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55
From: Current Clinical Urology, Urinary Stone Disease:
A Practical Guide to Medical and Surgical Management
Edited by: M. L. Stoller and M. V. Meng © Humana Press Inc., Totowa, NJ
4
Theories of Stone Formation
Hsiao-Jen Chung, MD, Harrison M. Abrahams, MD,
Maxwell V. Meng,
MD, and Marshall L. Stoller, MD
CONTENTS
INTRODUCTION
BASIC PHYSICAL CHEMISTRY
NUCLEATION
CRYSTAL AGGREGATION AND GROWTH
EPITAXY
MATRIX
INHIBITORS AND PROMOTERS
CRYSTAL RETENTION
CONCLUSIONS
REFERENCES
Key Words: Nephrolithiasis; etiology; saturation; crystal.
INTRODUCTION
Water is a pivotal element in digestion, circulation, elimination, and regulation of
body temperature. A critical function of the urinary system is the maintenance of normal
composition and volume of body fluid; this is accomplished by glomerular filtration,
tubular reabsorption, and tubular secretion of soluble and filterable plasma components.
By such means, urine contains water, electrolytes, minerals, hydrogen ions, end prod-
ucts of protein metabolism, and other compounds not useful to the metabolism, energy
requirements, or structure of the body. Under normal circumstances, urine will not
contain solid particles (stones).
Why do humans suffer from urinary stone disease? Although urinary stones have been
noted in human remains as old as 7000 years (1), the underlying etiology of stone
formation remains a mystery. The development of urinary calculi is most likely a mul-
tifactorial process and cannot be fully addressed by current theories. Fundamental knowl-
56 Chung et al.
edge of these theories is too complicated to entirely fit in this short chapter. Discussions
in the subsequent sections provide readers simplified general ideas developed from
current studies of urinary stone formation. This chapter will discuss the possible patho-
genesis of urinary stone formation, including the topics of basic physical chemistry,
nucleation, crystal aggregation and growth, epitaxy, matrix, and crystal retention.
BASIC PHYSICAL CHEMISTRY
When a small amount of sodium chloride is added to a glass of pure water at a given
pH and temperature, all of the sodium chloride will dissolve. With the addition of more
and more sodium chloride, a point will be reached at which the sodium chloride will no
longer dissolve. This type of solution is called a saturated solution. In a saturated solu-
tion, equilibrium exists between the dissociated ions and the solid compound. Some of
the solute is continuously crystallizing out of solution, and at the same time, a similar
amount of the solid dissolves into the solution. The equilibrium expression for this
reaction is (2):
K
eq
= [Na
+
][Cl
–
]/[NaCl] (1)
As long as solid sodium chloride remains, its effect on the equilibrium does not
change. The solubility product constant (K
sp
) is useful in predicting whether a precipitate
will form under specified conditions (2). The solubility product is a simplified equation
that only factors in the ionic concentrations.
K
sp
= K
eq
[NaCl] = [Na
+
][Cl
–
] (2)
In a real world situation, every ion in solution will interact with every other so the
solubility is altered accordingly. Strictly speaking, it is the ionic activities, and not the
ionic concentration, that govern the solubility principles described previously. Solubil-
ity product (solubility ion product) is therefore defined as the ion product at saturation
at a specific temperature. The ion product is a mathematical expression for overall ionic
activities (3).
If the numerous components of the urine and urinary stones are factored into the
equation, the concept becomes more complicated. Urine contains many electrically
active ions and small and macromolecular organic components. Some urinary constitu-
ents, referred to as inhibitors of crystal formation, enable the urine to retain more ions
in solution than at the level of saturation (1). For example, nephrocalcin can inhibit the
precipitation of calcium oxalate crystals in urine (4). This state is termed supersaturation,
operationally defined as the solute concentration in solution above that which would
ordinarily result in precipitation if the solution were held at equilibrium (3). In the study
of urolithiasis, the term formation product (formation ion product) is used to depict the
saturation ion product point at which the spontaneous crystal nucleation will occur.
When listing a formation product, environmental factors such as temperature, pH, time
of onset of nucleation, method of detection of nucleation, and surface of reaction con-
tainer must be specified, along with any unusual circumstances, such as cavitations from
stirring, strong magnetic or electric fields, and method of supersaturation generation (3).
