TOPOLOGICAL COMPLEXITY AND PREDICTABILITY IN THE DYNAMICS OF A TUMOR GROWTH MODEL WITH SHILNIKOV'S CHAOS

Dynamical systems modeling tumor growth have been investigated to determine the dynamics between tumor and healthy cells. Recent theoretical investigations indicate that these interactions may lead to different dynamical outcomes, in particular to homoclinic chaos. In the present study, we analyze both topological and dynamical properties of a recently characterized chaotic attractor governing the dynamics of tumor cells interacting with healthy tissue cells and effector cells of the immune system. By using the theory of symbolic dynamics, we first characterize the topological entropy and the parameter space ordering of kneading sequences from one-dimensional iterated maps identified in the dynamics, focusing on the effects of inactivation interactions between both effector and tumor cells. The previous analyses are complemented with the computation of the spectrum of Lyapunov exponents, the fractal dimension and the predictability of the chaotic attractors. Our results show that the inactivation rate of effector cells by the tumor cells has an important effect on the dynamics of the system. The increase of effector cells inactivation involves an inverse Feigenbaum (i.e. period-halving bifurcation) scenario, which results in the stabilization of the dynamics and in an increase of dynamics predictability. Our analyses also reveal that, at low inactivation rates of effector cells, tumor cells undergo strong, chaotic fluctuations, with the dynamics being highly unpredictable. Our findings are discussed in the context of tumor cells potential viability.

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Chaotic Behavior of One-Dimensional Cellular Automata Rule 24

Discrete Dynamics in Nature and Society ◽

10.1155/2014/304297 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Zujie Bie ◽

Qi Han ◽

Chao Liu ◽

Junjian Huang ◽

Lepeng Song ◽

...

Keyword(s):

Cellular Automata ◽

Characteristic Function ◽

Symbolic Dynamics ◽

Bernoulli Shift ◽

Chaotic Behavior ◽

Class Ii ◽

Chaotic Attractors ◽

One Dimensional ◽

Dynamical Behaviors ◽

Shift Map

Wolfram divided the 256 elementary cellular automata rules informally into four classes using dynamical concepts like periodicity, stability, and chaos. Rule 24, which is Bernoulliστ-shift rule and is member of Wolfram’s class II, is said to be simple as periodic before. Therefore, it is worthwhile studying dynamical behaviors of four rules, whether they possess chaotic attractors or not. In this paper, the complex dynamical behaviors of rule 24 of one-dimensional cellular automata are investigated from the viewpoint of symbolic dynamics. We find that rule 24 is chaotic in the sense of both Li-Yorke and Devaney on its attractor. Furthermore, we prove that four rules of global equivalenceε52of cellular automata are topologically conjugate. Then, we use diagrams to explain the attractor of rule 24, where characteristic function is used to describe the fact that all points fall into Bernoulli-shift map after two iterations under rule 24.

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CHAOTIC ATTRACTORS IN ONE-DIMENSION GENERATED BY A SINGULAR SHILNIKOV ORBIT

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127401004005 ◽

2001 ◽

Vol 11 (12) ◽

pp. 3059-3083 ◽

Cited By ~ 3

Author(s):

KRISTA J. TAYLOR ◽

BO DENG

Keyword(s):

Symbolic Dynamics ◽

Homoclinic Orbits ◽

One Dimension ◽

Chaotic Attractors ◽

Singularly Perturbed Systems ◽

One Dimensional ◽

Physical Systems ◽

Return Maps ◽

Singular Limits ◽

Natural Measures

Chaotic attractors containing Shilnikov's saddle-focus homoclinic orbits have been observed in many physical systems. Past and current researches of this type of Shilnikov homoclinic phenomena have focused on the orbit and nearby structures only. In this paper we will look at the role such orbits play in a type of attractor, which arises from one-dimensional return maps at the singular limits of some singularly perturbed systems. Results on symbolic dynamics, natural measures, and Lyapunov exponents are obtained for a sequence of a one-parameter caricature family of such attractors.

