Patolojik Dinlenme Tremorlerinin Kompleks Düzlemde Adaptif Tahmini

Öz

Bu çalışmada, Parkinson hastalarında sıklıkla görülen patolojik dinlenme tremorlerinin kompleks düzlemde adaptif tahmini gerçekleştirilmiştir. Bu kapsamda, ilk olarak anlık olarak ölçülen patolojik “sağ el ve sol el” veya “sağ bacak ve sol bacak” tremorleri kompleks düzlemde ifade edilmiş ve ardından, bu kompleks-değerli patolojik tremorler, bir-adım-ileri kesin linear (strcitly linear, SL) ve geniş linear (Widely linear, WL) tabanlı tahmin ediciler vasıtasıyla adaptif olarak tahmin edilmiştir. Burada, SL tabanlı tahmin edici, kompleks-değerli en küçük ortalama kare (Complex-valued least mean square, CLMS) algoritması ile eğitilirken, WL tabanlı tahmin edici ise artırılmış CLMS (Augmented CLMS) algoritması ile eğitilmiştir. Tahmin edicilerin başarımları, gerçek dünya verisi olan patolojik dinlenme tremorleri üzerinde mutlak hata ve tahmin kazancı açısından incelenmiştir. Yapılan benzetim sonuçları; kompleks-değerli patolojik dinlenme tremorlerinin dairesel olmayan davranış sergilediğini ve bu yüzden de WL tabanlı tahmin edicinin, SL versiyonuna kıyasla daha üstün bir başarım sergilediğini ortaya koymuştur.

Anahtar Kelimeler

• Parkinson hastalığı
• Dinlenme Tremorü
• Kompleks Düzlem
• Adaptif Tahmin
• Parkinson hastalığı, Dinlenme Tremorü, Kompleks Düzlem, Adaptif Tahmin

Adaptive Prediction of Pathological Resting Tremors in the Complex Domain

Öz

In this study, adaptive estimation of pathological resting tremors, which is frequently encountered in Parkinson’s patients, is performed in the complex domain. In this context, pathological “right hand and left hand” or “right leg and left leg” tremors, which were measured instantaneously, are first expressed in the complex domain. Then, these complex-valued pathological tremors are predicted adaptively using one-step-ahead strictly linear (SL) and widely linear (WL) based predictors. Here, the SL based predictor is trained by the Complex-valued least mean square (CLMS) algorithm, while the WL based predictor is trained by the augmented CLMS (ACLMS) algorithm. The performances of these predictors were examined in terms of absolute error and prediction gain on pathological resting tremors as real-world data. Simulation results reveal that complex-valued pathological resting tremors exhibit non-circular behavior and thus the WL based predictor outperforms the SL version.

Anahtar Kelimeler

• Parkinson’s disease
• Resting Tremor
• Complex Domain
• Adaptive Prediction
• Parkinson’s disease, Resting Tremor, Complex Domain, Adaptive Prediction

Kaynakça

1. Adali ,T., Haykin, S. 2010. Adaptive Signal Processing: Next Generation Solutions, Wiley: IEEE Press.
2. Adali, T., Calhoun, V. D.2007. “Complex ICA of medical imaging data”, IEEE Signal Proc. Mag., 24(5),136–139.
3. Adali, T., Schreier, P. J., Scharf,L. L. 2011. “Complex-valued signal processing: The proper way to deal with impropriety” , IEEE Trans. Signal Process., 59(11), 5101–5125.
4. Atashzar, S.F., Shahbazi, M., Samotus, O., Tavakoli, M., Jog, M.S. and Patel, R.V. (2016) . Characterization of Upper-Limb Pathological Tremors: Application to Design of An Augmented Haptic Rehabilitation System. IEEE J. Sel. Topics Signal Process., 10(5), pp. 888-903.
5. Elble, R. and Koller, W. (1990). Tremor, Johns Hopkins University Press, Baltimore,USA, (MD thesis).
6. Elble, R.J. (1997). The pathophysiology of tremor, in: R.L. Watts, W.C. Koller (Eds.), Movement Disorders: Neurologic Principles and Practice,McGraw-Hill, New York, pp. 405–417.
7. Goh, S. L., Chen, M. , Popovic,D. H., Aihara, K. , Obradovic, D., Mandic, D. P. 2006. “Complex-valued forecasting of wind profile,” Renewable Energy, 31, 1733–1750.
8. Javidi,S., Goh,S. L., Pedzisz, M., Mandic,D. P. 2008. “The augmented complex least mean square algorithm with application to adaptive prediction problems”, in Proc. 1st IARP Workshop Cogn. Inform. Process., 54–57.