Formation product is dependent on many factors making it difficult to reproduce experi-
mentally. Hence, it is graphically represented as a band-shaped region (Fig. 1).
Figure 1 illustrates the states of saturation as a general example of urinary stone
components. If the concentration product is less than the solubility product, the solution
is termed undersaturated, and crystal nucleation will not occur. The metastable region
Chapter 4 / Theories of Stone Formation 57
is the area between the solubility product and the formation product. Spontaneous nucle-
ation may occur in this region. A solution with a concentration product that is greater than
the formation product is quite unstable, and crystal nucleation will occur spontaneously.
One method to help prevent urinary stone formation is to avoid supersaturation. It is
important therefore to understand the states of urinary supersaturation in urinary-stone
patients. Calculation of urinary supersaturation is based on thermodynamics. From a
thermodynamic standpoint, urinary stone crystal formation is a spontaneous process and
occurs in the direction that decreases free energy. If there is available free energy, the
crystallization will occur. This driving force, expressed as free energy (∆G), can be
written:
∆G = RT ln (A
i
/A
o
) (3)
in which R is the universal gas constant, T is the temperature (in degrees Kelvin), and A
i
and A
o
are the activities of the un-ionized salt species in solution at any given condition
and equilibrium, respectively (5,6). The ratio A
i
/A
o
is termed relative supersaturation,
namely, the actual concentration product divided by the solubility product. Activity (A)
is related to concentration (C) through an activity coefficient (f) by:
A = f C (4)
In the above equations, only one salt is considered. Manual calculation of the relative
supersaturation of a salt in urine, which always contains multiple constituents, would be
tedious and impractical. To solve this problem, Finlayson developed a Fortran IV com-
puter program, EQUIL, for calculating ion equilibrium for solutions as complex as urine
(5). A BASIC language version of EQUIL, called EQUIL2, was also published (7).
Fig. 1. States of saturation. (See text for details.)
58 Chung et al.
Results of the calculation by these programs are suggested to be reasonably accurate
(5,7). These computer programs are useful for calculating not only urinary ion equilib-
rium but ion equilibrium in a variety of other solutions commonly used in biological
laboratories. However, kinetic considerations, such as how fast the crystallization pro-
cess occurs, are not factored into these programs nor consideration of aggregation,
retention, nucleation, and the role of matrix (7). Despite these shortfalls, the EQUIL and
EQUIL2 are powerful tools in the study of urinary stone formation. Many commercial
laboratories evaluating 24-h urinary constituents use these equations to calculate and
predict supersaturations.
NUCLEATION
Although the precise pathogenesis of urinary stone formation is unknown, most
believe it is related to crystal formation, especially in the early stages. Many crystalline
substances have been identified in urinary stones. The principal components are cal-
cium oxalate monohydrate (CaOx· H
2
O, whewellite), calcium oxalate dihydrate (CaOx·
2H
2
O, weddellite), basic calcium hydrogen phosphate (Ca
5
(PO
4
)
3
OH, apatite), calcium
hydrogen phosphate (CaHPO
4
· 2H
2
O, brushite), magnesium ammonium phosphate
(Mg(NH
4
)(PO
4
)· 6H
2
O, struvite), uric acid, and cystine (8). Urine is often saturated with
respect to the most common stone components. Even though all urinary stones are made
of crystals, not every stone former has crystalluria in their voided specimen (9). Con-
versely, crystalluria is very common in nonstone formers (10–15). There are overlaps
of the severity of crystalluria between stone formers and nonstone formers. Robertson
and Peacock, however, showed that stone formers tend to excrete larger crystal clumps
than nonstone formers (11). In addition, stone formers generally had calcium oxalate
dihydrate crystalluria, whereas nonstone formers generally had calcium oxalate mono-
hydrate crystalluria. The clinical significance of these findings is unknown.
Calcium oxalate is a major component of renal calculi. It is intriguing that calcium
oxalate crystalluria is typically in the dihydrate form whereas, in renal stones, it is most
commonly present in the monohydrate form. Calcium oxalate may exist in the monohy-
drate (COM), dihydrate (COD), or trihydrate (COT) configurations. Calcium oxalate
monohydrate is the most stable and the COT is the most unstable thermodynamically.