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Modeling of Tumor Growth Incorporating the Effects of Necrosis and the Effect of Bevacizumab

Complexity ◽

10.1155/2017/5985031 ◽

2017 ◽

Vol 2017 ◽

pp. 1-10 ◽

Cited By ~ 14

Author(s):

Dániel András Drexler ◽

Johanna Sápi ◽

Levente Kovács

Keyword(s):

Tumor Growth ◽

Tumor Cells ◽

Growth Models ◽

Colon Adenocarcinoma ◽

Extended Model ◽

Treatment Protocols ◽

Tumor Growth Model ◽

Physiological Processes ◽

Bevacizumab Treatment ◽

Tumor Growth Models

Tumor growth models are important to create an engineering background for cancer treatment either by using the models for simulations and evaluation of treatment protocols or, if combined with control engineering, by designing treatment protocols. A well-defined tumor growth model must describe the physiological processes and the measurements as well. Growing tumors are composed of dead tumor cells (forming the necrotic part) and living, proliferating tumor cells (forming the proliferating part); when tumor volume is measured, these parts are measured together. Most of the known tumor growth models do not consider the modeling of the necrotic part. Starting from a minimal model of the tumor growth under bevacizumab treatment, the aim of the current research is to extend it incorporating the volume and dynamics of the necrotic part and the pharmacodynamics and mixed-order pharmacokinetics of the applied drug. The extended model is validated using measurements with mice as hosts, colon adenocarcinoma as tumor, and bevacizumab as the drug used for treatment. The results show that the extended model can describe the important physiological phenomena and shows a good fit to the average of the measurements.

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Complex Dynamic Behaviors in Cellular Automata Rule 14

Discrete Dynamics in Nature and Society ◽

10.1155/2012/258309 ◽

2012 ◽

Vol 2012 ◽

pp. 1-12 ◽

Cited By ~ 2

Author(s):

Qi Han ◽

Xiaofeng Liao ◽

Chuandong Li

Keyword(s):

Cellular Automata ◽

Characteristic Function ◽

Fixed Points ◽

Symbolic Dynamics ◽

Bernoulli Shift ◽

Chaotic Attractors ◽

Complex Dynamic ◽

One Dimensional ◽

Dynamical Behaviors ◽

Shift Map

Wolfram divided the 256 elementary cellular automata rules informally into four classes using dynamical concepts like periodicity, stability, and chaos. Rule 14, which is Bernoulliστ-shift rule and is a member of Wolfram’s class II, is said to be simple as periodic before. Therefore, it is worthwhile studying dynamical behaviors of rule 14, whether it possesses chaotic attractors or not. In this paper, the complex dynamical behaviors of rule 14 of one-dimensional cellular automata are investigated from the viewpoint of symbolic dynamics. We find that rule 14 is chaotic in the sense of both Li-Yorke and Devaney on its attractor. Then, we prove that there exist fixed points in rule 14. Finally, we use diagrams to explain the attractor of rule 14, where characteristic function is used to describe that all points fall into Bernoulli-shift map after two iterations under rule 14.

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Mechanisms of syngeneic tumor rejection. Susceptibility of host-selected progressor variants to various immunological effector cells.

Journal of Experimental Medicine ◽

10.1084/jem.155.2.557 ◽

1982 ◽

Vol 155 (2) ◽

pp. 557-573 ◽

Cited By ~ 73

Author(s):

J L Urban ◽

R C Burton ◽

J M Holland ◽

M L Kripke ◽

H Schreiber

Keyword(s):

