Reverse engineering the kidney: modelling calcium oxalate monohydrate crystallization in the nephron

  • A. Borissova
  • G. E. Goltz
  • J. P. Kavanagh
  • T. A. Wilkins
Original Article

Abstract

Crystallization of calcium oxalate monohydrate in a section of a single kidney nephron (distal convoluted tubule) is simulated using a model adapted from industrial crystallization. The nephron fluid dynamics is represented as a crystallizer/separator series with changing volume to allow for water removal along the tubule. The model integrates crystallization kinetics and crystal size distribution and allows the prediction of the calcium oxalate concentration profile and the nucleation and growth rates. The critical supersaturation ratio for the nucleation of calcium oxalate crystals has been estimated as 2 and the mean crystal size as 1 μm. The crystal growth order, determined as 2.2, indicates a surface integration mechanism of crystal growth and crystal growth dispersion. The model allows the exploration of the effect of varying the input calcium oxalate concentration and the rate of water extraction, simulating real life stressors for stone formation such as dietary loading and dehydration.

Keywords

Crystallization Calcium oxalate Kidney Simulation Population balance 

Abbreviations

COM

Calcium oxalate monohydrate

CSD

Crystal size distribution

MSMPR

Mixed suspension, mixed product removal

PB

Population balance

WR

Fractional water removal rate

References

  1. 1.
    Andreassen JP, Hounslow MJ (2004) Growth and aggregation of vaterite in seeded-batch experiments. AIChE J 50:2772–2782CrossRefGoogle Scholar
  2. 2.
    Borissova A (2009) General systems modeling of multi-phase batch crystallization from solution. Chem Eng Process Process Intensif 48:268–278CrossRefGoogle Scholar
  3. 3.
    Bramley AS, Hounslow MJ, Ryall RL (1997) Aggregation during precipitation from solution. Kinetics for calcium oxalate monohydrate. Chem Eng Sci 52:747–757CrossRefGoogle Scholar
  4. 4.
    Brunsteiner M, Jones AG, Pratola F, Price SL, Simons SJR (2005) Toward a molecular understanding of crystal agglomeration. Cryst Growth Des 5:3–16CrossRefGoogle Scholar
  5. 5.
    Dean JA (ed) (1979) Lange’s handbook of chemistry, 12th edn. McGraw-Hill, New York, p 4–35Google Scholar
  6. 6.
    Fasano JM, Khan RK (2001) Intratubular crystallization of calcium oxalate in the presence of membrane vesicles: an in vitro study. Kidney Int 59:169–178CrossRefPubMedGoogle Scholar
  7. 7.
    Finlayson B (1972) The concept of a continuous crystallizer. Its theory and application to in vivo and in vitro urinary tract models. Investig Urol 9:258–263Google Scholar
  8. 8.
    Finlayson B, Reid F (1978) Expectation of free and fixed particles in urinary stone disease. Investig Urol 15:442–448Google Scholar
  9. 9.
    Garside J, Mersmann A, Nyvlt J (1990) Measurement of crystal growth rates. European Federation of Chemical Engineering, Working Party on Crystallization, Munich, p 37Google Scholar
  10. 10.
    Hartel RW, Randolph AD (1986) Mechanisms and kinetic modeling of calcium oxalate crystal aggregation in a urinelike liquor, part II: kinetic modeling. AIChE J 32:1186–1195CrossRefGoogle Scholar
  11. 11.
    Hartel RW, Gottung BE, Randolph AD, Drach GW (1986) Mechanisms and kinetic modeling of calcium oxalate crystal aggregation in a urinelike liquor, part I: mechanisms. AIChE J 32:1176–1185CrossRefGoogle Scholar
  12. 12.
    Hess B, Meinhardt U, Zipperle L, Giovanoli R (1995) Simultaneous measurements of calcium oxalate nucleation and aggregation: impact of various modifiers. Urol Res 23:231–238CrossRefPubMedGoogle Scholar
  13. 13.
    Højgaard I, Tiselius HG (1999) Crystallization in the nephron. Urol Res 27:397–403CrossRefPubMedGoogle Scholar
  14. 14.
    Højgaard I, Fornander A-M, Nilsson M-A, Tiselius HG (1999) The effect of pH changes on crystallization of calcium salts in solutions with an ion-composition corresponding to that in the distal tubule. Scanning Microsc 13:235–245Google Scholar
  15. 15.
    Hounslow MJ, Mumtaz HS, Collier AP, Barrick JP, Bramley AS (2001) A micro-mechanical model for the rate of aggregation during precipitation from solution. Chem Eng Sci 56:2543–2552CrossRefGoogle Scholar
  16. 16.
    Kafarov VV, Dorohov IN, Koltzova E (1983) Systems analysis of chemical technology processes. Processes of mass crystallization from solutions and gas phase. Nauka, MoscowGoogle Scholar
  17. 17.
    Kavanagh JP (1992) Methods for the study of calcium oxalate crystallization and their application to urolithiasis research. Scanning Microsc 6:685–705PubMedGoogle Scholar
