- Email: [email protected]
Calcium oxalate monohydrate renal calculi. Formation and development mechanism
ELSEVIER
Adv. Colloid Interface Sci., 59 (1995) l-17
ADVANCES IN COLLOID AND INTERFACE SCIENCE
Calcium oxalate monohydrate renal calculi. Formation and development mechanism* 0. SGhnel, F. Grases* University Illes Balears, Department
of Ch.emistry, 07071 Palma de Mallorca, Spain
Abstract Available information relevant to stone genesis on both calcium oxalate monohydrate crystallization and fine inner structure of papillary calculi is reviewed. Integration of attained facts facilitated formulating a feasible mechanism of papillary calculi formation and development. Medical implications of this mechanism are assessed.
Keywords:
Calcium oxalate monohydrate;
Papillar calculi; Formation mechanism
Introduction
The considerable effort devoted to studying human renal calculi composed predominantly of calcium oxalate has resulted in an enormous number of papers scattered over periodic literature. External appearance, chemical and phase composition, fine inner structure of calculi as well as the kinetics of nucleation, crystal growth and agglomeration of calcium oxalate have been extensively studied. Despite all this effort neither reliable criteria for identifying patients prone to stone formation nor efficient preventive and cure procedures have yet been formulated. 6 Dedicated to the memory of Professor B.V. Dejaguin. :I;Corresponding author. OOOl-8686/95/$29.00
0 1995 -
SSDZ OOOl-8686(95)00249-9
Elsevier Science B.V. All rights reserved.
2
0. Slihnel, F. GraseslAdv.
Colloid Interface Sci., 59 (1995) 1-17
An absence of concrete conclusions can certainly be attributed to the multidisciplinary character of this subject and ensuing lack of interdisciplinary communication. The objective of this paper is to formulate a feasible mechanism of calcium oxalate monohydrate (hereafter COM) calculi formation and development on the basis of synthesizing available information about COM crystallization and the structure of respective renal stones.
Crystallization
of COM
Results concerning COM crystallization reported in numerous papers are frequently contradictory, mostly due to widely different reaction conditions established in respective experiments. However, valuable qualitative information providing clues to papillary stone formation can be inferred from these results. A short account of the most important conclusions resulting from hitherto accumulated knowledge is given below. Supersaturation Urine is a complex solution containing inorganic cations and anions, mainly Na+, Ca2+, Mg 2+, Cl-, PO:-, HCO, dissociated organic compounds, such as oxalate, citric and uric acids, and macromolecules, mostly glycosaminoglycans and mucoproteins. Inorganic cations, i.e. Ca2+ and Mg2+, are partially bound in strong soluble complexes especially with citrate and hence concentration of free, i.e. unbound, ions is often considerably smaller than their analytical (total) concentration. Free ions represent ‘building units’ of COM crystal and therefore their concentrations in urine determine whether the system is supersaturated or not. Urine is always supersaturated with respect to COM. Since urinary concentration of calcium and oxalate ions is not in the stoichiometric ratio, supersaturation must be expressed as the second root of the product of respective free ions concentration [l]. Thus, to increase urinary supersaturation with respect to COM from 20 to 60 requires either three-fold simultaneous increase in calcium and oxalate free ions concentration or nine-fold increase in concentration of one ion maintaining the other ion concentration constant. The actual increase in the analytical concentration of a respective ion is higher than the required increase of the free ionic concentration (3 or 9 fold) due to complexation.
0. Siihnel, F. GraseslAdu.
Colloid Interface Ski., 59 (1995) 1-17
3
Nucleation Spontaneous nucleation of COM particles in urine bulk by homogeneous mechanism, i.e. spontaneous accretion of crystal building units proceeding in solution bulk, is negligible when supersaturation is lower than 59 [2]. Moreover, when analytical concentration of oxalate in whole urine drops below 0.16 mM, homogeneous nucleation does not proceed even at very large supersaturations [31. Urinary supersaturation with respect to COM hardly exceeds 20 [41 and practically cannot surpass the critical value for homogeneous nucleation since more than nine-fold increase, however temporary in urinary analytical concentration of either oxalate or calcium is hardly realistic. Thus COM particles originate in urine by spontaneous nucleation proceeding on a limited number of unspecified solid particles present in liquid, ie. by heterogeneous nucleation. This mechanism implies that a substantially lower number of crystals is formed in a unit volume of urine, around lOlo per m3, than by mechanism of homogeneous nucleation [ll .Since the kinetic order of COM heterogeneous nucleation equals unity [5], an occasional increase in urinary supersaturation leads just to a linear and not exponential increase in number of formed crystals as would be the case for homogeneous nucleation. Therefore, an abrupt occurrence of very high crystal concentration in the upper urinary tract is hardly ever likely. Furthermore, COM crystals can also be formed on crystalline particles of foreign substances that serve as nucleating substrate. The requisite condition for a foreign crystalline particle becoming a good substrate for nucleation is a misfit between lattice parameters of some crystal face of this compound and COM lower than about 10% [6]. Hydroxyapatite, brushite or uric acid satisfy this condition and thus serve as substrates for COM nucleation [7]. Crystal growth From crystal growth studies [EL111 it follows that COM crystals during their mean residence time in the nephron and collecting ducts, estimated to be around 5 min, cannot exceed size of approximately 10 urn. The surface reaction mechanism was recognized as controlling the growth of COM crystals and therefore their growth rate is not influenced by prevailing hydrodynamic conditions. That is, any conceivable change of urine production does not exert any significant effect on COM crystal growth.
4
0. Shhnel, F. GraseslAdv.
Colloid Interface Sci., 59 (1995) 1-17
Phase transition Transformation of metastable higher hydrates of calcium oxalate, ie. di- and trihydrate, into COM is a slow process requiring for completion a considerable time in the range of hundreds of hours 1121. Therefore, an idea that higher hydrates of calcium oxalate precipitate from urine first and only later transform into COM 113-151 is barely justified. COM generally represents the primary precipitated phase constituting COM calculi from the very beginning of the stone-forming process. Admixture
influence
A number of admixtures can either promote or inhibit nucleation and/or growth of COM crystals. Mucine particles present in the precipitating system serve as an effective substrate for nucleation and often several COM crystals originate on a single particle 1161. Admixtures reducing spontaneous nucleation through mechanism other than decreasing solution supersaturation by complexation, need not necessarily affect also formation of new crystals on a suitable substrate. Growth rate of COM crystals is reduced or completely suppressed by a number of substances, one of the most efficacious being phytic acid [17]. However, an admixture cannot stop crystal growth indefinitely unless forming an insoluble layer covering entire crystal surface 1181. If this is not the case, crystal resumes growth after period of stagnation, duration of which increases with increasing admixture concentration and a crystal develops through successive periods of growth and stagnation [19,20]. Since any admixture conceivably present in urine is unlikely to form insoluble layer totally covering the COM crystal surface, COM calculus development can be significantly retarded by these admixtures, but in no case stopped for good. Agglomeration Two different types of agglomeration must be distinguished, viz. primary and secondary agglomeration. Primary agglomeration represents a sort of crystal malgrowth that results in formation of a polycrystalline particle from the mother crystal (Fig. 1). New crystals originate on faces and tips of the mother crystal and can reach a similar size by subsequent regular growth 1211. Resulting agglomerates exhibit a complex inner structure dominated by wide-spread mutual connection of
0. SGhnel, F. GraseslAdv.
Collard Interface Sci., 59 (1995) 1-17
Fig. 1. Structure of typical COM particles formed by primary agglomeration.