There is supporting evidence that the COT is the first nucleated crystal phase of calcium
oxalate. Subsequently, COT is converted to COD and then to COM (16–18). COT is so
unstable that it is rarely detected in urine and urinary stones. COD can be transformed
to COM in a relatively short period of time (3.5 d) (19). Their solubility differs with COT
being the most soluble, COD intermediate, and COM being the least soluble. Despite the
fact that COM is the most stable crystal phase, COD can exist in urine for a prolonged
time; why this is so is unknown. Several factors in urine, however, favor the presence
of the COD. For example, the rate of transformation from COD to COM is reduced by
magnesium (20,21). Polyphosphate markedly inhibits the crystallization of COM but
has a much smaller effect on the formation of COD and COT (18). Some macromol-
ecules in urine favor formation of COD crystals (22).
Crystals in the urine result from nucleation, the initial step whereby the urinary con-
stituent transforms from a liquid to a solid phase in a supersaturated solution. When the
concentration product of the ions of the stone components is greater than the formation
product, ions begin to cluster close together to form the earliest nonsoluble crystal
structure. This cluster structure is a loose association and is initially not compact (23).
Chapter 4 / Theories of Stone Formation 59
Gradually the structure becomes more and more organized and finally resembles an
orderly crystal lattice structure (24). The term, nucleation, is used to depict this process.
There are two types of nucleation: homogeneous and heterogeneous. When the pro-
cess occurs spontaneously in a pure solution, homogeneous nucleation results. Because
impurities are always present in human urine, homogeneous nucleation is unlikely to
occur in vivo. The surfaces provided by the impurities can serve as a nidus in the nucle-
ation process, leading to heterogeneous nucleation. Heterogeneous nucleation will gen-
erally occur at a lower supersaturation level than that required for the induction of
homogeneous nucleation. The role of heterogeneous nucleation in stone formation is not
well understood. Nevertheless, several studies have reported that most stones are a
mixture of several different crystals with one or two prominent constituents (25–28).
These are indirect clues to support the inclusion of heterogeneous nucleation in the
process of stone formation.
A large proportion of urinary stones contain a mixture of calcium oxalate and calcium
phosphate. Crystallization of calcium oxalate is thought to start through the process of
heterogeneous nucleation, which is facilitated by a good fit for the calcium oxalate
lattice. Calcium phosphate may act as a nidus in this example (29–31). It has been
demonstrated that seed crystals of hydroxyapatite have the ability to induce the growth
of COM crystals from a metastable supersaturated solution of calcium oxalate (32).
Conversely , seed crystals of COM cannot induce the growth of hydroxyapatite crystals
(32). Hydroxyapatite is thermodynamically the most stable form of calcium phosphate
in alkaline urine. It is probably transformed from dicalcium phosphate dihydrate (33),
which is the most stable form in acidic urine (34). Dicalcium phosphate dihydrate also
has been found to induce the heterogeneous nucleation of calcium oxalate crystals (35).
These findings support the theory that renal stones composed of calcium salts start by
a heterogeneous nucleation in metastable supersaturated urine.
Formed crystals either can be excreted in the urine as crystalluria or grow and/or
aggregate to become clinically significant stones. If one takes into consideration the
speed of crystal nucleation and aggregation, and the transit time of urine through the
kidney (glomeruli to papillae, takes approx 2–3 min), one recognizes that crystal nucle-
ation alone cannot explain urinary stone formation. Indeed, Finlayson and Reid calcu-
lated the required time for free crystals to nucleate and grow, and concluded that before
free calcium oxalate particles could grow large enough to be trapped within the renal
tubules, they would be excreted in the urine rather than develop into calculi (36). Dif-
ferent types of crystals tend to nucleate in different parts of the nephron. Crystal nucle-
ation of calcium carbonate, calcium phosphate, and calcium oxalate are more likely to
occur in the loop of Henle, the late distal tubule, and the collecting ducts, respectively
(37,38). Although crystal nucleation is thought to be one of the prerequisites for uroli-
thiasis, it alone cannot explain stone disease, in which the stones are much larger than
the crystal nuclei. There must, therefore, be other mechanisms for crystals to grow and
be retained in the kidney to form stones before they are excreted in the urine.
CRYSTAL AGGREGATION AND GROWTH
Crystal nuclei will bind to each other to form larger particles. This process is called
aggregation or agglomeration. When one large particle is broken into many small par-
ticles in solution, energy must be consumed to overcome the forces holding the small
particles together. Conversely, the aggregation of small particles into large aggregates