Predicting the risk of kidney stone formation in the nephron by ‘reverse engineering’

  • Michael G. Hill
  • Erich KönigsbergerEmail author
  • Peter M. May
Original Paper


Although most kidney stones are found in the calyx, they are usually initiated upstream in the nephron by precipitation there of certain incipient mineral phases. The risk of kidney stone formation can thus be indicated by changes in the degree of saturation of these minerals in the nephron fluid. To this end, relevant concentration profiles in the fluid along the nephron have been calculated by starting with specified urine compositions and imposing constraints from the corresponding, much less variable, blood compositions. A model for supersaturation within ten sections of both long and short nephrons has accordingly been developed based on this ‘reverse engineering’ of the necessary substance concentrations coupled with chemical speciation distributions calculated by our Joint Expert Speciation System (JESS). This allows the likelihood of precipitation to be assessed based on Ostwald’s ‘Rule of Stages’. Differences between normal and stone-former profiles have been used to identify sections in the nephron where conditions seem most likely to induce heterogeneous nucleation.


Urinalysis Brushite Computer modelling Ostwald’s ‘Rule of Stages’ Joint Expert Speciation System 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Grases F, Costa-Bauzá A, Garcia-Ferragut L (1998) Biopathological crystallization: a general view about the mechanisms of renal stone formation. Adv Colloid Interface Sci 74:169–194CrossRefGoogle Scholar
  2. 2.
    Kallidonis P, Liourdi D, Liatsikos E (2011) Medical treatment for renal colic and stone expulsion. Eur Urol Suppl 10:415–422CrossRefGoogle Scholar
  3. 3.
    Tiselius HG (2011) Who forms stones and why? Eur Urol Suppl 10:408–414CrossRefGoogle Scholar
  4. 4.
    Hill MG, Königsberger E, May PM (2017) Mineral precipitation and dissolution in the kidney. Am Mineral 102:701–710CrossRefGoogle Scholar
  5. 5.
    Tiselius HG (1982) An improved method for the routine biochemical evaluation of patients with recurrent calcium oxalate stone disease. Clin Chim Acta 122:409–418CrossRefGoogle Scholar
  6. 6.
    Milosevic D, Batinic D, Konjevoda NBP, Stambuk N, Votava- Raic A, Fumic VBK, Rumenjak V, Stavljenic-Rukavina A, Nizic L, Vrljicak K (1998) Determination of urine supersaturation with computer program Equil 2 as a method for estimation of the risk of urolithiasis. J Chem Inf Comput Sci 38:646–650CrossRefGoogle Scholar
  7. 7.
    Laube N, Schneider A, Hesse A (2000) A new approach to calculate the risk of calcium oxalate crystallization from unprepared native urine. Urol Res 28:274–280CrossRefGoogle Scholar
  8. 8.
    Hill MG (2019) A chemical model to investigate the risk of kidney stone formation in humans in terms of urinary supersaturation. PhD thesis, Murdoch UniversityGoogle Scholar
  9. 9.
    Rodgers AL, Allie-Hamdulay S, Jackson G, Tiselius HG (2011) Simulating calcium salt precipitation in the nephron using chemical speciation. Urol Res 39:245–251CrossRefGoogle Scholar
  10. 10.
    Robertson WG (2015) Potential role of fluctuations in the composition of renal tubular fluid through the nephron in the initiation of Randall’s plugs and calcium oxalate crystalluria in a computer model of renal function. Urolithiasis 43(Supplement 1):S93–S107CrossRefGoogle Scholar
  11. 11.
    Tiselius H, Lindbäck B, Fornander AM, Nilsson MA (2009) Studies on the role of calcium phosphate in the process of calcium oxalate crystal formation. Urol Res 37:181–192CrossRefGoogle Scholar
  12. 12.
    Højgaard I, Tiselius HG (1999) Crystallization in the nephron. Urol Res 27:397–403CrossRefGoogle Scholar
  13. 13.
    Tiselius HG (1997) Estimated levels of supersaturation with calcium phosphate and calcium oxalate in the distal tubule. Urol Res 25:153–159CrossRefGoogle Scholar
  14. 14.
    Kok DJ (1997) Intratubular crystallization events. World J Urol 15:219–228CrossRefGoogle Scholar
  15. 15.
    Söhnel O, Grases F (1995) Calcium oxalate monohydrate renal calculi. Formation and development mechanism. Adv Colloid Interface Sci 59:1–17CrossRefGoogle Scholar
  16. 16.
    Grases F, Costa-Bauzá A, Gomila I, Ramis M, García-Raja A, Prieto RM (2012) Urinary pH and renal lithiasis. Urol Res 40:41–46CrossRefGoogle Scholar
  17. 17.
    Robertson WG, Scurr DS, Bridge CM (1981) Factors influencing the crystallisation of calcium oxalate in urine–critique. J Cryst Growth 53:182–194CrossRefGoogle Scholar
  18. 18.
    Tiselius HG (2011) A hypothesis of calcium stone formation: an interpretation of stone research during the past decades. Urol Res 39:231–243CrossRefGoogle Scholar
