Enteric Hyperoxaluria Secondary to Small Bowel Resection: Use of Computer Simulation to Characterize Urinary Risk Factors for Stone Formation and Assess Potential Treatment Protocols

Abstract

Background and Purpose:

We used computer modeling to investigate the influence of physicochemical stone risk factors on urinary supersaturation (SS) of calcium oxalate (CaOx) in patients with severe hyperoxaluria, relative hypocalciuria, hypocitraturia, and CaOx nephrolithiasis after extensive small bowel resection, usually performed for Crohn's disease. We also simulated different treatment strategies, including oral calcium supplements and citrate, in such patients.

Materials and Methods:

A baseline urine model was derived by consolidating data acquired by ourselves with those from another patient cohort. Calcium and oxalate excretions in this model were altered to obtain an extreme case. For comparison, additional models were based on published urine data from normal subjects (N) and idiopathic CaOx stone formers (SF). The Joint Expert Speciation System was used to simulate different urine situations based on reported compositional values.

Results:

[Ca²⁺][Ox²⁻] ionic concentration products and SS(CaOx) are substantially higher in enteric hyperoxaluric patients than in N and SF, despite their relatively lower calcium excretions. Molar Ca:Ox ratios are substantially lower in enteric hyperoxalurics than in N and SF. Oral calcium supplements can reduce SS(CaOx), but monitoring is required to avoid exceeding a safe dosing threshold. A simple calculation can alert the clinician that this threshold is being approached or even exceeded. Increasing urinary pH and citrate decreases SS(CaOx) but not to the same extent as decreasing Ox excretion.

Conclusions:

Calcium supplements can help reduce stone risk in patients with severe enteric hyperoxaluria, but initial efforts should be directed toward reducing urinary oxalate by reducing dietary oxalate. Citrate therapy that increases both urine pH and urinary citrate provides an additional therapeutic benefit.

Introduction

Recurrent calcium oxalate (CaOx) stone disease is a well-recognized consequence of extensive small bowel resection, usually performed for Crohn's disease.^1

–5 In such patients, urinary calcium excretion is often very low^1,2,5,6 and urinary oxalate excretion is typically very high.^3
–5 Notwithstanding the severe hyperoxaluria which prevails in these patients, it is intriguing that CaOx stones form despite such low levels of calcium excretion. Furthermore, since it has been suggested that CaOx crystallization occurs more efficiently as the Ca-to-Ox molar ratio approaches unity,^7,8 there is a further measure of intrigue related to how the magnitude of this ratio in these patients might be compared with that in other types of CaOx stone patients and in healthy individuals. It is, therefore, of interest to investigate ion products, supersaturation (SS) values, Ca-to-Ox molar ratios, and the prevailing chemical speciation in the urines of these different groups.

Irrespective of the nature of the chemical speciation that directs CaOx stone formation in severely hyperoxaluric patients, treatment strategies in these patients focus on reducing the magnitude of SS(CaOx). Such patients are usually treated with dietary oxalate restriction,⁹ but this often has limited success because patients cannot readily identify or avoid causative dietary constituents.¹⁰ Alternatively, they are treated with calcium supplements (often in large doses) to bind oxalate in the intestinal lumen and prevent its absorption.^11,12 A concern with the latter protocol is that despite some evidence to the contrary,¹³ a modest increase in urinary calcium (caused by the calcium supplementation) might offset any reduction in urinary oxalate. If this is a reality, it would be most helpful if clinicians had a guideline which could alert them when the critical level of calcium supplementation had been reached, so that supplementation beyond this point could be avoided.

As is well known, citrate is one of the interventions of choice in the management of idiopathic CaOx stone disease,¹⁴ by virtue of its capacity to increase urinary pH and decrease SS(CaOx).¹⁵ In patients with enteric hyperoxaluria and stones, baseline urinary citrate excretion is typically low² probably as a result of their mild metabolic acidosis, secondary to diarrhoea. The use of citrate is fairly standard in these patients. As such, it might be of interest to clinicians to know how citrate's efficacy in reducing SS(CaOx) would be compared with that of measures to decrease the urinary oxalate excretion.

