A 3-Dimentional Framework for Studying the Effects of Structural and Physical Properties of the Renal Outer Medulla on Urine Concentrating Mechanism

Saadatmand, Maryam; Saidi, Mohammad Said; Sohrabi, Salman; Banazadeh, Mohammad Hossein; Sadeghi Lafmejani, Saeed; Hamed, Hamid; Firoozabadi, Bahar

doi:10.22034/ijabbr.2021.44618

Document Type : Original Article

Authors

¹ Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran

² Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

https://doi.org/10.22034/ijabbr.2021.44618

Abstract

Background: Many theories and mathematical simulations have been proposed concerning urine concentrating mechanism (UCM). Due to significant effect of the tubule and vessel architecture in concentrating mechanism, the numerical analysis of UCM through a 3-Dimensional structure might be the answer to find a better consistency between the experimental and theoretical results.
Methods: In this paper we have investigated the effects of structural characteristics of the tubules and vessels on the urine concentrating mechanism in the outer medulla (OM) by developing a simple three-dimensional mathematical model. This model is a framework to attain a converged numerical solution for the momentum and species transport equations along with their stiff and coupled boundary conditions based on standard expressions for trans-tubular solutes and water transports on tubule’s membrane.
Results: The model structure and the number of the involved tubules have been assumed to be as simple as possible. The effects of slip boundary condition on membrane, Darcy permeability and solute’s diffusivity of the intermediate media on UCM have been studied. It has been shown that this approach can simply simulate preferential interactions and tubule’s confinement by radial diffusion coefficients.
Conclusions: All in all, the feasibility of the idea of completely 3-D modeling by employing the concept of diffusion coefficient and Darcy permeability has been explored and validated.

Graphical Abstract

Keywords

Main Subjects

Human Physiology

References

1. Qian, Q. (2018). Salt, water and nephron: Mechanisms of action and link to hypertension and chronic kidney disease. Nephrology, 23: 44-49.

2. Layton, AT. (2017). A new microscope for the kidney: mathematics. American Journal of Physiology-Renal Physiology, 312(4): F671-F672.

3. Layton, HE. (2002). Mathematical models of the mammalian urine concentrating mechanism. IMA VOLUMES IN MATHEMATICS AND ITS APPLICATIONS, 129(1): 233-272.

4. Sohrabi, S, Saidi, M.S, Saadatmand, M, Banazadeh, M.H, Firoozabadi, B. (2014). Three-dimensional simulation of urine concentrating mechanism in a functional unit of rat outer medulla. I. Model structure and base case results. Mathematical biosciences, 258: 44-56.

5. Burg, M, Green, N. (1973). Function of the thick ascending limb of Henle's loop. American Journal of Physiology-Legacy Content, 224(3): 659-668.

6. Rocha, AS, Kokko, JP. (1973). Sodium chloride and water transport in the medullary thick ascending limb of Henle. Evidence for active chloride transport. The Journal of clinical investigation, 52(3): 612-623.

7. Chou, C, Knepper, M. (1992). In vitro perfusion of chinchilla thin limb segments: segmentation and osmotic water permeability. American Journal of Physiology-Renal Physiology, 263(3): F417-F426.

8. Imai, M, Kokko, JP. (1974). Sodium chloride, urea, and water transport in the thin ascending limb of Henle. Generation of osmotic gradients by passive diffusion of solutes. The Journal of clinical investigation, 53(2): 393-402.

9. Marsh D, Azen, SP. (1975). Mechanism of NaCl reabsorption by hamster thin ascending limbs of Henle's loop. American Journal of Physiology-Legacy Content, 228(1): 71-79.

10. Yool, AJ, Brokl, OH, Pannabecker, TL, Dantzler, WH, Stamer, WD. (2002). Tetraethylammonium block of water flux in Aquaporin-1 channels expressed in kidney thin limbs of Henle's loop and a kidney-derived cell line. BMC physiology, 2(1): 4.

11. Stephenson, JL. (1972). Concentration of urine in a central core model of the renal counterflow system. Kidney international, 2(2): 85-94.

12. Kokko, J, Rector Jr, F. (1972). Countercurrent multiplication system without active transport in inner medulla. Kidney international, 2(4): 214-223.

13. Wang, X, Thomas, SR, Wexler, AS. (1998). Outer medullary anatomy and the urine concentrating mechanism. American Journal of Physiology-Renal Physiology, 274(2): F413-F424.

14. Wexler, AS, Kalaba, RE, Marsh, DJ. (1991). Three-dimensional anatomy and renal concentrating mechanism. I. Modeling results. American Journal of Physiology-Renal Physiology, 260(3): F368-F383.

15. Pannabecker, TL, Dantzler, WH, Layton, HE, Layton, AT. (2008). Role of three-dimensional architecture in the urine concentrating mechanism of the rat renal inner medulla. American Journal of Physiology-Renal Physiology, 295(5): F1271-F1285.

16. Zhai, XY, Thomsen, JS, Birn, H, Kristoffersen, IB, Andreasen, A, Christensen, E. (2006). Three-dimensional reconstruction of the mouse nephron. Journal of the American Society of Nephrology, 17(1): 77-88.

17. Layton, A.T, Layton, H.E. (2005). A region-based mathematical model of the urine concentrating mechanism in the rat outer medulla. I. Formulation and base-case results. American Journal of Physiology-Renal Physiology, 289(6): F1346-F1366.

