Skip to main content
Log in

Correlation Dimension Analysis of Doppler Signals in Children with Aortic Valve Disorders

  • Original Paper
  • Published:
Journal of Medical Systems Aims and scope Submit manuscript

Abstract

In this study, the correlation dimension analysis has been applied to the aortic valve Doppler signals to investigate the complexity of the Doppler signals which belong to aortic stenosis (AS) and aortic insufficiency (AI) diseases and healthy case. The Doppler signals of 20 healthy subjects, ten AS and ten AI patients were acquired via the Doppler echocardiography system that is a noninvasive and reliable technique for assessment of AS and AI diseases. The correlation dimension estimations have been performed for different time delay values to investigate the influence of time delay on the correlation dimension calculation. The correlation dimension of healthy group has been found lower those found in AI and AS disorder groups and the correlation dimension of AS group has also been found higher than those found in AI group, significantly. The results of this study have indicated that the aortic valve Doppler signals exhibit high level chaotic behaviour in AI and AS diseases than healthy case. Additionally, the correlation dimension analysis is sensitive to the time delay and has successfully characterized the blood flow dynamics for proper time delay value. As a result, the correlation dimension can be used as an efficient method to determine the healthy or pathological cases of aortic valve.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Glass, L., and Kaplan, D. T., Time series analysis of complex dynamics in physiology and medicine. Med. Prog. Technol. 19:115, 1993.

    Google Scholar 

  2. Haykin, S., and Li, X. B., Detection of signals in chaos. Proc. IEEE. 83:95, 1995. doi:10.1109/5.362751.

    Article  Google Scholar 

  3. Wagner, C. D., and Persson, P. B., Chaos in the cardiovascular system: an update. Cardiovasc. Res. 40:257, 1998. doi:10.1016/S0008-6363(98)00251-X.

    Article  Google Scholar 

  4. Akay, M., Nonlinear biomedical signal processing, volume 2: dynamic analysis and modelling. IEEE Press Series on Biomedical Engineering, New York, 2000.

    Book  Google Scholar 

  5. Stefanovska, A., and Bracic, M., Reconstructing cardiovascular dynamics. Control Eng. Pract. 7:161, 1999. doi:10.1016/S0967-0661(98)00185-3.

    Article  Google Scholar 

  6. Otto, C. M., Valvular heart disease. W.B. Saunders, Pennsylvania, 1999.

    Google Scholar 

  7. Nishimura, R. A., Aortic valve disease. Circulation. 106:770, 2002. doi:10.1161/01.CIR.0000027621.26167.5E.

    Article  Google Scholar 

  8. ACC/AHA, Practice guidelines for the management of patients with valvular heart disease: Executive Summary. A report of the American College of Cardiology/American Heart Association Task Force on Practice Guidelines (Writing committee to revise the 1998 guidelines fort he management of patients with valvular heart disease). J. Am. Coll. Cardiol. 48:598, 2006. doi:10.1016/j.jacc.2006.05.030.

    Article  Google Scholar 

  9. DeGroff, C. G., Doppler echocardiography. Pediatr. Cardiol. 23:307, 2002. doi:10.1007/s00246-001-0196-7.

    Article  Google Scholar 

  10. Hatle, L., and Angelsen, B., Doppler ultrasound in cardiology physical principles and clinical applications. Lea and Febiger, Philadelphia, USA, 1982.

    Google Scholar 

  11. Hoskins, P. R., McDiken, W. N., and Allan, P. L., Haemodynamics and blood flow. In: Allan, P. L., Dubbins, P. A., Pozniak, M. A., and McDiken, W. N. (Eds.), Clinical Doppler Ultrasound. London: Churchill Livingstone, p. 27, 2000.

    Google Scholar 

  12. Cannon, S. R., Richards, K. L., and Rollwit, W. T., Digital Fourier technique in the diagnosis and quantification of aortic stenosis with pulsed-Doppler echocardiography. J. Clin. Ultrasound. 10:101, 1982. doi:10.1002/jcu.1870100303.

    Article  Google Scholar 

  13. Güler, İ., Kara, S., Güler, N. F., and Kiymik, M. K., Application of autoregressive and fast Fourier transform spectral analysis to tricuspid and mitral valve stenosis. Comput. Methods Programs Biomed. 49:29, 1996. doi:10.1016/0169-2607(95)01702-X.

    Article  Google Scholar 

  14. Güler, İ., Hardalaç, F., and Müldür, S., Determination of aorta failure with the application of FFT, AR and wavelet methods to Doppler technique. Comput. Biol. Med. 32:435, 2001. doi:10.1016/S0010-4825(02)00021-5.

    Article  Google Scholar 

  15. Turkoglu, I., Arslan, A., and Ilkay, E., An intelligent system for diagnosis of the heart valve diseases with wavelet packet neural networks. Comput. Biol. Med. 33:319, 2003. doi:10.1016/S0010-4825(03)00002-7.