constituting crystals that evidently developed through an intensive random intergrowth, ie. crystals grow without any predominant orientation from surface of the others, and twinning. Secondary agglomeration, also termed von Smoluchowski agglomeration, proceeds by collisions of independent particles suspended in a liquid induced either by Brownian motion of particles or shear forces acting in a liquid [22]. Colliding particles remain attached and can be either cemented in their
6
0. Slihnel, F. GraseslAdv.
Colloid Interface Sci., 59 (1995) l-17
place or separated again by hydrodynamic forces. Resulting agglomerates are composed of weakly connected, often almost unconnected, randomly situated individual crystals and display a disordered structure distinctly different from structure of particles formed by primary agglomeration. COM particles originating especially during fast precipitation consist of crystals interconnected through twinning and/or intergrowth and correspond to agglomerates formed by primary agglomeration with perhaps a minor contribution of secondary agglomeration [23]. Crystal morphology
COM crystals of equilibrium morphology exhibit a polyhedral habit bounded by (loo), (021), (OlO), (121) and (001) faces 1241. Slowly grown COM crystals are limited by (loo), (OlO), (121) and sometimes also by (001) faces and display thus an equilibrium habit (see Fig. 2A). Crystals of COM precipitated from high ionic strength media form six-sided platelets bounded by (loo), (010) and (121) faces (see Fig. 2B), or in the presence of membrane vesicles form oval-shaped plates (see Fig. 2C). In contact with mother liquor for adequate time plate-like crystals gradually transform into typical COM polyhedral crystals or elongated multiple twins with acute edges at the ends.
100
Fig. 2. Morphology of COM crystals: (A) polyhedral habit; (B) six-sided plates; and (C) oval-shaped plates.
0. SGhnel, F. GraseslAdv.
Kidney morphology
Colloid Interface Sci., 59 (1995) 1-17
7
and urine composition
Kidney morphology is schematically summarized in Fig. 3. Urine is formed through filtration of the blood in the nephrons (Fig. 3, pos. 1)
Fig 3. The nephrons (1) are units in which urine is produced through processes of filtration and reabsorption of water and substances with low molecular weight. At the end of the nephron the resulting liquid is practically urine. Several nephrons are connected to the same collecting duct (2). The final part of the collecting duct is named Bellini’s duct. Several Bellini’s ducts terminate on the papillae tips (3). Papillae are little protuberances covered by a soft cubic epithelium. The rest of the inner part of the kidney is covered by a stronger transitional epithelium (4). Normally COM renal stones appear attached to papillae (5) or in renal cavities (6). Due to the body movement they can be detached and can appear in renal calix (71, renal pelvis (8) or ureter (9).
8
0. S6hne1, F. GraseslAdv.
Colloid Interface Sci., 59 (1995) 1-17
and basically contains water and soluble compounds (partially produced by metabolism) redundant for organism. The presence of considerable quantity of inorganic and organic ions, mainly Cl-, Na+, PO:-, Mg2+, HCO, and Ca2+, oxalate, citrate and urate, brings an average ionic strength of urine to around 0.33 mol/l. Urinary pH varies with urine composition within limits 4.5 and 7.5. Particular combinations of ions present in urine yield several compounds that under specific conditions can become sparingly soluble. Calcium and oxalate ions are always present in amounts exceeding solubility product of COM. Therefore, urine is always supersaturated with respect to COM but supersaturation is not usually sufficient to induce homogeneous nucleation of COM crystals [2,3]. Solubility of calcium phosphate and uric acid is pH dependent. The former compound becomes practically insoluble when pH exceeds 6 whereas the latter at pH lower than 5.5. Urine also contains a number of substances, such as citrate, pyrophosphate, glycoproteins and glycosaminoglycans that act as natural inhibitors of crystallization. The role of glycoproteins and glycosaminoglycans in urolithiasis, however, is not restricted exclusively to their inhibitory influence on crystallization. Taking into account urine composition, hydrodynamic conditions prevailing in the kidney and a near static state of the upper urinary tract, development of COM crystalline layer over almost entire internal surface of the kidney exposed to urine ought to be expected [25]. In contrast, crystalline concretions, if formed, develop only over a limited number of isolated areas. Therefore, a protective layer covering the internal renal walls that efficiently prevents crystal formation must be assumed. If this is the case, crystals can be formed only at places with destroyed, damaged or perhaps just reduced protective layer [26]. Experimental observations lend support to existence of such protective layer composed of glycosaminoglycans and also to crystal forming restricted to areas with defective layer. Glycosaminoglycans constituting protective layer can either (i) be excreted in the form of glycoproteins by the cells covering the internal renal epithelium, and/or (ii) be formed through metabolizing fragments of tissue proteoglycans. Glycosaminoglycans when excreted become bound to glycoproteins of the cellular membranes due to their similar nature. Existence of this antiadherent protective layer represents, without doubt, the most important factor hindering any papillary calculogenic process.
0. Shnel,
F. GraseslAdu.
Colloid Interface
Sci., 59 (1995) 1-17
9
COM calculi Two types of COM renal stones can be distinguished based on their structure: Type I: Stones attached to the papillae, termed also papillary stones (Fig. 3, pos. 5). These calculi contain a core, or stone nucleus, situated in the urolith interior and the shell constituting an outer part of the stone originating on the core, see Figs. 4A,B. Both parts exhibit distinctly different fine inner structure [27,28]. The core consists of platelike twinned and intergrown crystals of COM forming a loosely arranged aggregate, Fig. 5. Hardly any crystal within the core can be found unconnected to other crystals. The outer limit of core is usually covered with a layer of organic matter on which crystals constituting the shell developed. This shell shows a compact structure composed of columnar crystals radiating from the core limits towards the stone surface, Fig. 6. Organic matrix, representing about 2% of the stone weight, permeates through the entire shell filling the space between adjacent columnar crystals 1281. A stone inner structure clearly indicates that the core is formed first and later serves as a substrate for the shell development. Around 60% of these stones show distinct signs of attachment to the papillae [29]. Type II: Stones formed in the renal calix (Fig. 3, pos. 6). COM crystal constituting this stone type exhibits polyhedral habit bounded by (OlO), (121), (021) and (100) faces, see Fig. 7. Small crystals occurring in these stones originate on the surface of larger crystals, specifically on the (100) faces, in a manner typical for primary agglomeration, specifically epitaxy.
