DEVELOPMENT OF A DOSAGE METHOD FOR ELECTROCHEMICAL TREATMENT OF TUMOURS : A SIMPLIFIED MATHEMATICAL MODEL

Abstract If the principal destruction mechanism behind electrochemical treatment (ECT) of tumours is related to the destructive reaction products formed in the electrochemical processes at the electrodes, a mathematical model of these processes should be a powerful tool in developing a reliable dosage method. In this present study, a simplified mathematical model of the electrochemical processes, occurring during ECT, is presented. The model is based on electrode kinetics and transport equations of ionic species in dilute solutions. The analysis focuses on tissue surrounding a spherical platinum anode, which is treated as an aqueous solution of sodium chloride containing a bicarbonate buffer system. The considered electrochemical reactions are chlorine and oxygen evolution, while the considered homogeneous chemical reactions are the water protolysis and buffer reactions. The validity of the model is investigated by comparing simulated pH profiles with pH profiles and lesion sizes, reported from in vivo experiments. This paper indicates that by putting a proper set of input parameters into quite a simple mathematical model, it is possible to predict the size of a lesion produced through ECT. The model gives a very good qualitative and a fairly good quantitative description of the pH profile, obtained in tissue surrounding the anode after ECT treatment.