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J Urol. Author manuscript; available in PMC 2010 May 10.

Published in final edited form as:

Published online 2009 January 20. doi: 10.1016/j.juro.2008.10.141

PMCID: PMC2866055

NIHMSID: NIHMS195856

Center for Mineral Metabolism and Clinical Research, University of Texas Southwestern Medical Center, 5323 Harry Hines Boulevard, Dallas, TX 75390-8885

All correspondence should be addressed to Dr. Pak at the above address. Email: ude.nretsewhtuostu@kap.selrahc

The publisher's final edited version of this article is available at J Urol

The Equil 2 computer program has been questioned by the new Joint Expert Speciation System program (Mayhem Unit Trust and Council for Scientific and Industrial Research, Pretoria, South Africa) for estimating the urinary saturation of stone forming salts to gauge the propensity for stone formation. To attempt resolution the supersaturation index according to the Joint Expert Speciation System and the relative saturation ratio according to Equil 2 were compared with the semi-empirically derived concentration-to-product ratio.

Data were obtained from a recent article in The Journal of Urology®, in which pH, calcium and citrate were varied over a wide range in 72 urine samples. We calculated the relative saturation ratio and the supersaturation index of brushite, and compared them with the available concentration-to-product ratio derived from the growth or dissolution of synthetic brushite.

The mean concentration-to-product ratio did not differ from the supersaturation index but the concentration-to-product ratio and the supersaturation index were significantly lower than the relative saturation ratio (p <0.004). On the saturation value and urinary variable plot the relative saturation ratio could be readily distinguished from the concentration-to-product ratio because it was consistently and significantly higher. While the supersaturation index pattern was similar to the concentration-to-product ratio, the supersaturation index was slightly lower at high urinary pH and calcium, and slightly higher at lower urinary pH and calcium (p <0.001). When the Ca_{2}H_{2}(PO_{4})_{2} complex was deleted from the Joint Expert Speciation System, the corrected supersaturation index was not significantly different from the relative saturation ratio determined by Equil 2.

The relative saturation ratio overestimates brushite saturation by about 80%. The supersaturation index yields a good approximation of brushite saturation at modest degrees of saturation but it overestimates saturation at low pH or calcium (low saturation) and underestimates it at high pH or calcium (high saturation).

The use of outcome such as stone events requires long-term follow-up and is often impractical. Thus, the determination of urinary saturation of stone-forming salts is useful in gauging the propensity for stone formation and monitoring response to treatment.^{1} In the late 1960s, computer programs were developed to calculate ionic activities of stone constituents;^{2}^{,}^{3} urinary saturation was then estimated from activity products. In 1985, the Equil 2 computer program was introduced as an improved method for calculating urinary saturation of stone salts,^{4} including brushite (CaHPO_{4}·2H_{2}O) believed to be a precursor phase of hydroxyapatite.^{5} By then, a detailed analysis of urine for stone-forming constituents and ancillary components was being undertaken in stone research laboratories. By using such data, Equil 2 program derived concentration of Ca^{2+}(by subtracting known soluble complexes of calcium) and HPO_{4}^{2−} (from dissociation of phosphate and deletion of soluble phosphate complexes from total phosphate). The ionic activities of Ca^{2+} and HPO_{4}^{2−} were then calculated as an inverse function of ionic strength (derived from urinary components).

Since then, Equil 2 has been widely disseminated, becoming the tool of choice for estimating urinary saturation in both research and commercial clinical laboratories. Thus, this method has been used to assess stone-forming propensity of certain metabolic conditions (distal renal tubular acidosis^{6} and bowel diseases^{7}), dietary factors^{8} (salt, calcium, animal proteins and fruit juices), and drugs (thiazide and alkali therapy).^{6}^{,}^{8}^{,}^{9} Much of our current knowledge on the physicochemistry of stone formation and drug action has depended on the saturation data derived from Equil 2.

In 2006, Rodgers et al.^{10} introduced a new computer program JESS (Joint Expert Speciation System) to calculate urinary saturation of stone-forming salts. In contrast to EQUIL 2, the JESS software recognizes additional soluble complexes – Ca_{2}H_{2}(PO_{4})_{2} (dicalcium-dihydrogen phosphate) and (CaCitPO_{4})^{4−} (calcium phosphocitrate). About 25% of urinary calcium at baseline and greater than 50% of calcium after alkali treatment was reported to be complexed as Ca_{2}H_{2}(PO_{4})_{2} and (CaCitPO_{4})^{4−}. The formation of these complexes is dependent on pH and citrate. Thus, over a wide range of pH produced by alkali treatment, urinary saturation of brushite calculated by JESS was reported to be much lower and less dependent on pH, compared to that obtained by EQUIL 2.^{10} A current challenge in urolithiasis research is to ascertain the relative merits of the two computer programs.