Computer modeling is an extremely useful tool for obtaining theoretical answers to these questions, and it can be used to identify and focus questions to be addressed by clinical trials.¹⁶ With this approach, chemical speciation and SS values for all of the possible complexes in any particular urine are initially calculated using the measured total concentrations of the individual components. The input data are then varied systematically to model different pathological conditions or treatments, and chemical speciation and SS values are again calculated. A comparison of the various outputs provides insights into the processes that drive the achievement of chemical equilibria in the different models.

Materials and Methods

Calculations and modeling

Qualitative and quantitative information about the chemical complexes (speciation) in urine is extremely important for evaluating the SS of stone-forming salts. This parameter is the gold standard by which the risk of stone formation is assessed.¹⁷ Computer programs which have data bases of thermodynamic constants for the wide variety of complexes that might form from the known components in urine are required for calculating the concentrations of the various chemical species and concomitant SS values. Input for these programs is the concentration of components in the urine under investigation. For more than 35 years, the program EQUIL¹⁸ and its updated versions EQUIL2¹⁹ and EQUIL93²⁰ have been extensively and successfully used by urologists and others in clinical and research settings. The Joint Expert Speciation System (JESS) is a program which is similar to EQUIL in that it calculates SS values and the concentration of ionized calcium, but it has several advantages which include a bigger data base and the option of a wider range of calculations, including SS values for several different CaOx and CaP salts.^21,22 It has recently been applied in urolithiasis research.^15,23 Accordingly, it was selected for use in the present study to determine the type and concentration of different chemical species, to calculate SS of calcium oxalate monohydrate (COM), and to model different urinary scenarios

Baseline urine model

Typical urine compositional values for patients with severe hyperoxaluria arising from extensive small bowel resection, generally performed for Crohn's disease, were used as the baseline model for calculating SS values (Table 1). These data will henceforth be referred to as “baseline” or the “baseline model.” They were derived from 17 patients (6 patients were investigated by R.S. in the renal stone clinic at Vancouver General Hospital [VGH], and 11 were investigated by the research group from the Indiana University School of Medicine [IUPUI]⁵). All of the patients were CaOx stone formers; however, in one stone from VGH and one from IUPUI, ammonium urate was also present. None of the patients had low serum bicarbonate. Renal function was normal in 16 of the 17 patients; the remaining patient had a slightly reduced glomerular filtration rate of 51 mL/minute. In 16 of the patients, the bowel surgery was performed for Crohn's disease; in a single patient, the surgery was for other reasons. Most patients had had multiple small bowel resections; none had either a colostomy or an ileostomy at the time of study. Values in Table 1 for Mg and K are the means determined by R.S. in six patients. Values for ammonium, sulphate, and pH are the means of those reported in the Indiana study.⁵ Chloride and phosphate values were kindly provided by Elaine Worcester (University of Chicago) and Andrew Evan (Indiana University School of Medicine) in private correspondence. Other urinary parameters in the baseline model are the consolidated means of values determined in the two patient cohorts. Accordingly, our baseline model was considered being representative of patients with hyperoxaluria secondary to small bowel resection.

Table 1.

Typical 24-Hour Urine Compositional Values (“Baseline”)

Urinary parameter	Mean (range)
Calcium (mmol/24 hours)	2.71 (0.83–6.08)
Oxalate (mmol/24 hours)	0.79 (0.24–1.61)
Citrate (mmol/24 hours)	0.84 (0.10–2.30)
Uric acid (mmol/24 hours)	2.79 (1.5–4.4)
Sodium (mmol/24 hours)	173 (114–272)
Potassium (mmol/24 hours)	60 (30–75)
Magnesium (mmol/24 hours)	1.37 (1.05–1.70)
Ammonium (mmol/24 hours)	48 (31–69)
Sulphate (mmol/24 hours)	13.5 (3.5–20.5)
Phosphate (mmol/24 hours)	31.5 (10.6–70.3)
Chloride (mmol/24 hours)	197 (105–359)
pH	5.56 (5.14–6.05)
Volume (mL)	1495 (660–2470)

