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Introducción: La ferroptosis es un proceso no apoptótico de muerte celular regulada que depende de la presencia de iones hierro en el medio intracelular. Se caracterizada por la acumulación de especies reactivas de lípidos oxidados y radicales libres en las membranas celulares. Los inductores e inhibidores de este proceso inciden de manera circunstancial en él, con cuya respuesta celular se trabaja en función de elaborar modelos para el tratamiento del cáncer. Objetivo: Profundizar en el proceso de ferroptosis con un enfoque hacia los inductores e inhibidores, el establecimiento de modelos biofisicoquímicos y las estrategias terapéuticas para el tratamiento del cáncer. Métodos: Se realizó una revisión de los estudios más significativos sobre el tema, publicados en la Web of Science, PubMed, EBSCO, y Scopus. Resultados: Gracias al novedoso descubrimiento de la ferroptosis como impulsor de la muerte de células tumorales para tratar el cáncer, se han comenzado a desarrollar modelos teóricos que simulan el comportamiento de estas células y la complejidad en sistemas biológicos; que permiten encontrar procedimientos alternativos y menos invasivos contra esta y otras enfermedades. Conclusiones: Los inductores e inhibidores tienen una función primordial a la hora de predecir la influencia en la sensibilidad a la ferroptosis; por lo que se indagó en los mecanismos de funcionamiento de estos, que facilitará la forma de inducir en mayor o menor grado la muerte celular y disminuir la población de células cancerígenas(AU)

Introduction: Ferroptosis is a non-apoptotic process of regulated cell death that depends on the presence of iron ions in the intracellular medium. It is characterized by the accumulation of reactive species of oxidized lipids and free radicals in cell membranes. The inducers and inhibitors of this process circumstantially affect it, whose cellular response is used to develop models for cancer treatment. Objective: To deepen the ferroptosis process focusing on inducers and inhibitors, the establishment of biophysiochemical models and therapeutic strategies for cancer treatment. Methods: A review was carried out of the most significant studies on the subject, published in the Web of Science, PubMed, EBSCO and Scopus. Results: Thanks to the novel discovery of ferroptosis as a conductor of tumor cell death to treat cancer, theoretical models have begun to be developed that simulate the behavior of these cells and the complexity in biological systems; that allow finding alternative and less invasive procedures against this and other diseases. Conclusions: Inductors and inhibitors have a primary role in predicting the influence on sensitivity to ferroptosis; therefore, the mechanisms of operation of these were investigated, which will facilitate the way to induce cell death to a greater or lesser degree and reduce the population of cancer cells(AU)

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Introducción: La metástasis del cáncer es la transferencia de células tumorales de un órgano a otro mediante una serie de multipasos secuenciales interrelacionados. Este proceso es uno de los principales retos en el tratamiento del cáncer debido a su heterogeneidad biológica. El proceso de metástasis es considerado la principal causa de muerte en esta enfermedad, reportándose que más de 90 por ciento de las muertes por cáncer son debidos a esta etapa. Objetivo: Actualizar los conocimientos sobre metástasis en tumores sólidos y su asociación con transición epitelial-mesenquimal (EMT) en relación a la evolución y emergencia del cáncer. Método: Se realizó una revisión, no sistemática, de los estudios más significativos sobre el tema, publicados en la Web of Science, Pubmed, Ebsco, Scopus e Infomed. Conclusiones: La metástasis es la principal causa de muerte del cáncer, por lo que entender las bases del mecanismo de la formación de tumores metastásicos permitirá realizar terapias más eficaces para tratar el cáncer(AU)

Introduction: Cancer metastasis is the transfer of tumor cells from one organ to another through a series of interrelated sequential multi-steps. This process is one of the main challenges in cancer treatment due to the biological heterogeneity. The metastasis process is considered the main cause of death in this disease, accounting for more than 90 percent of cancer deaths. Objective: To identify the most recent advances on solid tumor metastasis and the association with epithelial-mesenchymal transition (EMT) in relation to the evolution and emergence of cancer. Method: A non-systematic review was carried out of the most significant studies on the subject, published in Web of Science, Pubmed, Ebsco, Scopus and Infomed. Conclusions: Metastasis is the main cause of cancer death, so understanding the bases of the mechanism for metastatic tumor formation will allow for more effective therapies(AU)

