<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Using the fractional calculus approach, we present the Laplace analysis of an equivalent electrical circuit for a multilayered system, which includes distributed elements of the Cole model type. The Bode graphs are obtained from the numerical simulation of the corresponding transfer functions using arbitrary electrical parameters in order to illustrate the methodology. A numerical Laplace transform is used with respect to the simulation of the fractional differential equations. From the results shown in the analysis, we obtain the formula for the equivalent electrical circuit of a simple spectrum, such as that generated by a real sample of blood tissue, and the corresponding Nyquist diagrams. In addition to maintaining consistency in adjusted electrical parameters, the advantage of using fractional differential equations in the study of the impedance spectra is made clear in the analysis used to determine a compact formula for the equivalent electrical circuit, which includes the Cole model and a simple RC model as special cases.</p></abstract>

Using the fractional calculus approach, we present the Laplace analysis of an equivalent electrical circuit for a multilayered system, which includes distributed elements of the Cole model type. The Bode graphs are obtained from the numerical simulation of the corresponding transfer functions using arbitrary electrical parameters in order to illustrate the methodology. A numerical Laplace transform is used with respect to the simulation of the fractional differential equations. From the results shown in the analysis, we obtain the formula for the equivalent electrical circuit of a simple spectrum, such as that generated by a real sample of blood tissue, and the corresponding Nyquist diagrams. In addition to maintaining consistency in adjusted electrical parameters, the advantage of using fractional differential equations in the study of the impedance spectra is made clear in the analysis used to determine a compact formula for the equivalent electrical circuit, which includes the Cole model and a simple RC model as special cases.

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

Journal of Electrical Bioimpedance

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Using the fractional calculus approach, we present the Laplace analysis of an equivalent electrical circuit for a multilayered system, which includes...

	Erythrocytes	Leukocytes	Plasma
γ	0.97	0.98	0.995
	0.975	0.99	0.99
	0.98	0.97	0.9997

	Erythrocytes	Leukocytes	Plasma
Rs	627.2	444.4	431.4
	673.7	475.6	496.5
	715.9	460.1	460.8
C_p	2.2081×10^-8	2.43×10^-8	2.4055×10^-8
	2.2900×10^-8	2.188×10^-8	2.1517×10^-8
	2.2575×10^-8	2.2336×10^-8	2.4114×10^-8
R_p	149970	358000	261960
	120710	341550	273750
	136930	332340	252250

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

Article Category: Articles

Online veröffentlicht: 27. Juli 2012

Seitenbereich: 2 - 11

Eingereicht: 12. Dez. 2011

DOI: https://doi.org/10.5617/jeb.225

Schlüsselwörter
Bioimpedance, fractional calculus, Nyquist and Bode diagrams, numerical Laplace transform

© 2012 F. Gómez, J. Bernal, J. Rosales, T. Cordova, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Fig. 2

Fig. 3

Fig.. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Exponent of the fractional differential equation that best fits the data

Values for the erythrocytes, leukocytes and plasma.

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

Article Category: Articles

Online veröffentlicht: 27. Juli 2012

Seitenbereich: 2 - 11

Eingereicht: 12. Dez. 2011

DOI: https://doi.org/10.5617/jeb.225

SchlüsselwörterBioimpedance, fractional calculus, Nyquist and Bode diagrams, numerical Laplace transform

© 2012 F. Gómez, J. Bernal, J. Rosales, T. Cordova, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Fig. 2

Fig. 3

Fig.. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Exponent of the fractional differential equation that best fits the data

Values for the erythrocytes, leukocytes and plasma.

Schlüsselwörter
Bioimpedance, fractional calculus, Nyquist and Bode diagrams, numerical Laplace transform