Advertisement

ARFIMA-GARCH Modeling of HRV: Clinical Application in Acute Brain Injury

  • Rute Almeida
  • Celeste Dias
  • Maria Eduarda Silva
  • Ana Paula RochaEmail author
Chapter

Abstract

In the last decade, several HRV based novel methodologies for describing and assessing heart rate dynamics have been proposed in the literature with the aim of risk assessment. Such methodologies attempt to describe the non-linear and complex characteristics of HRV, and hereby the focus is in two of these characteristics, namely long memory and heteroscedasticity with variance clustering. The ARFIMA-GARCH modeling considered here allows the quantification of long range correlations and time-varying volatility. ARFIMA-GARCH HRV analysis is integrated with multimodal brain monitoring in several acute cerebral phenomena such as intracranial hypertension, decompressive craniectomy and brain death. The results indicate that ARFIMA-GARCH modeling appears to reflect changes in Heart Rate Variability (HRV) dynamics related both with the Acute Brain Injury (ABI) and the medical treatments effects.

Notes

Acknowledgements

This work was supported in part by Portuguese funds through CIDMA UID/MAT/04106/2013 and CMUP UID/MAT/00144/2013, funded by the Portuguese Foundation for Science and Technology (FCT -Fundação para a Ciência e a Tecnologia), projects TEC2013-42140-R and TIN2014-53567-R from the MINECO with European Regional Development Fund (FEDER), Spain, and by Grupo Consolidado BSICoS (T-96) from DGA (Aragón, Spain) and European Social Fund (EU).

