Suppression of calculi growth based on the mathematical model of the pathogenesis of urolithiasis

So far various studies for the cause of the onset of urolithiasis has been made and the factors influencing the pathogenesis has been almost clear. On the other hand, though the understanding of individual factor influencing the pathogenesis has progressed biologically and clinically, theoretical study of the integrated dynamics leading to the calculus of urolithiasis through the crystal growth and aggregation from the crystal nucleation using a mathematical model has not been made yet. Then I derived the mathematical model of the process leading to the onset of urolithiasis so as to clarify how a variety of factors affecting urolithiasis influence the pathogenesis quantitatively. In the mathematical model, the process leading to the onset of urolithiasis is divided into the following three processes. (1) formation of crystal nuclei. (2) formation of calculi by growth of crystal nuclei. (3) bonding of calculi to urinary tract cells and growth of calculi. In addition, the parameters of the volume of the urinary tract, the flow rate of urine etc. are introduced to represent the characteristics of the urinary tract. As a result, for instance, in case of calcium oxalate calculi, the conditions that the calculus does not grow were shown analytically and numerically. And the dependence of the growth of the calculus on the volume of the urinary tract or the flow rate of urine was also clarified analytically and numerically. Then, based on the analysis of this mathematical model, we propose specific solutions in clinical.