Stone formation Contemporary
theory
Several theories of COM stone formation have been put forward during years of research. However, only the theory proposed by Finlayson [30,31] is based on sound experimental and theoretical grounds and therefore is exclusively considered further. According to this theory the possible mechanisms of renal stone formation can be broadly divided into two groups, viz. the mechanisms of free and fixed particle. The mechanism of free particle assumes that COM crystals nucleated in the nephron (Fig. 3, pos. 1) or the collecting duct (Fig. 3, pos. 2) acquire
10
0. Sbhnel, F. GraseslAdu.
Colloid Interface Sci., 59 (1995) 1-17
Fig 4. (A) Section of COM calculus displaying the central core and the surrounding compact shell (columnar zone). (B) Detail of the COM crystals forming the core. (SEM images).
0. Stihnel, F. GraseslAdv.
Fig. 5. Arrangement
Colloid Interface Sci., 59 (1995) 1-17
of COM crystals in the core.
Fig. 6. Columnar crystals constituting the shell.
11
12
0. Sbhnel, F. GraseslAdv.
Colloid Interface Sci., 59 (1995) l-17
Fig. 7. COM crystals observed in the central part of a calculus formed in cavities of the renal calix.
through growth proceeding during the residence time, a sufficient size for obstructing the Bellini’s duct, about 100 pm in diameter. A crystal entrapped in the Bellini’s duct represents a nidus for development of the stone core and later a full-sized calculus. Conversely, COM crystals may reach during residence in the kidney calix (Fig. 3, pos. 74) a size sufficient to preclude their being washed out from the upper urinary tract. Then, they sedimentate in calix and develop into a concretion inside the kidney. Recently, it was suggested [32,331, that secondary agglomeration of small COM crystals proceeding in the nephron and collecting duct brings about formation of sufficiently large particle that can obstruct the Bellini’s duct and then serve as a stone nidus. This eventuality was not considered in the original free particle theory. The fixed particle mechanism is based on the idea that crystals are either nucleated in urine and then attached to the urinary tract wall, mostly to papilla (Fig. 3, pos. 31, or formed directly on this wall. Particles adhering to the wall are prevented from being washed away from the kidney and can constitute a stone nidus.
0. SShnel, F. GraseslAdv.
Confrontation
with COM
Colloid Interface Ski., 59 (1995) 1-17
crystallization
13
behaviour
Several conclusions relevant to stone formation transpire from crystallization data: 1. Number concentration of COM crystals formed in the upper urinary tract during period of crystalluria is about lOlo per m3 of urine [31,331. This concentration well satisfies expectations of the heterogeneous nucleation and together with supersaturation considerations confirms this mechanism as responsible for COM crystal formation in upper urinary tract. Therefore, a significant, though temporary, increase of crystal concentration owing to conceivable changes in urine composition cannot be contemplated. 2. Formation of an entity sufficiently large to block Bellini’s duct through secondary agglomeration of crystals originating in urine is hardly conceivable. Crystal concentration required for formation of such agglomerate exceeds actual value by several orders of magnitude. Moreover, amount of COM necessary for establishing such crystal concentration is higher by a factor of about 50 than the mass actually available in urine [34]. Thus the free particle theory based on agglomeration is hardly realistic. 3. Individual COM crystals within the mean residence time in the upper urinary tract cannot reach size larger than about 10 pm. Such crystals are far too small to obstruct the Bellini’s duct and serve as a stone nidus. This fact, already recognised by Finlayson 130,311, led to rejection of the free particle mechanism as a feasible mechanism of COM papillary stone formation. 4. Specific admixtures present in urine can reduce calculus development but cannot stop it permanently. Therefore, a COM crystal fixed in the upper urinary tract and in permanent contact with supersaturated urine gives rise to a calculus despite presence of efficacious admixtures. 5. Admixtures influencing solely spontaneous nucleation of COM are of little consequence to concretions developing through primary agglomeration. That is, the effect of these admixtures on the core developing from mother crystal fixed in the kidney is inconsequential. 6. Oval-shaped plates of COM crystals constituting the papillary calculus core signify fast formation of such concretions resulting in a limited contact of formed crystals with urine. Conversely, a polyhedral habit of COM crystals comprising caliceal stones evidences a slow development of these stones allowing for lengthy contact of crystals with urine. 7. Structure of papillary urolith core corresponds to structure devel-
14
0. SGhnel, F. GraseslAdu.
Colloid Interface Sci., 59 (1995)
l-17
oping through primary agglomeration and is totally different from the structure likely to develop through secondary agglomeration. The structure of shell confirms its formation by regular crystal growth, though occasionally interrupted for a limited period of time. In addition, clinical observations suggest that stones are formed mostly in one and always the same kidney of a particular stone former [35] despite identical composition of urine produced in both kidneys. Therefore, propensity to papillary stone formation is connected with the actual state of the respective kidney rather than with the urine composition. Furthermore, experimental observations confirm formation of crystals in the kidney solely in places with damaged protective glycosaminoglycans layer 1261. Feasible formation
mechanism
Based on already presented considerations a realistic mechanism of papillary COM stone formation and development can now be assessed, see Fig. 8 [361. The first and decisive step in stone formation is an attachment of an appropriate solid particle present in urine to the walls of the renal papilla. This particle is either individual crystal or agglomerate of COM or a foreign substance having structure compatible with COM. Places with destroyed or damaged protective glycosaminoglycans layer covering the inner renal walls represent preferable locations for particle attachment. COM crystals can also be generated directly from urine on such sites. A particle attached to the inner kidney wall representing the stone nidus induces formation of new COM crystals. New crystals are formed by both nucleation on the particle surface and primary agglomeration. The latter mechanism can only become active from the very beginning of the process when the nidus is a COM crystal. Gradually, but relatively
Fig. 8. Proposed mechanism of COM papillary calculi formation. (A) Inner renal walls with a healthy glycosaminoglycans protective layer. (B) Damaged, destroyed or reduced glycosaminoglycans layer. (C) This situation will favour the formation of solid particles (calcium phosphates, uric acid, . ..) attached to the renal walls. (D) The solid particles will be able to induce the heterogeneous nucleation of COM on them. (E) A low inhibitory capacity of the urine will lead to the development of a COM calculus. Note: this scheme is not a scale drawing of the different parts.