  18. 18.
    Kavanagh JP (1999) Enlargement of a lower pole calcium oxalate stone: a theoretical examination of the role of crystal nucleation, growth and aggregation. J Endourol 13:605–610CrossRefPubMedGoogle Scholar
  19. 19.
    Kavanagh JP, Rao PN (2007) Lessons from a stone farm. AIP Conf Proc 900:159–169CrossRefGoogle Scholar
  20. 20.
    Kelman RB (1965) Longitudinal diffusion along the nephron during stop flow. Bull Math Biol 27:53–56Google Scholar
  21. 21.
    Kevrekidis PG, Whitaker N (2003) Effect of backleak in nephron dynamics. Phys Rev E 67:061911CrossRefGoogle Scholar
  22. 22.
    Kok DJ, Khan SR (1994) Calcium oxalate nephrolithiasis, a free or fixed particle disease. Kidney Int 46:847–854CrossRefPubMedGoogle Scholar
  23. 23.
    Königsberger E, Königsberger L-C (2001) Thermodynamic modelling of crystal deposition in humans. Pure Appl Chem 73:785–797CrossRefGoogle Scholar
  24. 24.
    Lide RD (ed) (1991). Handbook of chemistry & physics, 72nd edn. CRC Press, Boca Raton; Ann Arbor, Boston, p 4–49Google Scholar
  25. 25.
    Lieske JC, Leonard R, Toback FG (1995) Adhesion of calcium oxalate monohydrate crystals to renal epithelial cells is inhibited by specific anions. Am J Physiol Renal Physiol 268:F604–F612Google Scholar
  26. 26.
    May PM, Murray K (1991) JESS—a joint expert speciation system—I: raison d’être. Talanta 38:1409–1417CrossRefPubMedGoogle Scholar
  27. 27.
    May PM, Murray K (1991) JESS—a joint expert speciation system—II: the thermodynamic database. Talanta 38:1419–1426CrossRefPubMedGoogle Scholar
  28. 28.
    Mohan R, Myerson AS (2002) Growth kinetics: a thermodynamic approach. Chem Eng Sci 57:4277–4285CrossRefGoogle Scholar
  29. 29.
    Mullin JW (2001) Crystallization, 4th edn. Butterworth-Heinemann, OxfordGoogle Scholar
  30. 30.
    Petrova EV, Gvozdev NV, Rashkovich LN (2004) Growth and dissolution of calcium oxalate monohydrate (COM) crystals. J Optoelectron Adv Mater 6:261–268Google Scholar
  31. 31.
    Randolph AD, Larson MA (1971) Theory of particulate processes. Academic Press, New York/LondonGoogle Scholar
  32. 32.
    Rodgers AL, Allie-Hamdulay S, Jackson G (2006) Therapeutic action of citrate in urolithiasis by chemical speciation: increase in pH is the determinant factor. Nephrol Dial Transplant 21:361–369CrossRefPubMedGoogle Scholar
  33. 33.
    Schepers MSJ, Duim RAJ, Asselman M, Romijn JC, Schroder FH, Verkoelen CF (2003) Internalization of calcium oxalate crystals by renal tubular cells: a nephron segment-specific process? Kidney Int 64:493–500CrossRefPubMedGoogle Scholar
  34. 34.
    Sheng X, Ward MD, Wesson JA (2005) Crystal surface adhesion explains the pathological activity of calcium oxalate hydrates in kidney stone formation. J Am Soc Nephrol 16:1904–1908CrossRefPubMedGoogle Scholar
  35. 35.
    Simons SJR, Pratola F, Jones AG, Brunsteiner M, Price SL (2004) Towards a fundamental understanding of the mechanics of crystal agglomeration: a microscopic and molecular approach. Part Part Syst Charact 21:276–283CrossRefGoogle Scholar
  36. 36.
    Stephen H, Stephen T (1963) Solubility of inorganic and organic compounds, vol 1, part 1. Pergamon Press, Oxford, p 251Google Scholar
  37. 37.
    Vendel M, Rasmuson ÅC (1997) Mechanisms of initiation of incrustation. AIChE J 43:1300–1308CrossRefGoogle Scholar
  38. 38.
    Walker RA, Bott TR (1976) An approach to the prediction of fouling in heat exchanger tubes from existing data. Trans Inst Chem Eng 51:165–167Google Scholar
  39. 39.
    Werness PG, Brown CM, Smith LH, Findlayson B (1985) EQUIL 2: a basic computer programme for the calculation of urinary saturation. J Urol 134:1242–1244PubMedGoogle Scholar
  40. 40.
    Zauner R, Jones AG (2000) Determination of nucleation, growth, agglomeration and disruption kinetics from experimental precipitation data: the calcium oxalate system. Chem Eng Sci 55:4219–4232CrossRefGoogle Scholar

Copyright information

© International Federation for Medical and Biological Engineering 2010

Authors and Affiliations

  • A. Borissova
    • 1
  • G. E. Goltz
    • 1
    • 2
  • J. P. Kavanagh
    • 3
  • T. A. Wilkins
    • 4
  1. 1.Institute of Particle Science and EngineeringUniversity of LeedsLeedsUK
  2. 2.Keyworth InstituteUniversity of LeedsLeedsUK
  3. 3.Department of Minimally Invasive Urology and Stone ManagementSouth Manchester University Hospitals Foundation TrustManchesterUK
  4. 4.Nanomanufacturing InstituteUniversity of LeedsLeedsUK

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