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One-dimensional mathematical models for blood flow consist of advection-dominated systems of partial differential equations of hyperbolic/parabolic type. In this work we consider mathematical models for blood flow assuming a general velocity profile and a general tube law. We study conditions under which the models preserve some desirable mathematical properties such as hyperbolicity and genuine nonlinearity of characteristic fields. Furthermore, we derive coupling conditions for bifurcations/junctions of viscoelastic vessels and assess the role of the momentum correction factor on computed pressure and flow waveforms of the arterial and venous systems across a wide range of spatial scales.

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On the Role of Momentum Correction Factor and General Tube Law in One-Dimensional Blood Flow Models for Networks of Vessels

  • 会议论文

  • 发表日期：

    2026年

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  • Lucas O. Müller,
  • Eleuterio F. Toro

摘要

One-dimensional mathematical models for blood flow consist of advection-dominated systems of partial differential equations of hyperbolic/parabolic type. In this work we consider mathematical models for blood flow assuming a general velocity profile and a general tube law. We study conditions under which the models preserve some desirable mathematical properties such as hyperbolicity and genuine nonlinearity of characteristic fields. Furthermore, we derive coupling conditions for bifurcations/junctions of viscoelastic vessels and assess the role of the momentum correction factor on computed pressure and flow waveforms of the arterial and venous systems across a wide range of spatial scales.