Bulletin of Mathematical Biology

, Volume 78, Issue 5, pp 923–960 | Cite as

Transfer Function Analysis of Dynamic Blood Flow Control in the Rat Kidney

  • Ioannis SgouralisEmail author
  • Vasileios Maroulas
  • Anita T. Layton
Original Article


Renal blood flow is regulated by the myogenic response (MR) and tubuloglomerular feedback (TGF). Both mechanisms function to buffer not only steady pressure perturbations but also transient ones. In this study, we develop two models of renal autoregulation—a comprehensive model and a simplified model—and use them to analyze the individual contributions of MR and TGF in buffering transient pressure perturbations. Both models represent a single nephron of a rat kidney together with the associated vasculature. The comprehensive model includes detailed representation of the vascular properties and cellular processes. In contrast, the simplified model represents a minimal set of key processes. To assess the degree to which fluctuations in renal perfusion pressure at different frequencies are attenuated, we derive a transfer function for each model. The transfer functions of both models predict resonance at 45 and 180 mHz, which are associated with TGF and MR, respectively, effective autoregulation below \(\sim \)100 mHz, and amplification of pressure perturbations above \(\sim \)200 mHz. The predictions are in good agreement with experimental findings.


Kidney Hemodynamics Autoregulation Dynamic control  Transfer function System identification Complex system 



This work was conducted while I. Sgouralis was a Postdoctoral Fellow at 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. V. Maroulas was partially supported by a NIMBioS Mentor Grant. A. Layton is supported in part by the National Science Foundation through Grant DMS-1263995 and the National Institutes of Health through Grant DK089066.

Supplementary material

11538_2016_168_MOESM1_ESM.pdf (169 kb)
Supplementary material 1 (pdf 168 KB)


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Copyright information

© Society for Mathematical Biology 2016

Authors and Affiliations

  • Ioannis Sgouralis
    • 1
    Email author
  • Vasileios Maroulas
    • 2
  • Anita T. Layton
    • 3
  1. 1.National Institute for Mathematical and Biological SynthesisUniversity of TennesseeKnoxvilleUSA
  2. 2.Department of MathematicsUniversity of TennesseeKnoxvilleUSA
  3. 3.Department of MathematicsDuke UniversityDurhamUSA

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