Artificial intelligence applied to model the sulphur absorption process - a possible application in cure with sulphurous mineral water

Abstract

The presence of Sulphur in human body is estimated to be around .25 percent from total body weight. The modern therapy includes among others the usage of Sulphur us spring waters as crenotherapy or external use like - therapeutic and preventive treatment for a large category of diseases. High levels of hydrogen sulphide are extremely toxic and as result the model of absorption of Sulphur could be useful as predictor in a daily treatment during a cure with sulphurous mineral water. This quantity of chemical elements from a specific diet rich in these elements absorbed in human organism is one of the most important characteristics of a benefic cure in medical diseases. The most studied mechanisms of absorption were studied for Zinc, Magnesium, Iron and Calcium. The most common way to develop a mathematical model is to use the pharmacokinetic equations based on Michaelis-Menten approach (first order model) and to develop it thereafter for quantitative relations. In some cases, only experimental data can exists and the pharmacokinetic model is not completely elucidated or a simplified model doesn’t exist yet. A model based on genetic programming is proposed in order to discover a mathematical relationship between dietary sulphate (mmol/day) and total sulphate in ileostomy fluid (mmol/day) using experimental data published in literature. The set of terminals that are used in genetic programing – GP (using Polish notation) is reduced to basic operation (sum, difference, multiplication and division) along with the most plausible operations that could have physical meaning: rooted square, exponential and power. The formulas discovered by GP using experimental proved a good fit of data with discovered mathematical formula, e.g. the rooted mean square error below 1.5% and R2  94.36%. Mathematical formulas discovered by genetic programming can be used as an alternative to pharmacokinetic model in order to predict sulphate and sulphite absorption and excretion. The usage of this method is especially efficient when the mechanism of absorption in not elucidated enough to provide a compartmental model given by a set of equations. A correlation with pharmacokinetic equations in the case that these exist will help the improvement of terminals and alphabet used by genetic programming in order to have a model closer to one that have a physical meaning