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Modeling Blood Flow Control in the Kidney

  • Conference paper
Applications of Dynamical Systems in Biology and Medicine

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 158))

Abstract

A mathematical model of renal hemodynamics is developed in this study to investigate autoregulation in the rat kidney under physiological and pathophysiological conditions. The model simulates the blood supply to a nephron via the afferent arteriole, the filtration of blood through the glomerulus, and the transport of water and ions in the thick ascending limb of the short loop of Henle. The afferent arteriole exhibits the myogenic response, which induces changes in vascular smooth muscle tone in response to hydrostatic pressure variations. Chloride transport is simulated along the thick ascending limb, and the concentration of chloride at the macula densa provides the signal for the constriction or dilation of the afferent arteriole via tubuloglomerular feedback (TGF). With this configuration, the model predicts a stable glomerular filtration rate within a physiological range of perfusion pressure (60–180 mmHg). The contribution of TGF to overall blood flow autoregulation in the kidney is significant only within a narrow band of perfusion pressure values. Simulations of renal autoregulation under conditions of diabetes mellitus yield a > 60% increase in glomerular filtration rate, due in large part to the impairment of the voltage-gated Ca2+ channels of the afferent arteriole smooth muscle cells.

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References

  1. J. Arciero, B. Carlson, and T. Secomb, Theoretical model of metabolic blood flow autoregulation: roles of ATP release by red blood cells and conducted responses, Am J Physiol Heart Circ Physiol, 295 (2008), pp. H1562–H1571.

    Article  Google Scholar 

  2. K. Aukland and A. H. Oien, Renal autoregulation: models combining tubuloglomerular feedback and myogenic response, Am J Physiol: Renal Physiol, 252 (1987), pp. F768–F783.

    Google Scholar 

  3. N. Bank, P. Mower, H. S. Aynedjian, B. M. Wilkes, and S. Silverman, Sorbinil prevents glomerular hyperperfusion in diabetic rats, Am J Physiol, 256 (1989), pp. F1000–F1006.

    Google Scholar 

  4. M. Barfred, E. Mosekilde, and N. Holstein-Rathlou, Bifurcation analysis of nephron pressure and flow regulation, Chaos, 6 (1996), pp. 280–287.

    Article  Google Scholar 

  5. B. E. Carlson, J. C. Arciero, and T. W. Secomb, Theoretical model of blood flow autoregulation: roles of myogenic, shear-dependent, and metabolic responses, Am J Physiol Heart Circ Physiol, 295 (2008), pp. 1572–1579.

    Article  Google Scholar 

  6. P. K. Carmines, K. Ohishi, and H. Ikenaga, Functional impairment of renal afferent arteriolar voltage-gated calcium channels in rats with diabetes mellitus, J Clin Invest, 98 (1996), pp. 2564–2571.

    Article  Google Scholar 

  7. D. Casellas, M. Dupont, N. Bouriquet, L. Moore, A. Artuso, and A. Mimran, Anatomic pairing of afferent arterioles and renin cell distribution in rat kidneys, Am J Physiol (Renal Fluid Electrolyte Physiol 36), 267 (1994), pp. F931–F936.

    Google Scholar 

  8. J. Chen, I. Sgouralis, L. Moore, H. Layton, and A. Layton, A mathematical model of the myogenic response to systolic pressure in the afferent arteriole, Am J Physiol Renal Physiol, 300 (2011), pp. F669–F681.

    Article  Google Scholar 

  9. W. A. Cupples and B. Braam, Assessment of renal autoregulation, Am J Physiol Renal Physiol, 292 (2007), pp. F1105–F1123.

    Article  Google Scholar 

  10. S. Ditlevsen, K. Yip, D. Marsh, and N. Holstein-Rathlou, Parameter estimation of feedback gain in a stochastic model of renal hemodynamics: differences between spontaneously hypertensive and Sprague-Dawley rats, Am J Physiol Renal Physiol, 292 (2007), pp. F607–F616.

    Article  Google Scholar 

  11. R. Feldberg, M. Colding-Jèrgensen, and N. H. Holstein-Rathlou, Analysis of interaction between TGF and the myogenic response in renal blood flow autoregulation, Am J Physiol, 269 (1995), pp. F581–F593.

    Google Scholar 

  12. A. N. Ford Versypt, E. Makrides, J. Arciero, L. Ellwein, and A. T. Layton, Bifurcation study of blood flow control in the kidney. Math Biosci, 263 (2015), pp. 169–179.

    Article  MathSciNet  Google Scholar 

  13. N. Holstein-Rathlou, A closed-loop analysis of the tubuloglomerular feedback mechanism, Am J Physiol (Renal Fluid Electrolyte Physiol 30), 261 (1991), pp. F880–F889.

    Google Scholar 

  14. N. H. Holstein-Rathlou, Synchronization of proximal intratubular pressure oscillations: evidence for interaction between nephrons, Pflugers Arch, 408 (1987), pp. 438–443.

    Article  Google Scholar 

  15. N. H. Holstein-Rathlou and D. J. Marsh, Renal blood flow regulation and arterial pressure fluctuations: a case study in nonlinear dynamics, Physiol Rev, 74 (1994), pp. 637–681.

