What Supersaturation Is
Supersaturation is not some arcane computation lifted out of physical chemistry and placed on 24 hour urine kidney stone reports as a kind of flourish, or occasion for learned teaching. It is the sole driving force for crystallization, and, at least to me, the main variable I follow in my practice of stone prevention.
The superb and recent review of supersaturation I placed in the Science section makes clear its true physical meaning. You can saturate a solution easily. Simply stir it with an excess of any substance at a constant temperature, and eventually the concentration of the substance will come to some final and unchanging concentration. By excess, I mean there will be some of the solid phase present still, at the end of the process. That solution is at the solubility for that substance at that temperature. But no matter how much the excess you cannot drive more into solution. From the review I have published a key figure. It shows what happens if you do this experiment at different temperatures. You create the solubility curve for that solution and that substance, and such curves are available for many solution – substance pairs. For example, solubility is well known for the stone forming salts at body temperature.
Doing work on a solution
Change of temperature
Solubility falls with temperature, in general. If you lower the temperature of your solution, and do it slowly and carefully, it may remain clear even though the concentration of the salt is above solubility. To lower the temperature, you have moved heat from the solution. This means you have done work on it to move that heat. Some of the work is transformed into the energy stored in the supersaturation. In fact, the analogy to classical thermodynamics is accurate. The supersaturation is a free energy that will eventually release itself by forcing the salt into a state of lowered entropy – as a solid phase as opposed to a dissolved phase.
Another way to achieve supersaturation is to remove water, which can be accomplished by adding heat sufficient to convert water into its vapor phase so the volume of the aqueous solution is reduced. Once again, work has been done on the solution, and part of the work is transformed into the free energy of the supersaturation. Kidneys do not evaporate water. They use free energy from metabolism of substrates to power transporters that move ions and therefore drive movement of water from tubule fluid back into the blood. Though the pathways are specific to kidneys, the final effect is the same as if you had evaporated water; free energy is stored in the fluid as supersaturation.
Clinical urine samples
We let them cool yet they stay stable
When we collect 24 hour urines, temperature falls, usually, which will raise supersaturation even above what the kidney has accomplished. Most of the time we calculate the concentrations of the stone forming materials in that urine using concentrations of their constituents, and sets of equations that take into simultaneous consideration all of the relevant interactions between them. But although we measure what is in a much cooler urine, we assume body temperature. Even a urinalysis sample usually cools. So crystals under the microscope, and some losses of materials in a 24 hour urine are not unexpected. But surprisingly, up to several days, a urine will generally maintain very constant concentrations of calcium, oxalate, uric acid, phosphate, pH – all of the key variables that we use to calculate supersaturation. That is why it is practical to use 24 hour urines for patient care. These data, incidentally, speak for storing 24 hour urine samples at ambient temperature as opposed to refrigeration; the lower temperature will simply raise supersaturation more than room temperature will.
Urine contains abundant and varied crystal retardants
The stability of 24 hour urines is far greater than that of simple salt solutions because of its retardants which are, at least in part, the molecules that make up stone matrix. In the review, the diagram illustrates two important supersaturation zones. The first is that of metastable supersaturation, the space between the solubility curve and the Ostwald limit – take a look. Such a solution is like urine, clear for a time but prone to some eventual dissolution into solid phase. The other, above the limit, is unstable; crystals will form immediately. It is not the stone forming salts, and certainly not the small molecules of urine that permit the obvious and marked metastability of supersaturated urine; it is the kinetic retardation afforded by the urine proteome, and this vast mix of kinetic modifiers is as yet as poorly defined as the flora of the ocean deeps. We know some of them; we do not know most of them; and how they act together to retard crystallization is a massive open area of research.
The Ostwald limit, like the solubility curve itself, can only be determined experimentally. We have made such measures as have others, and find that stone formers have lower distances between their Ostwald limit and their supersaturation, meaning a higher risk for crystal formation from sudden surges of supersaturation. In particular this was true for the calcium phosphate (CaP) limit.
We published in our original papers that the concentration of urine citrate affected the Ostwald limit. Our recent re-analysis of the data – link above – identifies urine citrate and inorganic phosphate molarities as the main determinants of the limit for calcium phosphate, which seemed the more important one in terms of being related to stone formation. Inorganic phosphate itself can have no independent effect on the Ostwald limit as it is part of the actual measurement and fully accounted for. We propose it is inorganic pyrophosphate which may be the other critical inhibitor with citrate. Together, inorganic phosphate (pyrophosphate?) and citrate account for over 60% of the variation of the Ostwald limit, meaning it may not be only the large molecules which affect it.
What can supersaturation predict?
pH dependent supersaturation – males
In a perfectly defined laboratory experiment, supersaturation and crystallization are tightly enough linked to create the kinds of graphs shown in the review. But the mass of crystallization modifiers in urine so distances the force of supersaturation from its final manifestation in crystal formation that the measurement is itself very limited for clinicians.
But in one sense it is predictive. The this graph shows a general correspondence between urine supersaturation and stone composition. In the paper itself, groups of patients with defined stone types were analysed to determine the extent to which their average urine supersaturations corresponded with their predominant stone crystals.
In the figure, male uric acid and calcium phosphate stone formers exhibited higher than normal supersaturations with respect to the crystals in their stones, which is what one might imagine would be the case.
