The title accurately reflects the pragmatic value of the new research I review here. This work shows, for the first time, how one can use urine supersaturation measurements as an estimate of kidney stone risk. It also tests more rigorously than any study to date the urine supersaturation hypothesis that places supersaturation in a position of high primacy in kidney stone formation.

That test supports the primacy of supersaturation, and at the same time shows us how to use supersaturation as a graded risk factor, in the same way we use urine calcium, oxalate, citrate, and volume.

I wish to thank Drs Gary Curhan (Harvard) and John Asplin (Litholink) for their careful review and corrections to this article.

The beautiful thermodynamic partial differential equations expressing free energy changes with phase change comes from Phase separation of polymer mixtures induced by light and heat: A comparative study by light scattering, Advances in Natural Sciences: Nanoscience and Nanotechnology, 6(4):045002 · October 2015. 

The Urine Supersaturation Hypothesis

What Is the Hypothesis?

As far as a crystal is concerned, all of the established urine risk factors for stones act through supersaturation. A crystal cannot respond to calcium, oxalate, or urine volume directly, but only to the free energy produced by the calcium oxalate or calcium phosphate free ion product in relation to the solubility product – the supersaturation.

Given this, we generally base our practice and research upon the hypothesis that urine supersaturation is the efficient cause of stones, the force that compacts solution ions into crystal lattices. This has led to the clinical dictum first formulated by Dr John Asplin: ‘In someone who is producing new stones, urine supersaturations are too high with respect to the crystals forming. Therefore, whatever the supersaturation under that circumstance, lower it.

Supersaturation Does Not Act Alone

Anchored Sites

Of course urine supersaturation acts within a complex system. Randall’s plaque offers an anchored surface for nucleation of new stones, so urine supersaturation is not necessarily needed for de novo nucleation so much as growth of crystal on a preformed template. LIkewise, tubule plugs, almost always apatite, present their open ends to the urine and urine supersaturation acts to grow new crystals on that preformed surface.


Citrate, the fourth established urine risk factor, exemplifies another kind of mechanism. Citrate can directly attack the growth surface of calcium crystals, and interpose itself so as to disrupt growth and even force dissolution – a so called ‘crystal inhibitor‘. Citrate also acts on supersaturation, by binding calcium in a soluble complex so less is free to bind with oxalate or phosphate. Likewise, calcium bound citrate is not free to attack crystals. So the calcium – citrate ratio can be of importance in determining stone formation.

Macromolecular Crystallization Modifiers

Urine contains about 1800 individual proteins/peptides many of which attach to crystal surfaces and affect further nucleation, or growth, and can act as a matrix to bind crystals into stones – macromolecular inhibitors. Genetic or other modifications of these many large molecules could condition whether stones form, and much research has concerned the issue.


Like any free energy, supersaturation waits for opportunity to dissipate itself, in our case via phase transformation. In fact, it is no doubt citrate and the large molecule inhibitors that permit urine to maintain supersaturations over many days, as they do. So any drainage problems that raise the mean life of an element of urine within the kidney are apt to result in local dissipative crystallization. Medullary sponge kidney is a likely example of so called ‘stasis’ crystallization. Likewise for calyceal diverticula, and the common stones that form in bladders behind outflow obstructions.

Prior Tests of the Supersaturation Hypothesis

Given all of the factors that stand between supersaturation and its final expression in phase transformation – stones, empirical testing of the urine supersaturation hypothesis matters greatly. No one can quibble about what supersaturation is, or whether it is the necessary force for crystallization. But quibbles are plentiful when one says that urine supersaturation actually does express itself as a risk factor for stones, given the complexity of the renal and urinary systems. Against those quibbles, past scientists have placed their motes of positive argument.

Stone Crystals Match Urine Supersaturation

We have shown that stone crystal composition follows supersaturation. No doubt but that supersaturation is acting here as an agent of crystal formationBut this correspondence could be tested only for the pH sensitive calcium phosphate and uric acid phases. Had the observations failed to show matching, the hypothesis would have been rejected, so the data are not trivial. But the approach fails for calcium oxalate crystals that are insensitive to urine pH.