Additional urine models

In order to calculate and compare ion products, SS values, Ca-to-Ox molar ratios, and the prevailing chemical speciation in hyperoxaluric stone formers with those occurring in healthy subjects and in idiopathic CaOx stone patients, three additional urine models were identified: urine data from two published studies from the same research group constituted the normal (N) and idiopathic CaOx stone-forming (SF) models, respectively^24,25; finally, we altered our baseline composition for oxalate (790 to 1614 μmol/day) and for calcium (2.71 to 0.83 mmol/day) to provide a model of extreme hyperoxaluria accompanied by extreme hypocalciuria. These values were identified as the extreme excretions in our consolidated data base of urine chemistries (Table 1); in both cases, they (coincidentally) occurred in the Indiana cohort.⁵

Effect of oral calcium supplementation

With regard to the concern that the effect on SS(COM) of reducing urinary oxalate by administration of a calcium supplement might be compromised by concomitant increases in urinary calcium, simple physical chemistry principles dictate that since SS is directly dependent on the ion product [Ca²⁺][Ox²⁻], any decrease in the magnitude of this parameter caused by a decrease in the concentration of [Ox²⁻] will be offset when the concentration of [Ca²⁺] increases proportionately. On the basis of this inverse relationship, the critical Ca excretion can be predicted by applying the formula \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}{ \rm Ca}_{ \rm critical} = ( { \rm Ca}_{ \rm initial} ) / ( { \rm FO}_{ \rm x} ) ,\end{align*} \end{document}

where Ca_critical is the threshold Ca excretion at which the effect of a reduction in total Ox excretion on SS(COM) would be nullified, F_Ox is the numerical factor by which total oxalate excretion changes (from Ox_initial to Ox_final), and Ca_initial is the total calcium excretion before the commencement of treatment (with Ca supplementation). F_Ox itself is given by \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}( { \rm F}_{ \rm Ox} = { \rm Ox}_{ \rm final} / { \rm Ox}_{ \rm initial} )\end{align*} \end{document}

This argument is true only if there is a direct and precisely proportional relationship between the concentrations of total Ca and ionized [Ca²⁺] and between the concentrations of total Ox and ionized [Ox²⁻]. We undertook to investigate such relationships in the models of the present study and to test the robustness of our formula. Accordingly, we used JESS to calculate SS(COM) values for several different urine scenarios and interrogated them to ascertain the corresponding threshold Ca excretion values; these were then compared with our formula-derived values. In these models, urinary oxalate was set at levels constituting mild (400–500 μmol/day), severe (500–900 μmol/day), and extreme hyperoxaluria (900–1600 μmol/day); while urinary calcium was set at various levels between 1.0 and 6.0 mmols/day.

Comparison of treatment strategies

In order to compare the efficacy of raising urinary citrate excretion and pH relative to reducing urinary oxalate excretion, urinary Ox, Cit, and pH were systematically varied within each of their observed ranges (Ox: 400–1600 μmol/day, Cit: 0.10–2.50 mmol/day, pH: 5.1–6.0). As a part of the same modeling exercise, urinary Ca was also systematically varied over the range 1.0 to 6.0 mmol/day. In each case, values for SS(COM) were calculated and compared.

Results

Physicochemical stone risk factors

The concentrations of total and ionized Ca and Ox, their molar ratios, ion products and percentage ionic speciation, as well as the concomitant SS(COM) values for the four urine models that we defined as being representative of the range of different oxaluric scenarios are give in Table 2. The concentrations of different Ca and Ox chemical species are shown in Figures 1 and 2, respectively, while the corresponding percentage distributions of these species are shown in Figures 3 and 4, respectively.

FIG. 1.

Urinary calcium species expressed as molar concentrations in the different urine models.

FIG. 2.

Urinary oxalate species expressed as molar concentrations in the different urine models.

FIG. 3.

Urinary calcium species expressed as a percentage of total urinary calcium.

FIG. 4.

Urinary oxalate species expressed as a percentage of total urinary oxalate.

Table 2.

