Skip to main content

Advertisement

SpringerLink
Log in

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

  • Original Article
  • Published:
Medical & Biological Engineering & Computing Aims and scope Submit manuscript

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.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

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. Andreassen JP, Hounslow MJ (2004) Growth and aggregation of vaterite in seeded-batch experiments. AIChE J 50:2772–2782

    Article  CAS  Google Scholar 

  2. Borissova A (2009) General systems modeling of multi-phase batch crystallization from solution. Chem Eng Process Process Intensif 48:268–278

    Article  CAS  Google Scholar 

  3. Bramley AS, Hounslow MJ, Ryall RL (1997) Aggregation during precipitation from solution. Kinetics for calcium oxalate monohydrate. Chem Eng Sci 52:747–757

    Article  CAS  Google Scholar 

  4. Brunsteiner M, Jones AG, Pratola F, Price SL, Simons SJR (2005) Toward a molecular understanding of crystal agglomeration. Cryst Growth Des 5:3–16

    Article  CAS  Google Scholar 

  5. Dean JA (ed) (1979) Lange’s handbook of chemistry, 12th edn. McGraw-Hill, New York, p 4–35

  6. Fasano JM, Khan RK (2001) Intratubular crystallization of calcium oxalate in the presence of membrane vesicles: an in vitro study. Kidney Int 59:169–178

    Article  CAS  PubMed  Google Scholar 

  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 9:258–263

    CAS  Google Scholar 

  8. Finlayson B, Reid F (1978) Expectation of free and fixed particles in urinary stone disease. Investig Urol 15:442–448

    CAS  Google Scholar 

  9. Garside J, Mersmann A, Nyvlt J (1990) Measurement of crystal growth rates. European Federation of Chemical Engineering, Working Party on Crystallization, Munich, p 37

  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 32:1186–1195

    Article  CAS  Google Scholar 

  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 32:1176–1185

    Article  CAS  Google Scholar 

  12. Hess B, Meinhardt U, Zipperle L, Giovanoli R (1995) Simultaneous measurements of calcium oxalate nucleation and aggregation: impact of various modifiers. Urol Res 23:231–238

    Article  CAS  PubMed  Google Scholar 

  13. Højgaard I, Tiselius HG (1999) Crystallization in the nephron. Urol Res 27:397–403

    Article  PubMed  Google Scholar 

  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 13:235–245

    Google Scholar 

  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 56:2543–2552

    Article  CAS  Google Scholar 

  16. Kafarov VV, Dorohov IN, Koltzova E (1983) Systems analysis of chemical technology processes. Processes of mass crystallization from solutions and gas phase. Nauka, Moscow

  17. Kavanagh JP (1992) Methods for the study of calcium oxalate crystallization and their application to urolithiasis research. Scanning Microsc 6:685–705

    CAS  PubMed  Google Scholar 

  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 13:605–610

    Article  CAS  PubMed  Google Scholar 

  19. Kavanagh JP, Rao PN (2007) Lessons from a stone farm. AIP Conf Proc 900:159–169

    Article  Google Scholar 

  20. Kelman RB (1965) Longitudinal diffusion along the nephron during stop flow. Bull Math Biol 27:53–56

    CAS  Google Scholar 

  21. Kevrekidis PG, Whitaker N (2003) Effect of backleak in nephron dynamics. Phys Rev E 67:061911

    Article  CAS  Google Scholar 

  22. Kok DJ, Khan SR (1994) Calcium oxalate nephrolithiasis, a free or fixed particle disease. Kidney Int 46:847–854

    Article  CAS  PubMed  Google Scholar 

  23. Königsberger E, Königsberger L-C (2001) Thermodynamic modelling of crystal deposition in humans. Pure Appl Chem 73:785–797

    Article  Google Scholar 

  24. Lide RD (ed) (1991). Handbook of chemistry & physics, 72nd edn. CRC Press, Boca Raton; Ann Arbor, Boston, p 4–49

  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–F612

    CAS  Google Scholar 

  26. May PM, Murray K (1991) JESS—a joint expert speciation system—I: raison d’être. Talanta 38:1409–1417

    Article  CAS  PubMed  Google Scholar 

  27. May PM, Murray K (1991) JESS—a joint expert speciation system—II: the thermodynamic database. Talanta 38:1419–1426

    Article  CAS  PubMed  Google Scholar 

  28. Mohan R, Myerson AS (2002) Growth kinetics: a thermodynamic approach. Chem Eng Sci 57:4277–4285

    Article  CAS  Google Scholar 

  29. Mullin JW (2001) Crystallization, 4th edn. Butterworth-Heinemann, Oxford

    Google Scholar 

  30. Petrova EV, Gvozdev NV, Rashkovich LN (2004) Growth and dissolution of calcium oxalate monohydrate (COM) crystals. J Optoelectron Adv Mater 6:261–268

    CAS  Google Scholar 

  31. Randolph AD, Larson MA (1971) Theory of particulate processes. Academic Press, New York/London

    Google Scholar 

  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 21:361–369

    Article  CAS  PubMed  Google Scholar 

  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 64:493–500

    Article  CAS  PubMed  Google Scholar 

  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 16:1904–1908

    Article  CAS  PubMed  Google Scholar 

  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 21:276–283

    Article  CAS  Google Scholar 

  36. Stephen H, Stephen T (1963) Solubility of inorganic and organic compounds, vol 1, part 1. Pergamon Press, Oxford, p 251

    Google Scholar 

  37. Vendel M, Rasmuson ÅC (1997) Mechanisms of initiation of incrustation. AIChE J 43:1300–1308

    Article  CAS  Google Scholar 

  38. Walker RA, Bott TR (1976) An approach to the prediction of fouling in heat exchanger tubes from existing data. Trans Inst Chem Eng 51:165–167

    Google Scholar 

  39. Werness PG, Brown CM, Smith LH, Findlayson B (1985) EQUIL 2: a basic computer programme for the calculation of urinary saturation. J Urol 134:1242–1244

    CAS  PubMed  Google Scholar 

  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 55:4219–4232

    Article  CAS  Google Scholar 

Download references

Acknowledgements

The valuable comments, particularly on the estimation of the critical supersaturation ratio, of Professor D. Kashchiev of the Bulgarian Academy of Sciences and a Leverhulme Visiting Professor at the University of Leeds are gratefully acknowledged.

Author information

Authors and Affiliations

  1. Institute of Particle Science and Engineering, University of Leeds, Leeds, LS2 9JT, UK

    A. Borissova & G. E. Goltz

  2. Keyworth Institute, University of Leeds, Leeds, LS2 9JT, UK

    G. E. Goltz

  3. Department of Minimally Invasive Urology and Stone Management, South Manchester University Hospitals Foundation Trust, Manchester, M23 9LT, UK

    J. P. Kavanagh

  4. Nanomanufacturing Institute, University of Leeds, Leeds, LS2 9JT, UK

    T. A. Wilkins

Authors
  1. A. Borissova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. E. Goltz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. P. Kavanagh
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. T. A. Wilkins
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Borissova.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Borissova, A., Goltz, G.E., Kavanagh, J.P. et al. Reverse engineering the kidney: modelling calcium oxalate monohydrate crystallization in the nephron. Med Biol Eng Comput 48, 649–659 (2010). https://doi.org/10.1007/s11517-010-0617-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11517-010-0617-y

Keywords

Search

Navigation