Simulations of surface charge density changes during the untreated solid tumour growth.

Understanding untreated tumour growth kinetics and its intrinsic behaviour is interesting and intriguing. The aim of this study is to propose an approximate analytical expression that allows us to simulate changes in surface charge density at the cancer-surrounding healthy tissue interface during the untreated solid tumour growth. For this, the Gompertz and Poisson equations are used.

Efficacy of direct current generated by multiple-electrode arrays on F3II mammary carcinoma: experiment and mathematical modeling.

Background: The modified Gompertz equation has been proposed to fit experimental data for direct current treated tumors when multiple-straight needle electrodes are individually inserted into the base perpendicular to the tumor long axis. The aim of this work is to evaluate the efficacy of direct current generated by multiple-electrode arrays on F3II mammary carcinoma that grow in the male and female BALB/c/Cenp mice, when multiple-straight needle electrodes and multiple-pairs of electrodes are inserted in the tumor.

Methods: A longitudinal and retrospective preclinical study was carried out.

New formulation of the Gompertz equation to describe the kinetics of untreated tumors.

Background: Different equations have been used to describe and understand the growth kinetics of undisturbed malignant solid tumors. The aim of this paper is to propose a new formulation of the Gompertz equation in terms of different parameters of a malignant tumor: the intrinsic growth rate, the deceleration factor, the apoptosis rate, the number of cells corresponding to the tumor latency time, and the fractal dimensions of the tumor and its contour.

Methods: Furthermore, different formulations of the Gompertz equation are used to fit experimental data of the Ehrlich and fibrosarcoma Sa-37 tumors that grow in male BALB/c/Cenp mice.

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

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.

Antitumor effects of electrochemical treatment.

Electrochemical treatment is an alternative modality for tumor treatment based on the application of a low intensity direct electric current to the tumor tissue through two or more platinum electrodes placed within the tumor zone or in the surrounding areas. This treatment is noted for its great effectiveness, minimal invasiveness and local effect. Several studies have been conducted worldwide to evaluate the antitumoral effect of this therapy.

Modified Gompertz equation for electrotherapy murine tumor growth kinetics: predictions and new hypotheses.

Background: Electrotherapy 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.