Urinary Concentrations of Free and Ionized Calcium and Oxalate, Ion Products, and SS(COM) Values in Normal, Idiopathic Stone-Former, Hyperoxaluric, and Extreme Models

	N²⁴	SF²⁵	Present study baseline model	Present study extreme model
Ca (total) (mM)	3.62	3.42	1.81	0.55
Ox(total) (mM)	0.246	0.200	0.528	1.08
Cit (mM)	2.22	1.35	0.56	0.56
pH	6.01	6.13	5.56	5.56
Vol (l)	1.29	1.94	1.49	1.49
Ca²⁺ (mM)	1.07	1.16	0.773	0.236
Ox²⁻ (mM)	0.0817	0.0765	0.181	0.381
%Ca²⁺ (^a)	29	34	43	43
%Ox²⁻ (^b)	33	38	34	35
Ca_total/Ox_total	14.72	17.10	3.43	0.51
Ca²⁺/Ox²⁻	13.10	15.16	4.27	0.62
[Ca²⁺][Ox²]	8.74×10⁻⁸	8.87×10⁻⁸	1.40×10⁻⁷	0.90×10⁻⁷
SS(COM)	3.44	4.28	5.87	3.80

(^a)% of all Ca species which comprises Ca²⁺.

(^b)% of all Ox species that comprises Ox²⁻.

COM=calcium oxalate monohydrate; N=normal subjects; SF=stone formers; SS=supersaturation.

Effect of oral calcium supplementation

Although we completed numerous calculations to investigate possible conflict between the reduction in urinary oxalate and the accompanying increase in urinary calcium, we show only some of these in Table 3, in the interests of conserving column space. Here, we show decreases (Δ) in SS(COM) that are predicted to occur when total urinary oxalate excretion is incrementally decreased within different ranges, by 100, 200, and 300 μmol/day at certain levels of total Ca excretion (1.0, 2.0, and 3.0 mmol/day), and the corresponding critical increase in 24 hourly Ca excretion which would offset the decrease in urinary oxalate produced by the oral calcium supplement, as determined by our modeling with JESS and by application of our formula.

Table 3.

Critical Increase in 24 Hourly Calcium Excretion That Would Offset the Decrease in Urinary Oxalate Produced by an Oral Calcium Supplement, Determined by Modeling with Joint Expert Speciation System and by Application of the Proposed Formula

Initial Ca excretion (mmol/24 hours)	ΔOx Range (μmol/24 hours)	Actual ΔOx (μmol/24 hours)	ΔSS (COM)	Critical Ca excretion (JESS) (mmol/24 hours)	Critical Ca excretion (formula) (mmol/24 hours)
1.0	1200→900	300	3.40→2.56	1.34	1.33
	1100→900	200	3.13→2.56	1.23	1.22
	1000→900	100	2.84→2.56	1.12	1.11
2.0	1200→900	300	6.68→5.04	2.70	2.66
	1100→900	200	6.14→5.04	2.49	2.44
	1000→900	100	5.58→5.04	2.23	2.22
3.0	1200→900	300	9.84→7.40	4.10	3.99
	1100→900	200	9.02→7.40	3.72	3.66
	1000→900	100	8.20→7.40	3.36	3.33
1.0	900→600	300	2.56→1.71	1.51	1.50
	800→600	200	2.28→1.71	1.34	1.33
	700→600	100	2.00→1.71	1.18	1.17
2.0	900→600	300	5.04→3.36	3.06	3.00
	800→600	200	4.48→3.36	2.70	2.66
	700→600	100	3.92→3.36	2.36	2.34
3.0	900→600	300	7.40→4.94	4.66	4.50
	800→600	200	6.58→4.94	4.10	3.99
	700→600	100	5.75→4.94	3.54	3.51

JESS=Joint Expert Speciation System.

Comparison of treatment strategies

In order to compare the relative efficacy of reducing SS(COM) by increasing urinary citrate excretion and pH or by reducing urinary oxalate excretion, we modeled different scenarios in which these parameters as well as those of urinary Ca excretion were allowed to vary within their observed ranges. SS(COM) values obtained for some of these scenarios are given in Tables 4 and 5 while the full range of values are depicted in the column plots shown in Figures 5 and 6.

