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Philos Trans A Math Phys Eng Sci. 2016 May 13;374(2067). pii: 20150180. doi: 10.1098/rsta.2015.0180.

Multiple-input nonlinear modelling of cerebral haemodynamics using spontaneous arterial blood pressure, end-tidal CO2 and heart rate measurements.

Author information

Biomedical Engineering, University of Southern California, Los Angeles, CA, USA.
Bioengineering, McGill University, Montreal, Quebec, Canada
Institute for Exercise and Environmental Medicine, University of Texas Southwestern Medical Center, Dallas, TX, USA.


In order to examine the effect of changes in heart rate (HR) upon cerebral perfusion and autoregulation, we include the HR signal recorded from 18 control subjects as a third input in a two-input model of cerebral haemodynamics that has been used previously to quantify the dynamic effects of changes in arterial blood pressure and end-tidal CO2upon cerebral blood flow velocity (CBFV) measured at the middle cerebral arteries via transcranial Doppler ultrasound. It is shown that the inclusion of HR as a third input reduces the output prediction error in a statistically significant manner, which implies that there is a functional connection between HR changes and CBFV. The inclusion of nonlinearities in the model causes further statistically significant reduction of the output prediction error. To achieve this task, we employ the concept of principal dynamic modes (PDMs) that yields dynamic nonlinear models of multi-input systems using relatively short data records. The obtained PDMs suggest model-driven quantitative hypotheses for the role of sympathetic and parasympathetic activity (corresponding to distinct PDMs) in the underlying physiological mechanisms by virtue of their relative contributions to the model output. These relative PDM contributions are subject-specific and, therefore, may be used to assess personalized characteristics for diagnostic purposes.


dynamic nonlinear modelling; multi-input systems/models; principal dynamic modes; sympathetic and parasympathetic activity

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