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Introduction to Mathematical Modeling of Blood Flow Control in the Kidney

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Women in Mathematical Biology

Part of the book series: Association for Women in Mathematics Series ((AWMS,volume 8))

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Abstract

Besides its best known role in the excretion of metabolic wastes and toxins, the kidney also plays an indispensable role in regulating the balance of water, electrolytes, acid–base species, blood volume, and blood pressure. To properly fulfill its functions, it is crucial for the kidney to exercise hemodynamic control. In this review, we describe representative mathematical models that have been developed to better understand the kidney’s autoregulatory processes. In particular, we consider mathematical models that simulate renal blood flow regulation by means of key autoregulatory mechanisms: the myogenic response and tubuloglomerular feedback. We discuss the extent to which these modeling efforts have expanded the understanding of renal functions in health and diseases.

The original version of this chapter was revised. An erratum to this chapter can be found at https://doi.org/10.1007/978-3-319-60304-9_13

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Acknowledgements

This work is the product of a workshop and short-term visits supported by the National Institute for Mathematical and Biological Synthesis, an Institute sponsored by the National Science Foundation through NSF Award #DBI-1300426, with additional support from The University of Tennessee, Knoxville. Support was also provided by the National Institutes of Health: National Institute of Diabetes and Digestive and Kidney Diseases and by the National Science Foundation, via grants #DK089066 and #DMS-1263995 to AT Layton.

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Authors and Affiliations

  1. Department of Mathematics, Duke University, Durham, NC, 27708, USA

    Anita T. Layton

  2. Sorbonne Universités, UPMC Univ Paris 06, Université Paris Descartes, Sorbonne Paris Cité, INSERM UMRS 1138, CNRS ERL 8228, Centre de Recherche des Cordeliers, Paris, France

    Aurélie Edwards

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  1. Anita T. Layton
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Correspondence to Anita T. Layton .

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Editors and Affiliations

  1. Department of Mathematics, Duke University, Durham, North Carolina, USA

    Anita T. Layton

  2. Departments of Mathematics and Biology, University of North Carolina, Chapel Hill, North Carolina, USA

    Laura A. Miller

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Layton, A.T., Edwards, A. (2017). Introduction to Mathematical Modeling of Blood Flow Control in the Kidney. In: Layton, A., Miller, L. (eds) Women in Mathematical Biology. Association for Women in Mathematics Series, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-60304-9_4

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