0. Stihnel,
Fig. 8. Caption opposite.
F. GraseslAdv.
Colloid Interface
Sci., 59 (1995) 1-17
15
16
0. SGhnel, F. GraseslAdu.
Colloid Interface Sci., 59 (1995) 1-17
fast, a concretion consisting of loosely arranged twinned and inter-grown plate-like COM crystals is formed. Increasing outer surface of this concretion brings about decreasing rate of its vertical displacement. In a certain developing stage, when the displacement becomes sufficiently low, an organic material present in urine covers the concretion surface with a continuous layer. This layer prevents further contact of crystals with supersaturated urine and thus stops concretion growth that represents a complete calculus core. Organic layer, being an effective substrate for nucleation of COM crystals, induces formation of columnar COM crystals constituting the shell. If, for some reason, growth of columnar crystals is temporarily stopped, a layer of organic matter soon covers the calculus external surface. This layer is again an effective substrate for nucleation of COM crystals. When conditions prevailing in the kidney become again favourable for stone formation, a new calculus stratum of columnar crystals develops.
Medical implications Formulated mechanism of papillary COM stone formation has several important medical implications: 1. Defective glycosaminoglycans layer protecting the inner kidney wall is one of the main factors facilitating the COM papillary stone formation. Therefore, successful treatment of this kind of urolithiasis must be directed towards regeneration of the protective layer. 2. Urine composition is of secondary significance unless severe deviations, such as substantial deficit in citrate or a considerable excess of calcium and/or oxalate, resulting in high urinary supersaturation appear. However, even if this is the case, the protective layer must be defective, otherwise papillary stones would not be formed. In such situation, an adjustment of urinary composition leading to decrease of prevailing supersaturation, e.g. through altered diet, can improve stone incidence, but cannot fully eliminate their formation. 3. Administering inhibitors of COM crystal growth can prolong period between successive events of stone formation, but cannot bring this process to a complete halt. Inhibitors of COM nucleation are much more effective in preventing stone formation. 4. Any attempt to develop selective criteria for determining patients prone to papillary stone formation based exclusively on urine composition cannot be fully successful.
0. Siihnel, F. Grases IAdv. Colloid Interface Sci., 59 (1995) l-l 7
17
References [ll 121 131 141 151 161 171 181 191 1101 1111 1121 1131 1141 1151 1161 1171 1181 1191 1201 1211 1221 1231 1241 1251 1261 1271 1281 1291 1301 1311 1321 1331 1341 1351 1361
0. Sohnel and J. Garside, Precipitation. Butterworth, London, 1993. Ch.M. Brown, D.K. Ackermann, D.L. Purich and B. Finlayson, J. Cryst. Growth, 108 (1991) 455. Y. Berland, M. Olmer, M. Grandbuillemin, H.E.L. Madsen and R. Boistelle, J. Cryst. Growth, 87 (1987) 494. W.G. Robertson, D.S. Saw and C.M. Bridge, J. Cryst. Growth, 53 (1981) 182. J. Garside, Lj. Brecevic and J.W. Mullin, J. Cry&. Growth, 57 (1982) 233. D. Turnbull and B. Vonnegut, Ind. Eng. Chem., 44 (1952) 1292. K. Lonsdale, Nature, 217 (1968) 56. A.E. Nielsen, in: S.J. Jancic and E.J. DeJong (Eds.), Industrial Crystallization 81. North-Holland, Amsterdam, 1981. J.D. DeLong and D. Briedis, J. Cryst. Growth, 71(1985) 689. A. Costa-Bauza, F. Grases and 0. Sohnel, Cryst. Res. Technol., 28 (1993) 337. R.P. Singh, S.S. Gaur, D.J. White and G.H. Nancollas, J. Colloid Interface Sci., 118 (1987) 379. D. Skrtic, H. Ftierdi-Milhofer and M. Markovic, J. Cryst. Growth, 80 (1987) 113. R.I. Gibson, Am. Mineralogist, 59 (1974) 1177. B.T. Murphy and L.N. Pyrah, Br. J. Urol. 34 (1962) 129. H.H.Seyfart and B. Hahne, Jena Rev., 23 (1978) 182. F. Grases, L. Ma&ova, 0. Sohnel and A. Costa-Bauza, Br. J. Urol., 70 (1992) 240. F. Grases and P. March, Anal. Chim. Acta, 219 (1989) 89. H.A. O’Hara and R.C. Reid, Modelling Crystal Flow Rates from Solutions. Prentice Hall Inc., New Jersey, 1973. H. Human, Thesis, Catholic Univ. of Nijmegen, Nijmegen, 1981. S.T. Liu and G.H. Nancollas, J. Cryst. Growth, 6 (1970) 281. A.G. Jones, ICHEME, 5th Int. Symp. on Agglomeration, Symp. Ser. Rugby, 1989. M. Von Smoluchowski, Z. Physik. Chem., 92 (1918) 129. A. Millan, F. Grases, 0. Sohnel and I. Krivankova, Cryst. Res. Technol., 27 (1992) 31. F. Grases, 0. Sohnel, A. Millan and A. Costa-Bauza, Current Topics in Crystal Growth Research. In press. F. Grases, A. Costa-Bauza, J.G. March and 0. Sohnel, Nephron, 65 (1993) 77. W.A. See and R.D. Williams, J. Urol., 147 (1992) 541. 0. Sohnel and F. Grases, Nephron, 63 (1993) 176. H. Iwata, S. Nishio, A. Wakatsuki, K. Ochi and M. Takeuchi, J. Urol., 133 (1985) 334. J.S. Elliot, J. Urol., 109 (1973) 82. B. Finlayson, Urol. Clin. North Am., l(l974) 181. B. Finlayson and F. Reid, Invest. Urol., 15 (1978) 442. D.J. Kok, S.E. Papapoulos, O.L.M. Bijvoet, Kidney Int., 37 (1990) 51. D.J. Kok and S.R. Khan, Kidney Int., 46 (1994) 847. 0. Sohnel, F. Grases, and L. Garcia-Ferragut, Scanning Microscopy, 8 (1994) 513. B.M. Brenner and F.C. Rector, The Kidney. W.B. Saunders, Philadelphia, 1976. F. Grases, A. Costa-Bauza and A. Conte, Scanning Microscopy, 7 (1993) 1067.
