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Women in Mathematical Biology pp 101–113Cite as

Modeling Blood Flow and Oxygenation in a Diabetic Rat Kidney

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

Abstract

We use a highly detailed mathematical model of renal hemodynamics and solute transport to simulate medullary oxygenation in the kidney of a diabetic rat. Model simulations suggest that alterations in renal hemodynamics, which include diminished vasoconstrictive response of the afferent arteriole as a major factor, lead to glomerular hyperfiltration in diabetes. The resulting higher filtered Na+ load increases the reabsorptive work of the nephron, but by itself does not significantly elevate medullary oxygen consumption. The key explanation for diabetes-related medullary hypoxia may be impaired renal metabolism. Tubular transport efficiency is known to be reduced in diabetes, leading to increased medullary oxygen consumption, despite relatively unchanged active Na+ transport. The model predicts that interstitial fluid oxygen tension of the inner stripe, which is a particularly oxygen-poor region of the medulla, decreases by 18.6% in a diabetic kidney.

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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References

  1. Bagnasco, S., Good, D., Balaban, R., Burg, M.: Lactate production in isolated segments of the rat nephron. Am. J. Physiol. Ren. Physiol.248, F522–F526 (1985)

    Google Scholar 

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

    Google Scholar 

  3. Carmines, P., Inscho, E., Gensure, R.: Arterial pressure effects on preglomerular microvasculature of juxtamedullary nephrons. Am. J. Physiol.258, F94–F102 (1990)

    Google Scholar 

  4. Carmines, P.K., Ohishi, K., Ikenaga, H.: Functional impairment of renal afferent arteriolar voltage-gated calcium channels in rats with diabetes mellitus. J. Clin. Invest.98, F386–F395 (1996)

    Article  Google Scholar 

  5. Chen, J., Layton, A., Edwards, A.: A mathematical model of oxygen transport in the rat outer medulla: I. model formulation and baseline results. Am. J. Physiol. Ren. Physiol.297, F517–F536 (2009)

    Google Scholar 

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

    Article  Google Scholar 

  7. Cupples, W., Braam, B.: Assessment of renal autoregulation. Am. J. Physiol. Ren. Physiol.292, F1105–F1123 (2007)

    Article  Google Scholar 

  8. Dickman, K., Mandel, L.: Differential effects of respiratory inhibitors on glycolysis in proximal tubules. Am. J. Physiol.258, F1608–F1615 (1990)

    Google Scholar 

  9. Edwards, A., Layton, A.: Modulation of outer medullary NaCl transport and oxygenation by nitric oxide and superoxide. Am. J. Physiol. Ren. Physiol.301, F979–F996 (2011)

    Article  Google Scholar 

  10. Evans, R., Ince, C., Joles, J., Smith, D., May, C., O’Connor, P., Gardiner, B.: Haemodynamic influences on kidney oxygenation: the clinical implications of integrative physiology. Clin. Exp. Pharmacol. Physiol.40, 106–122 (2013)

    Article  Google Scholar 

  11. Evans, R., Harrop, G., Ngo, J., Ow, C., O’Connor, P.: Basal renal oxygen consumption and the efficiency of oxygen utilization for sodium reabsorption. Am. J. Physiol. Ren. Physiol.306, F551–F560 (2014)

    Article  Google Scholar 

  12. Foley, R.N., Collins, A.J.: End-stage renal disease in the United States: an update from the United States Rrenal Data System. J. Am. Soc. Nephrol.18, 2644–2648 (2007)

    Article  Google Scholar 

  13. Fry, B., Edward, A., Sgouralis, I., Layton, A.: Impact of renal medullary three-dimensional architecture on oxygen transport. Am. J. Physiol. Ren. Physiol.307, F263–F272 (2014)

    Article  Google Scholar 

  14. Fry, B., Edward, A., Layton, A.: Impacts of nitric oxide and superoxide on renal medullary oxygen transport and urine concentration. Am. J. Physiol. Ren. Physiol.308, F967–F980 (2015)

    Article  Google Scholar 

  15. Greger, R., Schlatter, E., Lang, F.: Evidence for electroneutral sodium chloride cotransport in the cortical thick ascending limb of Henle’s loop of rabbit kidney. Pflügers. Arch.396, 308–314 (1983)

    Article  Google Scholar 

  16. Hansell, P., Welch, W., Blantz, R., Palm, F.: Determinants of kidney oxygenation and their relationship to tissue oxygen tension in diabetes and hypertension. Clin. Exp. Pharmacol. Physiol.40, 123–137 (2013)

