Skip to main content
SpringerLink
Log in

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

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Notes

  1. Some entries in Table 3 were estimated from figures in the associated references. Those entries are marked with asterisks and, despite our efforts, may contain a degree of inaccuracy. Also, in several studies gain is reported in dB. In those cases, the values were computed using the reported formulas, or, when such formulas were not reported, assuming the standard one \(20\log _{10}|H(f)|\). Finally, to avoid complications introduced by the normalization of blood pressure time series, we have excluded studies in which the arterial blood pressure of the experimental models deviated substantially from 100 mmHg.

References

  • Abu-Amarah I, Ajikobi DO, Bachelard H, Cupples WA, Salevsky FC (1998) Responses of mesenteric and renal blood flow dynamics to acute denervation in anesthetized rats. Am J Physiol 275(5 Pt 2):R1543–R1552

    Google Scholar 

  • Ajikobi DO, Novak P, Salevsky FC, Cupples WA (1996) Pharmacological modulation of spontaneous renal blood flow dynamics. Can J Physiol Pharmacol 74(8):964–972

    Article  Google Scholar 

  • Arendshorst WJ (1979) Autoregulation of renal blood flow in spontaneously hypertensive rats. Circ Res 44(3):344–349

    Article  Google Scholar 

  • Bell TD, DiBona GF, Wang Y, Brands MW (2006) Mechanisms for renal blood flow control early in diabetes as revealed by chronic flow measurement and transfer function analysis. J Am Soc Nephrol 17(8):2184–2192

    Article  Google Scholar 

  • Bidani AK, Hacioglu R, Abu-Amarah I, Williamson GA, Loutzenhiser R, Griffin KA (2003) “Step” vs. “dynamic” autoregulation: implications for susceptibility to hypertensive injury. Am J Physiol Renal Physiol 285(1):F113–F120

    Article  Google Scholar 

  • Brink PR (1998) Gap junctions in vascular smooth muscle. Acta Physiol Scand 164(4):349–356

    Article  Google Scholar 

  • Brown DR, Cassis LA, Silcox DL, Brown LV, Randall David C (2006) Empirical and theoretical analysis of the extremely low frequency arterial blood pressure power spectrum in unanesthetized rat. Am J Physiol Heart Circ Physiol 291(6):H2816–H2824

    Article  Google Scholar 

  • Casellas D, Dupont M, Bouriquet N, Moore LC, Artuso A, Mimran A (1994) Anatomic pairing of afferent arterioles and renin cell distribution in rat kidneys. Am J Physiol 267(6 Pt 2):F931–F936

    Google Scholar 

  • Chen YM, Holstein-Rathlou NH (1993) Differences in dynamic autoregulation of renal blood flow between shr and wky rats. Am J Physiol 264(1 Pt 2):F166–F174

    Google Scholar 

  • Chen J, Sgouralis I, Moore LC, Layton HE, Layton AT (2011) A mathematical model of the myogenic response to systolic pressure in the afferent arteriole. Am J Physiol Renal Physiol 300(3):F669–F681

    Article  Google Scholar 

  • Chon KH, Zhong Y, Moore LC, Holstein-Rathlou NH, Cupples WA (2008) Analysis of nonstationarity in renal autoregulation mechanisms using time-varying transfer and coherence functions. Am J Physiol Regul Integr Comp Physiol 295(3):R821–R828

    Article  Google Scholar 

  • Cupples WA, Loutzenhiser RD (1998) Dynamic autoregulation in the in vitro perfused hydronephrotic rat kidney. Am J Physiol 275(1 Pt 2):F126–F130

    Google Scholar 

  • Cupples WA, Braam B (2007) Assessment of renal autoregulation. Am J Physiol Renal Physiol 292(4):F1105–F1123

    Article  Google Scholar 

  • Cupples WA, Novak P, Novak V, Salevsky FC (1996) Spontaneous blood pressure fluctuations and renal blood flow dynamics. Am J Physiol 270(1 Pt 2):F82–F89

    Google Scholar 

  • Cupples WA, Ajikobi DO, Wang X (2002) Kidney-specific responses of myogenic autoregulation to inhibition of nitric oxide synthase. In: Layton HE, Weinstein AM (eds) Membrane transport and renal physiology. Springer, Berlin

    Google Scholar 

  • Daniels FH, Arendshorst WJ, Roberds RG (1990) Tubuloglomerular feedback and autoregulation in spontaneously hypertensive rats. Am J Physiol 258(6 Pt 2):F1479–F1489