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The thermodynamical formalism of irreversible processes offers a theoretical framework appropriate to explain the complexity observed at the macroscopic level of dynamic systems. In this context, together with the theory of complex systems and systems biology, the thermodynamical formalism establishes an appropriate conceptual framework to address the study of biological systems, in particular cancer.The Chapter is organized as follows: In Subheading 1, an integrative view of these disciplines is offered, for the characterization of the emergence and evolution of cancer, seen as a self-organized dynamic system far from the thermodynamic equilibrium. Development of a thermodynamic framework, based on the entropy production rate, is presented in Subheading 2. Subheading 3 is dedicated to all tumor growth, as seen through a "phase transitions" far from equilibrium. Subheading 4 is devoted to complexity of cancer glycolysis. Finally, some concluding remarks are presented in Subheading 5.

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The regular nutritional intake of an expectant mother clearly affects the weight development of the fetus. Assuming the growth of the fetus follows a deterministic growth law, like a logistic equation, albeit dependent on the nutritional intake, the ideal solution is usually determined by the birth-weight being pre-assigned, for example, as a percentage of the mother's average weight. This problem can then be specified as an optimal control problem with the daily intake as the control, which appears in a Michaelis-Menten relationship, for which there are well-developed procedures to follow. The best solution is determined by requiring minimum total intake under which the preassigned birth weight is reached. The algorithm has been generalized to the case where the fetal weight depends in a detailed way on the cumulative intake, suitably discounted according to the history. The optimality system is derived and then solved numerically using an iterative method for the specific values of parameter. The procedure is generic and can be adapted to any growth law and any parameterisation obtained by the detailed physiology.

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In this work, a hyperchaotic system was used as a model for chronotherapy. We applied a periodic perturbation to a variable, varying the period and amplitude of forcing. The system, five-dimensional, has until three positive Lyapunov exponents. As a result, we get small periodical windows, but it was possible to get large areas of hyperchaos of two positive Lyapunov exponents from a chaotic behavior. In this chronotherapy model, chaos could be considered as a dynamical disease, and therapy goal must be to restore the hyperchaotic state.

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The mathematical modeling of tumor growth is an approach to explain the complex nature of these systems. A model that describes tumor growth was obtained by using a mesoscopic formalism and fractal dimension. This model theoretically predicts the relation between the morphology of the cell pattern and the mitosis/apoptosis quotient that helps to predict tumor growth from tumoral cells fractal dimension. The relation between the tumor macroscopic morphology and the cell pattern morphology is also determined. This could explain why the interface fractal dimension decreases with the increase of the cell pattern fractal dimension and consequently with the increase of the mitosis/apoptosis relation. Indexes to characterize tumoral cell proliferation and invasion capacities are proposed and used to predict the growth of different types of tumors. These indexes also show that the proliferation capacity is directly proportional to the invasion capacity. The proposed model assumes: i) only interface cells proliferate and invade the host, and ii) the fractal dimension of tumoral cell patterns, can reproduce the Gompertzian growth law.

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In this work, we propose a mesoscopic model for tumor growth to improve our understanding of the origin of the heterogeneity of tumor cells. In this sense, this stochastic formalism allows us to not only to reproduce but also explain the experimental results presented by Brú. A significant aspect found by the model is related to the predicted values for beta growth exponent, which capture a basic characteristic of the critical surface growth dynamics. According to the model, the value for growth exponent is between 0,25 and 0,5, which includes the value proposed by Kadar-Parisi-Zhang universality class (0,33) and the value proposed by Brú (0,375) related to the molecular beam epitaxy (MBE) universality class. This result suggests that the tumor dynamics are too complex to be associated to a particular universality class.

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