Mathematical models for drug diffusion through the compartments of blood and tissue medium

Khanday, M. A.; Rafiq, Aasma; Nazir, Khalid

doi:10.1016/j.ajme.2016.03.005

Cited by 46 publications

(69 citation statements)

References 10 publications

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“…Time delays in pharmacokinetics may be physiological or patho-physiological. In the latter case one may see Stijin et al [11]. In the present we consider physiological/harmless delays in drug distribution.…”

Section: Optimal Controlmentioning

confidence: 90%

A Model of Oral and Parenteral Drug Administration with Control

Nzerem¹,

H.C²

2018

(GLM)

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Drug administration is largely a frontier in pharmacokinetics and pharmacodynamics. Kinetics and dynamics are of science in general, and therefore issues on drug administration may be of interdisciplinary interest. This paper treated pharmacokinetics from the standpoints of a subject-specific drug administration and control. A compartment-based mathematical model of drug administration was presented. Besides the endearing impacts of drug administration, the optimal control of drug regimen is a sine qua non to the therapeutic benefits derivable from a drug at the physiologic site(s). This argument motivated the control method applied hereto. The variable of interest for control is the time-dependent drug concentration in the bloodstream. It was considered essential since the concentration of a drug in the body within a finite time horizon is partly a measure of therapeutic response. To this end, the optimal controller discussed here must be, and indeed is, the one that could furnish the concentration that is both therapy-effectual and time-minimizing. It is only when these two conditions are met that a drug regimen may be seen to have achieved the desired goal.

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Section: Optimal Controlmentioning

confidence: 90%

A Model of Oral and Parenteral Drug Administration with Control

Nzerem¹,

H.C²

2018

(GLM)

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“…To facilitate a meaningful contribution to the pharmacokinetics field, numerous mathematical models for drug delivery systems have been developed, which can be found in [17][18][19][20][21][22][23]. In [21], the established model described the mechanisms of how the human body handles nicardipine (NC)-cyclodextrin complexes injection in the gastrointestinal (GI) tract, distribution in plasma, and metabolism in the liver.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, [22] proposed a differential equation model to investigate the dynamic behavior drug resistance incorporating a delay in the process with conditions under which a Hopf bifurcation takes place, which leads to a periodic solution. The models in [23] outline the mechanisms of drug administration in the human body via oral and intravenous routes. To calculate the exact drug concentration in different compartments of blood and tissue medium, the Laplace transformation and eigenvalue method were applied.…”

Section: Introductionmentioning

confidence: 99%

“…To calculate the exact drug concentration in different compartments of blood and tissue medium, the Laplace transformation and eigenvalue method were applied. In this article, we solve the mathematical models of drug diffusion formulated by [20,21,23] numerically. The models were formulated based on the diffusion process by applying Fick's principle and the law of mass action.…”

Section: Introductionmentioning

confidence: 99%

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Stability analysis of a diagonally implicit scheme of block backward differentiation formula for stiff pharmacokinetics models

et al. 2020

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In this paper, we analyze the criteria for the stability of a method suited to the ordinary differential equations models. The relevant proof that the method satisfies the condition of stiff stability is also provided. The aim of this paper is therefore to construct an efficient two-point block method based on backward differentiation formula which is A-stable and converged. The new diagonally implicit scheme is formulated to approximate the solution of the pharmacokinetics models. By implementing the algorithm, the numerical solution to the models is compared with a few existing methods and established stiff solvers. It yields significant advantages when the diagonally implicit method with a lower triangular matrix and identical diagonal elements is considered. The formula is designed in such a way that it permits a maximum of one LU decomposition for each integration stage.

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“…where k is proportionality constant, u i denotes the mass of molecule and V i denotes the volume of the compartment i. We refer the interested reader to recent papers [10] and [20] for recent applications of compartment models. We are also inspired by another mathematical model in biology, a lake pollution model [1],…”

mentioning

confidence: 99%

A novel model for the contamination of a system of three artificial lakes

Hatipoğlu¹

2021

DCDS-S

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In this study, a new model has been developed to monitor the contamination in connected three lakes. The model has been motivated by two biological models, i.e. cell compartment model and lake pollution model. Haar wavelet collocation method has been proposed for the numerical solutions of the model containing a system of three linear differential equations. In addition to the solutions of the system, convergence analysis has been briefly given for the proposed method. The contamination in each lake has been investigated by considering three different pollutant input cases, namely impulse imposed pollutant source, exponentially decaying imposed pollutant source, and periodic imposed pollutant source. Each case has been illustrated with a numerical example and results are compared with the exact ones. Regarding the results in each case it has been seen that, Haar wavelet collocation method is an efficient algorithm to monitor the contamination of a system of lakes problem.

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Mathematical models for drug diffusion through the compartments of blood and tissue medium

Cited by 46 publications

References 10 publications

A Model of Oral and Parenteral Drug Administration with Control

A Model of Oral and Parenteral Drug Administration with Control

Stability analysis of a diagonally implicit scheme of block backward differentiation formula for stiff pharmacokinetics models

A novel model for the contamination of a system of three artificial lakes

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