Modeling Cerebral Blood Flow Velocity During Orthostatic Stress

Abstract

Cerebral autoregulation refers to the physiological process that maintains stable cerebral blood flow (CBF) during changes in arterial blood pressure (ABP). In this study, we propose a simple, nonlinear quantitative model with only four parameters that can predict CBF velocity as a function of ABP. The model was motivated by the viscoelastic-like behavior observed in the data collected during postural change from sitting to standing. Qualitative testing of the model involved analysis of dynamic responses to step-changes in pressure both within and outside the autoregulatory range, while quantitative testing was used to show that the model can fit dynamics observed in data measured from a healthy young and a healthy elderly subject. The latter involved analysis of structural and practical identifiability, sensitivity analysis, and parameter estimation. Results showed that the model is able to reproduce observed overshoot and adaptation and predict the different responses in the healthy young and the healthy elderly subject. For the healthy young subject, the overshoot was significantly more pronounced than for the elderly subject, but the recovery time was longer for the young subject. These differences resulted in different parameter values estimated using the two datasets.

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Acknowledgments

The authors would like to thank the Virtual Physiological Rat (VPR) project for supporting this work under NIH-NIGMS Grant 1P50-GM094503-01A0 subaward to North Carolina State University. In addition, Olufsen received partial support from the National Science Foundation under Grants NSF-DMS 1122424 and NSF-DMS 0636590, and Mahdi acknowledges the partial support of the EPSRC project EP/K036157/1. This study would not have been possible without the access to anonymized patient data provided by Dr. Lewis Lipsitz at the Hebrew SeniorLife in Boston, MA. The authors would also like to thank Prof. Johnny Ottesen for reading the manuscript and offering a number of helpful comments.

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Correspondence to Adam Mahdi.

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Associate Editor Aleksander S. Popel oversaw the review of this article.

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Mader, G., Olufsen, M. & Mahdi, A. Modeling Cerebral Blood Flow Velocity During Orthostatic Stress. Ann Biomed Eng 43, 1748–1758 (2015). https://doi.org/10.1007/s10439-014-1220-4

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Keywords

  • Cerebral autoregulation
  • Blood pressure
  • Structural identifiability
  • Practical identifiability
  • Viscoelasticity
  • Sensitivity analysis