References

  1. 1.
    Almeida, R., Gouveia, S., Rocha, A.P., Pueyo, E., Martínez, J.P., Laguna, P.: Exploring QT variability dependence from heart rate in coma and brain death on pediatric patients. IEEE Trans. Biomed. Eng. 53, 1317–1329 (2006)CrossRefPubMedGoogle Scholar
  2. 2.
    Almeida, R., Silva, M.J., Rocha, A.P.: Exploring QT variability dependence from heart rate in coma and brain death on pediatric patients. In: Proceedings of Computing in Cardiology Conference (CinC), 2013, pp. 61–64 (2013)Google Scholar
  3. 3.
    Baillie, R.T., Cecen, A.A., Erkal, C.: Normal heartbeat series are nonchaotic, nonlinear, and multifractal: new evidence from semiparametric and parametric tests. Chaos 19, 028503 (2009)CrossRefPubMedGoogle Scholar
  4. 4.
    Beran, J., Feng, Y., Ghosh, S., Kulik, R.: Statistics for Long-Memory Processes: Probabilistic Properties and Statistical Methods. Springer, New York (2012)Google Scholar
  5. 5.
    Bianchi, A.M., Mainardi, L.T., Cerutti, S.: Time-frequency analysis of biomedical signals. Trans. Inst. Meas. Control 22, 215–230 (2000)Google Scholar
  6. 6.
    Biswas, A.K., Scott, W.A., Sommerauer, J.F., Luckett, P.M.: Heart rate variability after acute traumatic brain injury in children. Crit. Care Med. 28(12), 3907–3912 (2000)CrossRefPubMedGoogle Scholar
  7. 7.
    Bolea, J., Almeida, R., Laguna, P., Sörnmo, L., Martínez, J.P.: BioSigBrowser, biosignal processing interface. In: Final Program and Abstract Book 9th International Conference on Information Technology and Applications in Biomedicine, ITAB 2009, Art. No. 5394301 (2009)Google Scholar
  8. 8.
    Bollerslev, T.: Generalized autoregressive conditional heteroscedasticity. J. Econ. 31, 307–327 (1986)CrossRefGoogle Scholar
  9. 9.
    Buchman, T.G., Stein, P.K., Goldstein, B.: Heart rate variability in critical illness and critical care. Curr. Opin. Crit. Care 8(4), 311–315 (2002)CrossRefPubMedGoogle Scholar
  10. 10.
    Dias, C., Maia, I., Cerejo, A., Varsos, G., Smielewski, P., Paiva, J.A., Czosnyka, M.: Pressures, flow, and brain oxygenation during plateau waves of intracranial pressure. Neurocrit. Care 21(1), 124–32 (2014)CrossRefPubMedGoogle Scholar
  11. 11.
    Dias, C., Silva, M.J., Pereira, E., Monteiro, E., Maia, I., Barbosa, S., Silva, S., Honrado, T., Cerejo, A., Aries, M.J.H., Smielewski, P., Paiva, J.A., Czosnyka, M.: Optimal cerebral perfusion pressure management at bedside: a single-center pilot study. Neurocrit. Care 23(1), 92–102 (2015)CrossRefPubMedGoogle Scholar
  12. 12.
    Dias, C., Almeida, R., Vaz Ferreira, A., Silva, J., Monteiro, E., Cerejo, A., Rocha, A.P.: Heart rate variability and multimodal brain monitoring before and after decompressive craniectomy in traumatic brain injury. Intensive Care Med. Exp. 4(Suppl 1), 30:209 (2016)Google Scholar
  13. 13.
    Gang, Y., Malik, M.L.: Heart rate variability in critical care medicine. Curr. Opin. Crit. Care 8(5): 371–375 (2002)CrossRefPubMedGoogle Scholar
  14. 14.
    Goldberger, A.L., Amaral, L.A.N., Glass, L., Hausdorff, J.M., Ivanov, P.C., Mark, R.G., Mietus, J.E., Moody, G.B., Peng, C.K., Stanley, H.E.: Physiobank, physiotoolkit and physionet: components of a new research resource for complex physiologic signals. Circulation 101, e215–e220 (2000)CrossRefPubMedGoogle Scholar
  15. 15.
    Haji-Michael, P.G., Vincent, J.L., Degaute, J.P., van de Borne, P.: Power spectral analysis of cardiovascular variability in critically ill neurosurgical patients. Crit. Care Med. 28(7), 2578–2583 (2000)CrossRefPubMedGoogle Scholar
  16. 16.
    Hosking, J.R.M.: Fractional differencing. Biometrika 68, 165–176 (1981)CrossRefGoogle Scholar
  17. 17.
    Hu, Y.M., Tsoukalas, C.: Conditional volatility properties of sleep-disordered breathing. Comput. Biol. Med. 36(3), 303–312 (2006)CrossRefPubMedGoogle Scholar
  18. 18.
    Hurvich, C.M., Ray, B.K.: Estimation of the memory parameter for nonstationary or noninvertible fractionally integrated processes. J. Time Ser. Anal. 16, 17–41 (1995)CrossRefGoogle Scholar
  19. 19.
    Kahraman, S., Dutton, R.P., Hu, P., Stansbury, L., Xiao, Y., Stein, D.M., Scalea, T.M.: Heart rate and pulse pressure variability are associated with intractable intracranial hypertension after severe traumatic brain injury. J. Neurosurg. Anesthesiol. 22(4), 296–302 (2010)CrossRefPubMedGoogle Scholar
