Development of a bivariate mathematical model to characterize simultaneously the dose-time-responses of pro-oxidant agents

The available data about the interference of oxidation compounds in the oxidation kinetics of process such as lipid oxidation chain reactions, the resistance of pharmaceutical drugs, the effects of free radical agents in cell tissue, the damage caused in DNA, etc, are examples of the many applications for in vivo and in vitro assays. However, often in these bio-assays, only semi-quantitative conclusions can be obtained, due to the use of quantification procedures disregarding kinetic considerations. A pseudo-mechanistic model is proposed which is based on the accumulative Weibull's function, and represents a formal transfer from the field of the dose-response relationships. It allows researchers to obtain the simultaneous solution of a series of oxidation activities as a function of concentration and time. It describes
satisfactorily simulations in which reaction compounds interact through a second order kinetic scheme. Its application is simple: it provides parametric estimates, which characterize the oxidative process; facilitates rigorous comparisons between the effects of distinct compounds in different systems; reduces the sensitivity to the experimental error; and its mathematical form constitutes a useful orientation to prepare more economic and efficient trial designs. The model was assayed, firstly, using the kinetic simulation of the oxidative process, and finally, it was applied to a variety of experimental data from other authors in different systems and conditions, obtaining highly satisfactory results in all cases. In all experimental data tested, the calculated parameters were always statistically significant (Student’s t-test, α = 0.05), the equations were consistent (Fisher’s F-test) and the goodness of fit (adj R2, adjusted coefficient of multiple determination) were up to 0.98.