Frequency response method in pharmacokinetics

Abstract

The paper presents the demonstration of applicability of the frequency response method in a bioavailability study. The frequency response method, common in system engineering, is based on an approximation of the frequency response of a linear dynamic system, calculated from input-output measurements, by a frequency model of the system transfer function in the frequency domain. In general, the influence of the system structure on the form of the system frequency response is much more distinct than on the form of the system output. This is of great advantage in modeling the system frequency response instead of the system output, commonly used in pharmacokinetics. After a brief theoretical section, the method is demonstrated on the estimation of the rate and extent of gentamicin bioavailability after intratracheal administration to guinea pigs. The optimal frequency model of the system describing the gentamicin pathway into the systemic circulation and point estimates of its parameters were selected by the approximation of the system frequency response in the frequency domain, using a noniterative algorithm. Two similar estimates of the system weighing function were independently obtained: the weighting function of the selected frequency model and the weighting function estimated by the numerical deconvolution procedure. Neither of the estimates of the weighting function does decrease monotonously after the maximum of about 2.2-2.5 unit of dose hr-1 recorded approximately 0.1 hr after drug administration. Both estimates show a marked additional peak approximately at 0.3 hr after administration and possible peaks in the further time period. We hypothesized that the loop found in the frequency response calculated and in the selected optimal frequency model, the high-order of this model, and several peaks identified in the estimates of the system weighting function indicated the complexity of the system and the presence of time delays. Three estimates of the extent of gentamicin intratracheal bioavailability obtained by the three different ways: directly from the calculated frequency response, calculated using the selected frequency model, and by the deconvolution method were 0.950, 0.934, and 0.907 respectively. Thus the conclusion can be made that gentamicin injected intratracheally to guinea pigs is almost completely available.

Untitled

“…selected with the AIC, modified for the use in the complex domain, [7,25] is described by the following equation:…”

“…In the first step, a pharmacokinetic dynamic system, denoted by H was defined in the complex domain, using the Laplace transform of the mathematically described mean serum concentration-time profile of acetaminophen of adult male Sprague-Dawley rats, denoted by (S) C and the Laplace transform of the mathematically described intramuscular administration of acetaminophen to adult male Sprague-Dawley rats, denoted by I(S) [6][7][8][9][10][11][12][13][14][15][16][17].…”

“…Throughout the current study the lower case letter " S " denotes the complex Laplace variable [7][8][9][10][11][12][13][14][15][16]. See the following equation:…”

“…In the fifth step, a mathematical model of the dynamic system H was developed using the computer program named CTDB [11] and the transfer function model In the sixth step, the transfer function H(S) was converted into equivalent frequency response function, denoted by ( ) j F iω [21,22]. In the seventh step, the non-iterative method described in the study published previously [22] was used to develop a mathematical model of the frequency response function was refined using the Monte-Carlo and the Gauss-Newton method in the time domain [23,24]; 2) the AIC, modified for the use in the complex domain, [7,25] …”

“…The current study is a companion piece of the study by Belander et al [1]. Therefore the data available in the study [1] was used with the objective to provide a further example showing a successful use of an advanced mathematical modeling method based on the theory of dynamic systems in mathematical modeling in pharmacokinetics [6][7][8][9][10][11][12][13][14][15][16]. Previous examples showing an advantageous use of the modeling method used in the current study can be found in the full-text journal articles available online, which can be downloaded completely, free of charge, from the following web sites of the author: http:// www.uef.sav.sk/durisova.htm and http://www.uef.sav.sk/ advanced.htm…”