Adv. Colloid Interface Sci., 59 (1995) l-17
ADVANCES IN COLLOID AND INTERFACE SCIENCE
Calcium oxalate monohydrate renal calculi. Formation and development mechanism* 0. SGhnel, F. Grases* University Illes Balears, Department
of Ch.emistry, 07071 Palma de Mallorca, Spain
Abstract Available information relevant to stone genesis on both calcium oxalate monohydrate crystallization and fine inner structure of papillary calculi is reviewed. Integration of attained facts facilitated formulating a feasible mechanism of papillary calculi formation and development. Medical implications of this mechanism are assessed.
Keywords:
Calcium oxalate monohydrate;
Papillar calculi; Formation mechanism
Introduction
The considerable effort devoted to studying human renal calculi composed predominantly of calcium oxalate has resulted in an enormous number of papers scattered over periodic literature. External appearance, chemical and phase composition, fine inner structure of calculi as well as the kinetics of nucleation, crystal growth and agglomeration of calcium oxalate have been extensively studied. Despite all this effort neither reliable criteria for identifying patients prone to stone formation nor efficient preventive and cure procedures have yet been formulated. 6 Dedicated to the memory of Professor B.V. Dejaguin. :I;Corresponding author. OOOl-8686/95/$29.00
0 1995 -
SSDZ OOOl-8686(95)00249-9
Elsevier Science B.V. All rights reserved.
2
0. Slihnel, F. GraseslAdv.
Colloid Interface Sci., 59 (1995) 1-17
An absence of concrete conclusions can certainly be attributed to the multidisciplinary character of this subject and ensuing lack of interdisciplinary communication. The objective of this paper is to formulate a feasible mechanism of calcium oxalate monohydrate (hereafter COM) calculi formation and development on the basis of synthesizing available information about COM crystallization and the structure of respective renal stones.
Crystallization
of COM
Results concerning COM crystallization reported in numerous papers are frequently contradictory, mostly due to widely different reaction conditions established in respective experiments. However, valuable qualitative information providing clues to papillary stone formation can be inferred from these results. A short account of the most important conclusions resulting from hitherto accumulated knowledge is given below. Supersaturation Urine is a complex solution containing inorganic cations and anions, mainly Na+, Ca2+, Mg 2+, Cl-, PO:-, HCO, dissociated organic compounds, such as oxalate, citric and uric acids, and macromolecules, mostly glycosaminoglycans and mucoproteins. Inorganic cations, i.e. Ca2+ and Mg2+, are partially bound in strong soluble complexes especially with citrate and hence concentration of free, i.e. unbound, ions is often considerably smaller than their analytical (total) concentration. Free ions represent ‘building units’ of COM crystal and therefore their concentrations in urine determine whether the system is supersaturated or not. Urine is always supersaturated with respect to COM. Since urinary concentration of calcium and oxalate ions is not in the stoichiometric ratio, supersaturation must be expressed as the second root of the product of respective free ions concentration [l]. Thus, to increase urinary supersaturation with respect to COM from 20 to 60 requires either three-fold simultaneous increase in calcium and oxalate free ions concentration or nine-fold increase in concentration of one ion maintaining the other ion concentration constant. The actual increase in the analytical concentration of a respective ion is higher than the required increase of the free ionic concentration (3 or 9 fold) due to complexation.
0. Siihnel, F. GraseslAdu.
Colloid Interface Ski., 59 (1995) 1-17
3
Nucleation Spontaneous nucleation of COM particles in urine bulk by homogeneous mechanism, i.e. spontaneous accretion of crystal building units proceeding in solution bulk, is negligible when supersaturation is lower than 59 [2]. Moreover, when analytical concentration of oxalate in whole urine drops below 0.16 mM, homogeneous nucleation does not proceed even at very large supersaturations [31. Urinary supersaturation with respect to COM hardly exceeds 20 [41 and practically cannot surpass the critical value for homogeneous nucleation since more than nine-fold increase, however temporary in urinary analytical concentration of either oxalate or calcium is hardly realistic. Thus COM particles originate in urine by spontaneous nucleation proceeding on a limited number of unspecified solid particles present in liquid, ie. by heterogeneous nucleation. This mechanism implies that a substantially lower number of crystals is formed in a unit volume of urine, around lOlo per m3, than by mechanism of homogeneous nucleation [ll .Since the kinetic order of COM heterogeneous nucleation equals unity [5], an occasional increase in urinary supersaturation leads just to a linear and not exponential increase in number of formed crystals as would be the case for homogeneous nucleation. Therefore, an abrupt occurrence of very high crystal concentration in the upper urinary tract is hardly ever likely. Furthermore, COM crystals can also be formed on crystalline particles of foreign substances that serve as nucleating substrate. The requisite condition for a foreign crystalline particle becoming a good substrate for nucleation is a misfit between lattice parameters of some crystal face of this compound and COM lower than about 10% [6]. Hydroxyapatite, brushite or uric acid satisfy this condition and thus serve as substrates for COM nucleation [7]. Crystal growth From crystal growth studies [EL111 it follows that COM crystals during their mean residence time in the nephron and collecting ducts, estimated to be around 5 min, cannot exceed size of approximately 10 urn. The surface reaction mechanism was recognized as controlling the growth of COM crystals and therefore their growth rate is not influenced by prevailing hydrodynamic conditions. That is, any conceivable change of urine production does not exert any significant effect on COM crystal growth.
4
0. Shhnel, F. GraseslAdv.
Colloid Interface Sci., 59 (1995) 1-17
Phase transition Transformation of metastable higher hydrates of calcium oxalate, ie. di- and trihydrate, into COM is a slow process requiring for completion a considerable time in the range of hundreds of hours 1121. Therefore, an idea that higher hydrates of calcium oxalate precipitate from urine first and only later transform into COM 113-151 is barely justified. COM generally represents the primary precipitated phase constituting COM calculi from the very beginning of the stone-forming process. Admixture
influence
A number of admixtures can either promote or inhibit nucleation and/or growth of COM crystals. Mucine particles present in the precipitating system serve as an effective substrate for nucleation and often several COM crystals originate on a single particle 1161. Admixtures reducing spontaneous nucleation through mechanism other than decreasing solution supersaturation by complexation, need not necessarily affect also formation of new crystals on a suitable substrate. Growth rate of COM crystals is reduced or completely suppressed by a number of substances, one of the most efficacious being phytic acid [17]. However, an admixture cannot stop crystal growth indefinitely unless forming an insoluble layer covering entire crystal surface 1181. If this is not the case, crystal resumes growth after period of stagnation, duration of which increases with increasing admixture concentration and a crystal develops through successive periods of growth and stagnation [19,20]. Since any admixture conceivably present in urine is unlikely to form insoluble layer totally covering the COM crystal surface, COM calculus development can be significantly retarded by these admixtures, but in no case stopped for good. Agglomeration Two different types of agglomeration must be distinguished, viz. primary and secondary agglomeration. Primary agglomeration represents a sort of crystal malgrowth that results in formation of a polycrystalline particle from the mother crystal (Fig. 1). New crystals originate on faces and tips of the mother crystal and can reach a similar size by subsequent regular growth 1211. Resulting agglomerates exhibit a complex inner structure dominated by wide-spread mutual connection of
0. SGhnel, F. GraseslAdv.
Collard Interface Sci., 59 (1995) 1-17
Fig. 1. Structure of typical COM particles formed by primary agglomeration.