In 1969, we introduced a semi-empirical approach for measuring brushite saturation, based on the ratio of activity products or concentration products before and after incubation with synthetic brushite.^{3} Although this method revealed a more direct estimate of saturation from the extent of actual growth (supersaturation) or dissolution (undersaturation) of added brushite, we abandoned it in the mid-80’s due to its complexity (requiring 2 days of incubation).

Recently, we simplified the method for the concentration product ratio (CPR) by reducing the time of incubation with synthetic brushite to 5 hours.^{11} To test the new approach, we assessed the effect of varying urinary pH, calcium and citrate on brushite saturation. In this report, we took the data from the aforementioned study, and calculated brushite saturation values by Equil 2 as relative saturation ratio (RSR) and by JESS as supersaturation index (SI). We then compared RSR and SI with the corresponding CPRs.

From our recent publication is this Journal,^{11} we took values for CPR of brushite obtained by a new, simplified method over a wide range of pH (by titration with dilute HCl or KOH to 5.67, 6.0, 6.35 and 6.7), calcium (by addition of calcium chloride to 2.5, 3.75, 5.0, and 6.25 mmol/L) and added citrate (0, 1, 2, and 3 mmol potassium citrate/L). In this manuscript, the corresponding RSR and SI of brushite were calculated by Equil 2 and JESS, respectively.^{4}^{,}^{10} In 6 urine samples tested at four ranges of pH, calcium or citrate (n = 72), CPR was compared with SI and RSR. Moreover, the JESS software program was modified by deleting Ca_{2}H_{2}(PO_{4})_{2} complex alone, or both Ca_{2}H_{2}(PO_{4})_{2} and (CaCitPO_{4})^{4−} complexes. SI obtained with and without deletion of above complexes was then compared with RSR. For technical reasons, we could not add the above complexes to the Equil 2 program.

The significant difference in saturation ratios at each level of urinary variable (pH, calcium or citrate) was assessed by repeated measures analysis of variance using a mixed linear model approach. In the whole group of 72 samples, or the subgroup of 24 samples (for each urinary variable), each 24-hour urine collection had been adjusted to yield 4 ranges of urinary pH, calcium or citrate. Thus, a mixed linear model was used to assess differences in saturation ratios in the whole group or subgroups. The subject was included as a random effect in these models to account for the lack of independence between observations obtained from the same individuals. Adjustments for multiple comparisons were made using the adjust=simulate option of SAS Proc Mixed LSMEANS.^{12}

The slopes of the relationship between brushite saturation and varying pH, calcium and citrate were determined; they were compared between the saturation variables by using a random coefficient model. For data derived from changes in urinary pH, calcium and citrate, taken separately or combined, the dependence of RSR and SI on CPR was determined by linear regression analysis. Only the relationship for the combined data are presented here, since the same pattern was observed for separate urinary variables. Statistical analysis was performed using SAS 9.1.3 (SAS Institute, Cary, NC).

Individual values for CPR are compared with corresponding RSR and SI in Fig. 1. For each variable (pH, calcium or citrate), data from 24 samples (6 urine samples at four ranges) are shown. For all three variables, CPR was lower than RSR, but similar to SI, in most of the samples. When the group means were compared for each variable, CPR was nearly identical and non-significantly different from SI (p > 0.9). Both CPR and SI were significantly lower than RSR (p < 0.003).

In Fig. 2, the relationship between brushite saturation and urinary variable is displayed. For all three methods of assessing saturation, a direct association was depicted between brushite saturation and urinary pH or calcium, and an inverse association was shown between brushite saturation and urinary citrate. This pattern of change in RSR was distinct from that of CPR or SI, with RSR being significantly higher than CPR or SI (p = 0.05–0.001) at most levels of all three urinary variables (p < 0.0001 from linear model). However, the pattern of change in SI merged with that of CPR, especially with added citrate (Fig. 2, right). Compared to CPR, SI tended to be slightly lower at high ranges of urinary pH and calcium, and slightly higher at lower ranges (Fig. 2, left and middle). The slope of the lines for SI was less steep than those for CPR (p < 0.003).

For the combined data (n = 72), RSR was highly correlated with CPR, with the intercept near zero and the slope of 1.79 (Fig. 3). Thus, at a broad range of brushite saturation, RSR was about 80 percent higher than CPR.

Dependence of RSR on CPR and of SI on CPR. Dotted line indicated identity. Regression lines for RSR vs. CPR (solid) and SI vs. CPR (dashed) are displayed.

SI was also highly correlated with CPR. However, the intercept was near 1 and the slope was much lower at 0.53 (Fig. 3). Thus, SI closely approximated RSR at modest degrees of brushite saturation, but was higher than CPR at low saturation ranges and lower than CPR at high saturation ranges.