  20. 20.
    Kakar, V., Nagaria, J., John Kirkpatrick P.: The current status of decompressive craniectomy. Br. J. Neurosurg. 23(2), 147–157 (2009)CrossRefPubMedGoogle Scholar
  21. 21.
    Kamath, M.V., Watanabe, M., Upton, A. (eds.): Heart Rate Variability (HRV) Signal Analysis: Clinical Applications. CRC Press, Boca Raton (2013)Google Scholar
  22. 22.
    Leite, A., Rocha, A.P., Silva, M.E., Costa, O.: Modelling long-term heart rate variability: an ARFIMA approach. Biomed. Tech. 51, 215–219 (2006)CrossRefGoogle Scholar
  23. 23.
    Leite, A., Rocha, A.P., Silva, M.E., Gouveia, S., Carvalho, J., Costa, O.: Long-range dependence in heart rate variability data: ARFIMA modelling vs detrended fluctuation analysis. Proc. Comput. Cardiol. 34, 21–24 (2007)Google Scholar
  24. 24.
    Leite, A., Rocha, A.P., Silva, M.E.: Long memory and volatility in HRV: an ARFIMA-GARCH approach. Proc. Comput. Cardiol. 36, 165–168 (2009)Google Scholar
  25. 25.
    Leite, A., Rocha, A.P., Silva, M.E.: Beyond long memory in heart rate variability: an approach based on fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity. Chaos 23(2), 023103 (2013)CrossRefPubMedGoogle Scholar
  26. 26.
    Leite, A., Silva, M.E., Rocha, A.P.: Scaling exponents in heart rate variability. In: Lita da Silva, J., Caeiro, F., Natário, I., Braumann, C.A. (eds.) Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications, pp. 259–267. Springer, Berlin (2013)Google Scholar
  27. 27.
    Leite, A., Rocha, A.P., Silva, M.E.: Modeling volatility in heat rate variability. In: 2016 Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC). IEEE Engineering in Medicine and Biology Society Conference Proceedings, pp. 3582–3585 (2016)Google Scholar
  28. 28.
    Ljung, G.M., Box, G.E.P.: On a measure of lack of fit in time series models. Biometrika 65, 297–303 (1978)CrossRefGoogle Scholar
  29. 29.
    Luis, A., Santos, A.S., Dias, C., Almeida, R., Rocha, A.P.: Heart rate variability during plateau waves of intracranial pressure: a pilot descriptive study. In: 2015 Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC). IEEE Engineering in Medicine and Biology Society Conference Proceedings, pp. 6142–6145 (2015)Google Scholar
  30. 30.
    Maddala, G.S., Kim, I.M.: Unit Roots, Cointegration, and Structural Change (Themes in Modern Econometrics). Cambridge University Press, Cambridge (1999)CrossRefGoogle Scholar
  31. 31.
    Mainardi, L.T., Bianchi, A.M., Cerutti, S.: Time-frequency and time-varying analysis for assessing the dynamic responses of cardiovascular control. Crit. Rev. Biomed. Eng. 30, 175–217 (2002)CrossRefPubMedGoogle Scholar
  32. 32.
    Martínez, J.P., Almeida, R., Olmos, S., Rocha, A.P., Laguna, P.: Wavelet-based ECG delineator: evaluation on standard databases. IEEE Trans. Biomed. Eng. 51, 570–581 (2004)CrossRefPubMedGoogle Scholar
  33. 33.
    Mazzeo, A.T., LaMonaca, E., DiLeo, R., Vita, G., Santamaria, L.B.: Heart rate variability: a diagnostic and prognostic tool in anesthesia and intensive care. Acta Anaesthesiol. Scand. 55(7), 797–811 (2011)CrossRefPubMedGoogle Scholar
  34. 34.
    Mowery, N.T., Norris, P.R., Riordan, W., Jenkins, J.M., Williams, A.E., Morris Jr., J.A.: Cardiac uncoupling and heart rate variability are associated with intracranial hypertension and mortality: a study of 145 trauma patients with continuous monitoring. J. Trauma 65(3), 621–627 (2008)CrossRefPubMedGoogle Scholar
  35. 35.
    Nakagawa, T., Ashwal, S., Mathur, M., Mysore, M.: Guidelines for the determination of brain death in infants and children: an update of the 1987 task force recommendations-executive summary. Ann. Neurol. 71(4), 573–585 (2012)CrossRefPubMedGoogle Scholar
  36. 36.
    Neidzwiecki, M.: Identification of Time-Varying Processes. Wiley, New York (2000)Google Scholar
  37. 37.
    Norris, P.R., Morris, J.A., Ozdas, A., Groga, E.L., Williams, A.E.: Heart rate variability predicts trauma patient outcome as early as 12 h: implications for military and civilian triage. J. Surg. Res. 129(1), 122–128 (2005)CrossRefPubMedGoogle Scholar
