A combined transport-kinetics model for the growth of renal calculi

Abstract

Renal stone disease is not only a concern on the Earth but could conceivably pose a serious risk to the astronauts' health and safety in Space. In this study, a combined transport-kinetics model for the growth of calcium oxalate (CaOx) crystals is presented. The model is used to parametrically investigate the growth of renal calculi in urine with a focus on the coupled effects of transport and surface reaction on the ionic concentrations at the surface of the crystal and their impact on the resulting growth rates. It is shown that under nominal conditions of low solution supersaturation and low Damköhler number that typically exist on the Earth, the surface concentrations of calcium and oxalate approach their bulk solution values in the urine and the growth rate is most likely limited by the surface reaction kinetics. But for higher solution supersaturations and large Damköhler numbers that may be prevalent in the microgravity environment of Space, the calcium and oxalate surface concentrations tend to shift more towards their equilibrium or saturation values and thus the growth process may be limited by the transport through the medium. Furthermore, it is shown that as the crystal size increases a shift towards a transport-limited growth process is likely. In this situation beyond a critical radius that is a function of the physiochemical parameters of the renal environment, the growth rate will not be independent of the radius as in a reaction-limited situation but will decrease as the crystal size increases.