Phonographic signal with a fractional-order chaotic system: a novel and simple algorithm for analyzing residual arteriovenous access stenosis


To detect the early developmental stages of arteriovenous access (AVA) stenosis in hemodialysis patients, this study explored a stenosis detector based on the Burg method and the fractional-order chaos system (FOCS). The bruit developed by the blood flowing through AVA can be a viable noninvasive strategy for monitoring AVA functions. We used the Burg method of the autoregressive model to estimate the frequency spectra of phonographic signals recorded by an electronic stethoscope in patients’ AVAs and to identify the spectral peaks in the region of 25–800 Hz. The frequency spectra differed significantly between normal and stenosis statuses in AVA. We found that the frequency and amplitude in power spectra analysis varied in accordance with the severity of AVA stenosis. However, the correlation of these parameters for classifying the degree of stenosis is limited when only using the Burg method. Therefore, we used an FOCS to monitor the differing frequency spectra between the normal condition and AVA stenosis. The variances of these two conditions were dynamic errors that were the coupling variables that tracked the responses between the master system and the slave system. A total of 42 patients who had received percutaneous transluminal angioplasty (PTA) for their failing AVAs was recruited for this study. In this study, the dynamic error, Index Ψ, was used to calculate the frequency spectrum redistribution in patients undergoing PTA. In addition, ΔImp was the index used to evaluate improvements in the luminal diameter between pre- and post-PTA. Therefore, we used linear regression to model the relationship between ΔImp and Index Ψ. The findings indicate that the proposed method has enhanced efficiency, especially in the venous anastomosis (V-site). The FOCS is a novel and simple algorithm for analyzing the residual AVA stenosis of PTA treatment.

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  1. 1.

    U S Renal Data System (USRDS) (2011) Annual Data Report: Atlas of Chronic Kidney Disease and End-Stage Renal Disease in the United States. NIDDK 2:294–302

    Google Scholar 

  2. 2.

    Tsai JC, Chen SC, Hwang SJ et al (2010) Prevalence and risk factors for CKD in spouses and relatives of hemodialysis patients. Am J Kidney Dis 55:856–866

    PubMed  Article  Google Scholar 

  3. 3.

    Fillinger MF, Reinitz ER, Schwartz RA et al (1989) Beneficial effects of banding on venous intimal-medial hyperplasia in arteriovenous loop grafts. Am J Surg 11:87–94

    Article  Google Scholar 

  4. 4.

    Vesquez PO, Marco MM, Mandersson B (2009) Arteriovenous fistula stenosis detection using wavelets and support vector machines. Proc IEEE Eng Med Biol Soc 1298–1301

  5. 5.

    Kumbar L, Karim J, Besarab A (2012) Surveillance and monitoring of dialysis access. Int J Nephrol 2012:9

  6. 6.

    Allon M, Robbin ML (2009) Hemodialysis vascular access monitoring: current concepts. Hemodial Int 13(2):153

    PubMed  Article  Google Scholar 

  7. 7.

    Loth F, Fischer PF, Bassiouny HS (2008) Blood flow in end-to-side anastomoses. Annu Rev Fluid Mech 40:367–393

    Article  Google Scholar 

  8. 8.

    Beathard GA (2004) A practitioner’s Guide to Physical Examination of Dialysis Vascular Access, ESRD Network 13

  9. 9.

    Akay YM, Akay M, Welkowitz W et al (1993) Non-invasive acoustical detection of coronary artery disease: a comparative study of signal processing methods. IEEE Trans Bio Med Eng 40(6):571–578

    Article  CAS  Google Scholar 

  10. 10.

    Chen WL, Lin CH, Chen T, Chen PJ, Kan CD (2012) Stenosis detection algorithm using the Burg method of autoregressive model for hemodialysis patients: evaluation of arteriovenous shunt stenosis. J Med Biol Eng. doi:10.5405/jmbe.1173

  11. 11.

    Collomb C (2009) Linear Prediction and Levinson-Durbin Algorithm. Available online at

  12. 12.

    Chen HK (2005) Synchronization of two different chaotic systems: a new system and each of the dynamical systems Lorenz. Chaos, Solitons Fractals 23(5):1245–1251

    Google Scholar 

  13. 13.

