Is cancer a pure growth curve or does it follow a kinetics of dynamical structural transformation?

BACKGROUND: Unperturbed tumor growth kinetics is one of the more studied cancer topics; however, it is poorly understood. Mathematical modeling is a useful tool to elucidate new mechanisms involved in tumor growth kinetics, which can be relevant to understand cancer genesis and select the most suitable treatment. METHODS: The classical Kolmogorov-Johnson-Mehl-Avrami as well as the modified Kolmogorov-Johnson-Mehl-Avrami models to describe unperturbed fibrosarcoma Sa-37 tumor growth are used and compared with the Gompertz modified and Logistic models. Viable tumor cells (1×105) are inoculated to 28 BALB/c male mice. RESULTS: Modified Gompertz, Logistic, Kolmogorov-Johnson-Mehl-Avrami classical and modified Kolmogorov-Johnson-Mehl-Avrami models fit well to the experimental data and agree with one another. A jump in the time behaviors of the instantaneous slopes of classical and modified Kolmogorov-Johnson-Mehl-Avrami models and high values of these instantaneous slopes at very early stages of tumor growth kinetics are observed. CONCLUSIONS: The modified Kolmogorov-Johnson-Mehl-Avrami equation can be used to describe unperturbed fibrosarcoma Sa-37 tumor growth. It reveals that diffusion-controlled nucleation/growth and impingement mechanisms are involved in tumor growth kinetics. On the other hand, tumor development kinetics reveals dynamical structural transformations rather than a pure growth curve. Tumor fractal property prevails during entire TGK.

DNA overstretching transition induced by melting in a dynamical mesoscopic model.

We present a phenomenological dynamical model describing the force induced melting as responsible for the DNA overstretching transition. The denaturation mechanism is developed under the framework of the mesoscopic one-dimensional Peyrard-Bishop-Dauxois (PBD) picture which models the melting features of a polymer chain by means of a Morse potential and the stacking interaction. We find a good agreement with both the experimental overstretching curve and the asymmetric hysteretic properties with different simulation times. The comparison of the standard PBD model with a modification of the Morse potential which takes into account the interaction with the solvent has been also successfully investigated.

3D Stationary electric current density in a spherical tumor treated with low direct current: an analytical solution.

Electrotherapy with direct current delivered through implanted electrodes is used for local control of solid tumors in both preclinical and clinical studies. The aim of this research is to develop a solution method for obtaining a three-dimensional analytical expression for potential and electric current density as functions of direct electric current intensity, differences in conductivities between the tumor and the surrounding healthy tissue, and length, number and polarity of electrodes. The influence of these parameters on electric current density in both media is analyzed. The results show that the electric current density in the tumor is higher than that in the surrounding healthy tissue for any value of these parameters. The conclusion is that the solution method presented in this study is of practical interest because it provides, in a few minutes, a convenient way to visualize in 3D the electric current densities generated by a radial electrode array by means of the adequate selection of direct current intensity, length, number, and polarity of electrodes, and the difference in conductivity between the solid tumor and its surrounding healthy tissue.

Tissue Damage, Temperature, and pH Induced by Different Electrode Arrays on Potato Pieces (Solanum tuberosum L.).

One of the most challenging problems of electrochemical therapy is the design and selection of suitable electrode array for cancer. The aim is to determine how two-dimensional spatial patterns of tissue damage, temperature, and pH induced in pieces of potato (Solanum tuberosum L., var. Mondial) depend on electrode array with circular, elliptical, parabolic, and hyperbolic shape. The results show the similarity between the shapes of spatial patterns of tissue damage and electric field intensity, which, like temperature and pH take the same shape of electrode array. The adequate selection of suitable electrodes array requires an integrated analysis that involves, in a unified way, relevant information about the electrochemical process, which is essential to perform more efficiently way the therapeutic planning and the personalized therapy for patients with a cancerous tumor.