Scaling Phenomena in Biological and Medical Systems
References

Larry S. Liebovitch
Florida Atlantic University
http://www.ccs.fau.edu/~liebovitch/larry.html

Part I: Overview of fractal properties:

-L. S. Liebovitch. 1998. Fractals and Chaos Simplified for the Life Sciences. Oxford University Press, NY.

-L. S. Liebovitch, et al. 1999. When using the mean is meaningless: Examples from probability theory and cardiology. In Handbook of Methods for Research in Learning and Teaching Science and Mathematics, Eds. A. E. Kelly and R. Lesh, Kluwer, in press.

Part II: Fractals in the timing of heart attacks:

-L. S. Liebovitch et al. 1999. Nonlinear properties of cardiac rhythm abnormalities. Physical Review E59:3312-3319.

Part III: Fractals in the timing of the switching of conformational states in ion channel proteins in the cell membrane:

-L. S. Liebovitch and A. T. Todorov. 1996. Using fractals and nonlinear dynamics to determine the physical properties of ion channel proteins. Critical Reviews in Neurobiology 10:169-187.

-L. S. Liebovitch. 1996. Ion channel kinetics. In Fractal Geometry in Biological Systems, ed. P. M. Iannaccone and M. Khokha, CRC Press, Boca Raton FL.

-L. S. Liebovitch et al. 1987. Ion channel kinetics: a model based on fractal scaling rather than multistate Markov processes. Mathematical Biosciences 84:37-68.

-L. S. Liebovitch. 1989. Analysis of fractal ion channel gating kinetics: kinetic rates, energy levels, and activation energies. Mathematical Biosciences, 93:97-115.

-L. S. Liebovitch and T. I. Toth. 1991. Distributions of activation energy barriers that produce stretched exponential probability distributions for the time spent in each state of the two state reaction A-B. Bulletin of Mathematical Biology, 53:443-455.

-L. S. Liebovitch and T. I. Toth. 1990. The Akaike information criterion (AIC) is not a sufficient condition to determine the number of ion channel states from single channel recordings, Synapse 5:134-138.

-L. S. Liebovitch et al. 1994. Neural networks to compute molecular dynamics. J. Biological Systems, 2:193-228.

-L. S. Liebovitch and M. Zochowski. 1997. Dynamics of neural networks relevant to properties of proteins. Physical Review E56:931-935.

Part IV: Other biomedical applications of fractals:

-L. S. Liebovitch. 1998. Fractals and Chaos Simplified for the Life Sciences. Oxford University Press, NY.

-J. B. Bassingthwaighte, L. S. Liebovitch, and B. J. West. 1994. Fractal Physiology. Oxford University Press, NY.

-P. M. Iannaccone and M. Khokha. 1996. Fractal Geometry in Biological Systems, CRC Press, Boca Raton FL.

 

1999-2000 Reactive Flow and Transport Phenomena