FIG. 5.

Supersaturation of calcium oxalate monohydrate (SS(COM)) as a function of total 24-hourly excretion of calcium and citrate, and urinary pH at baseline oxalate excretion.

FIG. 6.

Supersaturation of calcium oxalate monohydrate (SS(COM)) as a function of total 24-hourly excretion of oxalate and citrate, and urinary pH at baseline calcium excretion.

Table 4.

Calcium Oxalate Monohydrate Supersaturation (SS(COM)) as a Function of 24-Hour Urinary Calcium and Citrate Excretion and pH at Baseline 24-Hour Urinary Oxalate Excretion

	Citrate (mmol/24 hours)
Calcium (mmol/24 hours)	0.10	1.00	2.00	2.50
pH 5.10
1.0	2.48	2.38	2.27	2.22
2.0	4.88	4.69	4.50	4.40
4.0	9.40	9.10	8.75	8.59
6.0	13.52	13.12	12.68	12.47
pH 6.00
1.0	2.12	1.95	1.77	1.69
2.0	4.04	3.76	3.47	3.33
4.0	7.41	7.01	6.61	6.40
6.0	10.33	9.89	9.42	9.18

Table 5.

Calcium Oxalate Monohydrate Supersaturation (SS(COM)) as a Function of 24-Hour Urinary Oxalate and Citrate Excretion at Baseline 24-Hour Urinary Calcium Excretion

	Citrate (mmol/24 hours)
Oxalate (μmol/24 hours)	0.10	1.00	2.00	2.50
pH 5.10
400	3.32	3.20	3.07	3.01
600	4.95	4.78	4.58	4.49
900	7.41	7.14	6.85	6.71
1100	9.04	8.71	8.36	8.18
1300	10.67	10.28	9.86	9.66
1350	11.07	10.67	10.23	10.02
1600	13.06	12.59	12.08	11.86
pH 6.00
400	2.69	2.52	2.34	2.26
600	4.02	3.77	3.50	3.37
900	6.01	5.64	5.25	5.06
1100	7.35	6.89	6.40	6.18
1300	8.67	8.13	7.55	7.29
1350	8.99	8.43	7.83	7.57
1600	10.64	9.98	9.27	8.95

Discussion

Qualitative and quantitative interrogation of the chemical speciation generated in the urine models of the present study is required to provide insights into stone pathogenesis and optimal treatment strategies in patients with enteric hyperoxaluria.

The concentration of ionized [Ca²⁺] in the urine of hyperoxaluric patients (baseline model) is lower than that in the urine of N and idiopathic CaOx SF (Table 2 and Fig. 1). Although this is consistent with the fact that the concentration of total Ca in the latter two models is ∼2x greater (Table 2), the relative concentrations of [Ca²⁺] do not differ by the same factors, nor do those of the other Ca species (Fig. 1), indicating that the total concentration of Ca is not the sole determinant of the concentration of ionized [Ca²⁺].

The same is not true for Ox. Here, we note that the concentration of total Ox in the baseline model is 2.1x and 2.6x greater than that in the N and SF models, respectively (Table 2) and that the concentrations of [Ox²⁻] are greater by approximately the same factors (2.2x and 2.4x) (Table 2 and Fig. 2). Of course, the concentration of [Ox²⁻] is dependent on the concentrations of all of the other Ox species (Fig. 2), but the concentration of total Ox appears to be the dominant determinant.

These observations can be used to account for the relative differences in SS(COM) of the different urine models (Table 2). SS(COM) in hyperoxaluric patients (5.87) (baseline model) is substantially greater than that which occurs typically in the urine of N (3.44) and idiopathic CaOx SF subjects (4.28). Since the concentration of [Ca²⁺] is lower in the baseline model, the higher SS(COM) value in this group can be solely attributed to its higher concentration of ionized [Ox²⁻], as is apparent from the higher value for the ion product [Ca²⁺][Ox²⁻] (Table 2).