    Article  Google Scholar 

  16. Barişçi, N., Topal, E., Hardalaç, F., and Güler, İ., Classification of aorta insufficiency and stenosis using neuro-fuzzy system. J. Med. Syst. 29:155, 2005. doi:10.1007/s10916-005-3003-9.

    Article  Google Scholar 

  17. Amit, G., Gavriely, N., Lessick, J., and Intrator, N., Automatic extraction of physiological features from vibro-acoustic heart signals: correlation with echo-Doppler, 32nd Annual International Conference on Computers in Cardiology 32, 299. Lyon, France, 2005.

    Google Scholar 

  18. Kara, S., Classification of mitral stenosis from Doppler signals using short time Fourier transform and artificial neural networks. Exp. Syst. Appl. 31:229, 2007.

    MathSciNet  Google Scholar 

  19. Keunen, R. W. M., Vliegen, J. H. R., Stam, C. J., and Tavy, D. L., Nonlinear transcranial Doppler analysis demonstrates age-related changes of cerebral hemodynamics. Ultrasound Med. Biol. 22:383, 1996. doi:10.1016/0301-5629(96)00035-X.

    Article  Google Scholar 

  20. Güler, İ., and Übeyli, E. D., Detecting variability of internal carotid arterial Doppler signals by Lyapunov exponents. Med. Eng. Phys. 26:763, 2004. doi:10.1016/j.medengphy.2004.06.007.

    Article  Google Scholar 

  21. Ozturk, A., and Arslan, A., Classification of transcranial Doppler signals using their chaotic invariant measures. Comput. Methods Programs Biomed. 86:171, 2007. doi:10.1016/j.cmpb.2007.02.004.

    Article  Google Scholar 

  22. Abarbanel, H. D. I., Brown, R., Sidorowich, J. J., and Tsimring, L. S., The analysis of observed chaotic data in physical systems. Rev. Mod. Phys. 65:1331, 1993. doi:10.1103/RevModPhys.65.1331.

    Article  MathSciNet  Google Scholar 

  23. Parlitz, U., Nonlinear time series analysis. In: Suykens, J. A. K., and Vandewalle, J. (Eds.), Nonlinear Modelling—Advanced Black-Box Techniques. Kluwer: Academic, p. 209, 1998.

    Google Scholar 

  24. Hentschel, H. G. E., and Procaccia, I., The infinite number of generalized dimensions of fractals and strange attractors. Physica D. 8:435, 1983. doi:10.1016/0167-2789(83)90235-X.

    Article  MathSciNet  MATH  Google Scholar 

  25. Grassberger, P., and Procaccia, I., Measuring the strangenes of strange attractors. Physica D. 9:189, 1983. doi:10.1016/0167-2789(83)90298-1.

    Article  MathSciNet  MATH  Google Scholar 

  26. Carvajal, R., Wessel, N., Vallverdu, M., Caminal, P., and Voss, A., Correlation dimension analysis of heart rate variability in patients with dilated cardiomyopathy. Comput. Methods Programs Biomed. 78:133, 2005. doi:10.1016/j.cmpb.2005.01.004.

    Article  Google Scholar 

  27. Evans, D. H., McDicken, W. N., Skidmore, R., and Woodcock, J. P., Doppler ultrasound: physics, instrumentation and clinical applications. Chichester, Wiley, 1989.

    Google Scholar 

  28. Sigel, B., A brief history of Doppler ultrasound in the diagnosis of peripheral vascular disease. Ultrasound Med. Biol. 24:169, 1998. doi:10.1016/S0301-5629(97)00264-0.

    Article  Google Scholar 

  29. Papadimitriou, S., and Bezerianos, A., Nonlinear analysis of the performance and reliability of wavelet singularity detection based denoising for Doppler ultrasound fetal heart rate signals. Int. J. Med. Inform. 53:43, 1999. doi:10.1016/S1386-5056(98)00102-6.

    Article  Google Scholar 

  30. Zhang, Y., Wang, Y., Wang, W., and Liu, B., Doppler ultrasound signal denoising based on wavelet frames. IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 48:709, 2001. doi:10.1109/58.920698.

    Article  Google Scholar 

  31. Donoho, D. L., De-noising by soft-thresholding. IEEE Trans. Inf. Theory. 41:613, 1995. doi:10.1109/18.382009.

    Article  MathSciNet  MATH  Google Scholar 

  32. Daubechies, I., Ten lectures on wavelets. SIAM, Philadelphia, PA, 1992.

    MATH  Google Scholar 

  33. Donoho, D. L., and Johnstone, I. M., Ideal spatial adaptation via wavelet shrinkage. Biometrika. 81:425, 1994. doi:10.1093/biomet/81.3.425.