T Cell ◽

Tumor Growth ◽

Natural Killer ◽

Tumor Cells ◽

Killer Cell ◽

Tumor Rejection ◽

Cell Mediated Immunity ◽

Killer Activity ◽

Effector Cells ◽

Parental Tumor

The ultraviolet radiation-induced fibrosarcoma 1591 generally is rejected by normal syngeneic mice and only rarely exhibits progressive growth. We isolated five of these rare progressor tumors from normal animals to determine the selective pressures that had been exerted upon the parental tumor by normal immunocompetent hosts. We found that the variant tumor cell lines could neither induce nor be killed by tumor-specific lymphocytes, suggesting that selection had been exerted against tumor cells expressing the tumor-specific antigen. In contrast, no selection against natural killer cell activity or against nonspecific T cell-mediated immunity seems to have occurred because progressor tumor cells were highly sensitive to these types of effector cells and in fact induced these effector cells more effectively than did the parental tumor. Nude mice were found to be as capable as normal mice in generating natural killer activity in response to a challenge with progressor tumor cells, but they were unable to mount a nonspecific T lymphocyte response. This may account for the fact that the progressor tumors grew at a significantly faster rate in nude animals than in normal mice. Thus, our study shows that in this tumor system nonspecific T cell-mediated immunity may play a role in retarding tumor growth, but the absolute resistance of normal animals to progressive tumor growth critically depends upon the presence of T cell-mediated tumor-specific immunity. Furthermore, neither NK cells nor nonspecific cytotoxic T lymphocytes appear to play a role in immunoselection against this tumor in normal immunocompetent hosts.

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Melatonin modifies tumor hypoxia and metabolism by inhibiting HIF-1α and energy metabolic pathway in the in vitro and in vivo models of breast cancer

Melatonin Research ◽

10.32794/mr11250042 ◽

2019 ◽

Vol 2 (4) ◽

pp. 83-98 ◽

Cited By ~ 2

Author(s):

André De Lima Mota ◽

Bruna Vitorasso Jardim-Perassi ◽

Tialfi Bergamin De Castro ◽

Jucimara Colombo ◽

Nathália Martins Sonehara ◽

...

Keyword(s):

Breast Cancer ◽

Glucose Metabolism ◽

Tumor Growth ◽

Tumor Cells ◽

Carbonic Anhydrases ◽

In Vivo Models ◽

Ca Ix ◽

Gene And Protein Expression

Breast cancer is the most common cancer among women and has a high mortality rate. Adverse conditions in the tumor microenvironment, such as hypoxia and acidosis, may exert selective pressure on the tumor, selecting subpopulations of tumor cells with advantages for survival in this environment. In this context, therapeutic agents that can modify these conditions, and consequently the intratumoral heterogeneity need to be explored. Melatonin, in addition to its physiological effects, exhibits important anti-tumor actions which may associate with modification of hypoxia and Warburg effect. In this study, we have evaluated the action of melatonin on tumor growth and tumor metabolism by different markers of hypoxia and glucose metabolism (HIF-1α, glucose transporters GLUT1 and GLUT3 and carbonic anhydrases CA-IX and CA-XII) in triple negative breast cancer model. In an in vitro study, gene and protein expressions of these markers were evaluated by quantitative real-time PCR and immunocytochemistry, respectively. The effects of melatonin were also tested in a MDA-MB-231 xenograft animal model. Results showed that melatonin treatment reduced the viability of MDA-MB-231 cells and tumor growth in Balb/c nude mice (p <0.05). The treatment significantly decreased HIF-1α gene and protein expression concomitantly with the expression of GLUT1, GLUT3, CA-IX and CA-XII (p <0.05). These results strongly suggest that melatonin down-regulates HIF-1α expression and regulates glucose metabolism in breast tumor cells, therefore, controlling hypoxia and tumor progression.

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ANTITUMOR EFFECT OF COLLOIDAL SILVER BISILICATE IN EXPERIMENTAL IN VITRO AND IN VIVO STUDIES

Problems in oncology ◽

10.37469/0507-3758-2019-65-5-760-765 ◽

2019 ◽

Vol 65 (5) ◽

pp. 760-765

Author(s):

Margarita Tyndyk ◽

Irina Popovich ◽

A. Malek ◽

R. Samsonov ◽

N. Germanov ◽

...

