Modeling Blood Flow and Oxygenation in a Diabetic Rat Kidney

Conference paper
First Online:
Part of the Association for Women in Mathematics Series book 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.

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

Notes

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.

References

  1. 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. 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. 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. 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)CrossRefGoogle Scholar
  5. 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. 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)CrossRefGoogle Scholar
  7. 7.
    Cupples, W., Braam, B.: Assessment of renal autoregulation. Am. J. Physiol. Ren. Physiol.292, F1105–F1123 (2007)CrossRefGoogle Scholar
  8. 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. 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)CrossRefGoogle Scholar
  10. 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)CrossRefGoogle Scholar
  11. 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)CrossRefGoogle Scholar
  12. 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)CrossRefGoogle Scholar
  13. 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)CrossRefGoogle Scholar
  14. 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)CrossRefGoogle Scholar
  15. 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)CrossRefGoogle Scholar
  16. 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)CrossRefGoogle Scholar
  17. 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. 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. 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. 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. 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)CrossRefGoogle Scholar
  22. 22.
    Leehey, D., Singh, A., Alavi, N., Singh, R.: Role of angiotensin II in diabetic nephropathy. Kidney Int.58(Suppl 77), S93–S98 (2000)CrossRefGoogle Scholar
  23. 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)CrossRefGoogle Scholar
  24. 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)CrossRefGoogle Scholar
  25. 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)CrossRefGoogle Scholar
  26. 26.
    Sgouralis, I., Layton, A.: Theoretical assessment of renal autoregulatory mechanisms. Am. J. Physiol. Ren. Physiol.306, F1357–F1371 (2014)CrossRefGoogle Scholar
  27. 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. 28.
    Thomson, S.C., Vallon, V., Blantz, R.C.: Resetting protects efficiency of tubuloglomerular feedback. Kidney Int. Suppl.67, S65–S70 (1998)CrossRefGoogle Scholar
  29. 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. 30.
    Vallon, V.: The proximal tubule in the pathophysiology of the diabetic kidney. Am. J. Physiol. Regul. Integr. Comp. Physiol.300, R1009–R1022 (1996)CrossRefGoogle Scholar
  31. 31.
    Vallon, V.: The proximal tubule in the pathophysiology of the diabetic kidney. Am. J. Physiol. Regul. Integr. Comp. Physiol.300, 1009–1022 (2011)CrossRefGoogle Scholar
  32. 32.
    Vallon, V.: The mechanisms and therapeutic potential of SGLT2 inhibitors in diabetes mellitus. Annu. Rev. Med.66, 255–270 (2015)CrossRefGoogle Scholar
  33. 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)CrossRefGoogle Scholar
  34. 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. 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. 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)CrossRefGoogle Scholar

Copyright information

© The Author(s) and the Association for Women in Mathematics 2017

Authors and Affiliations

  1. 1.NIMBioSUniversity of Tennessee KnoxvilleKnoxvilleUSA
  2. 2.Department of MathematicsDuke UniversityDurhamUSA

Personalised recommendations