    Chen JH (2008) Controlling chaos and chaotification in the Chen–Lee system by multiple time delays. Chaos Solitons Fractals 36(4):843–852

    Google Scholar 

  14. 14.

    Hwang C, Leu JF, Tsay SY (2002) A note on time-domain simulation of feedback fractional-order systems. IEEE Trans Automat Control 47:625–631

    Article  Google Scholar 

  15. 15.

    Ma C, Hori Y (2007) Fractional-order control: theory and applications in motion control. IEEE Ind Electron Mag 1(4):6–16

    Google Scholar 

  16. 16.

    Ge ZM, Hsu MY (2007) Chaos in a generalized Van Der Pol system and in its fractional order system. Chaos, Solitons Fractals 33:1711–1745

    Article  Google Scholar 

  17. 17.

    Chen JH (2008) Controlling chaos and chaotification in the Chen–Lee system by multiple time delays. Chaos, Solitons Fractals 36(4):843–852

    Article  Google Scholar 

  18. 18.

    Chen JH, Chen HK, Lin YK (2009) Synchronization and anti-synchronization coexist in Chen–Lee chaotic systems. Chaos, Solitons Fractals 39(2):707–716

    Article  Google Scholar 

  19. 19.

    Ge ZM, Hsu MY (2007) Chaos in a generalized Van Der Pol system and in its fractional order system. Chaos, Solitons Fractals 33(5):1711–1745

    Article  Google Scholar 

  20. 20.

    Miller KS, Ross B (1993) An introduction to the fractional calculus and fractional differential equations. Wiley, New York

    Google Scholar 

  21. 21.

    Podlubny I (1999) Fractional differential equations. Mathematics in Science and Engineering, vol 198, Academic Press, New York

  22. 22.

    Stroud JS, Berger SA, Saloner D (2000) Influence of stenosis morphology on flow through severely stenotic vessels: implications for plaque rupture. J Biomech 33:443–455

    PubMed  Article  CAS  Google Scholar 

  23. 23.

    van der Linden J, Smits JH, Assink JH, Wolterbeek DW, Zijlstra JJ, de Jong GH, van den Dorpel MA, Blankestijn PJ (2002) Short- and long-term functional effects of percutaneous transluminal angioplasty in hemodialysis vascular access. J Am Soc Nephrol 13(3):715–720

    PubMed  Google Scholar 

  24. 24.

    Andrew M, Forauer R, Eric M, Hoffer K, Karen Homa P (2008) Dialysis access venous stenosis: treatment with balloon angioplasty-1-versus 3-minute inflation times. Radiology 249(1):375–381

    Article  Google Scholar 

  25. 25.

    Akay M (1997) Wavelet applications in medicine. Spectr IEEE 34(5):50–56

    Article  Google Scholar 

  26. 26.

    Akay M, Welkowitz W, Semmlow JL (1991) Application of the ARMA method to acoustic detection of coronary artery disease. Med Biol Eng Comput 29(4):365–372

    PubMed  Article  CAS  Google Scholar 

  27. 27.

    Doyle DJ, Mandell DM, Richardson RM (2002) Monitoring hemodialysis vascular access by digital phonoangiography. Ann Biomed Eng 30(7):982

    PubMed  Article  Google Scholar 

  28. 28.

    Grama M, Olesena JT, Riisa HC (2011) Stenosis detection algorithm for screening of arteriovenous fistulae. In: 15th NBC on biomedical engineering and medical physic, pp 241–244

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This study was supported and conducted by the Multidisciplinary Centre of Excellence for Clinical Trials and Research at National Cheng Kung University Hospital. In addition, this study was supported by the research grant DOH99-TD-B-111-002. We are grateful to Wei-Ming Wang for providing the statistical consulting services from the Biostatistics Consulting Center, National Cheng Kung University Hospital.

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Correspondence to Chung-Dann Kan.

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Chen, WL., Chen, T., Lin, CH. et al. Phonographic signal with a fractional-order chaotic system: a novel and simple algorithm for analyzing residual arteriovenous access stenosis. Med Biol Eng Comput 51, 1011–1019 (2013).

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  • Arteriovenous access (AVA) stenosis
  • Phonographic signal
  • Fractional-order chaotic system (FOCS)
  • Venous anastomosis (V-site)
  • Percutaneous transluminal angioplasty (PTA)