Keyword(s):

Antitumor Activity ◽

Tumor Growth ◽

Tumor Cells ◽

Human Tumor ◽

Significant Inhibition ◽

In Vivo Studies ◽

Ehrlich Carcinoma ◽

In Vivo Experiments

The paper presents the results of the research on the antitumor activity of a new drug - atomic clusters of silver (ACS), the colloidal solution of nanostructured silver bisilicate Ag6Si2O7 with particles size of 1-2 nm in deionized water. In vitro studies to evaluate the effect of various ACS concentrations in human tumor cells cultures (breast cancer, colon carcinoma and prostate cancer) were conducted. The highest antitumor activity of ACS was observed in dilutions from 2.7 mg/l to 5.1 mg/l, resulting in the death of tumor cells in all studied cell cultures. In vivo experiments on transplanted Ehrlich carcinoma model in mice consuming 0.75 mg/kg ACS with drinking water revealed significant inhibition of tumor growth since the 14th day of experiment (maximally by 52% on the 28th day, p < 0.05) in comparison with control. Subcutaneous injections of 2.5 mg/kg ACS inhibited Ehrlich's tumor growth on the 7th and 10th days of the experiment (p < 0.05) as compared to control.

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Immunomodulating nano-adaptors potentiate antibody-based cancer immunotherapy

Nature Communications ◽

10.1038/s41467-021-21497-6 ◽

2021 ◽

Vol 12 (1) ◽

Cited By ~ 1

Author(s):

Cheng-Tao Jiang ◽

Kai-Ge Chen ◽

An Liu ◽

Hua Huang ◽

Ya-Nan Fan ◽

...

Keyword(s):

T Cells ◽

T Cell ◽

Immune Responses ◽

Cancer Immunotherapy ◽

Tumor Cells ◽

Noncovalent Interactions ◽

Killer Cell ◽

Antibody Immobilization ◽

Effector Cells ◽

Nanoparticle Surface

AbstractModulating effector immune cells via monoclonal antibodies (mAbs) and facilitating the co-engagement of T cells and tumor cells via chimeric antigen receptor- T cells or bispecific T cell-engaging antibodies are two typical cancer immunotherapy approaches. We speculated that immobilizing two types of mAbs against effector cells and tumor cells on a single nanoparticle could integrate the functions of these two approaches, as the engineered formulation (immunomodulating nano-adaptor, imNA) could potentially associate with both cells and bridge them together like an ‘adaptor’ while maintaining the immunomodulatory properties of the parental mAbs. However, existing mAbs-immobilization strategies mainly rely on a chemical reaction, a process that is rough and difficult to control. Here, we build up a versatile antibody immobilization platform by conjugating anti-IgG (Fc specific) antibody (αFc) onto the nanoparticle surface (αFc-NP), and confirm that αFc-NP could conveniently and efficiently immobilize two types of mAbs through Fc-specific noncovalent interactions to form imNAs. Finally, we validate the superiority of imNAs over the mixture of parental mAbs in T cell-, natural killer cell- and macrophage-mediated antitumor immune responses in multiple murine tumor models.

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Quantitative Experimental and Theoretical Investigations on the Interaction of Shock Waves with Magnetic Fields

Zeitschrift für Naturforschung A ◽

10.1515/zna-1969-1002 ◽

1969 ◽

Vol 24 (10) ◽

pp. 1449-1457

Author(s):

H. Klingenberg ◽

F. Sardei ◽

W. Zimmermann

Keyword(s):

Magnetic Fields ◽

Shock Waves ◽

Physical Model ◽

Spectroscopic Method ◽

Experimental Results ◽

Dimensional Theory ◽

One Dimensional ◽

Theoretical Investigations ◽

Theoretical Predictions ◽

Interaction Of Shock Waves

Abstract In continuation of the work on interaction between shock waves and magnetic fields 1,2 the experiments reported here measured the atomic and electron densities in the interaction region by means of an interferometric and a spectroscopic method. The transient atomic density was also calculated using a one-dimensional theory based on the work of Johnson3 , but modified to give an improved physical model. The experimental results were compared with the theoretical predictions.

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