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Modeling and Simulation of Equivalent Circuits in Description of Biological Systems - A Fractional Calculus Approach Cover

Modeling and Simulation of Equivalent Circuits in Description of Biological Systems - A Fractional Calculus Approach

Journal of Electrical Bioimpedance
Volume 3 (2012): Issue 1 (January 2012)
By: F. Gómez,  J. Bernal,  J. Rosales and  T. Cordova  
Open Access
|Jul 2012

Figures & Tables

Fig. 1

Equivalent electrical circuit to the biological system.
Equivalent electrical circuit to the biological system.

Fig. 2

Equivalent electrical circuit to the first layer of the model.
Equivalent electrical circuit to the first layer of the model.

Fig. 3

Bode diagram for the first layer.
Bode diagram for the first layer.

Fig.. 4

Bode diagram for the first, second and third layers.
Bode diagram for the first, second and third layers.

Fig. 5

Bode diagram corresponding to the first layer, fractional exponent γ=0.95
Bode diagram corresponding to the first layer, fractional exponent γ=0.95

Fig. 6

Bode diagram comparison corresponding to the first layer, integer order and fractional exponent γ=0.95 and γ=0.98.
Bode diagram comparison corresponding to the first layer, integer order and fractional exponent γ=0.95 and γ=0.98.

Fig. 7

Equivalent electrical circuit for data of blood tissue, erythrocytes, leukocytes and plasma.
Equivalent electrical circuit for data of blood tissue, erythrocytes, leukocytes and plasma.

Fig. 8

Nyquist diagram for erythrocytes showing reactance as a function of resistance.
Nyquist diagram for erythrocytes showing reactance as a function of resistance.

Fig. 9

Nyquist diagram for leukocytes showing reactance as a function of resistance.
Nyquist diagram for leukocytes showing reactance as a function of resistance.

Fig. 10

Nyquist diagram for plasma showing reactance as a function of resistance.
Nyquist diagram for plasma showing reactance as a function of resistance.

Exponent of the fractional differential equation that best fits the data

ErythrocytesLeukocytesPlasma
γ0.970.980.995
0.9750.990.99
0.980.970.9997

Values for the erythrocytes, leukocytes and plasma_

ErythrocytesLeukocytesPlasma
Rs627.2444.4431.4
673.7475.6496.5
715.9460.1460.8
Cp2.2081×10-82.43×10-82.4055×10-8
2.2900×10-82.188×10-82.1517×10-8
2.2575×10-82.2336×10-82.4114×10-8
Rp149970358000261960
120710341550273750
136930332340252250
DOI: https://doi.org/10.5617/jeb.225 | Journal eISSN: 1891-5469
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Language: English
Page range: 2 - 11
Submitted on: Dec 12, 2011
Published on: Jul 27, 2012
Published by: University of Oslo
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
Bioimpedance,
fractional calculus,
Nyquist and Bode diagrams,
numerical Laplace transform
Related subjects:
Engineering,
Bioengineering and biomedical engineering,
Biomedical electronics,
Life sciences,
Biophysics,
Medicine,
Biomedical engineering,
Physics,
Spectroscopy and metrology

© 2012 F. Gómez, J. Bernal, J. Rosales, T. Cordova, published by University of Oslo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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