Simplified estimates of ion-activity products of calcium oxalate and calcium phosphate in mouse urine

Abstract

This study aimed at formulating simplified estimates of ion-activity products of calcium oxalate (AP_CaOx) and calcium phosphate (AP_CaP) in mouse urineto find the most important determinants in order to limit the analytical work-up. Literature data on mouse urine composition was used to determine the relative effect of each urine variable on the two ion-activity products. AP_CaOx and AP_CaP were calculated by iterative approximation with the EQUIL2 computerized program. The most important determinants for AP_CaOx were calcium, oxalate and citrate and for AP_CaP calcium, phosphate, citrate, magnesium and pH. Urine concentrations of the variables were used. A simplified estimate of AP_CaOx (AP(CaOx)-index_MOUSE) that numerically approximately corresponded to 10⁸ × AP_CaOx was given the following expression:

$$ {\text{AP(CaOx)-index}}_{\text{MOUSE}} = 0.70 \times {\text{Calcium}}^{1.05} \times {\text{Oxalate}}^{0.95} (0.90 - 0.0225 \times {\text{Citrate}}) + (6.6 \times 10^{ - 8} \times {\text{Citrate}}^{3.98} ) $$

For a series of urine samples with various composition the coefficient of correlation between AP(CaOx)-index_MOUSE and 10⁸ × AP_CaOx was 0.99 (p = 0.00000). A similar estimate of AP_CaP (AP(CaP)-index_MOUSE) was formulated so that it approximately would correspond numerically to 10¹⁴ × AP_CaP taking the following form:

$$ {\text{AP(CaP)-index}}_{\text{MOUSE}} = \frac{{0.05 \times {\text{Calcium}}^{1.17} \times {\text{Phosphate}}^{0.85} \times {\text{Magnesium}}^{0.18}\times ({\text{pH}} - 4.5)^{6.8} }}{{{\text{Citrate}}^{0.76} }} $$

For a series of variations in urine composition the coefficient of correlation was 0.95 (p = 0.00000). The two approximate estimates shown in this article are simplified expressions of AP_CaOx and AP_CaP. The intention of these theoretical calculations was not to get methods for accurate information on the saturation levels in urine, but to have mathematical tools useful for rough conclusions on the outcome of different experimental situations in mice. It needs to be emphasized that the accuracy will be negatively influenced if urine variables not included in the formulas differ very much from basic concentrations.