    Google Scholar 

  16. N. H. Holstein-Rathlou, O. V. Sosnovtseva, A. N. Pavlov, W. A. Cupples, C. M. Sorensen, and D. J. Marsh, Nephron blood flow dynamics measured by laser speckle contrast imaging, Am J Physiol Renal Physiol, 300 (2011), pp. F319–F329.

    Article  Google Scholar 

  17. N. H. Holstein-Rathlou, A. J. Wagner, and D. J. Marsh, Tubuloglomerular feedback dynamics and renal blood flow autoregulation in rats, AJP Renal Physiology, 260 (1991), pp. F53–F68.

    Google Scholar 

  18. A. Hope, G. Clausen, and L. Rosivall, Total and local renal blood flow and filtration in the rat during reduced renal arterial blood pressure, Acta Physiol Scand, 113 (1981), pp. 455–463.

    Article  Google Scholar 

  19. P. Johnson, The myogenic response, in Handbook of Physiology. The Cardiovascular System. Vascular Smooth Muscle, Am Physiol Soc, Bethesda, MD, 1981, pp. 409–442.

    Google Scholar 

  20. A. Layton, Feedback-mediated dynamics in a model of a compliant thick ascending limb, Math Biosci, 228 (2010), pp. 185–194.

    Article  MathSciNet  MATH  Google Scholar 

  21. H. Layton, E. Pitman, and L. Moore, Bifurcation analysis of TGF-mediated oscillations in SNGFR, Am J Physiol (Renal Fluid Electrolyte Physiol 30), 261 (1991), pp. F904–F919.

    Google Scholar 

  22. N. H. Holstein-Rathlou, A. J. Wagner, and D. J. Marsh,, Limit-cycle oscillations and tubuloglomerular feedback regulation of distal sodium delivery, Am J Physiol Renal Physiol, 278 (2000), pp. F287–F301.

    Google Scholar 

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

    Article  Google Scholar 

  24. D. J. Marsh, O. V. Sosnovtseva, K. H. Chon, and N. H. Holstein-Rathlou, Nonlinear interactions in renal blood flow regulation, Am J Physiol Regul Integr Comp Physiol, 288 (2005), pp. R1143–R1159.

    Article  Google Scholar 

  25. D. J. Marsh, O. V. Sosnovtseva, A. N. Pavlov, K. P. Yip, and N. H. Holstein-Rathlou, Frequency encoding in renal blood flow regulation, Am J Physiol Regul Integr Comp Physiol, 288 (2005), pp. R1160–R1167.

    Article  Google Scholar 

  26. D. J. Marsh, I. Toma, O. V. Sosnovtseva, J. Peti-Peterdi, and N.-H. Holstein-Rathlou, Electrotonic vascular signal conduction and nephron synchronization, Am J Physiol Renal Physiol, 296 (2009), pp. F751–F761.

    Article  Google Scholar 

  27. L. Moore, J. Schnermann, and S. Yarimizu, Feedback mediation of SNGFR autoregulation in hydropenic and DOCA- and salt-loaded rats, Am J Physiol Renal Physiol, 237 (1979), pp. F63–F74.

    Google Scholar 

  28. L. C. Moore, A. Rich, and D. Casellas, Ascending myogenic autoregulation: interactions between tubuloglomerular feedback and myogenic mechanisms, Bull Math Biol, 56 (1994), pp. 391–410.

    Article  MATH  Google Scholar 

  29. B. D. Myers, W. M. Deen, and B. M. Brenner, Effects of norepinephrine and angiotensin ii on the determinants of glomerular ultrafiltration and proximal tubule fluid reabsorption in the rat, Circ Res, 37 (1975), pp. 101–110.

    Article  Google Scholar 

  30. L. G. Navar, E. W. Inscho, J. D. Imig, and K. D. Mitchell, Heterogeneous activation mechanisms in the renal microvasculature., Kidney Int Suppl, 67 (1998), pp. S17–S21.

    Article  Google Scholar 

  31. P. O’Connor, Renal oxygen delivery: matching delivery to metabolic demand, Clin Exp Pharmacol Physiol, 33 (2006), pp. 961–967.

    Article  Google Scholar 

  32. W. Pfaller, Structure Function Correlation on Rat Kidney: Quantitative Correlation of Structure and Function in the Normal and Injured Rat Kidney, Springer-Verlag, New York, 1982.

    Book  Google Scholar 

  33. A. R. Pries, T. W. Secomb, T. Gessner, M. B. Sperandio, J. F. Gross, and P. Gaehtgens, Resistance to blood flow in microvessels in vivo, Circ Res, 75 (1994), pp. 904–915.

    Article  Google Scholar 

  34. R. J. Roman, Abnormal renal hemodynamics and pressure-natriuresis relationship in Dahl salt-sensitive rats., Am J Physiol: Renal Physiol, 251 (1986), pp. F57–F65.

    Google Scholar 

  35. R. J. Roman and A. W. Cowley, Jr, Characterization of a new model for the study of pressure-natriuresis in the rat, Am J Physiol, 248 (1985), pp. F190–F198.