constituting crystals that evidently developed through an intensive random intergrowth, ie. crystals grow without any predominant orientation from surface of the others, and twinning. Secondary agglomeration, also termed von Smoluchowski agglomeration, proceeds by collisions of independent particles suspended in a liquid induced either by Brownian motion of particles or shear forces acting in a liquid [22]. Colliding particles remain attached and can be either cemented in their
6
0. Slihnel, F. GraseslAdv.
Colloid Interface Sci., 59 (1995) l-17
place or separated again by hydrodynamic forces. Resulting agglomerates are composed of weakly connected, often almost unconnected, randomly situated individual crystals and display a disordered structure distinctly different from structure of particles formed by primary agglomeration. COM particles originating especially during fast precipitation consist of crystals interconnected through twinning and/or intergrowth and correspond to agglomerates formed by primary agglomeration with perhaps a minor contribution of secondary agglomeration [23]. Crystal morphology
COM crystals of equilibrium morphology exhibit a polyhedral habit bounded by (loo), (021), (OlO), (121) and (001) faces 1241. Slowly grown COM crystals are limited by (loo), (OlO), (121) and sometimes also by (001) faces and display thus an equilibrium habit (see Fig. 2A). Crystals of COM precipitated from high ionic strength media form six-sided platelets bounded by (loo), (010) and (121) faces (see Fig. 2B), or in the presence of membrane vesicles form oval-shaped plates (see Fig. 2C). In contact with mother liquor for adequate time plate-like crystals gradually transform into typical COM polyhedral crystals or elongated multiple twins with acute edges at the ends.
100
Fig. 2. Morphology of COM crystals: (A) polyhedral habit; (B) six-sided plates; and (C) oval-shaped plates.
0. SGhnel, F. GraseslAdv.
Kidney morphology
Colloid Interface Sci., 59 (1995) 1-17
7
and urine composition
Kidney morphology is schematically summarized in Fig. 3. Urine is formed through filtration of the blood in the nephrons (Fig. 3, pos. 1)
Fig 3. The nephrons (1) are units in which urine is produced through processes of filtration and reabsorption of water and substances with low molecular weight. At the end of the nephron the resulting liquid is practically urine. Several nephrons are connected to the same collecting duct (2). The final part of the collecting duct is named Bellini’s duct. Several Bellini’s ducts terminate on the papillae tips (3). Papillae are little protuberances covered by a soft cubic epithelium. The rest of the inner part of the kidney is covered by a stronger transitional epithelium (4). Normally COM renal stones appear attached to papillae (5) or in renal cavities (6). Due to the body movement they can be detached and can appear in renal calix (71, renal pelvis (8) or ureter (9).
8
0. S6hne1, F. GraseslAdv.
Colloid Interface Sci., 59 (1995) 1-17
and basically contains water and soluble compounds (partially produced by metabolism) redundant for organism. The presence of considerable quantity of inorganic and organic ions, mainly Cl-, Na+, PO:-, Mg2+, HCO, and Ca2+, oxalate, citrate and urate, brings an average ionic strength of urine to around 0.33 mol/l. Urinary pH varies with urine composition within limits 4.5 and 7.5. Particular combinations of ions present in urine yield several compounds that under specific conditions can become sparingly soluble. Calcium and oxalate ions are always present in amounts exceeding solubility product of COM. Therefore, urine is always supersaturated with respect to COM but supersaturation is not usually sufficient to induce homogeneous nucleation of COM crystals [2,3]. Solubility of calcium phosphate and uric acid is pH dependent. The former compound becomes practically insoluble when pH exceeds 6 whereas the latter at pH lower than 5.5. Urine also contains a number of substances, such as citrate, pyrophosphate, glycoproteins and glycosaminoglycans that act as natural inhibitors of crystallization. The role of glycoproteins and glycosaminoglycans in urolithiasis, however, is not restricted exclusively to their inhibitory influence on crystallization. Taking into account urine composition, hydrodynamic conditions prevailing in the kidney and a near static state of the upper urinary tract, development of COM crystalline layer over almost entire internal surface of the kidney exposed to urine ought to be expected [25]. In contrast, crystalline concretions, if formed, develop only over a limited number of isolated areas. Therefore, a protective layer covering the internal renal walls that efficiently prevents crystal formation must be assumed. If this is the case, crystals can be formed only at places with destroyed, damaged or perhaps just reduced protective layer [26]. Experimental observations lend support to existence of such protective layer composed of glycosaminoglycans and also to crystal forming restricted to areas with defective layer. Glycosaminoglycans constituting protective layer can either (i) be excreted in the form of glycoproteins by the cells covering the internal renal epithelium, and/or (ii) be formed through metabolizing fragments of tissue proteoglycans. Glycosaminoglycans when excreted become bound to glycoproteins of the cellular membranes due to their similar nature. Existence of this antiadherent protective layer represents, without doubt, the most important factor hindering any papillary calculogenic process.
0. Shnel,
F. GraseslAdu.
Colloid Interface
Sci., 59 (1995) 1-17
9
COM calculi Two types of COM renal stones can be distinguished based on their structure: Type I: Stones attached to the papillae, termed also papillary stones (Fig. 3, pos. 5). These calculi contain a core, or stone nucleus, situated in the urolith interior and the shell constituting an outer part of the stone originating on the core, see Figs. 4A,B. Both parts exhibit distinctly different fine inner structure [27,28]. The core consists of platelike twinned and intergrown crystals of COM forming a loosely arranged aggregate, Fig. 5. Hardly any crystal within the core can be found unconnected to other crystals. The outer limit of core is usually covered with a layer of organic matter on which crystals constituting the shell developed. This shell shows a compact structure composed of columnar crystals radiating from the core limits towards the stone surface, Fig. 6. Organic matrix, representing about 2% of the stone weight, permeates through the entire shell filling the space between adjacent columnar crystals 1281. A stone inner structure clearly indicates that the core is formed first and later serves as a substrate for the shell development. Around 60% of these stones show distinct signs of attachment to the papillae [29]. Type II: Stones formed in the renal calix (Fig. 3, pos. 6). COM crystal constituting this stone type exhibits polyhedral habit bounded by (OlO), (121), (021) and (100) faces, see Fig. 7. Small crystals occurring in these stones originate on the surface of larger crystals, specifically on the (100) faces, in a manner typical for primary agglomeration, specifically epitaxy.