The results of the extreme model demonstrate that notwithstanding the very low Ca excretion, SS(COM) is greater than that for normal individuals (Table 2), albeit by a small amount only. This arises because of the very high Ox excretion (and concomitantly high concentration of [Ox²⁻]) in the former group that offsets the potential protective effect of the lower Ca excretion. Thus, our initial speculation of possible intrigue about stone formation in the presence of very low Ca excretion is partially unfounded; our results demonstrate that there is still sufficient Ca to constitute a relatively high value for SS(COM) in extreme cases of hyperoxaluria. Nevertheless, the lower SS(COM) in the extreme model relative to the SF and baseline models suggests that stone formation in this hypothetical group would be less severe than that in the other groups because of its extremely low Ca excretion.

The percentage distributions of the Ca (Fig. 3) and Ox (Fig. 4) species provide further insights into the physicochemical aspects of stone formation in severely hyperoxaluric patients. We note that the percentage of calcium species comprising ionized [Ca²⁺] is the same in the two hyperoxaluric models (43% and 43%), but greater than that which occurs in N (29%) and idiopathic CaOx SF (34%) (Table 2 and Fig. 3). Conversely, the percentages of [Ox²⁻] in the two hyperoxaluric models also have similar values (34% and 35%), and they are approximately equal to those that occur in the other two models (33% and 38%) (Table 2 and Fig. 4). This suggests that the driving force toward achieving chemical equilibrium in hyperoxaluric patients is urinary calcium, possibly because it is the limiting reactant in these patients, unlike that in idiopathic CaOx stone formers in whom urinary oxalate generally plays this role. It therefore follows hypothetically that it may be advantageous to reduce urinary Ca when treating severely hyperoxaluric patients, though this may be difficult to achieve. Thiazide diuretics may not be an ideal option, as they could exacerbate electrolyte problems such as hypokalemia associated with diarrhea in these patients. Judicious salt restriction may be a better alternative.

The finding described earlier that the percentage of [Ca²⁺] in the two hyperoxaluric models (43% and 43%) is greater than that which occurs in N (29%) and idiopathic CaOx SF (34%) might appear to be counterintuitive, as the total calcium excretions in the former models are lower than those in the latter. However, the percentage distribution of calcium (and all other) species depends on numerous factors, including those of pH and ionic strength. As such, a direct relationship between the excretion of total Ca and the percentage of ionized Ca²⁺ is not necessarily expected.

Regarding the suggestion that a Ca:Ox molar ratio approaching unity might be indicative of a relatively higher risk of crystallization (and hence stone formation),^7,8 our values (Table 2) show that the ratios in the enteric hyperoxaluric models (3.43 and 0.51) are much lower than those in the N and SF models (14.72 and 17.10 respectively) and that a similar trend is apparent in the ratio of the ionized species. Since stone formation in patients with enteric hyperoxaluria tends to be more severe than in idiopathic CaOx stone formers,²⁶ the notion of the ratio being an indicator of stone risk is consistent with our results. Our SS(COM) values also reveal a higher risk in the baseline hyperoxaluric model than in N and SF (5.87 vs. 3.44 and 4.28, respectively). However, the value for our extreme model (3.80) lies between that for N and SF and is, therefore, in disagreement with this notion. While the SS(COM) prediction for our extreme model is probably closer to reality than that obtained from the molar ratios, the broad agreement between the ratio and SS approaches is interesting because the former is based on kinetic data⁸ while SS is a thermodynamic property. This agreement on the prediction of stone risk based on kinetic and thermodynamic principles is encouraging

