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Register a new userFerroptosis as a Biological Phase Transition I: avascular and vascular tumor growth
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Herewith we discuss a network model of the ferroptosis avascular and vascular tumor growth based on our previous proposed framework. Chiefly, ferroptosis should be viewed as a first order phase transition characterized by a supercritical Andronov Hopf bifurcation, with the emergence of limit cycle. The increase of the population of the oxidized PUFA fragments, take as the control parameter, involves an inverse Feigenbaum, (a cascade of saddle foci Shilnikovs bifurcations) scenario, which results in the stabilization of the dynamics and in a decrease of complexity.
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The comprehension of tumor growth is a intriguing subject for scientists. New researches has been constantly required to better understand the complexity of this phenomenon. In this paper, we pursue a physical description that account for some experimental facts involving avascular tumor growth. We have proposed an explanation of some phenomenological (macroscopic) aspects of tumor, as the spatial form and the way it growths, from a individual-level (microscopic) formulation. The model proposed here is based on a simple principle: competitive interaction between the cells dependent on their mutual distances. As a result, we reproduce many empirical evidences observed in real tumors, as exponential growth in their early stages followed by a power law growth. The model also reproduces the fractal space distribution of tumor cells and the universal behavior presented in animals and tumor growth, conform reported by West, Guiot {it et. al.}cite{West2001,Guiot2003}. The results suggest that the universal similarity between tumor and animal growth comes from the fact that both are described by the same growth equation - the Bertalanffy-Richards model - even they does not necessarily share the same biophysical properties.
Prediction and control of cancer invasion is a vital problem in medical science. This paper proposes a modern geometric Ricci-flow and entropy based model for control of avascular multicellular tumor spheroid growth and decay. As a tumor growth/decay control tool, a monoclonal antibody therapy is proposed. Keywords: avascular tumor growth and decay, multicellular tumor spheroid, Ricci flow and entropy, nonlinear heat equation, monoclonal antibody cancer therapy
A first principles approach to the theoretical description of the development of biological forms, from a fertilized egg to a functioning embryo, remains a central challenge to applied physics and theoretical biology. Rather than refer to principles of self-organization and non-equilibrium statistical mechanics to describe a developing embryo from its active cellular constituents, a purely geometric theory is constructed that references the properties of the ambient space that the embryo occupies. In 1975 the Fields laureate Ren{e} Thom developed a system of techniques and local dynamical models that are capable of reconstructing the local dynamic of an embryo at each new growth event of the system. Each new growth event (the development of a limb, for example) is a topological change in the dynamic of the system that can be classified only according to the properties of space. The local models can be non-conservative flows with robust attractor behavior that serve as organizing centers for systems development. Hamiltonian flows can also be considered with novel, self-reproducing vague attractor behavior. The set of growth events become an unfolding space related to the differentiable manifold of states. The set of growth events, which Thom refers to as the catastrophe set, has special algebraic properties which permit these models to be low dimensional--the local model contains few parameters. We present Thoms work as a research program outlining a framework for the construction of these local models, and, ultimately, the synthesis of these models into a full theoretical description of a developing biological organism. We give examples of the application of selected models to key growth events in the process of gastrulation.
Tumor growth has long been a target of investigation within the context of mathematical and computer modelling. The objective of this study is to propose and analyze a two-dimensional probabilistic cellular automata model to describe avascular solid tumor growth, taking into account both the competition between cancer cells and normal cells for nutrients and/or space and a time-dependent proliferation of cancer cells. Gompertzian growth, characteristic of some tumors, is described and some of the features of the time-spatial pattern of solid tumors, such as compact morphology with irregular borders, are captured. The parameter space is studied in order to analyze the occurrence of necrosis and the response to therapy. Our findings suggest that transitions exist between necrotic and non-necrotic phases (no-therapy cases), and between the states of cure and non-cure (therapy cases). To analyze cure, the control and order parameters are, respectively, the highest probability of cancer cell proliferation and the probability of the therapeutic effect on cancer cells. With respect to patterns, it is possible to observe the inner necrotic core and the effect of the therapy destroying the tumor from its outer borders inwards.
A connection is established between discrete stochastic model describing microscopic motion of fluctuating cells, and macroscopic equations describing dynamics of cellular density. Cells move towards chemical gradient (process called chemotaxis) with their shapes randomly fluctuating. Nonlinear diffusion equation is derived from microscopic dynamics in dimensions one and two using excluded volume approach. Nonlinear diffusion coefficient depends on cellular volume fraction and it is demonstrated to prevent collapse of cellular density. A very good agreement is shown between Monte Carlo simulations of the microscopic Cellular Potts Model and numerical solutions of the macroscopic equations for relatively large cellular volume fractions. Combination of microscopic and macroscopic models were used to simulate growth of structures similar to early vascular networks.
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