Information Technology & Software

This model simulates several basic cellular and global functions of immune systems.

A mathematical model that represents several physical and mental behaviors has been developed to enable the phenomenological description of basic functions of immune systems. This development is part of a continuing effort to improve the autonomy of robots and spacecraft by use of computational methods that exploit paradigms of human immune systems. The model can serve as a formalism for building artificial immune systems for computing and for other forms of information processing.

The discipline of artificial immune systems is a rapidly growing field of information processing based upon immune- inspired paradigms of nonlinear dynamics. The interest in immunesystems paradigms stems from the observation that an immune system serves as an excellent model of adaptive processes that occur at the local (cellular) and of useful behavior emerging at the global level.

Although artificial immune systems have many features in common with artificial neural networks, there are some differences that arise from the fact that immune systems perform many different functions simultaneously and, in comparison with neural networks, they are more complex and more diverse. In contradistinction to a neural network, an immune system, from the perspective of nonlinear dynamics, can be considered as a multibody system (the bodies being cells) in which the bodies are interconnected via flows of information. Inasmuch as these flows and the responses to them may be distorted, delayed, or incomplete, the motion of each cell becomes stochastic and can be simulated as a controlled random walk.

One of the main challenges in modeling living systems is to distinguish random walks of physical origin (for instance, Brownian motions) from those of biological origin. Following a line of reasoning from prior research, it was assumed, in the development of the present model, that a biological random walk must be nonlinear. The model is intended, more specifically, to simulate the main immune-system functions based on the dynamics of body cells interacting with invader cells. In contradistinction to prior stochastic models, the present model incorporates the concept of reflection; that is, the human ability to observe one’s own thoughts. This concept renders the model more adaptable to the world of biological and social evolutionary processes.

The model consists of (1) a generator of stochastic processes that represents motor dynamics in the form of nonlinear random walks and (2) a simulator of the nonlinear version of the Fokker-Planck equation, representing the mental dynamics. Thus, the model is one of coupled mental/motor dynamics incorporating the concept of self-image. It has been demonstrated that the model can simulate such basic functions of immune systems (and of cells within immune systems) as selfidentification, self/nonself discrimination, self-repair, formation of acquired immunity, self-organization, predator/ prey pursuit, and reproduction.

This work was done by Michail Zak of Caltech for NASA’s Jet Propulsion Laboratory. For further information, access the Technical Support Package (TSP) free on-line at under the Information Sciences category. NPO-21039

This Brief includes a Technical Support Package (TSP).

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