Stone formation Contemporary
theory
Several theories of COM stone formation have been put forward during years of research. However, only the theory proposed by Finlayson [30,31] is based on sound experimental and theoretical grounds and therefore is exclusively considered further. According to this theory the possible mechanisms of renal stone formation can be broadly divided into two groups, viz. the mechanisms of free and fixed particle. The mechanism of free particle assumes that COM crystals nucleated in the nephron (Fig. 3, pos. 1) or the collecting duct (Fig. 3, pos. 2) acquire
10
0. Sbhnel, F. GraseslAdu.
Colloid Interface Sci., 59 (1995) 1-17
Fig 4. (A) Section of COM calculus displaying the central core and the surrounding compact shell (columnar zone). (B) Detail of the COM crystals forming the core. (SEM images).
0. Stihnel, F. GraseslAdv.
Fig. 5. Arrangement
Colloid Interface Sci., 59 (1995) 1-17
of COM crystals in the core.
Fig. 6. Columnar crystals constituting the shell.
11
12
0. Sbhnel, F. GraseslAdv.
Colloid Interface Sci., 59 (1995) l-17
Fig. 7. COM crystals observed in the central part of a calculus formed in cavities of the renal calix.
through growth proceeding during the residence time, a sufficient size for obstructing the Bellini’s duct, about 100 pm in diameter. A crystal entrapped in the Bellini’s duct represents a nidus for development of the stone core and later a full-sized calculus. Conversely, COM crystals may reach during residence in the kidney calix (Fig. 3, pos. 74) a size sufficient to preclude their being washed out from the upper urinary tract. Then, they sedimentate in calix and develop into a concretion inside the kidney. Recently, it was suggested [32,331, that secondary agglomeration of small COM crystals proceeding in the nephron and collecting duct brings about formation of sufficiently large particle that can obstruct the Bellini’s duct and then serve as a stone nidus. This eventuality was not considered in the original free particle theory. The fixed particle mechanism is based on the idea that crystals are either nucleated in urine and then attached to the urinary tract wall, mostly to papilla (Fig. 3, pos. 31, or formed directly on this wall. Particles adhering to the wall are prevented from being washed away from the kidney and can constitute a stone nidus.
0. SShnel, F. GraseslAdv.
Confrontation
with COM
Colloid Interface Ski., 59 (1995) 1-17
crystallization
13
behaviour
Several conclusions relevant to stone formation transpire from crystallization data: 1. Number concentration of COM crystals formed in the upper urinary tract during period of crystalluria is about lOlo per m3 of urine [31,331. This concentration well satisfies expectations of the heterogeneous nucleation and together with supersaturation considerations confirms this mechanism as responsible for COM crystal formation in upper urinary tract. Therefore, a significant, though temporary, increase of crystal concentration owing to conceivable changes in urine composition cannot be contemplated. 2. Formation of an entity sufficiently large to block Bellini’s duct through secondary agglomeration of crystals originating in urine is hardly conceivable. Crystal concentration required for formation of such agglomerate exceeds actual value by several orders of magnitude. Moreover, amount of COM necessary for establishing such crystal concentration is higher by a factor of about 50 than the mass actually available in urine [34]. Thus the free particle theory based on agglomeration is hardly realistic. 3. Individual COM crystals within the mean residence time in the upper urinary tract cannot reach size larger than about 10 pm. Such crystals are far too small to obstruct the Bellini’s duct and serve as a stone nidus. This fact, already recognised by Finlayson 130,311, led to rejection of the free particle mechanism as a feasible mechanism of COM papillary stone formation. 4. Specific admixtures present in urine can reduce calculus development but cannot stop it permanently. Therefore, a COM crystal fixed in the upper urinary tract and in permanent contact with supersaturated urine gives rise to a calculus despite presence of efficacious admixtures. 5. Admixtures influencing solely spontaneous nucleation of COM are of little consequence to concretions developing through primary agglomeration. That is, the effect of these admixtures on the core developing from mother crystal fixed in the kidney is inconsequential. 6. Oval-shaped plates of COM crystals constituting the papillary calculus core signify fast formation of such concretions resulting in a limited contact of formed crystals with urine. Conversely, a polyhedral habit of COM crystals comprising caliceal stones evidences a slow development of these stones allowing for lengthy contact of crystals with urine. 7. Structure of papillary urolith core corresponds to structure devel-
14
0. SGhnel, F. GraseslAdu.
Colloid Interface Sci., 59 (1995)
l-17
oping through primary agglomeration and is totally different from the structure likely to develop through secondary agglomeration. The structure of shell confirms its formation by regular crystal growth, though occasionally interrupted for a limited period of time. In addition, clinical observations suggest that stones are formed mostly in one and always the same kidney of a particular stone former [35] despite identical composition of urine produced in both kidneys. Therefore, propensity to papillary stone formation is connected with the actual state of the respective kidney rather than with the urine composition. Furthermore, experimental observations confirm formation of crystals in the kidney solely in places with damaged protective glycosaminoglycans layer 1261. Feasible formation
mechanism
Based on already presented considerations a realistic mechanism of papillary COM stone formation and development can now be assessed, see Fig. 8 [361. The first and decisive step in stone formation is an attachment of an appropriate solid particle present in urine to the walls of the renal papilla. This particle is either individual crystal or agglomerate of COM or a foreign substance having structure compatible with COM. Places with destroyed or damaged protective glycosaminoglycans layer covering the inner renal walls represent preferable locations for particle attachment. COM crystals can also be generated directly from urine on such sites. A particle attached to the inner kidney wall representing the stone nidus induces formation of new COM crystals. New crystals are formed by both nucleation on the particle surface and primary agglomeration. The latter mechanism can only become active from the very beginning of the process when the nidus is a COM crystal. Gradually, but relatively
Fig. 8. Proposed mechanism of COM papillary calculi formation. (A) Inner renal walls with a healthy glycosaminoglycans protective layer. (B) Damaged, destroyed or reduced glycosaminoglycans layer. (C) This situation will favour the formation of solid particles (calcium phosphates, uric acid, . ..) attached to the renal walls. (D) The solid particles will be able to induce the heterogeneous nucleation of COM on them. (E) A low inhibitory capacity of the urine will lead to the development of a COM calculus. Note: this scheme is not a scale drawing of the different parts.
