An Example of the Use of Complexity Theory in the

Một phần của tài liệu The biomedical engineering handbook (Trang 178 - 183)

Consciousness can be viewed as an emergent behavior arising from the interactions among a very large number of local agents, which, in this case, range from electrons through neurons and glial cells to networks of neurons. The hierarchical organization of the brain [Churchland and Sejnowski, 1992;

Newell, 1990], which exists and evolves on a multitude of spatial and temporal scales, is a good example of the scaling characteristics found in many complex dynamic systems. There is no master controller for this emergent behavior, which results from the intricate interactions among a very large number of local agents.

A model that duplicates the global dynamics of the induction of unconsciousness in humans due to cerebral ischemia produced by linear acceleration stress (G-LOC) was constructed using some of the tenets of complexity [Cammarota, 1994]. It was an attempt to provide a theory that could both replicate historical human acceleration tolerance data and present a possible underlying mechanism. The model coupled the realization that an abrupt loss of consciousness could be thought of as a phase transition from consciousness to unconsciousness with the proposed neurophysiologic theory of G-LOC [Whinnery, 1989]. This phase transition was modeled using a percolation network to evaluate the connectivity of neural pathways within the central nervous system.

In order to construct the model, several hypotheses had to be formulated to account for the unobservable interplay among the local elements of the central nervous system. The inspiration for the characteristics of the locally interacting elements (the nodes of the percolation lattice) was provided by the physiologic mechanism of arousal (the all-or-nothing aspect of consciousness), the utilization of oxygen in neural tissue during ischemia, and the response of neural cells to metabolic threats. The neurophysiologic theory of acceleration tolerance views unconsciousness as an active protective mechanism that is triggered by a metabolic threat which in this case is acceleration-induced ischemia. The interplay among the local systems is determined by using a percolation network that models the connectivity of the arousal mechanism (the reticular activating system). When normal neuronal function is suppressed due to local cerebral ischemia, the corresponding node is removed from the percolation network. The configuration of the percolation network varies as a function of time. When the network is no longer able to support arousal, unconsciousness results.

The model simulated a wide range of human data with a high degree of fidelity. It duplicated the population response (measured as the time it took to lose consciousness) over a range of stresses that varied from a simulation of the acute arrest of cerebral circulation to a gradual application of acceleration stress. Moreover, the model was able to offer a possible unified explanation for apparently contradictory historical data. An analysis of the parameters responsible for the determination of the time of LOC indicated that there is a phase transition in the dynamics that was not explicitly incorporated into the construction of the model. The model spontaneously captured an interplay of the cardiovascular and neurologic systems that could not have been predicted based on existing data.

The keys to the model’s success are the reasonable assumptions that were made about the characteristics and interaction of the local dynamic subsystems through the integration of a wide range of human and animal physiologic data in the design of the model. None of the local parameters was explicitly tuned to produce the global (input–output) behavior. By successfully duplicating the observed global behavior of humans under acceleration stress, however, this model provided insight into some (currently) unobserv- able inner dynamics of the central nervous system. Furthermore, the model suggests new experimental protocols specifically aimed at exploring further the microscopic interplay responsible for the macroscopic (observable) behavior.

Defining Terms

1/f process: Signals or systems that exhibit spectra which attenuate following a fractional power dependence on frequency.

Cellular automata: Composite discrete-time and discrete space dynamic systems defined on a regular lattice. Neighborhood rules determine the state transitions of the individual local elements (cells).

Chaos: A state the produces a signal that resembles noise and is aperiodic, well-bounded, and very sensitive to initial conditions but is governed by a low-order deterministic differential or difference equation.

Complexity: Complexity theory is concerned with systems that have many degrees of freedom (com- posite systems), are spatially extended (systems with both spatial and temporal degrees of freedom), and are dissipative as well as nonlinear due to the rich interactions among the local components (agents). Some of the terms associated with such systems are emergent global behavior, collective behavior, cooperative behavior, self-organization, critical phenomena, and scale invariance.

Criticality: A state of a system where spatial and/or temporal characteristics are scale invariant.

Emergent global behavior: The observable behavior of a system that cannot be deduced from the prop- erties of constituent components considered in isolation and results from the collective (cooperative or competitive) evolution of local events.

Fractal: Refers to physical objects or dynamic processes that reveal new details on space or time magnification. Fractals lack a characteristic scale.