    Google Scholar 

  • Flemming B, Arenz N, Seeliger E, Wronski T, Steer K, Persson PB (2001) Time-dependent autoregulation of renal blood flow in conscious rats. J Am Soc Nephrol 12(11):2253–2262

    Google Scholar 

  • Griffin KA, Hacioglu R, Abu-Amarah I, Loutzenhiser R, Williamson GA, Bidani AK (2004) Effects of calcium channel blockers on dynamic and steady-state step renal autoregulation. Am J Physiol Renal Physiol 286(6):F1136–F1143

    Article  Google Scholar 

  • Hayashi K, Epstein M, Loutzenhiser R, Forster H (1992) Impaired myogenic responsiveness of the afferent arteriole in streptozotocin-induced diabetic rats: role of eicosanoid derangements. J Am Soc Nephrol 2(11):1578–1586

    Google Scholar 

  • He J, Marsh DJ (1993) Effect of captopril on fluctuations of blood pressure and renal blood flow in rats. Am J Physiol 264(1 Pt 2):F37–F44

    Google Scholar 

  • Holstein-Rathlou NH (1987) Synchronization of proximal intratubular pressure oscillations: evidence for interaction between nephrons. Pflugers Arch 408(5):438–443

    Article  Google Scholar 

  • Holstein-Rathlou NH, Marsh DJ (1994a) A dynamic model of renal blood flow autoregulation. Bull Math Biol 56(3):411–429

    Article  MATH  Google Scholar 

  • Holstein-Rathlou NH, Marsh DJ (1994b) Renal blood flow regulation and arterial pressure fluctuations: a case study in nonlinear dynamics. Physiol Rev 74(3):637–681

    Google Scholar 

  • Holstein-Rathlou NH, Wagner AJ, Marsh DJ (1991) Tubuloglomerular feedback dynamics and renal blood flow autoregulation in rats. Am J Physiol 260(1 Pt 2):F53–F68

    Google Scholar 

  • Holstein-Rathlou NH, He J, Wagner AJ, Marsh DJ (1995) Patterns of blood pressure variability in normotensive and hypertensive rats. Am J Physiol 269(5 Pt 2):R1230–R1239

    Google Scholar 

  • Holstein-Rathlou N-H, Sosnovtseva OV, Pavlov AN, Cupples WA, Sorensen CM, Marsh DJ (2011) Nephron blood flow dynamics measured by laser speckle contrast imaging. Am J Physiol Renal Physiol 300(2):F319–F329

    Article  Google Scholar 

  • Janssen BJ, Oosting J, Slaaf DW, Persson PB, Struijker-Boudier HA (1995) Hemodynamic basis of oscillations in systemic arterial pressure in conscious rats. Am J Physiol 269(1 Pt 2):H62–H71

    Google Scholar 

  • Just A (2007) Mechanisms of renal blood flow autoregulation: dynamics and contributions. Am J Physiol Regul Integr Comp Physiol 292(1):R1–R17

    Article  Google Scholar 

  • Just A, Arendshorst WJ (2003) Dynamics and contribution of mechanisms mediating renal blood flow autoregulation. Am J Physiol Regul Integr Comp Physiol 285(3):R619–R631

    Article  Google Scholar 

  • Just A, Wittmann U, Ehmke H, Kirchheim HR (1998) Autoregulation of renal blood flow in the conscious dog and the contribution of the tubuloglomerular feedback. J Physiol 506(Pt 1):275–290

    Article  Google Scholar 

  • Just A, Ehmke H, Wittmann U, Kirchheim HR (1999) Tonic and phasic influences of nitric oxide on renal blood flow autoregulation in conscious dogs. Am J Physiol 276(3 Pt 2):F442–F449

    Google Scholar 

  • Just A, Ehmke H, Wittmann U, Kirchheim HR (2002) Role of angiotensin II in dynamic renal blood flow autoregulation of the conscious dog. J Physiol 538(Pt 1):167–177

    Article  Google Scholar 

  • Karlsen FM, Andersen CB, Leyssac PP, HolsteinRathlou NH (1997) Dynamic autoregulation and renal injury in dahl rats. Hypertension 30(4):975–983

    Article  Google Scholar 

  • Kirchheim HR, Ehmke H, Hackenthal E, Löwe W, Persson P (1987) Autoregulation of renal blood flow, glomerular filtration rate and renin release in conscious dogs. Pflugers Arch 410(4–5):441–449