  19. 19.
    Rodgers A, Webber D, Hibberd B (2015) Experimental determination of multiple thermodynamic and kinetic factors for nephrolithiasis in the urine of healthy controls and calcium oxalate stone formers: does a universal discriminator exist? Urolithiasis 43:479–487CrossRefGoogle Scholar
  20. 20.
    Coe FL, Evan A, Worcester E (2011) Pathophysiology-based treatment of idiopathic calcium kidney stones. Clin J Am Soc Nephrol 6:2083–2092CrossRefGoogle Scholar
  21. 21.
    Baumann JN, Affolter B (2014) From crystaluria to kidney stones, some physicochemical aspects of calcium nephrolithiasis. World J Nephrol 3:256–267CrossRefGoogle Scholar
  22. 22.
    Söhnel O, Grases F (2011) Supersaturation of body fluids, plasma and urine, with respect to biological hydroxyapatite. Urol Res 39:429–436CrossRefGoogle Scholar
  23. 23.
    Asplin JR, Mandel NS, Coe FL (1996) Evidence for calcium phosphate supersaturation in the loop of Henle. Am J Physiol 270:F604–F613PubMedGoogle Scholar
  24. 24.
    Luptak J, Bek-Jensen H, Fornander AM, Højgaard I, Nilsson MA, Tiselius H (1994) Crystallization of calcium oxalate and calcium phosphate at superstauration levels corresponding to those in different parts of the nephron. Scan Microsc 8:47–62Google Scholar
  25. 25.
    Grases F, Villacampa AI, Söhnel O, Königsberger E, May PM (1997) Phosphate composition of precipitates from urine-like liquors. Cryst Res Technol 32:707–715CrossRefGoogle Scholar
  26. 26.
    Johnsson MSA, Nancollas GH (1992) The role of brushite and octacalcium phosphate in apatite formation. Crit Rev Oral Biol Med 3:61–82CrossRefGoogle Scholar
  27. 27.
    Pak CYC (1969) Physicochemical basis for formation of renal stones of calcium phosphate origin: calculation of the degree of saturation of urine with respect to brushite. J Clin Investig 48:1914–1922CrossRefGoogle Scholar
  28. 28.
    Pak CYC (1981) Potential etiologic role of brushite in the formation of calcium (renal) stones. J Cryst Growth 53:202–208CrossRefGoogle Scholar
  29. 29.
    Pak CYC, Rodgers K, Poindexter JR, Sakhaee K (2008) New methods of assessing crystal growth and saturation of brushite in whole urine: effect of pH, calcium and citrate. J Urol 180:1532–1537CrossRefGoogle Scholar
  30. 30.
    Coe FL, Parks JH, Nakagawa Y (1992) Inhibitors and promoters of calcium oxalate crystallization. their relationship to the pathogenesis and treatment of nephrolithiasis. In: Coe FL, Favus MJ (eds) Disorders of bone and mineral metabolism, vol 35. Raven Press Ltd, New York, pp 757–799Google Scholar
  31. 31.
    Rabadjieva D, Tepavitcharova S, Sezanova K, Gergulova R (2016) Chemical equilibria modeling of calcium phosphate precipitation and transformation in simulated physiological solutions. J Solut Chem 45:1620–1633CrossRefGoogle Scholar
  32. 32.
    Sawada K (1997) The mechanisms of crystallization and transformation of calcium carbonates. Pure Appl Chem 69:921–928CrossRefGoogle Scholar
  33. 33.
    Zhang J, Wang L, Putnis C (2019) Underlying role of brushite in pathological mineralization of hydroxyapatite. J Phys Chem B 123:2874–2881CrossRefGoogle Scholar
  34. 34.
    Atherton JC (2006) Function of the nephron and the formation of urine. Anaesth Intensive Care Med 7:221–226CrossRefGoogle Scholar
  35. 35.
    Good DW, Knepper MA (1985) Ammonia transport in the mammalian kidney. Am J Physiol 248:F459–F471PubMedGoogle Scholar
  36. 36.
    May PM, Murray K (1991) JESS, a Joint Expert Speciation System—I. Raison d’être. Talanta 38:1409–1417CrossRefGoogle Scholar
  37. 37.
    May PM, Murray K (1991) JESS, a Joint Expert Speciation System—II. The thermodynamic database. Talanta 38:1419–1426CrossRefGoogle Scholar
  38. 38.
    May PM (2015) JESS at thirty: strengths, weaknesses and future needs in the modelling of chemical speciation. Appl Geochem 55:3–16CrossRefGoogle Scholar
  39. 39.
    May PM, Rowland D (2018) JESS, a Joint Expert Speciation System—VI: thermodynamically-consistent standard Gibbs energies of reaction for aqueous solutions. N J Chem 42:7617–7629CrossRefGoogle Scholar
  40. 40.
    Cavan D, Hovorka R, Hejlesen O, Andreassen S, Sonksen P (1996) Use of the DIAS model to predict unrecognised hypoglycaemia in patients with insulin dependent diabetes. Comput Methods Prog Biomed 50:241–246CrossRefGoogle Scholar
  41. 41.
    Hill M (2010) A personal experience of using computer technology to assist with the treatment of diabetes. In: Proceedings of the UKACC international conference on control, Coventry, UK, pp 417–422.

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.ChemistryMurdoch UniversityMurdochAustralia

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