Fractional brownian motion: A generalization of the random function created by the record of the motion of a “brownian particle” executing random walk. Brownian motion is commonly used to model diffusion in constraint-free media. Fractional brownian motion is often used to model diffusion of particles in constrained environments or anomalous diffusion.

Percolation: A simple mathematical construct commonly used to measure the extent of connectedness in a partially occupied (site percolation) or connected (bond percolation) lattice structure.

Phase transition: Any abrupt change between the physical and/or the dynamic states of a system, usually between ordered and disordered organization or behavior.

Renormalization: Changing the characteristic scale of a measurement though a process of systematic averaging applied to the microscopic elements of a system (also referred to as coarse graining).

Scaling: Structures or dynamics that maintain some form of exact or statistical invariance under transformations of scale.

Self-organization: The spontaneous emergence of order. This occurs without the direction of a global controller.

Self-similarity: A subset of objects and processes in the scaling category that remain invariant under ordinary geometric similarity.

References

Akansu A.N. and Haddad R.A. 1992. Multiresolution Signal Decomposition: Transforms, Subbands, and Wavelets. New York, Academic Press.

Bagley R. and Calico R. 1991. Fractional order state equations for the control of viscoelastic damped structures. J. Guid. 14: 304.

Bak P., Tang C., and Wiesenfeld K. 1988. Self-organized criticality. Phys. Rev. A. 38: 364.

Bak P. and Chen K. 1991. Self-organized. Sci. Am. J.: 45.

Barnsley M.F. 1993. Fractals Everywhere, 2nd ed. New York, Academic Press.

Barnsley M.F. and Hurd L.P. 1993. Fractal Image Compression. Wellesley, AK Peters.

Basseville M., Benveniste A., Chou K.C. et al. 1992. Modeling and estimation of multiresolution stochastic processes. IEEE Trans. Inf. Theor. 38: 766.

Cammarota J.P. 1994. A Dynamic Percolation Model of the Central Nervous System under Acceleration (+Gz) Induced/Hypoxic Stress. Ph.D. thesis, Drexel University, Philadelphia.

Churchland P.S. and Sejnowski T.J. 1992. The Computational Brain. Cambridge, Mass., MIT Press.

Daniel V. 1967. Dielectric Relaxation. New York, Academic Press.

Devaney R.L. 1992. A First Course in Chaotic Dynamical Systems: Theory and Experiment. Reading, Mass., Addison-Wesley.

Falconer K. 1990. Fractal Geometry: Mathematical Foundations and Applications. New York, John Wiley &

Sons.

Feder J. 1988. Fractals. New York, Plenum Press.

Forrest S. 1990. Emergent computation: self-organization, collective, and cooperative phenomena in natural and artificial computing networks. Physica D 42: 1.

Goldberg D.E. 1989. Genetic Algorithms in Search, Optimization, and Machine Learning. Reading, Mass., Addison-Wesley.

Harvey R.L. 1994. Neural Network Principles. Englewood Cliffs, NJ, Prentice-Hall.

Langton C.G. 1989. Artificial Life: Proceedings of an Interdisciplinary Workshop on the Synthesis and Simulation of Living Systems, September 1987, Los Alamos, New Mexico, Redwood City, Calif, Addison-Wesley.

Langton C.G. 1990. Computation at the edge of the chaos: Phase transitions and emergent computation.

Physica D 42: 12.

Langton C.G., Taylor C., Farmer J.D., and Rasmussen S. 1992. Artificial Life II: Proceedings of the Workshop on Artificial Life, February 1990, Sante Fe, New Mexico. Redwood City, Calif, Addison-Wesley.

Mandelbrot B. 1967. Some noises with 1/f spectrum, a bridge between direct current and white noise.

IEEE Trans. Inf. Theor. IT-13: 289.

Mandelbrot B. 1983. The Fractal Geometry of Nature. New York, WH Freeman.

Meyer Y. 1993. Wavelets: Algorithms and Applications. Philadelphia, SIAM.

Newell A. 1990. Unified Theories of Cognition. Cambridge, Mass., Harvard University Press.

Orbach R. 1986. Dynamics of fractal networks. Science 231: 814.

Peitgen H.O. and Richter P.H. 1986. The Beauty of Fractals. New York, Springer-Verlag.