Computations were made from combined data compiled from all urine samples at four ranges of pH, calcium and citrate (n = 72). SI was not significantly different from CPR (p = 1.0), but RSR was significantly higher than CPR (p < 0.0001)(Fig. 4). When Ca_{2}H_{2}(PO_{4})_{2} complex was deleted from JESS program, the corrected SI increased significantly from the original value (p < 0.0001), to attain a value slightly lower numerically but not significantly different than RSR (p = 0.9). When both Ca_{2}H_{2}(PO_{4})_{2} and (CaCitPO_{4})^{4−} complexes were deleted, the corrected SI was numerically higher but not significantly different than RSR (p = 0.8).

From data derived from a recent report in this Journal,^{11} urinary saturation of brushite was calculated by Equil 2 and JESS computer programs^{4}^{,}^{10} as RSR and SI, respectively, during wide changes in urinary pH, calcium and citrate. RSR and SI were then compared with the corresponding semi-empirically derived CPR. Overall, SI provided a good approximation of CPR, but RSR did not.

The JESS program differs from Equil 2 by inclusion of additional soluble complexes.^{4}^{,}^{10} Principal complexes relevant to calculation of brushite saturation are: Ca_{2}H_{2}(PO_{4})_{2} and (CaCitPO_{4})^{4−}. By diverting some of total calcium and phosphate to soluble ligands, these complexes reduce the amount of ionized calcium and phosphate and hence the saturation of brushite. Thus, Rodgers et al.^{10} reported a much lower value for brushite saturation when calculated by JESS rather than by Equil 2.

In contrast to the above computer-derived methods, CPR is obtained semi-empirically,^{11} where the ratio of concentration products are obtained by a simple computation, before and after experimentally incubating urine with synthetic brushite. CPR has a “physicochemical reality,” since supersaturation is obtained from the actual growth of added brushite, and undersaturation by dissolution of brushite. Thus, we believe that CPR of brushite can be used to validate the results of computer-derived approaches.

This study disclosed that RSR yields a poor approximation of CPR, being higher by 70–80 percent and showing wider variation with changes in urinary pH, calcium or citrate. In contrast, SI gave a good approximation of CPR. For all 72 samples and for each set of separate urinary variables (n = 24), the mean SI values were nearly identical and not significantly different from corresponding CPR values. On closer inspection, SI was slightly lower at higher levels of pH and calcium, and slightly higher at lower levels, compared with CPR. Though small, the above differences were significant (p < 0.001 for the slopes). These effects canceled each other to yield the group mean values of SI that were nearly identical to CPR.

The above findings (by random coefficient model) were affirmed by a different statistical analysis (regression analysis). While both RSR and SI were highly correlated with CPR, the slope for RSR was higher at 1.79 with the intercept originating near zero. The results indicated that RSR overestimated CPR by about 80 percent at a wide range of brushite saturation. In contrast, the slope for SI was much lower, and the intercept was near 1. SI was therefore higher than CPR at low ranges of brushite saturation, and lower than CPR at high ranges of saturation. Brushite saturation is decreased at low urinary pH and calcium, and increased at high urinary pH and calcium. Thus, at low ranges of brushite saturation (correponding to low urinary pH and calcium), SI probably overestimates brushite saturation. Conversely, at high ranges of brushite saturation (high urinary pH and calcium), SI probably underestimates it.

To understand the basis for the above results, SI was recalculated after omitting key soluble complexes contained in JESS but not in Equil 2 program. For all urine samples, the deletion of Ca_{2}H_{2}(PO_{4})_{2} complex from the JESS program yielded SI of brushite that approached the corresponding RSR value. The deletion of both Ca_{2}H_{2}(PO_{4})_{2} and (CaCitPO_{4})^{4−} complexes produced SI value slightly higher numerically than the RSR value. Thus, the overestimation of brushite saturation by RSR is probably due mainly to the omission of Ca_{2}H_{2}(PO_{4})_{2} complex in Equil 2. Other complexes or varying stability constants employed by the two programs may account for the different slopes of the relationship between brushite saturation and urinary variables. To be sure, actual identification of these complexes in urine would be required. Future studies must also focus on why SI deviates from CPR at extremes of urinary pH, calcium or brushite saturation.

The method for CPR is too labor intensive for routine clinical application, even though it has been simplified.^{11} We suggest that in a routine setting, RSR may be substituted by SI to estimate brushite saturation in urine. Alternatively, RSR might be corrected by dividing it by 1.8. However, the use of CPR is recommended for research purposes, until SI method is further refined or validated.

This work was supported by USPHS grant P01-DK20543 from the National Institutes of Health. The authors would like to thank Kathy Rodgers for technical assistance and Faye Britton for administrative support.

- CPR
- Concentration product ratio, a measure of brushite saturation derived by a semi-empirical method
- RSR
- Relative saturation ratio, a measure of brushite saturation calculated by Equil 2 computer program
- SI
- Supersaturation index, a measure of brushite saturation calculated by JESS computer program
- JESS
- Joint Expert Speciation System, a new computer program for estimating urinary saturation of stone salts
- Ca
^{2+} - Ionized calcium
- HPO
_{4}^{2−} - Ionized divalent phosphate

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