Abstract
BackgroundElectrotherapy effectiveness at different doses has been demonstrated in preclinical and clinical studies; however, several aspects that occur in the tumor growth kinetics before and after treatment have not yet been revealed. Mathematical modeling is a useful instrument that can reveal some of these aspects. The aim of this paper is to describe the complete growth kinetics of unperturbed and perturbed tumors through use of the modified Gompertz equation in order to generate useful insight into the mechanisms that underpin this devastating disease.MethodsThe complete tumor growth kinetics for control and treated groups are obtained by interpolation and extrapolation methods with different time steps, using experimental data of fibrosarcoma Sa-37. In the modified Gompertz equation, a delay time is introduced to describe the tumor's natural history before treatment. Different graphical strategies are used in order to reveal new information in the complete kinetics of this tumor type.ResultsThe first stage of complete tumor growth kinetics is highly non linear. The model, at this stage, shows different aspects that agree with those reported theoretically and experimentally. Tumor reversibility and the proportionality between regions before and after electrotherapy are demonstrated. In tumors that reach partial remission, two antagonistic post-treatment processes are induced, whereas in complete remission, two unknown antitumor mechanisms are induced.ConclusionThe modified Gompertz equation is likely to lead to insights within cancer research. Such insights hold promise for increasing our understanding of tumors as self-organizing systems and, the possible existence of phase transitions in tumor growth kinetics, which, in turn, may have significant impacts both on cancer research and on clinical practice.
Highlights
Electrotherapy effectiveness at different doses has been demonstrated in preclinical and clinical studies; several aspects that occur in the tumor growth kinetics before and after treatment have not yet been revealed
tumor growth kinetics (TGK) The complete growth kinetics of unperturbed fibrosarcoma Sa-37 tumors are generated by interpolation of the experimental data for REG-II and the extrapolation process for REG-I using Equation 5 with values for a, b, τ, and Vo from the control group (CG) (Table 1)
TGK exhibits a characteristic S shape with three stages (SI, SII, and SIII), which are well defined for all Δt values, as shown in Figure 1 for Δt = 1/3 days
Summary
Electrotherapy effectiveness at different doses has been demonstrated in preclinical and clinical studies; several aspects that occur in the tumor growth kinetics before and after treatment have not yet been revealed. Significant research has been done in the modeling of tumors using theoretical models and computer simulations in order to describe and predict various aspects of tumor growth kinetics (TGK). Predicting tumor growth is important in the planning and evaluation of screening programs, clinical trials, and epidemiological studies, as well as in the adequate selection of dose-response relationships regarding the proliferative potential of tumors [2,3,4,5]. The biological behavior of a malignant tumor is highly influenced by its growth rate, which is determined by many intratumoral and micro-environmental factors. The space-time permanent growth is probably the most characteristic feature of a malignant tumor
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