Ross B. 1977. Fractional calculus. Math. Mag. 50: 115.

Shroeder M. 1990. Fractals, Chaos, Power Laws. New York, WH Freeman.

Simpson P.K. 1990. Artificial Neural Systems: Foundations, Paradigms, Applications, and Implementations.

New York, Pergamon Press.

Stauffer D. and Aharony A. 1992. Introduction to Percolation. 2nd ed. London, Taylor & Francis.

Toffoli T. and Margolus N. 1987. Cellular Automata Machines: A New Environment for Modeling.

Cambridge, Mass., MIT Press.

Tsonis P.A. and Tsonis A.A. 1989. Chaos: Principles and implications in biology. Comput. Appl. Biosci.

5: 27.

Vaidyanathan P.P. 1993. Multi-Rate Systems and Filter Banks. Englewood Cliffs, NJ, Prentice-Hall.

West B.J. 1990. Physiology in fractal dimensions: error tolerance. Ann. Biomed. Eng. 18: 135.

West B.J. 1994. Scaling statistics in biomedical phenomena. In Proceedings of the IFAC Conference on Modeling and Control in Biomedical Systems, Galveston, Texas.

West B.J. and Goldberger A. 1987. Physiology in fractal dimensions. Am. Scientist 75: 354.

West B.J. and Shlesinger M. 1989. On the ubiquity of 1/f noise. Int J. Mod. Phys. 3: 795.

Whinnery J.E. 1989. Observations on the neurophysiologic theory of acceleration (+Gz) induced loss of consciousness. Aviat. Space Environ. Med. 60: 589.

Wilson K.G. 1983. The renormalization group and critical phenomena. Rev. Mod. Phys. 55: 583.

Wornell G.W. 1993. Wavelet-based representations for the 1/f family of fractal processes. IEEE Proc.

81: 1428.

9

Future Directions:

Biomedical Signal Processing and Networked Multimedia Communications

Banu Onaral

Drexel University

9.1 Public Switched Network and Asynchronous Transfer Mode . . . 9-2 9.2 Wireless Communication . . . 9-2 9.3 Photonics . . . 9-3 9.4 Virtual Reality . . . 9-3 Acknowledgment. . . 9-3 Defining Terms . . . 9-3 References . . . 9-4 The long anticipated“information age” is taking shape at the cross-section of multimedia signal processing and telecommunications-based networking. By defying the traditional concepts of space and time, these emerging technologies promise to affect all facets of our lives in a pervasive and profound manner [Mayo, 1992]. The physical constraints of location have naturally led, over the centuries, to the creation of the conventional patient care services and facilities. As the “information superhighway” is laid down with branches spanning the nation, and eventually the world via wired and wireless communication channels, we will come closer to a bold new era in health care delivery, namely, the era of remote monitoring, diagnosis, and intervention.

Forward-looking medical industries are engaging in research and development efforts to capitalize on the emerging technologies. Medical institutions in particular recognize the transforming power of the impending revolution. A number of hospitals are undertaking pilot projects to experiment with the potentials of the new communication and interaction media that will constitute the foundations of futuristic health care systems. There is consensus among health care administrators that the agility and

9-1

effectiveness with which an institution positions itself to fully embrace the new medical lifestyle will decide its viability in the next millennium.

Although multimedia communications is yet in its infancy, recent developments foretell a bright future. Many agree that multimedia networking is becoming a reality thanks to advances in digital signal- processing research and development. Trends toward implementation of algorithms by fewer components are leading to decreasing hardware complexity while increasing processing functionality [Andrews, 1994].

The vast and vibrant industry producing multimedia hardware and software ranging from application- specific digital signal processors and video chip sets to videophones and multimedia terminals heavily relies on digital signal processing know-how.

As in the case of generic digital signal processing, biomedical signal processing is expected to play a key role in mainstreaming patient care at a distance. Earlier in this section, emerging methods in biomedical signal analysis that promise major enhancements in our ability to extract information from vital signals were introduced. This chapter provides a glimpse of the future — when biomedical signals will be integ- rated with other patient information and transmitted via networked multimedia — by examining trends in key communications technologies, namely, public switched-network protocols, wireless communications, photonics, and virtual reality.

Một phần của tài liệu The biomedical engineering handbook (Trang 178 - 183)

Tải bản đầy đủ (PDF)

(611 trang)