Numerical Solution of Fuzzy Fractional Pharmacokinetics Model Arising from Drug Assimilation into the Bloodstream

Ahmadian, Ali; Senu, Norazak; Larki, Farhad; Salahshour, Soheil; Suleiman, Mohamed; Islam, Md. Shabiul

doi:10.1155/2013/304739

Cited by 15 publications

(6 citation statements)

References 73 publications

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“…Fuzzy logic approaches appear promising in preclinical applications and might be useful in drug discovery and design. In this regards, Ahmadian et al [20] developed a tau method based on the Jacobi operational matrix to numerically solve the pharmacokinetics-pharmacodynamic equation, arising from drug assimilation into the bloodstream. The comparison of the results shows that the present method is a powerful mathematical tool for finding the numerical solutions of a generalized linear fuzzy fractional pharmacokinetics-pharmacodynamic equation.…”

Section: Introductionmentioning

confidence: 99%

A survey on fuzzy fractional differential and optimal control nonlocal evolution equations

Agarwal

Băleanu

Nieto

et al. 2018

Journal of Computational and Applied Mathematics

148

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We survey some representative results on fuzzy fractional differential equations, controllability, approximate controllability, optimal control, and optimal feedback control for several different kinds of fractional evolution equations. Optimality and relaxation of multiple control problems, described by nonlinear fractional differential equations with nonlocal control conditions in Banach spaces, are considered.

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Section: Introductionmentioning

confidence: 99%

A survey on fuzzy fractional differential and optimal control nonlocal evolution equations

Agarwal

Băleanu

Nieto

et al. 2018

Journal of Computational and Applied Mathematics

148

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“…Pharmacokinetics is a process involving the absorption, distribution, bioavailability, metabolism, and elimination of a drug through the body's biological systems. Bioavailability is the fraction of a drug absorbed into the systemic circulation, the volume of distribution and refers to measures of the apparent space in the body available to contain the drug, while clearance indicates the body's ability to eliminate the drug [1].…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, the fractional order system can be adjusted to fit real data by selecting a suitable value of non-integer order to better predict the reaction of the drugs. Thus, some researchers are interested to study the simulations of the fractional pharmacokinetics model [1,[11][12][13][14]. Some studies concentrate on providing the solutions to the fractional pharmacokinetics model dealing with the Mittag-Leffler, Riemann-Liouville, and Caputo fractional derivatives [15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulations of One-Directional Fractional Pharmacokinetics燤odel

Noor¹,

Yatim²,

Ruhaiyem³

2022

Computers, Materials &Amp; Continua

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In this paper, we present a three-compartment of pharmacokinetics model with irreversible rate constants. The compartment consists of arterial blood, tissues and venous blood. Fick's principle and the law of mass action were used to develop the model based on the diffusion process. The model is modified into a fractional pharmacokinetics model with the sense of Caputo derivative. The existence and uniqueness of the model are investigated and the positivity of the model is established. The behaviour of the model is investigated by implementing numerical algorithms for the numerical solution of the system of fractional differential equations. MATLAB software is used to plot the graphs for illustrating the variation of drug concentration concerning time. Therefore, the numerical simulations of the model are presented for different values of α which verified the theoretical analysis. Besides, we also observed the pattern of the simulations at the three-compartment of the model by using different values of initial conditions.

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“…The two‐compartmental fractional model with a commensurate order was investigated in Petráš and Magin 16 and Copot et al 17 and solved numerically by using the Grünwald–Letnikov (GL) approximation. Ahmadian et al 18 proposed a Jacobi tau method to simulate the concentration of drug in blood for the fuzzy fractional pharmacokinetics. And then in order to solve the fuzzy fractional differential equation arising in the drug delivery model, Ahmadian et al 19 also gave a numerical method based on Legendre operational matrix.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of a two‐compartmental fractional model in pharmacokinetics and parameters estimation

Qiao

2021

Math Methods in App Sciences

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Compartmental model is the classic and widely used approach in pharmacokinetics. Recently, fractional calculus is introduced to describe the time course of drugs in human body which follow the anomalous diffusion mechanism. To consider the different fractional order transmission process, the two‐compartmental fractional model has been proposed and studied. And it will be of great significance to find out a simple and efficient numerical method to solve the model and estimate model parameters. This work investigates two numerical methods of the two‐compartmental fractional model using finite difference schemes, which are based on the shifted Grünwald–Letnikov approximate formula and L1 formula, respectively. The hybrid Nelder–Mead simplex search and particle swarm optimization, denoted as NMSS–PSO, is provided to estimate the fractional model parameters. Comparison between the numerical solution and the solution by the numerical inverse Laplace transform method establishes the validity of the developed numerical algorithms. Then the influence of the order of fractional derivative on the drug amount in human body is also discussed. Finally, the two‐compartmental fractional model is applied to fit the amiodarone pharmacokinetics data based on the NMSS–PSO algorithms. This work will be of importance for the development of fractional pharmacokinetics.

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Numerical Solution of Fuzzy Fractional Pharmacokinetics Model Arising from Drug Assimilation into the Bloodstream

Cited by 15 publications

References 73 publications

A survey on fuzzy fractional differential and optimal control nonlocal evolution equations

A survey on fuzzy fractional differential and optimal control nonlocal evolution equations

Numerical Simulations of One-Directional Fractional Pharmacokinetics燤odel

Numerical simulation of a two‐compartmental fractional model in pharmacokinetics and parameters estimation

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