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Mathematical Modeling of Blood Flow in the Cardiovascular System

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Quantification of Biophysical Parameters in Medical Imaging

Abstract

This chapter gives a short overview of the mathematical modeling of blood flow at different resolutions, from the large vessel scale (three-dimensional, one-dimensional, and zero-dimensional modeling) to microcirculation and tissue perfusion. The chapter focuses first on the formulation of the mathematical modeling, discussing the underlying physical laws, the need for suitable boundary conditions, and the link to clinical data. Recent applications related to medical imaging are then discussed, in order to highlight the potential of computer simulation and of the interplay between modeling, imaging, and experiments in order to improve clinical diagnosis and treatment. The chapter ends presenting some current challenges and perspectives.

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Acknowledgments

The authors are grateful to C. Bertoglio, D. Lombardi, and L. O. Müller for the useful discussions.

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Authors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    Alfonso Caiazzo

  2. INRIA Paris, Paris, France

    Irene E. Vignon-Clementel

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  1. Alfonso Caiazzo
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  2. Irene E. Vignon-Clementel
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Correspondence to Alfonso Caiazzo .

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Editors and Affiliations

  1. Department of Radiology, Humboldt University of Berlin Charité University Hospital, Berlin, Germany

    Ingolf Sack

  2. Medical Physics and Metrological Information Technology, Physikalisch-Technische Bundesanstalt , Berlin, Germany

    Tobias Schaeffter

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Caiazzo, A., Vignon-Clementel, I.E. (2018). Mathematical Modeling of Blood Flow in the Cardiovascular System. In: Sack, I., Schaeffter, T. (eds) Quantification of Biophysical Parameters in Medical Imaging. Springer, Cham. https://doi.org/10.1007/978-3-319-65924-4_3

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