Mathematical model application to the kinetic study of tumor markers

In order to overcome the inefficient cutoff criterion in the management of neoplastic patients after therapy, in follow-up, in recurrence and in monitoring treatment, we have analysed some mathematical models to evaluate serial determinations of tumor markers, with the aim to ascertain the radicality of surgery or the presence of recurrences. Since a tracer study of the biological system of tumor markers is impossible, some information, such as rate factor and half-life, is obtained by determination of the marker after radical treatment. In steady state with two or more samples in time it is possible with adequate statistical models to establish a significant increase in the marker. In recurrence, if it is true that the secretion rate of the marker by a tumor is proportional to tumor mass, then increasing concentrations of the tumor marker would be a phenotypic expression of tumor growth. Therefore some mathematical models are proposed to evaluate the kinetics of tumor growth.