    Article  Google Scholar 

  • Kleinstreuer N, David T, Plank MJ, Endre Z (2008) Dynamic myogenic autoregulation in the rat kidney: a whole-organ model. Am J Physiol Renal Physiol 294(6):F1453–F1464

    Article  Google Scholar 

  • Knudsen T, Elmer H, Morten H K, Holstein-Rathlou N-H, Jakob S (2004) Dynamic modeling of renal blood flow in Dahl hypertensive and normotensive rats. IEEE Trans Biomed Eng 51(5):689–697

    Article  Google Scholar 

  • Layton HE, Pitman EB, Moore LC (1991) Bifurcation analysis of TGF-mediated oscillations in SNGFR. Am J Physiol 261(5 Pt 2):F904–F919

    Google Scholar 

  • Layton HE, Pitman EB, Moore LC (1997) Spectral properties of the tubuloglomerular feedback system. Am J Physiol 273(4 Pt 2):F635–F649

    Google Scholar 

  • Lessard A, Salevsky FC, Bachelard H, Cupples WA (1999) Incommensurate frequencies of major vascular regulatory mechanisms. Can J Physiol Pharmacol 77(4):293–299

    Article  Google Scholar 

  • Leyssac PP (1986) Further studies on oscillating tubulo-glomerular feedback responses in the rat kidney. Acta Physiol Scand 126(2):271–277

    Article  Google Scholar 

  • Loutzenhiser R, Bidani A, Chilton L (2002) Renal myogenic response: kinetic attributes and physiological role. Circ Res 90(12):1316–1324

    Article  Google Scholar 

  • Loutzenhiser R, Griffin K, Williamson G, Bidani A (2006) Renal autoregulation: new perspectives regarding the protective and regulatory roles of the underlying mechanisms. Am J Physiol Regul Integr Comp Physiol 290(5):R1153–R1167

    Article  Google Scholar 

  • Marsh DJ, Osborn JL, Cowley AW Jr (1990) 1/f fluctuations in arterial pressure and regulation of renal blood flow in dogs. Am J Physiol 258(5 Pt 2):F1394–F1400

    Google Scholar 

  • Marsh DJ, Sosnovtseva OV, Chon KH, Holstein-Rathlou N-H (2005) Nonlinear interactions in renal blood flow regulation. Am J Physiol Regul Integr Comp Physiol 288(5):R1143–R1159

    Article  Google Scholar 

  • Moss NG, Kopple TE, Arendshorst WJ (2016) Modulation of the myogenic mechanism: concordant effects of NO synthesis inhibition and O\(_2\)-dismutation on renal autoregulation in the time and frequency domains. Am J Physiol Renal Physiol. doi:10.1152/ajprenal.00461.2015

  • Nordsletten DA, Blackett S, Bentley MD, Ritman EL, Smith NP (2006) Structural morphology of renal vasculature. Am J Physiol Heart Circ Physiol 291(1):H296–H309

    Article  Google Scholar 

  • Oien AH, Aukland K (1983) A mathematical analysis of the myogenic hypothesis with special reference to autoregulation of renal blood flow. Circ Res 52(3):241–252

    Article  Google Scholar 

  • Pires SL, Barrès C, Sassard J, Julien C (2001) Renal blood flow dynamics and arterial pressure lability in the conscious rat. Hypertension 38(1):147–152

    Article  Google Scholar 

  • Rothe CF, Nash FD, Thompson DE (1971) Patterns in autoregulation of renal blood flow in the dog. Am J Physiol 220(6):1621–1626

    Google Scholar 

  • Sakai T, Hallman E, Marsh DJ (1986) Frequency domain analysis of renal autoregulation in the rat. Am J Physiol 250(2 Pt 2):F364–F373

    Google Scholar 

  • Sandgaard NCF, Andersen JL, Holstein-Rathlou N-H, Bie P (2002) Aortic blood flow subtraction: an alternative method for measuring total renal blood flow in conscious dogs. Am J Physiol Regul Integr Comp Physiol 282(5):R1528–R1535

    Article  Google Scholar 

  • Scully CG, Mitrou N, Braam B, Cupples WA, Chon KH (2013) Detecting physiological systems with laser speckle perfusion imaging of the renal cortex. Am J Physiol Regul Integr Comp Physiol 304(11):R929–R939