    Article  MathSciNet  MATH  Google Scholar 

  34. William, G. P., Chaos Theory Tamed. Taylor and Francis, London, 1997.

    Google Scholar 

  35. Takens, F., Detecting strange attractors in turbulence. Lect. Notes Math. 898:366, 1981. doi:10.1007/BFb0091924.

    Article  MathSciNet  Google Scholar 

  36. Fraser, A. M., and Swinney, H. L., Independent coordinates for strange attractors from mutual information. Phys. Rev. A. 33:1134, 1986. doi:10.1103/PhysRevA.33.1134.

    Article  MathSciNet  MATH  Google Scholar 

  37. Sauer, T., Yorke, J., and Casdagli, M., Embedology. J. Stat. Phys. 65:579, 1994. doi:10.1007/BF01053745.

    Article  MathSciNet  Google Scholar 

  38. Theiler, J., Estimating fractal dimension. J. Opt. Soc. Am. A. 7:1055, 1990. doi:10.1364/JOSAA.7.001055.

    Article  MathSciNet  Google Scholar 

  39. Merkwirth, C., Partliz, U., and Lauterborn, W., TSTOOL—A software package for nonlinear time series analysis. Proc. Int. Workshop on Advanced Black-Box Techniques for Nonlinear Modelling (Katholieke Universiteit, Leuven, Belgium, July 8–10) p. 144, 1998.

  40. Ding, M., Grebogi, C., Ott, E., Sauer, T., and Yorke, J. A., Estimating correlation dimension from chaotic time series: when does plateau occur? Physica D. 69:404, 1993. doi:10.1016/0167-2789(93)90103-8.

    Article  MathSciNet  MATH  Google Scholar 

  41. Eckmann, J. P., and Ruelle, D., Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems. Physica D. 56:185, 1992. doi:10.1016/0167-2789(92)90023-G.

    Article  MathSciNet  MATH  Google Scholar 

  42. Kantz, H., and Schreiber, T., Nonlinear time series analysis, 2nd edition. Cambridge University Press, Cambridge, 2003.

    Book  Google Scholar 

  43. May, P., Arrouvel, C., Revol, M., Servant, J. M., and Vicaut, E., Detection of hemodynamic turbulence in experimental stenosis: an in vivo study in the rat carotid artery. J. Vasc. Res. 39:21, 2002. doi:10.1159/000048990.

    Article  Google Scholar 

  44. Parthimos, D., Osterloh, K., Pires, A. R., and Griffith, T. M., Deterministic nonlinear characteristics of in vivo blood flow velocity and arteriolar diameter fluctuations. Phys. Med. Biol. 49:1789, 2004. doi:10.1088/0031-9155/49/9/014.

    Article  Google Scholar 

  45. Almog, Y., Oz, O., and Akselrod, S., Correlation dimension estimation: Can this nonlinear description contribute to the characterization of blood pressure control in rats? IEEE Trans. Biomed. Eng. 46:535, 1999. doi:10.1109/10.759054.

    Article  Google Scholar 

  46. Theiler, J., Statistical precision of dimension estimators. Phys. Rev. A. 41:3038, 1990. doi:10.1103/PhysRevA.41.3038.

    Article  Google Scholar 

  47. Young, J. B., Quinones, M. A., Waggoner, A. D., and Miller, R. R., Diagnosis and quantification of aortic stenosis with pulsed Doppler echocardiography. Am. J. Cardiol. 45:987, 1980. doi:10.1016/0002-9149(80)90167-8.

    Article  Google Scholar 

  48. Yearwood, T. L., Misbach, G. A., and Chandran, K. B., Experimental fluid dynamics of aortic stenosis in a model of human aorta. Clin. Physiol. Meas. 10:11, 1989. doi:10.1088/0143-0815/10/1/002.

    Article  Google Scholar 

  49. Ruelle, D., and Takens, F., On the nature of turbulence. Commun. Math. Phys. 20:167 and 23, 343, 1971.

    Article  MathSciNet  MATH  Google Scholar 

  50. Barclay, K. D., Klassen, G. A., and Young, C., A method for detecting chaos in canine myocardial microcirculatory red cell flux. Microcirculation. 7:335, 2000. doi:10.1038/sj.mn.7300116.

    Google Scholar 

  51. Schulz, S., Bauernschmitt, R., Schwarzhaupt, A., Vahl, C. F., and Kiencke, U., Nonlinear dynamic analysis of hemodynamic signals for identifying transitions between ventriculoarterial coupling states. Comput. Cardiol. 26:507, 1999.

    Google Scholar 

Download references

Acknowledgement

The authors would like to thank Prof. Dr. N. Kürşad Tokel the cardiologist of Pediatric Cardiology Department of Başkent University Ankara Hospital for recording data and his contributions.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to N. Fatma Güler.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yılmaz, D., Güler, N.F. Correlation Dimension Analysis of Doppler Signals in Children with Aortic Valve Disorders. J Med Syst 34, 931–939 (2010). https://doi.org/10.1007/s10916-009-9308-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10916-009-9308-3

Keywords

Navigation