18. Layton, AT, Pannabecker, TL, Dantzler, WH, Layton, HE. (2010). Functional implications of the three-dimensional architecture of the rat renal inner medulla. American Journal of Physiology-Renal Physiology, 298(4): F973-F987.

19. Bentley, M, Jorgensen, S, Lerman, L, Ritman, E, Romero, J. (2007). Visualization of three‐dimensional nephron structure with microcomputed tomography. ANAT. REC, 290(3): 277-283.

20. Kriz, W, Kaissling, B. (1992). Structural organization of the mammalian kidney. The kidney: physiology and pathophysiology, 3: 587-654.

21. Pannabecker, TL, Dantzler, WH. (2004). Three-dimensional lateral and vertical relationships of inner medullary loops of Henle and collecting ducts. American Journal of Physiology-Renal Physiology, 287(4): F767-F774.

22. Layton, AT, Layton, HE. (2003). A region-based model framework for the rat urine concentrating mechanism. Bulletin of mathematical biology, 65(5): 859-901.

23. Layton, AT, Vallon, V. (2018). Renal tubular solute transport and oxygen consumption: insights from computational models. Current opinion in nephrology and hypertension, 27(5): 384-389.

24. Layton, AT. (2017). Tracking the Distribution of a Solute Bolus in the Rat Kidney Women in Mathematical Biology (pp. 115-136): Springer.

25. Chen, Y, Fry, B, Layton, A. (2017). Modeling glucose metabolism and lactate production in the kidney. Mathematical biosciences, 289: 116-129.

26. Sgouralis, I, Layton, AT. (2015). Mathematical modeling of renal hemodynamics in physiology and pathophysiology. Mathematical biosciences, 264: 8-20.

27. Layton, AT, Laghmani, K, Vallon, V, Edwards, A. (2016). Solute transport and oxygen consumption along the nephrons: effects of Na+ transport inhibitors. American Journal of Physiology-Renal Physiology, 311(6): F1217-F1229.

28. Sgouralis, I, Layton, AT. (2017). Modeling blood flow and oxygenation in a diabetic rat kidney Women in Mathematical Biology (pp. 101-113): Springer.

29. Wexler, AS, Marsh, DJ. (1991). Numerical methods for three-dimensional models of the urine concentrating mechanism. Applied mathematics and computation, 45(2): 219-240.

30. Sohrabi S, Saidi M S, Saadatmand M, Banazadeh M H, Firoozabadi B. (2014). Three-dimensional simulation of urine concentrating mechanism in a functional unit of rat outer medulla. I. Model structure and base case results. Mathematical biosciences, 258: 44-56.

31. Kriz, W., Kaissling,, B. (2000). Structural organization of the mammalian kidney The kidney physiology and Pathophysiology (3d ed). Philadelphia: Lippincott Williams Wilkins: 588-654

32. Layton H E. (2002). Mathematical Models of the Mammalian Urine Concentrating Mechanism. Membrane Transport and Renal Physiology, 129.

33. Stephenson, J. L., Zhang, Y., Eftekhari, A., Tewarson, R. (1987). Electrolyte transport in a central core model of the renal medulla. Am J Physiol, 253(5 Pt 2): F982-997.

34. Mirbagheri, S.A, Saidi, M.S, Sohrabi, S, Firoozabadi, B, Banazadeh, M.H. (2016). Effects of hypertension on Intima-Media Thickness (IMT); application to a human carotid artery. Scientia Iranica, 23(4): 1731-1740.

35. Kedem, O, Katchalsky, A. (1963). Permeability of composite membranes. Part 1.—Electric current, volume flow and flow of solute through membranes. Transactions of the Faraday Society, 59: 1918-1930.

36. Sani M, SAEIDI, MS. (2010). Rayan: A polyhedral grid co-located incompressible finite volume solver (part I: basic design features).

37. Sani M, Saidi, MS. (2009). A set of particle locating algorithms not requiring face belonging to cell connectivity data. Journal of Computational Physics, 228(19): 7357-7367.

38. Sani M, Saidi, MS. (2010). A lagged implicit segregated data reconstruction procedure to treat open boundaries. Journal of Computational Physics, 229(14): 5418-5431.

39. Lide, D.R. . (2001). CRC Handbook of Chemistry and Physics. 82th edn. Cleveland, OH: CRC.

40. Sani, M, Saidi, MS. (2010). A lagged implicit segregated data reconstruction procedure to treat open boundaries. Journal of Computational Physics, 229(14): 5418-5431.

41. Sohrabi, S, Nemati Mehr, S.M, Falsafi, P. (2013). A Novel Approach for Compensating the Significance of Tubule’s Architecture in Urine Concentrating Mechanism of Renal Medulla. Paper presented at the ASME 2013 International Mechanical Engineering Congress and Exposition.

International Journal of Advanced Biological and Biomedical Research

A 3-Dimentional Framework for Studying the Effects of Structural and Physical Properties of the Renal Outer Medulla on Urine Concentrating Mechanism

References

References

Volume 9, Issue 1 - Serial Number 1
January 2021
Pages 28-47

A 3-Dimentional Framework for Studying the Effects of Structural and Physical Properties of the Renal Outer Medulla on Urine Concentrating Mechanism

References

References

Volume 9, Issue 1 - Serial Number 1January 2021Pages 28-47

Volume 9, Issue 1 - Serial Number 1
January 2021
Pages 28-47