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.

Haptoglobin, acid phosphatase and demographic factors: obesity risk

The aim of this work is to study the risk of obesity posed by two genetic factors: haptoglobin phenotype and acid phosphatase phenotype, one enzymatic activity: acid phosphatase activity (ACP1), age and gender. Haptoglobin (Hp) is a protein of the immune system, and three phenotypes of Hp are found in humans: Hp1-1, Hp2-1, and Hp2-2. This protein is associated with a susceptibility to common pathological conditions, such as obesity. ACP1 is an intracellular enzyme The phenotypes of ACP1 (AA, AB, AC, BB, BC, CC) are also considered. We took a sample of 127 subjects with complete data from 714 registers. Since we intend to identify risk factors for obesity, an ordinal regression model is adjusted, using the Body Mass Index, BMI, to define weight categories. Haptoglobin phenotype, enzymatic activity of ACP1, acid phosphatase phenotype, age and gender are considered as regressor variables. We found three factors associated with an increased risk of obesity: phenotype Hp2-1 of haptoglobin (estimated odds ratio OR 11.54), phenotype AA of acid phosphatase (OR 33.788) and age (OR 1.39). The interaction between phenotype Hp2-1 and phenotype AC is associated with a decreased risk of obesity (OR 0.032); The interaction between phenotype AA and ACP1 activity is associated with a decreased risk of obesity (OR 0.954).

Avoiding healthy cells extinction in a cancer model

We consider a dynamical model of cancer growth including three interacting cell populations of tumor cells, healthy host cells and immune effector cells. For certain parameter choice, the dynamical system displays chaotic motion and by decreasing the response of the immune system to the tumor cells, a boundary crisis leading to transient chaotic dynamics is observed. This means that the system behaves chaotically for a finite amount of time until the unavoidable extinction of the healthy and immune cell populations occurs. Our main goal here is to apply a control method to avoid extinction. For that purpose, we apply the partial control method, which aims to control transient chaotic dynamics in the presence of external disturbances. As a result, we have succeeded to avoid the uncontrolled growth of tumor cells and the extinction of healthy tissue. The possibility of using this method compared to the frequently used therapies is discussed. (C) 2014 Elsevier Ltd. All rights reserved.