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

Gómez-Aguilar, J. F.; Bernal, J. J.; Rosales, J. J.; Cordova, T. T.

doi:10.5617/jeb.225

Cited by 60 publications

(24 citation statements)

References 29 publications

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“…Go´mez et al 2 proposed a work on modeling and simulation of equivalent circuits in description of biological systems, in which a fractional calculus approach was used in the modeling of the biological system into equivalent electrical system. It also illustrates that in the biological system, there is no conversion of electrical energy into magnetic energy.…”

Section: Literature Surveymentioning

confidence: 99%

RETRACTED: Restricted release of skin cancer medicine based on fascination and dispersion rates using proportional–integral–derivative controller

Jagadeesan¹,

Dhanasekar²,

2019

Measurement and Control

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Skin cancer is the most common of all cancers. About 35 million cases of skin cancer are diagnosed every year. Malignant melanoma is a dangerous type of skin cancer and it is difficult to treat. Early diagnosis and treatment can increase the survival rate from melanoma. However, the therapeutic treatment is the main option but still it is not feasible for most of the cases. The conventional method of drug release may cause damage to the normal cells present near the abnormal cells due to improper dosage of drug. In order to reduce the impact of drug in normal cells, the flow rate of the drug has to be controlled and the fascination rate of the drug by abnormal cells should be made maximum by targeted drug delivery. The proposed work is to convert the biological system comprising three layers like dermis, subcutaneous tissues, and bones and muscular layers into an equivalent electrical system. The mathematical model for the biological system is determined with its equivalent electrical system, and the tool PSPICE is used to evaluate the fascination and dispersion rate of the drug. In addition to evaluation of fascination and dispersion rate using PSPICE, the fascination rate of drug is measured individually for the three layers as well as for the combination of first two layers (dermis and subcutaneous layers) and for all the three layers using MATLAB. The comparison of the fascination and dispersion rates is done for all the three layers and the same has been analyzed by incorporating a conventional proportional-integral-derivative controller to minimize the dispersion rate.

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Section: Literature Surveymentioning

confidence: 99%

RETRACTED: Restricted release of skin cancer medicine based on fascination and dispersion rates using proportional–integral–derivative controller

Jagadeesan¹,

Dhanasekar²,

2019

Measurement and Control

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“…It is evident that absolute error of the enhanced algorithm (21) is lower as the exponential is to the power of À4 when compared to power of À2 for the single approximations (19). In contrast to initial works, 6,7 where Euler transformation was applied, here, the method has been further improved by incorporating the qd algorithm of Rutishauser to accelerate the convergence of the in¯nite series in (20) and providing a higher stability to the proposed NILT method, see Ref.…”

Section: Analysis and Simulation Resultsmentioning

confidence: 99%

“…11 The form and properties of fractional-order derivatives as mathematical description can be found in the monographs by Podlubny, 12 Herrman 13 and Meerschaert and Sikorskii, 14 while the theoretical models and experimental applications are available and published. 15 Some applications are in¯elds that include bioengineering, [16][17][18][19] lters, 20 control theory, 21 signal processing, 22 oscillators, [23][24][25][26][27][28][29] transmission lines (TLs) [30][31][32][33] and potentially many others.…”

Section: Introductionmentioning

confidence: 99%

Application of Numerical Inverse Laplace Transform Methods for Simulation of Distributed Systems with Fractional-Order Elements

R‐Smith

Kartci

Brančík

2018

J CIRCUIT SYST COMP

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The paper presents a computationally e±cient method for modeling and simulating distributed systems with lossy transmission line (TL) including multiconductor ones, by a less conventional method. The method is devised based on 1D and 2D Laplace transforms, which facilitates the possibility of incorporating fractional-order elements and frequency-dependent parameters. This process is made possible due to the development of e®ective numerical inverse Laplace transforms (NILTs) of one and two variables, 1D NILT and 2D NILT. In the paper, it is shown that in high frequency operating systems, the frequency dependencies of the system ought to be included in the model. Additionally, it is shown that incorporating fractional-order elements in the modeling of the distributed parameter systems compensates for losses along the wires, provides higher degrees of°exibility for optimization and produces more accurate and authentic modelling of such systems. The simulations are performed in the Matlab environment and are e®ectively algorithmized.

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“…In the last decade, using fractional operators which explain the events, situations or modes between two different stages or the phenomena with memory provide more accurate models in many branches of science and engineering including chemistry, biology, biomedical devices, nanotechnology, diffusion, diffraction, and economics [12][13][14][15][16][17][18][19][20][21]. In [22,23], the modeling and comparison of the countries in the sense of economics and its parameters are implemented.…”

Section: Introductionmentioning

confidence: 99%

Deep Assessment Methodology Using Fractional Calculus on Mathematical Modeling and Prediction of Gross Domestic Product per Capita of Countries

Karaçuha¹,

Tabatadze²,

Karaçuha³

et al. 2020

Preprint

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In this study, by using Least Square Method, the dataset for the Gross Domestic Product per capita is modeled as a function satisfying the fractional differential equation. The function itself is assumed to be the finite summation of its previous values and the derivatives with unknown coefficients. Then, the prediction for the upcoming years is done by having an approach dividing the dataset into 4 regions corresponding to four different tasks. The mathematical model of the Gross Domestic Product (GDP) per capita of the countries (and union) which are Brazil, China, European Union (EU), India, Italy, Japan, UK, the USA, Spain, and Turkey is constructed with a new methodology called as the deep assessment method which comes from the expressing an arbitrary function modeling the dataset as the finite summation of its previous values and the derivatives with unknown coefficient. The method uses the fractional calculus properties combining with Least Square Method and is compared to Long short-term memory (LSTM) algorithm which is a special type of neural network used for time sequences in general.

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

Cited by 60 publications

References 29 publications

RETRACTED: Restricted release of skin cancer medicine based on fascination and dispersion rates using proportional–integral–derivative controller

RETRACTED: Restricted release of skin cancer medicine based on fascination and dispersion rates using proportional–integral–derivative controller

Application of Numerical Inverse Laplace Transform Methods for Simulation of Distributed Systems with Fractional-Order Elements

Deep Assessment Methodology Using Fractional Calculus on Mathematical Modeling and Prediction of Gross Domestic Product per Capita of Countries

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