Our modeling of reductions in oxalate excretion with simultaneous increases in Ca excretion shows that decreases in SS(COM) achieved by the former effect can, indeed, be offset by the latter effect (Table 3). This is particularly apparent when the initial Ca excretion level is low, irrespective of the magnitude of ΔOx. For example, consider a patient whose initial Ca excretion is 1 mmol/24 hours and in whom a decrease in oxalate excretion of 300 μmol/day is achieved. Such a patient will benefit by a substantial decrease in SS(COM) from 3.40 to 2.56 if the initial oxalate excretion is 1200 μmol/day and from 2.56 to 1.71 if the initial oxalate excretion is 900 μmol/day, but these effects will be nullified if the Ca excretion undergoes a modest increase from its initial level of 1 mmol/day to a critical level of 1.34 or 1.51 mmol/24 hours, respectively (Table 3). On the other hand, a patient who has an initial Ca excretion of 3 mmol/day and whose Ox excretion also decreases by 300 μmol/day will be more tolerant of increases in Ca excretion as the latter would have to undergo a substantial increase from an initial level of 3.0 mmol/day to a critical level of 4.10 when the initial oxalate excretion is 1200 μmol/day and to a critical level of 4.66 when the initial oxalate excretion is 900 μmol/day, to offset the benefit of the decrease in SS(COM). Alternatively, it can be argued that these calculations demonstrate that it is the fractional increase in calcium excretion that matters, rather than the absolute increase. When viewed in this way, it becomes apparent that the magnitudes of the critical increases in calcium are about the same, regardless of the baseline urine calcium.

Our formula for calculating the critical Ca excretion yields values that correlate well with those predicted by JESS, particularly when the initial Ca excretion is relatively low (Table 3), but it tends to marginally underestimate the JESS predictions as concentrations of the latter increase toward higher levels. Notwithstanding these small deviations, our simple formula should be useful for alerting clinicians to the approaching Ca threshold level.

Our results, therefore, suggest that clinicians should be wary of administering Ca supplementation in severely hyperoxaluric patients who have low initial Ca excretion levels (≤2 mmol/day), as a relatively small absolute increase in Ca excretion will nullify the effect of decreases in oxaluria. Alternative treatments may be required in these cases. At relatively higher initial Ca excretion levels, calcium supplementation can be administered, but our formula should be applied to routinely check whether the critical Ca level is approaching. Regular monitoring of Ca and Ox excretions is therefore advised. Clinicians can refer directly to Table 3 if their patients' urinary Ca and Ox values fall within the listed ranges, or can perform the calculation themselves for values lying outside of these ranges. An attractive feature of applying our formula is that it does not require ongoing calculation of SS values throughout the treatment period. The latter would itself require the measurement of several urinary components, which is costly, and application of speciation software, which may not be readily available to practising clinicians.

Regarding the possibility of administering citrate in the treatment of these patients, our results show that as citrate increases at any given pH and at any given initial calcium excretion, SS(COM) decreases (Table 4 and Fig. 5). Similarly, as pH increases at any given initial citrate excretion and at any given Ca excretion, SS(COM) decreases (Table 4 and Fig. 5). These results are not surprising and are predictable on the basis of simple physiochemical principles. However, the magnitudes of the effects are of interest in the context of comparisons with other protocols such as those in which decreases in urinary oxalate are strategically targeted. We note that irrespective of the initial Ca excretion level, decreases in SS(COM) per mmol of citrate are relatively modest (<U) when the latter is increased within a range of values that could be feasibly achieved in a clinical setting (0.10–2.50 mmol/24 hours). On the other hand, more impressive decreases in SS(COM) are achieved when pH is increased across the empirically determined range for this variable in these patients (pH 5.10–6.00). This supports our previously reported conclusion that decreases in SS(COM) after citrate administration are due to increases in pH rather than to increases in citrate excretion.¹⁵

Our modeling has also enabled us to compare the individual effects of urinary citrate, oxalate, and pH on SS(COM) (Table 5). These results again demonstrate that relatively modest decreases in SS(COM) are achieved per mmol of citrate when it is increased within its empirically determined range, and that larger decreases are achieved when pH is raised to levels that have been empirically recorded in these patients. However, Table 5 also shows that the largest decreases in SS(COM) (per mmol) are achieved when urinary oxalate is decreased across its empirically determined excretion range at any given level of pH or citrate excretion. Thus, protocols that attempt to reduce urinary oxalate appear to be more efficacious than those which attempt to increase urinary citrate or pH.