Use of Trial Data

In prospective trials, one can ask if reduced stones correlate with reduced supersaturations. In one diet trial, by Borghi, and one trial of hydration, I have pointed out that the active treatment patients who formed fewer stones had lower urine supersaturations.

The authors of a new study obtained the full data set from the abovementioned Borghi diet trial and could associate initial supersaturations and treatment changes in supersaturation from baseline with new stone outcome in the active (low sodium high calcium) arm. They were able to extract a quantitative relationship between change in supersaturation with respect to calcium oxalate and new stones.

This use of the trial data could not have falsified the supersaturation hypothesis. Within the original trial, the low sodium high calcium group formed fewer stones than did its control diet group, and in keeping with the supersaturation hypothesis had the lower urine supersaturation. Failure to find a smooth correlation to predict new stones from baseline supersaturations could have reflected simply variabilities that the original trial design did not seek to minimize. Therefore, that the results of the study supported the supersaturation hypothesis is not of crucial importance.

Case Control Risk Factor Evidence

The Curhan group at Harvard has tested the hypothesis that urine calcium, oxalate, citrate, volume, and other characteristics are causes of stones using a powerful epidemiological design.

Three cohorts, two of them female (red in the figure below) and one male (blue) contributed large amounts of information to investigators at Harvard over decades of life. Included in this was kidney stone onset. From a well chosen subset of people who formed stones and people who did not form stones, the Curhan group collected 24 hour urine samples submitted for comprehensive assessment of the usually recognized risk factors and the additional data needed to calculate supersaturation.

For each, the tests were two: Do the stone formers differ from the controls? Does the relative risk of becoming a stone former increase with the magnitude of the proposed risk factor – dose effect?

In each case, this group was testing hypotheses that the factor was a cause of stones. Failure to find an effect in their case control design would be powerfully against the hypothesis in question.

Now, the same group has provided us equivalent data concerning the supersaturations.

Graphing Conventions Used Here

The top of each bar in the graph below is the relative risk within a given urine risk factor grouping (for example, a range of urine calcium excretions in the upper left panel) compared to a reference range (for calcium, less than 100 mg/day). The bottom of each bar, visually emphasized by the solid filled bars, is the lower 95th percentile of the relative risk.

When the lower 95th percentile fails to cross 1 (the dashed horizontal line), the probability that risk is not increased is below 5%.

For protective urine measurements, urine citrate and volume, the process is simply reversed: The mean relative risk compared to the highest urine value is plotted downward, and the top 95th percentile upward from that. When that top 95th percentile of risk lies below 1, the likelihood that risk is not reduced is below 5%.

In each graph below, the two female cohorts are in red, the one male cohort in blue.

Prior Established Graded Risk Factors

The most important prior outcome of the the entire work has been to prove that four urine measurements satisfy the predictions: Differs between stone formers vs. controls, and shows a dose effect. Urine calcium, oxalate, citrate, and volume – the four panels at the left and center of the figure – show both characteristics.

This work has replaced older and mainly incorrect cutpoints with real information linking a particular measurement to relative risk.

Effects of Supersaturation

Dr Megan Prochaska, in the Curhan group and using the same three cohorts, has provided us with crucial tests concerning stone incidence and urine supersaturations. I have graphed her new findings as in the other four risk factors, using the right hand panels of the figure.

Supersaturation Calculation

Everywhere else on this site, and in most publications, supersaturations are calculated from urine free ion products and established solubility products using programs such as EQUIL – 2. This work differs in that the free ion activity product from EQUIL – 2 is divided by the mean value derived from a group of normal non stone forming controls. This creates a ratio of the calculated calcium oxalate and calcium phosphate supersaturations from EQUIL-2 to the corresponding means of the normals, and that ratio is called the ‘relative supersaturation ratio (RSS)’. Because the transformation of supersaturation to RSS involves only multiplication by a single number (the reciprocals of the means for calcium oxalate and calcium phosphate, respectively) it can only alter the magnitude of the numbers, but not their relative positions one to another. So risk in relation to RSS or to supersaturation will be the same.