  38. 38.
    Rajendra Acharya, U., Paul Joseph, K., Kannathal, N., Lim, C.M., Suri, J.S.: Heart rate variability: a review. Med. Biol. Eng. Comput. 44(12), 1031–1051 (2006)CrossRefPubMedGoogle Scholar
  39. 39.
    Robinson, P.M.: Gaussian semiparametric estimation of long range dependence. Ann. Stat. 23(5), 1630–1661 (1995)CrossRefGoogle Scholar
  40. 40.
    Rocha, A.P., Leite, A., Gouveia, S., Lago, P., Costa, O., Freitas, A.F.: Spectral characterization of long-term ambulatory heart rate variability signals. In: 5th IMA Conference on Mathematics in Signal Processing (2000)Google Scholar
  41. 41.
    Rocha, A.P., Almeida, R., Leite, A., Silva, M.J., Silva, M.E.: Long-term HRV in critically ill pediatric patients: comma versus brain death. Comput. Cardiol. 41, 89–92 (2014)Google Scholar
  42. 42.
    Rocha, A.P., Leite, A., Silva, M.E.: Volatility leveraging in heart rate: health vs disease. Proc. Comput. Cardiol. 43, 25–28 (2016)Google Scholar
  43. 43.
    Ryan, M.L., Thorson, C.M., Otero, C.A., Vu, T., Proctor, K.G.: Clinical applications of heart rate variability in the triage and assessment of traumatically injured patients. Anesthesiol. Res. Pract. 2011, 416590 (2011)Google Scholar
  44. 44.
    Sassi, R., Cerutti, S., Lombardi, F., Malik, M., Huikuri, H., Peng, C.-K., Schmidt, G., Yamamoto, Y.: Advances in heart rate variability signal analysis: joint position statement by the e-Cardiology ESC Working Group and the European Heart Rhythm Association co-endorsed by the Asian Pacific Heart Rhythm Society. Europace 17(9), 1341–1353 (2015)CrossRefPubMedGoogle Scholar
  45. 45.
    Signorini, M.G., Sassi, R., Cerutti, S.: Working on the NOLTISALIS database: measurement of nonlinear properties in heart rate variability signals. In: Proceedings of IEEE- EMBS International Conference, 2001, pp. 547–550 (2001)Google Scholar
  46. 46.
    Stein, P.K., Bosner, M.S., Kleiger, R.E., Conger, B.M.: Heart rate variability: a measure of cardiac autonomic tone. Am. Heart J. 127(5), 1376–1381 (1994)CrossRefPubMedGoogle Scholar
  47. 47.
    Sykora, M., Czosnyka, M., Liu, X., Donnelly, J., Nasr, N., Diedler, J., et al.: Autonomic impairment in severe traumatic brain injury: a multimodal neuromonitoring study. Crit. Care Med. 44(6), 1173–1181 (2016)CrossRefPubMedGoogle Scholar
  48. 48.
    Tarvainen, M.P., Ranta-Aho, P.O., Karjalainen, P.A.: An advanced detrending method with application to HRV analysis. IEEE Trans. Biomed. Eng. 49(2):172–175 (2002)CrossRefPubMedGoogle Scholar
  49. 49.
    Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology: Heart rate variability. Standards of measurement, physiological interpretation, and clinical use. Eur. Heart J. 17(3), 354–381 (1996)Google Scholar
  50. 50.
    Vallbona, C., Cardus, D., Spencer, W.A., Hoff, H.E.: Patterns of sinus arrhythmia in patients with lesions of the central nervous system. Am. J. Cardiol. 16(3), 379–89 (1965)CrossRefPubMedGoogle Scholar
  51. 51.
    Vanderlei, L.C., Pastre, C.M., Hoshi, R.A., Carvalho, T.D., Godoy, M.F.: Basic notions of heart rate variability and its clinical applicability. Rev. Bras. Cir. Cardiovasc. 24(2), 205–217 (2009)CrossRefPubMedGoogle Scholar
  52. 52.
    Velasco, C.: Gaussian semiparametric estimation of nonstationary time series. J. Time Ser. Anal. 20, 87–127 (1999)CrossRefGoogle Scholar
  53. 53.
    Wijdicks, E.F.M.: The diagnosis of brain death. N. Engl. J. Med. 344, 1215–1221 (2001)CrossRefPubMedGoogle Scholar
  54. 54.
    Wilcox, R.R.: Fundamentals of Modern Statistical Methods, 2nd edn. Academic Press, New York (2010)CrossRefGoogle Scholar
  55. 55.
    Winchell, R.J., Hoyt, D.B.: Spectral analysis of heart rate variability in the ICU: a measure of autonomic function. J. Surg. Res. 63(1), 11–16 (1996)CrossRefPubMedGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Rute Almeida
    • 1
  • Celeste Dias
    • 2
  • Maria Eduarda Silva
    • 3
  • Ana Paula Rocha
    • 4
    Email author
  1. 1.CMUP and BSICoSUniversidade do PortoPortoPortugal
  2. 2.CHSJ and FMUPUniversidade do PortoPortoPortugal
  3. 3.CIDMA and FEPUniversidade do PortoPortoPortugal
  4. 4.CMUP and FCUPUniversidade do PortoPortoPortugal

Personalised recommendations