    Google Scholar 

  36. H. Ryu and A. Layton, Effect of tubular inhomogeneities on feedback-mediated dynamics of a model of a thick ascending limb, Med Math Biol, 30 (2012), pp. 191–212.

    Article  MathSciNet  Google Scholar 

  37. W. E. Schiesser, The Numerical Method of Lines: Integration of Partial Differential Equations, Academic Press, San Diego, 1991.

    MATH  Google Scholar 

  38. J. Schnermann and J. Briggs, Function of the juxtaglomerular apparatus: Control of glomerular hemodynamics and renin secretion, in Seldin and Giebisch’s The Kidney: Physiology and Pathophysiology, A. RJ and H. SC, eds., Elsevier Academic Press, Amsterdam; Boston, 4th ed., 2008, pp. 589–626.

    Google Scholar 

  39. I. Sgouralis and A. Layton, Autoregulation and conduction of vasomotor responses in a mathematical model of the rat afferent arteriole, Am J Physiol Renal Physiol, 33 (2012), pp. F229–F239.

    Article  Google Scholar 

  40. W. E. Schiesser,, Control and modulation of fluid flow in the rat kidney, Bull Math Biol, in press, (2013).

    Google Scholar 

  41. W. E. Schiesser,,, Theoretical assessment of renal autoregulatory mechanisms, Am J Physiol Renal Physiol, in press, (2014).

    Google Scholar 

  42. L. Shampine and S. Thompson, Solving DDEs in MATLAB, Applied Numerical Mathematics, 37 (2001), pp. 441–458.

    Article  MathSciNet  MATH  Google Scholar 

  43. C. M. Sorensen, P. P. Leyssac, O. Skott, and N. H. Holstein-Rathlou, Role of the renin-angiotensin system in regulation and autoregulation of renal blood flow, Am J Physiol Regul Integr Comp Physiol, 279 (2000), pp. R1017–R1024.

    Google Scholar 

  44. S. Thomas, A. Layton, H. Layton, and L. Moore, Kidney moeling: status and perspectives, Proceedings of the IEEE, 94 (2006), pp. 740–752.

    Article  Google Scholar 

  45. V. Vallon, R. C. Blantz, and S. Thomson, Glomerular hyperfiltration and the salt paradox in early [corrected] type 1 diabetes mellitus: a tubulo-centric view, J Am Soc Nephrol, 14 (2003), pp. 530–537.

    Article  Google Scholar 

  46. V. Vallon, K. Richter, R. C. Blantz, S. Thomson, and H. Osswald, Glomerular hyperfiltration in experimental diabetes mellitus: potential role of tubular reabsorption, J Am Soc Nephrol, 10 (1999), pp. 2569–2576.

    Google Scholar 

  47. S. J. Van Dijk, P. A. C. Specht, J. Lazar, H. J. Jacob, and A. P. Provoost, Synergistic QTL interactions between Rf-1 and Rf-3 increase renal damage susceptibility in double congenic rats., Kidney Int, 69 (2006), pp. 1369–1376.

    Google Scholar 

  48. A. Vander, Renal Physiology, McGraw-Hill, New York, 5 ed., 1995.

    Google Scholar 

  49. G. Williamson, R. Loutzenhiser, X. Wang, K. Griffin, and A. Bidani, Systolic and mean blood pressures and afferent arteriolar myogenic response dynamics: a modeling approach, Am J Physiol Regul Integr Comp Physiol, 295 (2008), pp. R1502–R1511.

    Article  Google Scholar 

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Acknowledgements

The first three authors “Julia Arciero, Laura Ellwein, and Ashlee N. Ford Versypt” contributed equally. The work of the first author “Julia Arciero” was supported in part by the National Science Foundation (NSF), grant DMS-1224195. The work of the fifth author “Anita T. Layton” was supported in part by the NSF, grant DMS-1263995, and by the National Institutes of Health: National Institute of Diabetes and Digestive and Kidney Diseases, grant DK089066.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, Indianapolis, IN, 46202, USA

    Julia Arciero

  2. Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA, 23284, USA

    Laura Ellwein

  3. Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Ashlee N. Ford Versypt

  4. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    Elizabeth Makrides

  5. Department of Mathematics, Duke University, Durham, NC, 27705, USA

    Anita T. Layton

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  1. Julia Arciero
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  2. Laura Ellwein
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  3. Ashlee N. Ford Versypt
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  4. Elizabeth Makrides
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  5. Anita T. Layton
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Correspondence to Julia Arciero .

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Editors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, Michigan, USA

    Trachette Jackson

  2. Department of Mathematics, Pomona College, Claremont, California, USA

    Ami Radunskaya

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Arciero, J., Ellwein, L., Versypt, A.N.F., Makrides, E., Layton, A.T. (2015). Modeling Blood Flow Control in the Kidney. In: Jackson, T., Radunskaya, A. (eds) Applications of Dynamical Systems in Biology and Medicine. The IMA Volumes in Mathematics and its Applications, vol 158. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2782-1_3

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