0893-6080(93)90009-L. DOI

Schmidt W., Davis J. Pattern recognition properties of various feature spaces for higher order neural networks. IEEE Transactions on Pattern Analysis and Machine Intelligence. 1993;15(8):795–801. doi: 10.1109/34.236250. DOI

Kosmatopoulos E. B., Polycarpou M. M., Christodoulou M. A., Ioannou P. A. High-order neural network structures for identification of dynamical systems. IEEE Transactions on Neural Networks. 1995;6(2):422–431. doi: 10.1109/72.363477. PubMed DOI

Heywood M., Noakes P. Framework for improved training of Sigma-Pi networks. IEEE Transactions on Neural Networks. 1995;6(4):893–903. doi: 10.1109/72.392251. PubMed DOI

Marquardt D. W. An algorithm for least-squares estimation of nonlinear parameters. SIAM Journal of Applied Mathematics. 1963;11(2):431–441.

Moré J. J. Numerical Analysis. Vol. 630. Berlin, Germany: Springer; 1978. The Levenberg-Marquardt algorithm: implementation and theory; pp. 105–116. (Lecture Notes in Mathematics). DOI

Morgado D. F., Antunes A., Vieira J., Mota A. Implementing the Levenberg-Marquardt algorithm on-line: a sliding window approach with early stopping. Proceedings of the 2nd IFAC Workshop on Advanced Fuzzy/Neural Control; 2004.

Dias F. M., Antunes A., Vieira J., Mota A. M. On-line training of neural networks: a sliding window approach for the Levenberg-Marquardt algorithm. Proceedings of the 1st International Work-Conference on the Interplay Between Natural and Artificial Computation (IWINAC '05); June 2005; Las Palmas, Spain. pp. 577–585. DOI

Ichiji K., Sakai M., Homma N., Takai Y., Yoshizawa M. SU-HH-BRB-10: adaptive seasonal autoregressive model based intrafractional lung tumor motion prediction for continuously irradiation. Medical Physics. 2010;37:3331–3332.

Dias F. M., Antunes A., Vieira J., Mota A. M. On-line training of neural networks: a sliding window approach for the Levenberg-Marquardt algorithm. Proceedings of the 1st International Work-Conference on the Interplay Between Natural and Artificial Computation (IWINAC 2005); June 2005; Las Palmas, Spain. pp. 577–585. DOI

Bukovsky I., Ichiji K., Homma N., Yoshizawa M., Rodriguez R. Testing potentials of dynamic quadratic neural unit for prediction of lung motion during respiration for tracking radiation therapy. Proceedings of the IEEE WCCI International Joint Conference on Neural Networks; July 2010; Barcelona, Spain.

Mandic D. P. A generalized normalized gradient descent algorithm. IEEE Signal Processing Letters. 2004;11(2):115–118. doi: 10.1109/LSP.2003.821649. DOI

Widrow B., Stearns S. D. Adaptive Signal Processing. Englewood Cliffs, NJ, USA: Prentice-Hall; 1985.

Bukovsky I., Homma N., Cejnek M., Ichiji K. Study of learning entropy for novelty detection in lung tumor motion prediction for target tracking radiation therapy. Proceedings of the International Joint Conference on Neural Networks; 2014; Beijing, China.