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Theoretical analysis of arterial hemodynamics including the influence of bifurcations

Part I: Mathematical model and prediction of normal pulse patterns

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Abstract

Based on earlier theoretical studies, a new mathematical model is developed for the prediction of the pressure and flow pulses propagating in the arterial system. This model permits a more realistic simulation of bifurcation and stenoses than was possible previously. By making use of a computer, it allows us to calculate the pulse shapes along branching arteries. It is based on the assumption that each arterial conduit can be represented by a suitable combination of three basic segments, namely segments with no or only small-calibre side branches, short segments with big side branches, and short segments with pathological changes of the conduit. Along segments of the first type, the pulse propagation is calculated with the aid of the method of characteristics and a first order integration. For the other two types, the linearized mass balance and momentum equations are utilized together with the boundary conditions to determine the pressure and flow values at the ends of the segment. A standard case for the human arterial conduit extending from the heart to the foot, with eight major branches, is defined using published data and prescribing the ejection pattern from the heart. The computed pulse shapes and their changes with propagation exhibit the characteristic features observed in man under normal conditions.

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Author notes

  1. J. C. Stettler

    Present address: Department of Mechanical Engineering, University of Houston, 77004, Houston, Texas

Authors and Affiliations

  1. Institute of Biomedical Engineering, University of Zurich, Moussonstrasse 18, CH-8044, Zurich, Switzerland

    J. C. Stettler, P. Niederer & M. Anliker

  2. Swiss Federal Institute of Technology, Moussonstrasse 18, CH-8044, Zurich, Switzerland

    J. C. Stettler, P. Niederer & M. Anliker

Authors
  1. J. C. Stettler
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  2. P. Niederer
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  3. M. Anliker
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Additional information

This work was supported in part by Grant 3. 121.–0.77 from the Swiss National Science Foundation.

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Stettler, J.C., Niederer, P. & Anliker, M. Theoretical analysis of arterial hemodynamics including the influence of bifurcations. Ann Biomed Eng 9, 145–164 (1981). https://doi.org/10.1007/BF02363533

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