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Physicochemical Aspects of Uro-crystallization and Stone Formation

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Urinary Tract Stone Disease

Abstract

Urinary stones are predominantly crystalline and the precipitation of uro-crystals must obey the physical-chemical principles applicable to crystallization in a broader sense. Key amongst these is the requirement for supersaturation to be generated, providing the necessary thermodynamic driving force for crystallization. The three main processes of nucleation, growth, and aggregation are all dependent on the degree of supersaturation. Nucleation of uro-crystals will be heterogeneous (occurring at a surface) and can only be sustained at a supersaturation above the equilibrium condition. Once nucleation has occurred, growth and aggregation can proceed until a saturated equilibrium is achieved, although in the continuous flow of the urinary system the supersaturation may be maintained by replenishment with fresh solute. A new crystallization process has recently been recognized involving the ordered clustering of nanocrystals, which brings together elements of nucleation, growth, and aggregation. The relevance of this to uro-crystallization is not yet clear. Of established significance is the presence of crystallization inhibitors and promoters in urine. These might act through changes in supersaturation or directly at the interface between crystals and solution or crystals and their nucleating substrate.

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Abbreviations

a:

activity

Δa :

activity driving force (supersaturation)

A :

pre-exponential factor (in Arrhenius reaction rate equation)

c :

concentration

Δc :

concentration driving force (supersaturation)

CaOx:

calcium oxalate (crystalline)

ΔG :

Gibbs energy change

ΔG het :

Gibbs energy change for heterogeneous nucleation

ΔG hom :

Gibbs energy change for homogeneous nucleation

ΔG s :

Gibbs energy change for production of new crystal surface

ΔG v :

Gibbs energy change for production of new crystal volume

ΔG crit :

Gibbs energy change for production of a critical nucleus

g :

growth rate

I :

ionic strength

J :

nucleation rate

k :

growth rate constant

k sp :

solubility product

k :

Boltzmann constant

FP :

formation product

L :

particle size

L crit :

size of critical nucleus

M :

strength factor of aggregation bridge

ML:

metastable limit

N:

Avogadro’s number

n :

growth rate reaction order

pK a :

-log (acid dissociation constant)

r :

radius

r crit :

radius of critical nucleus

R :

gas constant

R agg :

aggregation rate

R coll :

aggregate collision rate

R con :

aggregate consolidation rate

R disp :

aggregate dispersion rate

S :

supersaturation ratio

T :

absolute temperature

v m :

molecular volume

(x):

concentration of species x

[x]:

activity of species x

z :

valency

α :

volume shape factor

β :

surface shape factor

γ :

activity coefficient

γ Ss :

interfacial energy (between substratum and solution phase)

γ cs :

interfacial energy (between crystal and solution phase)

γ Sc :

interfacial energy (between substratum and crystal phase)

θ :

contact angle

μ 0 :

chemical potential at the standard state

μ :

chemical potential

Δμ :

thermodynamic driving force

σ :

relative supersaturation

Ï„ :

induction time

Φ :

reaction affinity (positive form of Δμ)

Φ /N :

reaction affinity per molecule

Ï• :

heteronucleation factor

Ψ :

aggregation efficiency factor

c:

crystals

eq:

equilibrium

s:

solution

S:

substratum

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Authors and Affiliations

  1. Department of Urology, University Hospital of South Manchester, Manchester, UK

    John P. Kavanagh

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  1. John P. Kavanagh
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Correspondence to John P. Kavanagh .

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Editors and Affiliations

  1. Dept. Urology, Spire Manchester Hospital, Russell Road, Manchester, M16 8AJ, United Kingdom

    Nagaraja P. Rao

  2. Division of Urologic Surgery, Duke University Medical Center, Durham, 27710, North Carolina, USA

    Glenn M. Preminger

  3. Department of Urology, South Manchester University Hospitals, Manchester, M20 2LR, United Kingdom

    John P. Kavanagh

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Kavanagh, J.P. (2010). Physicochemical Aspects of Uro-crystallization and Stone Formation. In: Rao, N., Preminger, G., Kavanagh, J. (eds) Urinary Tract Stone Disease. Springer, London. https://doi.org/10.1007/978-1-84800-362-0_3

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  • DOI: https://doi.org/10.1007/978-1-84800-362-0_3

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