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


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.


Crystallization Calcium oxalate Kidney Simulation Population balance 



Calcium oxalate monohydrate


Crystal size distribution


Mixed suspension, mixed product removal


Population balance


Fractional water removal rate



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.


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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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