9. Jelfs,B., Mandic, D. P., Douglas, S. C. 2012. “An adaptive approach for the identification of improper complex signals,” Signal Process., 92, 335–344.
10. Khalili, A., Rastegarnia, A., Bazzi, W. M., Yang,Z. 2014. “Derivation and analysis of incremental augmented complex leastmean square algorithm” , IET Signal Process., 9(4), 312–319.
11. Mandic, D. P., Goh, S. L. 2009. Complex Valued Nonlinear Adaptive Filters: Noncircularity Widely Linear and Neural Models. United Kingdom: Wiley.
12. Maneski, L. P. et al. (2011). Electrical stimulation for the suppression of pathological tremor. Medical and Biological Engineering and Computing, 49(10), pp. 1187–1193.
13. Mengüç, E. C., Çınar, S., Xiang, M., & Mandic, D. P. (2021). Online Censoring Based Weighted-Frequency Fourier Linear Combiner for Estimation of Pathological Hand Tremors. IEEE Signal Processing Letters, 28, 1460-1464.
14. Mengüç, E.C ve Rezayi, N. (2019). Estimation of Pathological Hand Signals by Fourier Linear Combiner Based Online Censoring LMS Algorithm, in: IEEE 27.Sinyal İşleme ve İletişim Uygulamaları Kurultayı. Sivas. pp. 1-4.
15. Mengüç, E.C., Acır, N. 2017. “An augmented complex-valued Lyapunov stability theory based adaptive filter algorithm,” Signal Processing., 137, 10–21.
16. Mengüç, E.C., Acır, N. 2018. “An augmented complex-valued least-mean kurtosis algorithm for the filtering of noncircular signals,” IEEE Transactions on Signal Processing, 66(2), 438-448.
17. O’Connor, R. J. and Kini, M. U. (2011). Non-pharmacological and nonsurgical interventions for tremor: a systematic review. Parkinsonism and Related Disorders, 17(7), pp. 509–515.
18. Ollila, E. (2008). On the circularity of a complex random variable. IEEE Signal Processing Letters, 15, 841-844. Picinbono, B. , Chevalier, P. 1995. “Widely linear estimation with complex data,” IEEE Trans. Signal Process., 43(8),2030– 2033.
19. Reeke, G. N. 2005. “Modeling in the Neurosciences: From Biological Systems to Neuromimetic Robotics”, CRC Press, [online] Available: https://www.motusbioengineering.com/.
20. Rezayi, N. and Mengüç, E. C. (2018) Performances of LMS-based adaptive Fourier linear combiners on the estimation of pathological hand tremors. in: National Conf. on Electr. Electron. and Biomed. Engineering, pp. 543-547.
21. Riviere, C. N. and Thakor, N. V. (1996). Modeling and canceling tremor in human-machine interfaces. in: IEEE Eng. Med., Biol. Mag., 15(3), pp. 29– 36.
22. Riviere, C. N., Rader, R. S. and Thakor, N. V. (1998). Adaptive cancelling of physiological tremor for improved precision in microsurgery. in: IEEE Trans. Biomed. Engineering, 45(7), pp. 839–846.
23. Riviere, C.N., Ang, W.T. and Khosla, P.K. (2003). Toward active tremor canceling in handheld microsurgical instruments. IEEE Trans. Robot. Automat. 19(5), pp. 793–800.
24. Riviere,C. N., Reich, S. G. and Thakor, N. V. (1997)Adaptive fourier modeling for quantification of tremor1. Journal of Neuroscience Methods, vol. 74, no. 1, pp. 77–87.
25. Rocon, E., Belda-Lois, J., Ruiz, A., Manto, M., Moreno, J. C. and Pons, J. (2007a). Design and validation of a rehabilitation robotic exoskeleton for tremor assessment and suppression. in: IEEE Transactions on Neural Systems and Rehabilitation Engineering, 15(3), pp. 367–378.
26. Rocon, E., Manto, M., Pons, J., Camut, S. and Belda, J. M. (2007b). Mechanical suppression of essential tremor. The Cerebellum, 6(1), pp. 73–78.
27. Schreier ,P. J., Scharf, L. L. 2010. Statistical Signal Processing of Complex- Valued Data: The Theory of Improper and Noncircular Signals (1.Basım). Cambridge, U.K.: Cambridge Univ. Press.
28. Stott, A., Kanna, S., Mandic, D. P. 2018. "Widely linear complex partial least squares for latent subspace regression", Signal Processing, 152, 350-362.
29. Vaz, C., Kong, X. and Thakor, N. (1994). An adaptive estimation of periodic signals using a Fourier linear combiner. in: IEEE Trans. Signal Process., 42(1), pp. 1-10.
30. Veluvolu, K. and Ang, W. (2010). Estimation and filtering of physiological tremor for real-time compensation in surgical robotics applications. The International Journal of Medical Robotics and Computer Assisted Surgery, 6(3), pp. 334–342.
31. Veluvolu, K. C., Tan, U.-X., Latt, W. T., Shee, C. and Ang, W. T. (2007). Bandlimited multiple fourier linear combiner for real-time tremor compensation. in: IEEE Annual Engineering in Medicine and Biology Society (EMBS) Conference, pp. 2847– 2850. Veluvolu, K., Latt, W. and Ang, W. (2010). Double adaptive bandlimited multiple fourier linear combiner for real-time estimation/filtering of physiological tremor. Biomedical Signal Processing and Control, 5(1), pp. 37–44.
32. Wang, S., Gao, Y., Zhao, J. and Cai, H. (2014). Adaptive sliding bandlimited multiple fourier linear combiner for estimation of pathological tremor, Biomedical Signal Processing and Control, 10, pp. 260– 274.
33. Widrow, B. , McCool, J. , Ball, M. 1975. “The complex LMS algorithm” , Proceedings of the IEEE, 63(4), 719–720.
34. Xia, Y., Douglas, S.C., Mandic, D.P. 2012. “Adaptive frequency estimation in smart grid applications: exploiting noncircularity and widely linear adaptive estimators” , IEEE Signal Process. 29(5), 44–54 .
35. Xu, L. , Pearlson, G. D., Calhoun, V. D. 2008 “Joint source based morphometry to identify sources of gray matter and white matter relative differences in schizophrenia versus healthy controls ” In Proc. ISMRM, Toronto.