Prediction of renal crystalline size distributions in space using a PBE analytic model. 2. Effect of dietary countermeasures.

An analytic Population Balance Equation model is used to assess the efficacy of citrate, pyrophosphate, and augmented fluid intake as dietary countermeasures aimed at reducing the risk of renal stone formation for astronauts. The model uses the measured biochemical profile of the astronauts as input and predicts the steady-state size distribution of the nucleating, growing, and agglomerating renal calculi subject to biochemical changes brought about by administration of these dietary countermeasures. Numerical predictions indicate that an increase in citrate levels beyond its average normal ground-based urinary values is beneficial but only to a limited extent. Unfortunately, results also indicate that any decline in the citrate levels during space travel below its normal urinary values on Earth can easily move the astronaut into the stone-forming risk category. Pyrophosphate is found to be an effective inhibitor since numerical predictions indicate that even at quite small urinary concentrations, it has the potential of shifting the maximum crystal aggregate size to a much smaller and plausibly safer range. Finally, our numerical results predict a decline in urinary volume below 1.5 liters/day can act as a dangerous promoter of renal stone development in microgravity while urinary volume levels of 2.5-3 liters/day can serve as effective space countermeasures.