Biomedical Engineering Reference
In-Depth Information
blood flow can be discerned based on their respective fractal prop-
erties
(18)
. Moreover,
H
values for white and gray matters and
within parenchymal regions of the rat brain cortex were distinctly
different
(17)
.
In our human studies, fractal analysis revealed age and gen-
der related stiffening of the cerebral vasculature
(15)
. We found
that the hemodynamics of the borderline regions in between the
frontal and temporal lobes (i.e. between the vascular territories
of the ACA and MCA) has a fractal pattern which is noisier than
their neighbors' suggesting that vascular segments in these areas
contain less efficient “arterial pumps”. This can potentially render
these regions more vulnerable to hypoperfusion.
It seems that normal, physiological biological complexity
presents itself within a restricted range of
H
or
values, while
their values outside this range can indicate disease states or
progress towards pathology.
β
Acknowledgments
The authors gratefully acknowledge the contribution of Ms.
Andrea Mile to the human LED Imager study and Drs. Fahmeed
Hyder, Ikuhiro Kida and Basavaraju G. Sanganahalli to the MRI
study. This work was supported by the Hungarian Research Foun-
dation (OTKA) by its grants T016953, T34122 and the High
Performance Computing of the Hungarian National Information
Infrastructure Development Program.
References
1. Norris, V., Cabin, A. and Zemirline, A. (2005)
Hypercomplexity.
Acta Biotheor
5
3, 313-330.
2. Krone, G., Mallot, H., Palm, G. and Schuz,
A. (1986) Spatiotemporal receptive fields: A
dynamical model derived from cortical archi-
tectonics.
Proc R Soc Lond B Biol Sci
2
26,
421-444.
3. Grassberger, P. and Procaccia, I. (1983) Mea-
suring the strangeness of strange attractors.
Physica D
9
, 189-208.
4. Kaplan, D. and Glass, L. (1997)
Understand-
ing
8. Bassingthwaighte, J., Liebovitch, L. and West,
B. (1994)
Fractal Physiology
. Oxford Univer-
sity Press, New York, Oxford.
9. Mandelbrot, B. (1983)
The Fractal Geometry
of Nature
. WH Freeman, San Francisco.
10. Avnir, D., Biham, O., Lidar, D. and Malcai,
O. (1998) Is the geometry of nature fractal?
Science
2
79, 39-40.
11. Mandelbrot,
B.
(1985)
Self-affine
Fractals
and
Fractal
Dimension.
Phys
Scripta
3
2,
257-260.
12. Dunn, A. K., Bolay, H., Moskowitz, M. A.
and Boas, D. A. (2001) Dynamic Imaging Of
Cerebral Blood Flow Using Laser Speckle.
J
Cereb Blood Flow Metab
2
1, 195-201.
13. Eke, A. (2003)
Fractal
,
chaos
,
physiological
complexity
.In:
Studia Physiologica
(Series Ed.:
A. Juhasz-Nagy)
1
3,1-157, Scientia Kiado,
Budapest.
14. Eke, A., Herman, P., Bassingthwaighte, J. B.,
Raymond, G. M., Percival, D. B., Cannon, M.,
Balla, I. and Ikrenyi, C. (2000) Physiological
Nonlinear
Dynamics
.
Springer-Verlag,
New York.
5. Falconer, K. (1990)
Fractal geometry: Mathe-
matical Foundations and Applications
. Wiley,
Chichester, New York.
6. Eke, A., Herman, P., Kocsis, L. and Kozak,
L. R. (2002) Fractal characterization of com-
plexity in temporal physiological signals.
Phys-
iol Meas
2
3, R1-38.
7. Beran, J. (1994)
Statistics for Long Memory
Processes
. Chapman and Hall, New York.