    Article  Google Scholar 

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

    Google Scholar 

  18. Komers, R., Lindsley, J., Oyama, T., Allison, K., Anderson, S.: Role of neuronal nitric oxide synthesis (NOS1) in the pathoegensis of renal hemodynamic changes in diabetes. Am. J. Physiol.279, F573–F583 (2000)

    Google Scholar 

  19. Layton, A.: A mathematical model of the urine concentrating mechanism in the rat renal medulla: I. formulation and base-case results. Am. J. Physiol. Ren. Physiol.300, F356–F371 (2011)

    Google Scholar 

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

    Google Scholar 

  21. Layton, A., Dantzler, W., Pannabecker, T.: Urine concentrating mechanism: impact of vascular and tubular architecture and a proposed descending limb urea-Na+ cotransporter. Am. J. Physiol. Ren. Physiol.302, F591–F605 (2012)

    Article  Google Scholar 

  22. Leehey, D., Singh, A., Alavi, N., Singh, R.: Role of angiotensin II in diabetic nephropathy. Kidney Int.58(Suppl 77), S93–S98 (2000)

    Article  Google Scholar 

  23. Moss, R., Layton, A.: Dominant factors that govern pressure natriuresis in diuresis and antidiuresis: a mathematical model. Am. J. Physiol. Ren. Physiol.306, F952–F969 (2014)

    Article  Google Scholar 

  24. Nieves-Gonzalez, A., Clausen, C., Layton, A., Layton, H., Moore, L.: Transport efficiency and workload distribution in a mathematical model of the thick ascending limb. Am. J. Physiol. Ren. Physiol.304, F653–F664 (2013)

    Article  Google Scholar 

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

    Article  Google Scholar 

  26. Sgouralis, I., Layton, A.: Theoretical assessment of renal autoregulatory mechanisms. Am. J. Physiol. Ren. Physiol.306, F1357–F1371 (2014)

    Article  Google Scholar 

  27. Stokes, J., Grupp, C., Kinne, R.: Purification of rat papillary collecting duct cells: functional and metabolic assessment. Am. J. Physiol.253, F251–F262 (1987)

    Google Scholar 

  28. Thomson, S.C., Vallon, V., Blantz, R.C.: Resetting protects efficiency of tubuloglomerular feedback. Kidney Int. Suppl.67, S65–S70 (1998)

    Article  Google Scholar 

  29. Uchida, S., Endou, H.: Substrate specificity to maintain cellular ATP along the mouse nephron. Am. J. Physiol. Ren. Physiol.255, F977–F983 (1988)

    Google Scholar 

  30. Vallon, V.: The proximal tubule in the pathophysiology of the diabetic kidney. Am. J. Physiol. Regul. Integr. Comp. Physiol.300, R1009–R1022 (1996)

    Article  Google Scholar 

  31. Vallon, V.: The proximal tubule in the pathophysiology of the diabetic kidney. Am. J. Physiol. Regul. Integr. Comp. Physiol.300, 1009–1022 (2011)

    Article  Google Scholar 

  32. Vallon, V.: The mechanisms and therapeutic potential of SGLT2 inhibitors in diabetes mellitus. Annu. Rev. Med.66, 255–270 (2015)

    Article  Google Scholar 

  33. Vallon, V., Thomson, S.: Renal function in diabetic disease models: the tubular system in the pathophysiology of the diabetic kidney. Annu. Rev. Physiol.74, 351–375 (2012)

    Article  Google Scholar 

  34. Vallon, V., Blantz, R., Thomson, S.: Homeostatic efficiency of tubuloglomerular feedback is reduced in established diabetes mellitus in rats. Am. J. Physiol. (Renal Fluid Electrolyte Physiol 38)269, F876–F883 (1995)

    Google Scholar 

  35. Weinstein, A.: A mathematical model of the inner medullary collecting duct of the rat: pathways for Na and K transport. Am. J. Physiol. (Renal Physiol 43)274, F841–F855 (1998)

    Google Scholar 

  36. Zeidel, M., Silva, P., Seifter, J.: Intracellular pH regulation and proton transport by rabbit renal medullary collecting duct cells: role of plasma membrane proton adenosine triphosphatase. J. Clin. Invest.77, 113–120 (1986)

    Article  Google Scholar 

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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. NIMBioS, University of Tennessee Knoxville, Knoxville, TN, 37996, USA

    Ioannis Sgouralis

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

    Anita T. Layton

Authors
  1. Ioannis Sgouralis
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  2. Anita T. Layton
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Correspondence to Ioannis Sgouralis .

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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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Sgouralis, I., Layton, A.T. (2017). Modeling Blood Flow and Oxygenation in a Diabetic Rat 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_6

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