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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.

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In this study, the influence of defined extrusion-like treatment conditions on the denaturation behavior and kinetics of single- and multi-component protein model systems at a protein concentration of 70% (w/w) was investigated. α-Lactalbumin (αLA) and β-Lactoglobulin (βLG), and whey protein isolate (WPI) were selected as single- and multi-component protein model systems, respectively. To apply defined extrusion-like conditions, treatment temperatures in the range of 60 and 100 °C, shear rates from 0.06 to 50 s⁻1, and treatment times up to 90 s were chosen. While an aggregation onset temperature was determined at approximately 73 °C for WPI systems at a shear rate of 0.06 s⁻1, two significantly different onset temperatures were determined when the shear rate was increased to 25 and 50 s⁻1. These two different onset temperatures could be related to the main fractions present in whey protein (βLG and αLA), suggesting shear-induced phase separation. Application of additional mechanical treatment resulted in an increase in reaction rates for all the investigated systems. Denaturation was found to follow 2.262 and 1.865 order kinetics for αLA and WPI, respectively. The reaction order of WPI might have resulted from a combination of a lower reaction order in the unsheared system (i.e., fractional first order) and higher reaction order for sheared systems, probably due to phase separation, leading to isolated behavior of each fraction at the local level (i.e., fractional second order).

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