Mathematical modeling of calcium phosphate precipitation in biologically relevant systems: scoping review

Biologically guided precipitation of calcium phosphates is important for the formation of calcified human tissues, such as bone and teeth, and is of practical significance in numerous industrial and agricultural processes, such as wastewater treatment and dairy ultrafiltration. Mineral precipitation is physicochemically complex and becomes even more complex in the presence of biological materials. The theoretical foundation of phase transition in general has been developed and is vital for many applications, such as metallurgy and weather prediction. The goal of this scoping review was to identify and evaluate established mathematical approaches developed to describe the formation of calcium precipitates in biological systems. A scoping review was conducted using MathSciNet, Scopus, and Web of Science databases to retrieve eligible mathematical modeling papers on calcium precipitates in biological systems. From the 2096 studies screened, 115 studies were included. The major biological systems of interest were tissues of the human body (49/115), water research (38/115), and agricultural and earth sciences applications (17/115). The majority of studies described precipitation of calcium phosphate (79/115), followed by calcium carbonate (22/115). Mathematical modeling of calcium precipitation was dominated by classical nucleation (64/115) and kinetic (38/115) theories. Only a minority of studies explicitly modeled chemical reactions in the aqueous phase (33/115). Biological components were explicitly described in 45/115 studies and included as physicochemical limitations in 70/115 studies. The majority of the studies (91/115) attempted to quantitatively compare the model predictions to the experimental data, with 59/115 reporting good to reasonable fit. This scoping review suggests that broad theories, such as classical nucleation and kinetic theories, may be adapted for modeling calcium precipitation in biologically relevant systems; however, detailed mathematical descriptions of biological, chemical, and physicochemical aspects of calcium precipitation are required.