Calcium Oxalate Supersaturation

Compared to kidney stone rates in people whose urine had calcium oxalate RSS<1, risk of stones was already significantly increased in the cohorts with urine calcium oxalate RSS between 1 and 1.9 (upper right panel). Thereafter, risk increases with RSS in a progressive manner with p values for trend analysis of <0.001 in all three cohorts. Since the bottoms of the bars do not cross 1 in even the lowest RSS range, risk is almost certainly increased at any RSS above 1.

Calcium Phosphate Supersaturation

For Calcium phosphate (lower right panel), the same, except that risk is not certain in the lowest RSS group for one of the three cohorts. Also, only one of the cohorts provided sufficient data for analysis in the highest RSS group. Even so, trend p values were <0.001 for all three cohorts.

Uric Acid Supersaturation

Dr Prochaska provided data for uric acid RSS which showed progressive stone risk for two of the three cohorts, but I did not graph it. Uric acid chemistry is such that crystallization is rapid as urine pH falls, and treatment is aimed at urine pH. The group does not have stone analysis data, and uric acid stones could therefore not reliably be separated from calcium stones.

Orders of Magnitude

I have made the calcium, oxalate, and two supersaturation scales identical, from 0-7, so as to compare the four risk factors. CaOx RSS and urine calcium match well, the range of risk for oxalate and CaP supersaturation is much smaller, though all four are progressive.

Importance of the New Findings

Critical Test of the Supersaturation Hypothesis

The obvious importance is that this stringent test of the supersaturation hypothesis is not negative. Had it proven negative, one would have had to radically revise our thinking. Perhaps Karl Popper would have been happy with such an outcome, perhaps I might have been, too, but it is easier to have a positive result.

Risk Begins at Modest Calcium Oxalate Supersaturations

The Special Supersaturations Available Here

The RSS values we have for the new work arise from decisions made by Professor Charles Pak. Charles wished to construct a visually clear representation of calcium oxalate, calcium phosphate and other supersaturations on a single graph, and achieved that aim by scaling each supersaturation by the mean of the corresponding supersaturation found in normal – non stone forming – people. The resulting RSS values for each supersaturation therefore run in multiples of a normal population and can fit into a single graph range.

For calcium oxalate, his normals had a mean calcium oxalate ion activity product of 7.3×10-9 M2, the core measure from which supersaturation derives. The solubility activity product is 2.2 x 10-9 M2. This means that his normals had a supersaturation of 7.3/2.2 or 3.31. In the scale Prochaska had available, therefore, the first supersaturation range ran from 3.3 to 6.3 (3.3 x 1.9). Risk was first evident therefore within this range. If we are using standard supersaturations for our clinical work we therefore can approximate that risk begins at above 3.3 and rises thereafter exactly in proportion to her graph.

For calcium phosphate as brushite, the Pak normals had a mean value of 2.35 x 10-7 M2. In EQUIL the solubility product for brushite is almost identical: 2.35 x 10-7 M2. So the RSS and SS values for brushite are the same, and risk from calcium phosphate supersaturation begins above 1.

I wish to specially thank Dr John Asplin for providing the two equilibrium solubility products used above which he obtained from EQUIL and from a difficult to obtain book: Urinary Calculi  LC Delatte, A rapadp, A Hodgkinson eds, 1973.

Upper Limit of Metastability Can Mislead Us

Brilliant work by Dr Charles Pak showed us long ago that for calcium oxalate one needs for crystallization to raise supersaturation above an empirical upper limit – the so called upper limit of metastable supersaturation (ULM). Among others, I have explored the significance of the ULM by testing its ability to distinguish between stone formers and well matched controls. 

Among both men and women (references to primary publications in the above linked article), I found the critical difference between the measured calcium oxalate ULM and the actual urine supersaturation for calcium oxalate was not impressively different between patients and controls. Likewise I could not find important differences between patients and controls for urine supersaturation. But my two small trials may have lacked power.