0. Stihnel,
Fig. 8. Caption opposite.
F. GraseslAdv.
Colloid Interface
Sci., 59 (1995) 1-17
15
16
0. SGhnel, F. GraseslAdu.
Colloid Interface Sci., 59 (1995) 1-17
fast, a concretion consisting of loosely arranged twinned and inter-grown plate-like COM crystals is formed. Increasing outer surface of this concretion brings about decreasing rate of its vertical displacement. In a certain developing stage, when the displacement becomes sufficiently low, an organic material present in urine covers the concretion surface with a continuous layer. This layer prevents further contact of crystals with supersaturated urine and thus stops concretion growth that represents a complete calculus core. Organic layer, being an effective substrate for nucleation of COM crystals, induces formation of columnar COM crystals constituting the shell. If, for some reason, growth of columnar crystals is temporarily stopped, a layer of organic matter soon covers the calculus external surface. This layer is again an effective substrate for nucleation of COM crystals. When conditions prevailing in the kidney become again favourable for stone formation, a new calculus stratum of columnar crystals develops.
Medical implications Formulated mechanism of papillary COM stone formation has several important medical implications: 1. Defective glycosaminoglycans layer protecting the inner kidney wall is one of the main factors facilitating the COM papillary stone formation. Therefore, successful treatment of this kind of urolithiasis must be directed towards regeneration of the protective layer. 2. Urine composition is of secondary significance unless severe deviations, such as substantial deficit in citrate or a considerable excess of calcium and/or oxalate, resulting in high urinary supersaturation appear. However, even if this is the case, the protective layer must be defective, otherwise papillary stones would not be formed. In such situation, an adjustment of urinary composition leading to decrease of prevailing supersaturation, e.g. through altered diet, can improve stone incidence, but cannot fully eliminate their formation. 3. Administering inhibitors of COM crystal growth can prolong period between successive events of stone formation, but cannot bring this process to a complete halt. Inhibitors of COM nucleation are much more effective in preventing stone formation. 4. Any attempt to develop selective criteria for determining patients prone to papillary stone formation based exclusively on urine composition cannot be fully successful.
0. Siihnel, F. Grases IAdv. Colloid Interface Sci., 59 (1995) l-l 7
17
References [ll 121 131 141 151 161 171 181 191 1101 1111 1121 1131 1141 1151 1161 1171 1181 1191 1201 1211 1221 1231 1241 1251 1261 1271 1281 1291 1301 1311 1321 1331 1341 1351 1361
0. Sohnel and J. Garside, Precipitation. Butterworth, London, 1993. Ch.M. Brown, D.K. Ackermann, D.L. Purich and B. Finlayson, J. Cryst. Growth, 108 (1991) 455. Y. Berland, M. Olmer, M. Grandbuillemin, H.E.L. Madsen and R. Boistelle, J. Cryst. Growth, 87 (1987) 494. W.G. Robertson, D.S. Saw and C.M. Bridge, J. Cryst. Growth, 53 (1981) 182. J. Garside, Lj. Brecevic and J.W. Mullin, J. Cry&. Growth, 57 (1982) 233. D. Turnbull and B. Vonnegut, Ind. Eng. Chem., 44 (1952) 1292. K. Lonsdale, Nature, 217 (1968) 56. A.E. Nielsen, in: S.J. Jancic and E.J. DeJong (Eds.), Industrial Crystallization 81. North-Holland, Amsterdam, 1981. J.D. DeLong and D. Briedis, J. Cryst. Growth, 71(1985) 689. A. Costa-Bauza, F. Grases and 0. Sohnel, Cryst. Res. Technol., 28 (1993) 337. R.P. Singh, S.S. Gaur, D.J. White and G.H. Nancollas, J. Colloid Interface Sci., 118 (1987) 379. D. Skrtic, H. Ftierdi-Milhofer and M. Markovic, J. Cryst. Growth, 80 (1987) 113. R.I. Gibson, Am. Mineralogist, 59 (1974) 1177. B.T. Murphy and L.N. Pyrah, Br. J. Urol. 34 (1962) 129. H.H.Seyfart and B. Hahne, Jena Rev., 23 (1978) 182. F. Grases, L. Ma&ova, 0. Sohnel and A. Costa-Bauza, Br. J. Urol., 70 (1992) 240. F. Grases and P. March, Anal. Chim. Acta, 219 (1989) 89. H.A. O’Hara and R.C. Reid, Modelling Crystal Flow Rates from Solutions. Prentice Hall Inc., New Jersey, 1973. H. Human, Thesis, Catholic Univ. of Nijmegen, Nijmegen, 1981. S.T. Liu and G.H. Nancollas, J. Cryst. Growth, 6 (1970) 281. A.G. Jones, ICHEME, 5th Int. Symp. on Agglomeration, Symp. Ser. Rugby, 1989. M. Von Smoluchowski, Z. Physik. Chem., 92 (1918) 129. A. Millan, F. Grases, 0. Sohnel and I. Krivankova, Cryst. Res. Technol., 27 (1992) 31. F. Grases, 0. Sohnel, A. Millan and A. Costa-Bauza, Current Topics in Crystal Growth Research. In press. F. Grases, A. Costa-Bauza, J.G. March and 0. Sohnel, Nephron, 65 (1993) 77. W.A. See and R.D. Williams, J. Urol., 147 (1992) 541. 0. Sohnel and F. Grases, Nephron, 63 (1993) 176. H. Iwata, S. Nishio, A. Wakatsuki, K. Ochi and M. Takeuchi, J. Urol., 133 (1985) 334. J.S. Elliot, J. Urol., 109 (1973) 82. B. Finlayson, Urol. Clin. North Am., l(l974) 181. B. Finlayson and F. Reid, Invest. Urol., 15 (1978) 442. D.J. Kok, S.E. Papapoulos, O.L.M. Bijvoet, Kidney Int., 37 (1990) 51. D.J. Kok and S.R. Khan, Kidney Int., 46 (1994) 847. 0. Sohnel, F. Grases, and L. Garcia-Ferragut, Scanning Microscopy, 8 (1994) 513. B.M. Brenner and F.C. Rector, The Kidney. W.B. Saunders, Philadelphia, 1976. F. Grases, A. Costa-Bauza and A. Conte, Scanning Microscopy, 7 (1993) 1067.