For example, male normals (M normal on figure) had a brushite (CaHPO4) supersaturation (along the left hand axis) of about 1.6 whereas male calcium phosphate stone formers whose stones were either pure calcium phosphate (M CaP) or admixed with calcium oxalate (M CaP/CaOx) had much higher calcium phosphate supersaturations of 2.4 and 2.3 respectively. Likewise, males whose stones were pure uric acid (M UA) or mixed uric acid and calcium oxalate (M mixed) had much higher uric acid supersaturations (front axis of plot; 1.7 and 2.3, respectively) compared to male normals (M normal; 1.3 supersaturation). Likewise, the treated patients with either calcium phosphate or uric acid containing stones had much lower supersaturations than those untreated; compare RX bars with corresponding non RX labeled bars for the same groups.
pH independent supersaturations – males
By contrast, calcium oxalate supersaturation of male patients (M CaOx) did not differ from that of normal males (M normal), yet the stones were predominantly calcium oxalate by selection. Here is a paradox, and an important exception to what would seem an invariable rule. In physical chemical terms, supersaturation is the driving force for crystal formation, and there is one physics, so what applies in the closed and narrowed environment of a laboratory experiment applies in humans. But the lack of difference of supersaturations points to the necessity of assuming other important factors intervene between the driving force and its expression.
An obvious candidate is the myriad of urine crystal modifier molecules I have discussed above and in the post on stone matrix. This is a working hypothesis that has not been testable until the advent of proteomic methods that can sort out and quantify these molecules in patients and normal people and begin to show in what ways they might diverge from one another.
Another possibility is that calcium oxalate is itself not an initial crystal phase even in stones in which it is the predominant crystal. Future posts on this site will bring forward evidence about this idea, which is gradually acquiring some support: An initial calcium phosphate deposit is required to anchor the nascent calcium oxalate crystal on the papillary surface. The clinical implication of the idea, if true, is obvious. It would be important to control not only calcium oxalate but also calcium phosphate supersaturations in calcium oxalate stone formers.
One important point of the figure, however, concerns the average supersaturation of treated calcium oxalate stone formers. It is much lower than normal, and lower than pre-treatment. On the whole, treatments for calcium oxalate stones such as fluids, thiazide, and potassium citrate are effective and we use these conventional treatments as do other groups; so the lower supersaturation is in a group of patients whose stone rates are lower than they had been before.
Are women different from men?
They are. The adjacent figure follows the exact form of the prior one but differs in its content. The pH dependent supersaturations, for calcium phosphate and uric acid are higher in patients than in normals, as in men. But unlike the case in men, calcium oxalate supersaturation of stone formers exceeds normal. So women do not pose the calcium oxalate anomaly men pose; the stone formers are more supersaturated with respect to pH dependent and pH independent crystals. This may well be clue, long term, to real differences in the biology of stone formation.
But even though the anomaly is not present, these data are all mean values. The tables from the original paper make clear that these means, as is always the case, are accompanied by considerable variability as evidenced by standard deviations. In other words it is not hard to find a man or a woman stone former whose urine supersaturations fall within the range of same sex normal people.
What should we do?
We treat patients every day, and it may take years to clarify all of the factors involved in stone formation. But we can measure at least this one factor, supersaturation, and know that in measuring it we are observing a principle physical driving force for crystal formation. How we can best use supersaturation given the gaps and irregularities I have shown here is not completely obvious. But to me, the most sensible approach has been articulated by my colleague Dr. John Asplin: ‘The supersaturations of active stone formers are too high with respect to the crystals in their stones and should be lowered’ (Personal communication). He proposes lowering them by half, and that seems as reasonable as any other quantitative proposal.
To use his proposal we need to know three things: the crystals in the stones formed; whether a patient is an active stone former; and measurements of urine supersaturation that are clinically relevant.
Crystals in stones formed
I have already emphasized the key importance of stone analysis and in fact of even sequential and ongoing analysis. Here is more of the argument for such a course of action. You cannot use supersaturation except in relation to crystals in stones, so knowing those crystals is of primary importance.
Is the patient an active stone former?
What is meant by active and what one does to determine activity are hardly the same. Active is by way of metaphor – ‘forming new stones under the present conditions’ would be a kind of translation into something one might attempt to measure. But in reality we mean by new stones those passed or removed or appearing on a radiograph and not present on a prior radiograph. Think about that. The timing is entirely in relation to what images we have available. CT scans are most reliable for counting stones, but entail consequential radiation exposure so we limit them. Therefore there are appreciable gaps, and altogether a determination of activity is rough at best. My view is conservative; if stones seem active, I consider them so and act accordingly.
Are supersaturation measurements relevant?
The case I included in my account of how I practice illustrates the problem. My patient was a nurse with a complex work life and therefore variable hydration and diet. What 24 hour urine should I take as germane? In the case, I assumed what I was receiving – weekend collections – were not relevant, and worked out a way of proceeding with treatment and with correspondingly usable urine collections. Often we have to regularize diet and fluid habits before we can even make measurements to rely on.
This is an area in which patients have to help us to help them. They know their own lives, and they know when a collection is valid or simply what can be accomplished over a weekend off. It is up to us to understand the problem and understand their lives. It is up to them to be sure, once informed about the issues, to get us representative samples under conditions which they themselves believe will be achievable long term and reliably over the working week.
This is also an area in which clinical acumen reigns supreme, wherein the finest physicians may earn their crown imperial. Nothing less will suffice than a full understanding of the patient and the life lived, habits truly followed, motivations feigned and real, desires articulated and desires powerful enough to alter the warp and woof of daily living. It might be said, if I were given to an extreme of expression, that it is in assessment of stone activity I am, at least, most a physician in this odd, technical, and demanding corner of medicine.