Modeling the cardiovascular system using a nonlinear additive autoregressive model with exogenous input

M. Riedl, A. Suhrbier, H. Malberg, T. Penzel, G. Bretthauer, J. Kurths, N. Wessel

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10 Citations (Scopus)


The parameters of heart rate variability and blood pressure variability have proved to be useful analytical tools in cardiovascular physics and medicine. Model-based analysis of these variabilities additionally leads to new prognostic information about mechanisms behind regulations in the cardiovascular system. In this paper, we analyze the complex interaction between heart rate, systolic blood pressure, and respiration by nonparametric fitted nonlinear additive autoregressive models with external inputs. Therefore, we consider measurements of healthy persons and patients suffering from obstructive sleep apnea syndrome (OSAS), with and without hypertension. It is shown that the proposed nonlinear models are capable of describing short-term fluctuations in heart rate as well as systolic blood pressure significantly better than similar linear ones, which confirms the assumption of nonlinear controlled heart rate and blood pressure. Furthermore, the comparison of the nonlinear and linear approaches reveals that the heart rate and blood pressure variability in healthy subjects is caused by a higher level of noise as well as nonlinearity than in patients suffering from OSAS. The residue analysis points at a further source of heart rate and blood pressure variability in healthy subjects, in addition to heart rate, systolic blood pressure, and respiration. Comparison of the nonlinear models within and among the different groups of subjects suggests the ability to discriminate the cohorts that could lead to a stratification of hypertension risk in OSAS patients.

Original languageEnglish
Article number011919
Number of pages9
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Issue number1
Publication statusPublished - Jul 2008


  • heart-rate-variability
  • baroreflex sensitivity
  • blood-pressure
  • dynamics
  • sleep
  • hypertension

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