Given that calcium oxalate stones may well form anchored to plaque or perhaps to tubule plugs, and given that plaque and plugs provide initial crystal substrate that abrogates the ULM altogether, it may well be that very modest calcium oxalate supersaturation is enough in those who form more abundant plaque or plugs and thereby become stone formers.

Likewise, modern work has revealed that calcium phosphate may play a special role in calcium oxalate stones by acting as a link between plaque and perhaps open plug ends and the initial calcium oxalate crystal formation. 

Supersaturation is a Progressive Risk Factor

The progressive nature of the calcium oxalate supersaturation is compatible with growth on plaque or plugs. This is because even if nucleation in solution no longer matters, there being an anchored substrate, one needs supersaturation to grow the calcium oxalate phase, so growth – and manifest stone risk – will be proportional to supersaturation as in the new data.

Risk Begins at Any Supersaturation for Calcium Phosphate

Originating Species

With the exception of one cohort (females in the lower right hand panel of the figure shown above), any CaP supersaturation raises stone risk, and this is also compatible with what we know otherwise. Interstitial plaque is not affected by urine concentrations, but plaque exposed to urine first overgrows with calcium phosphates of urine origin. Thereafter, calcium oxalate nucleates over the initial calcium phosphate layers. Plugs are almost always calcium phosphate as apatite, so they require some CaP supersaturation.


Brushite is a special case that amplifies this peculiar role for calcium phosphate in calcium oxalate stone disease.

Pak showed clearly that brushite is the first crystal phase to form in urine as one raises supersaturations, and this crystal may be very important in nucleation of calcium oxalate. Oxalate in solution can pirate calcium off of the brushite lattice, cannibalizing brushite to make itself – at least in vitro. We measure CaP supersaturation as brushite, the most soluble form of calcium phosphate regularly found in urine. Even slight supersaturation can be enough to nucleate brushite, creating a possible source of high calcium concentration to foster calcium oxalate.

Any CaP SS may be Enough

Altogether CaP supersaturation is like the match more than the tinder, so any at all is very likely enough for calcium oxalate stone formation. In order for calcium phosphate to predominate as the main stone type, one needs higher CaP supersaturation. Possibly, the progressive nature of CaP supersaturation results from people whose stones had higher CaP mineral contents; we cannot know.

Clinical Meaning

Because of what it can do, most of us work to lower CaP supersaturation below 1 in every case we can. These new data encourage us in that practice and add some experimental heft to the proposition that CaP supersaturation may be generally important, even for the common CaOx stones.

But perhaps more importance is that the new data confer on patients and physicians a new fluency and sophistication in the use of calcium oxalate supersaturation. Just as we have abandoned clinical cut point definitions such as ‘hypercalciuria’, ‘hyperoxaluria’, ‘hypocitraturia’ and ‘low urine volume’ as diagnoses, and replaced them by using actual measured values to assess potential stone risk, we can do the same with supersaturations.

A value, for example, of 2 is a lot less risky than a value of 6, for calcium oxalate. This makes supersaturation more like blood pressure, and other graded risk factors, and allows us to stop using such phrases as ‘high supersaturation’ instead of the more nuanced statistical risk the supersaturation implies. Given the 3.3 multiplier to convert RSS to the commonly used SS, the key SS values for clinicians are (rounded): below 3.3 (lowest risk); 3.3 – <6.6, increased risk is present; 6.6 – <9.9, medium risk; 9.9 – 13.1, high risk; >13.1 very high risk.

These values can be used to amplify the Asplin dictum. If stones are forming, supersaturation with respect to the crystals in the stones formed are too high and should be lowered to below the Prochaska delimiters of 3.3 for calcium oxalate and 1, of course, for calcium phosphate.

This is a Major Contribution

The new work provides a critical test of the supersaturation hypothesis. The positive result means we can continue to use that hypothesis as an integral part of our working theory of stone pathogenesis and treatment. For clinicians, the present result offers a clear message: Measure supersaturation, lower it: Aim below 3.3 for calcium oxalate, and 1 for calcium phosphate.

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