    Article  Google Scholar 

  • Scully CG, Mitrou N, Braam B, Cupples WA, Chon KH (2014) Segmentation of renal perfusion signals from laser speckle imaging into clusters with phase synchronized dynamics. IEEE Trans Biomed Eng 61(7):1989–1997

    Article  Google Scholar 

  • Sgouralis I, Layton AT (2012) Autoregulation and conduction of vasomotor responses in a mathematical model of the rat afferent arteriole. Am J Physiol Renal Physiol 303(2):F229–F239

    Article  Google Scholar 

  • Sgouralis I, Layton AT (2013) Control and modulation of fluid flow in the rat kidney. Bull Math Biol 75(12):2551–2574. doi:10.1007/s11538-013-9907-5

  • Sgouralis I, Layton AT (2014) Theoretical assessment of renal autoregulatory mechanisms. Am J Physiol Renal Physiol 306(11):F1357–F1371. doi:10.1152/ajprenal.00649.2013

  • Sgouralis I, Layton AT (2015) Mathematical modeling of renal hemodynamics in physiology and pathophysiology. Math Biosci 264:8–20

  • Sgouralis I, Layton AT (2016) Conduction of feedback-mediated signal in a computational model of coupled nephrons. Math Med Biol 33(1):87–106. doi:10.1093/imammb/dqv005

  • Shi Y, Wang X, Chon KH, Cupples WA (2006) Tubuloglomerular feedback-dependent modulation of renal myogenic autoregulation by nitric oxide. Am J Physiol Regul Integr Comp Physiol 290(4):R982–R991

    Article  Google Scholar 

  • Shipley RE, Study RS (1951) Changes in renal blood flow, extraction of inulin, glomerular filtration rate, tissue pressure and urine flow with acute alterations of renal artery blood pressure. Am J Physiol 167(3):676–688

    Google Scholar 

  • van Dokkum RP, Sun CW, Provoost AP, Jacob HJ, Roman RJ (1999) Altered renal hemodynamics and impaired myogenic responses in the fawn-hooded rat. Am J Physiol 276(3 Pt 2):R855–R863

    Google Scholar 

  • Wagner CD, Persson PB (1994) Two ranges in blood pressure power spectrum with different 1/f characteristics. Am J Physiol 267(2 Pt 2):H449–H454

    Google Scholar 

  • Wang X, Cupples WA (2001) Interaction between nitric oxide and renal myogenic autoregulation in normotensive and hypertensive rats. Can J Physiol Pharmacol 79(3):238–245

    Article  Google Scholar 

  • Wang X, Salevsky FC, Cupples WA (1999) Nitric oxide, atrial natriuretic factor, and dynamic renal autoregulation. Can J Physiol Pharmacol 77(10):777–786

    Article  Google Scholar 

  • Wang X, Ajikobi DO, Salevsky FC, Cupples WA (2000) Impaired myogenic autoregulation in kidneys of brown norway rats. Am J Physiol Renal Physiol 278(6):F962–F969

    Google Scholar 

  • Wang X, Loutzenhiser RD, Cupples WA (2007) Frequency modulation of renal myogenic autoregulation by perfusion pressure. Am J Physiol Regul Integr Comp Physiol 293(3):R1199–R1204

    Article  Google Scholar 

  • Welch P (1967) The use of fast fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans Audio Electroacoust 15:70–73

    Article  MathSciNet  Google Scholar 

  • Young DK, Marsh DJ (1981) Pulse wave propagation in rat renal tubules: implications for GFR autoregulation. Am J Physiol 240(5):F446–F458

    Google Scholar 

Download references

Acknowledgments

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.

Author information

Authors and Affiliations

  1. National Institute for Mathematical and Biological Synthesis, University of Tennessee, Knoxville, TN, USA

    Ioannis Sgouralis

  2. Department of Mathematics, University of Tennessee, Knoxville, TN, USA

    Vasileios Maroulas

  3. Department of Mathematics, Duke University, Durham, NC, USA

    Anita T. Layton

Authors
  1. Ioannis Sgouralis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vasileios Maroulas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Anita T. Layton
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ioannis Sgouralis.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (pdf 168 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sgouralis, I., Maroulas, V. & Layton, A.T. Transfer Function Analysis of Dynamic Blood Flow Control in the Rat Kidney. Bull Math Biol 78, 923–960 (2016). https://doi.org/10.1007/s11538-016-0168-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-016-0168-y

Keywords

Search

Navigation