Since in vivo increases in urinary citrate and pH are inextricably linked, we recognize that it is important to model their combined effect and to factor it into the current modeling exercise in which we are assessing different treatment protocols. The results (Table 5 and Fig. 6) enable us to do this. We note that a patient suffering with the worst case scenario (corresponding to highest oxalate and lowest citrate) at pH=5.10, who is treated with citrate, is predicted to reduce his SS(COM) from 13.06 to 8.95 if his urinary citrate excretion is raised from 0.10 to 2.50 mmol/24 hours and his pH is raised from 5.10 to 6.00, but that approximately the same outcome is achieved (i.e., a decrease in SS(COM) from 13.06 to 9.04) if his urinary oxalate excretion is decreased from 1600 to 1100 μmol/24 hours without any increases in urinary pH and citrate being required. On the other hand, if the patient achieves all of the treatment goals mentioned earlier simultaneously (increase in citrate excretion to 2.50 mmols/24 hours, increase in pH to 6.00, and reduction in oxalate excretion to 1100 μmol/24 hours), SS(COM) will decrease from 13.06 to 6.18. While fundamental principles in physical chemistry could have predicted this outcome qualitatively, the magnitude of the additional decrease in SS(COM) (from 9.04 to 6.18) achieved by increasing citrate excretion and pH makes a compelling argument for administering citrate in combination with dietary interventions to reduce oxalate excretion, not only in patients with hypocitraturia, but also in all patients with severe enteric hyperoxaluria, regardless of their baseline urinary citrate excretion.

In evaluating various treatments, we have considered only decreases in SS as a goal of therapy. However, other protective mechanisms may also be relevant. For example, raising urinary citrate may have benefits beyond complexing urinary Ca, as it can also act a priori as an inhibitor of heterogeneous nucleation or as an inhibitor of crystallization processes such as growth and aggregation. It is important to make the point that urinary saturation and crystallisation inhibition are fundamentally different physicochemical processes; the first is based on thermodynamic principles, while the second is driven by kinetic factors. As with other speciation programs, JESS does not take into account kinetic phenomena; hence, in the present study, we modeled only saturation, but the potential role of kinetic factors needs to be acknowledged. We also acknowledge that focusing on SS may divert attention from other pathologies besides stone formation which may be occurring in these patients. For example, low urine Ca may be an indicator of poor mineral absorption and, as such, it may be an additional reason to provide Ca supplements beyond that of lowering urine oxalate, while severe hyperoxaluria may be toxic to the kidney, independent of stone formation.

It is important to recognize that we have presented here several models of the risk of CaOx crystallization under various physiological and pathological conditions. By definition, a model is a simplified approximation of a natural phenomenon that should stimulate scientific debate.²⁷ Our results must be viewed in this light. In this article, our models of different levels of hyperoxaluria have demonstrated how changes occur in SS(COM) when specific urinary conditions, clinically associated with these pathologies, are changed. Whether these are clinically significant and whether our proposed treatment strategies are clinically feasible or not highlights the purpose of performing modeling calculations in the first place, namely to conjure questions that are of interest and which may invite the challenge of empirical investigation.

Conclusions

Treating patients with severe enteric hyperoxaluria and CaOx nephrolithiasis is challenging. Existing treatment options have associated concerns and limitations. We undertook to use computer modeling to assess the relative efficacies of these by investigating their respective effects on the SS of CaOx.

Results confirmed that treatment with oral calcium supplements is potentially helpful but that careful monitoring of urinary calcium excretion is necessary to avoid exceeding a safe threshold. A simple formula is provided for checking whether this threshold has been reached. Treatment with citrate also reduces SS(CaOx), but not to the same extent as lowering oxalate excretion. The best outcome is achieved by combining dietary restriction of oxalate with citrate therapy and judicious use of oral calcium supplements.

These results provide clinicians with guidelines for optimizing and monitoring the treatment of patients with enteric hyperoxaluria, CaOx nephrolithiasis, and extreme urine chemistries.

Footnotes

Acknowledgments

The authors thank Dr. Elaine Worcester (University of Chicago) and Dr. Andrew Evan (Indiana University School of Medicine) for providing urinary chloride and phosphate data.

This work was financially supported by the South African National Research Foundation, the South African Medical Research Council, and the University of Cape Town.

Disclosure Statement

The authors declare that there are no conflicts of interest.

Abbreviations Used

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