Mathematical modeling of formation of nanocrystalline calcium oxalate under physiological conditions

Abstract

For the first time, a physicochemical model of the formation of poorly soluble compounds in the kidney nephron was developed on the basis of a mathematical description of the ideal displacement reactor. As a result of mathematical modeling, it was found that under normal physiological conditions, the formation of a solid phase is not the dominant process, which explains the absence of crystalline formations in the kidneys in healthy people. An increase in the concentration of precipitate-forming ions, corresponding to certain conditions of the human body, leads to the occurrence of local high supersaturations in certain areas of the nephron, which can lead to the formation of solid phase nuclei, their fixation and further growth. It is shown that the calculations of material balances, flow movements, as well as the concentration profiles of components in the nephron determine the possibility of predicting the behavior of the model system with variations in the parameters and conditions that affect the course of the crystallization process (concentration, fluid flow, hydrodynamic regime, etc.), which will allow developing effective methods for the prevention and treatment of urolithiasis, including the dissolution of already formed aggregates.

Keywords

• crystallization
• calcium oxalates
• saline
• model
• plug flow reactor
• nephron
• material graph