Pulse Wave Velocity Prediction and Compliance Assessment in Elastic Arterial Segments

  • Jeffrey S. Lillie
  • Alexander S. Liberson
  • Doran Mix
  • Karl Q. Schwarz
  • Ankur Chandra
  • Daniel B. Phillips
  • Steven W. Day
  • David A. BorkholderEmail author


Pressure wave velocity (PWV) is commonly used as a clinical marker of vascular elasticity. Recent studies have increased clinical interest in also analyzing the impact of heart rate, blood pressure, and left ventricular ejection time on PWV. In this article we focus on the development of a theoretical one-dimensional model and validation via direct measurement of the impact of ejection time and peak pressure on PWV using an in vitro hemodynamic simulator. A simple nonlinear traveling wave model was developed for a compliant thin-walled elastic tube filled with an incompressible fluid. This model accounts for the convective fluid phenomena, elastic vessel deformation, radial motion, and inertia of the wall. An exact analytical solution for PWV is presented which incorporates peak pressure, ejection time, ejection volume, and modulus of elasticity. To assess arterial compliance, the solution is introduced in an alternative form, explicitly determining compliance of the wall as a function of the other variables. The model predicts PWV in good agreement with the measured values with a maximum difference of 3.0%. The results indicate an inverse quadratic relationship (\(R^{2} = .99\)) between ejection time and PWV, with ejection time dominating the PWV shifts (12%) over those observed with changes in peak pressure (2%). Our modeling and validation results both explain and support the emerging evidence that, both in clinical practice and clinical research, cardiac systolic function related variables should be regularly taken into account when interpreting arterial function indices, namely PWV.


Left ventricular ejection time Systemic vascular resistance Pulse wave velocity Peak pressure Blood pressure Wave propagation 



The authors would like to thank Matt Waldron and Cody Cziesler for their many hours of data processing and algorithm enhancements. In addition we’d like to thank John Snyder for his insightful statistical guidance and discussions. This work was supported by a grant from the National Semiconductor Corporation.

Conflict of Interest

Jeffrey S. Lillie, Alexander S. Liberson, Doran Mix, Karl Q. Schwarz, Ankur Chandra, Daniel B. Phillips, Steven W. Day, and David A. Borkholder declare that they have no conflict of interest.

Human and Animal Rights and Informed Consent

This article does not contain any studies with human or animal subjects performed by any of the authors.

Supplementary material

13239_2014_202_MOESM1_ESM.docx (121 kb)
Supplementary material 1 (DOCX 99 kb)


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Copyright information

© Biomedical Engineering Society 2014

Authors and Affiliations

  • Jeffrey S. Lillie
    • 1
  • Alexander S. Liberson
    • 1
  • Doran Mix
    • 2
  • Karl Q. Schwarz
    • 2
  • Ankur Chandra
    • 2
  • Daniel B. Phillips
    • 1
  • Steven W. Day
    • 1
  • David A. Borkholder
    • 1
    • 2
    Email author
  1. 1.Rochester Institute of TechnologyRochesterUSA
  2. 2.University of RochesterRochesterUSA

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