A Compartmental Model Predicts That Dietary Potassium Affects Lithium Dynamics in Rats

Abstract

Lithium is the treatment of choice for manic depression, but therapy often results in nephrogenic diabetes insipidus and lithium intoxication. To investigate the effects of dietary potassium on potential side effects of lithium therapy, a mathematical model was built using the modeling program SAAM (Simulation, Analysis, And Modeling). Experimental data modeled were from adult male Sprague-Dawley rats fed diets with or without lithium and one of three levels of potassium for 17 d. A five-compartment model of lithium dynamics was built that was consistent with data from rats fed a lithium-containing diet adequate in potassium. This model was then compared with data from rats fed the other two lithium-containing diets. The model predicts that both the fractional transfer coefficient and rate of transport of lithium to the serum compartment from the kidney compartment are lower in rats fed the potassium-adequate diet than in those fed the potassium-deficient diet, and even lower in those fed the potassium-supplemented diet. In addition, fractional transfer coefficients into the serum compartment from the sampled and simulated tissue compartments changed differently with time depending on the amount of dietary potassium. The model also predicts that there would be less accumulation of lithium in the kidney, sampled tissue and simulated tissue compartments with supplemental dietary potassium. The model suggests that potassium supplementation, after a 7-d delay, protects against nephrogenic diabetes insipidus and the potentially toxic accumulation of lithium by decreasing the reabsorption of lithium from the kidneys and increasing lithium efflux from the tissues.