In this work, we studied the individual and combined effect of inhibitors such as citrate ions and magnesium ions on crystallization of calcium oxalate. It is the main constituent of more than 70% of urinary stones. In order to optimize the number of experiments with the help of a suitable mathematical model, an experimental design was developed. The crystallization of CaC 2 O 4 with and without inhibitors, at physiological concentrations, was studied by turbidimetry at 37• C. The inhibition effect was evaluated through the induction time (nucleation) and the turbidimetrical slope (crystalline growth). The experimental design enabled the investigation of the effect of citrate ions, magnesium ions, and their combination on the inhibition rate. The obtained results showed that the inhibition power increases with inhibitor concentration when it is tested alone. This inhibition also affected the delay on nucleation. Thus, the induction time varied from 0.22 min without inhibitor to 4.73 min with citrate ions and 1.96 min with magnesium ions. The two inhibitors were more effective on nucleation and on crystalline growth when they were used in combination compared to one of them tested alone. The mathematical model fitted the experimental results well with a minimum of trials. 

Our objective is to study the interaction between calcium oxalate (CaOx) low molecular weight inhibitors such as aluminum and pyrophosphate and to analyze their effect on nucleation and crystal growth while combined two by two to citrate. At physiological concentrations, CaOx crystallization, with or without inhibitors, was studied by spectrophotometry at 620 nm. All experiments were undergone at 37 °C. A mathematical model was used in order to optimize the number of experiments. Results showed that the inhibition power increases with inhibitor concentration when the molecule is tested alone. We obtained an important inhibition reaching a maximum of 93.9% for a citrate concentration of 2.5 mM, an inhibition of 87.8% for an aluminum concentration of 0.528 mM and an inhibition of only 34% for a 0.2 mM concentration of pyrophosphate. Citrate and aluminum act on nucleation, crystal growth and aggregation, while pyrophosphate acts weakly on crystal growth. The induction time is more or less constant. Results show that at any combined citrate pyrophosphate concentration, the effects are higher than those obtained for the inhibitors taken alone. The induction time for the combined inhibitors is more important than for a single inhibitor, thus triggering delay in nucleation. The citrate-pyrophosphate combination gives a synergetic effect at any used concentrations, whereas the effect of citrate-aluminum combination depends of the used concentrations of the two inhibitors. The results allow to quantify the contribution of inhibitors in the overall inhibition. The mathematical models fitted the experimental results well with a minimum of trials