Mathematical Models of the Pharmacokinetic Behavior of Digoxin in Five Healthy Subjects following Rapid Intravenous Injection of 1 mg of Digoxin

Abstract

Keywords: Digoxin; Intravenous injection; Mathematical model IntroductionDigoxin is widely used in clinical practice for treatment of congestive heart failure (CHF) and atrial fibrillation (AF) or an acute coronary syndrome (ACS) [1][2][3][4]. Pharmacokinetics of digoxin was investigated in the previous study by Kramer et al. in five healthy male volunteers after a rapid intravenous injection of 1.0 mg of digoxin [1]. The current study is a companion piece of the previous study by Kramer et al. [1], therefore the data published in the previous study by Kramer et al. [1] are used, with the main objective to provide a further example which shows a successful use of an advanced mathematical modeling method based on the theory of dynamic systems in mathematical modeling in pharmacokinetics [5][6][7][8][9][10][11][12][13][14][15][16]. An additional objective was to motivate researchers working in the field of pharmacokinetics to use of an alternative modeling method, namely a modeling method based on the theory of dynamic systems in the development pharmacokinetic models. Previous examples presenting an advantageous use of the modeling method used in the current study can be found in the articles available online, which can be downloaded free of cost from the following web pages of the author: http://www.uef.sav.sk/durisova.htm and http://www.uef.sav.sk/advanced.htm. The current study continued to inform pharmacokinetic community about benefits linked to the use of computational tools from the theory of dynamic systems in mathematical modeling in pharmacokinetics. MethodsAs stated previously, an advanced mathematical modeling method based on the theory of dynamic systems was employed to develop mathematical models of the pharmacokinetic behavior of digoxin in the volunteers investigated in the previous study by Kramer et al. [1], and in the current study. The development of a mathematical model of the pharmacokinetic behavior of digoxin in each volunteer was performed in the following steps:In the first step of the model development process, a pharmacokinetic dynamic system, here denoted as H, was defined for the volunteer by relating the Laplace transform of volunteer's plasma concentration time profile of digoxin, here denoted as C(S), and the Laplace transform of the intravenous injection (input) of 1.0 mg of digoxin into the body of the volunteer, here denoted as I(S).The following simplifying assumptions were introduced prior the model development process: a) initial conditions of each pharmacokinetic dynamic system H were zero; b) pharmacokinetic processes occurring in the body after the intravenous injection of digoxin were linear and time-invariant; c) concentrations of digoxin were the same throughout all subsystems of the pharmacokinetic dynamic system H (where each subsystem was an integral part of the pharmacokinetic dynamic system H); d) no barriers to the distribution and/or elimination of digoxin existed.In the second step of the model development process, the pharmacokinetic dynamic system H, was used...

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“…Reference [7] conducted research on Mathematical Models of Digoxin Pharmacokinetic Behavior in Five Healthy Subjects Following Rapid Intravenous Injection of 1 mg of Digoxin. They came up with models that successfully described the pharmacokinetic behavior of digoxin after its intravenous injection into healthy male adult volunteers, thus motivating researchers working in the field of pharmacokinetics to use a mathematical modeling method based on the theory of dynamic systems in their research work.…”