In recent years, several new methods for the mathematical modeling have gradually emerged in pharmacokinetics, and the development of pharmacokinetic models based on these methods has become one of the most rapidly growing and exciting application-oriented sub-disciplines of the mathematical modeling. The goals of our MiniReview are twofold: i) to briefly outline fundamental ideas of some new modeling methods that have not been widely utilized in pharmacokinetics as yet, i.e. the methods based on the following concepts: linear time-invariant dynamic system, artificialneural-network, fuzzy-logic, and fractal; ii) to arouse the interest of pharmacological, toxicological, and pharmaceutical scientists in the given methods, by sketching some application examples which indicate the good performance and perspective of these methods in solving pharmacokinetic problems.It often occurs in science that tools, knowledge, or techniques developed in one field enable advances in other fields. This applies also to methods for building mathematical models, i.e. tools that have been developed predominantly in the field of mathematics, computer science, and system engineering. In contrast to animal or disease models commonly used in pharmacology, mathematical models are mathematical structures which, on abstracting from reality, allow formulations in mathematical terms of essential assumptions believed to underlie particular actual-world problems. The mathematical modeling relies on: i) the sound understanding and appreciation of the problem under study; ii) the realistic mathematical representation of the important phenomena; iii) the finding of useful solutions; iv) the interpretation of the mathematical results, the model-based prediction or simulation, and so on. All that is required for the practical use of mathematical models is to understand these models properly and then to apply them to study phenomena of the interest in various fields of science, including pharmacokinetics. In the latter field, mathematical models have historically played a vital role, and methods for the development models such as deterministic linear compartment models, physiologically-based models, and population models have become quite common. Along with this, other modeling methods have gradually emerged in pharmacokinetics over recent years, and the Author for correspondence: Mária Ď urišová, Institute of Experimental Pharmacology, Slovak Academy of Sciences, Dubravska cesta 9, SK-841 04 Bratislava 4, Slovak Republic (fax π42 12 5477 5928, e-mail maria.durisova/savba.sk).development of pharmacokinetic models has become one of the most rapidly growing and exciting applicationoriented sub-disciplines of the mathematical modeling.The goals of this MiniReview are twofold: i) to briefly outline fundamental ideas of some mathematical methods that have not been widely utilized in pharmacokinetics so far, i.e. the methods based on the following concepts: linear time-invariant dynamic system, artificial-neural-network, fuzzy-logic, and fractal; ...

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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.

In this retrospective study 351 children (<16.0 years) with end-stage renal disease (ESRD) accepted for renal replacement therapy (RRT) in the four Dutch pediatric centers were analyzed for the period 1987-2001. The data were compared with a previous study performed in 1979-1986. Eighty patients were of non-Dutch origin. An annual ESRD incidence of 5.8 patients per million of the child population (p.m.c.p.) was calculated, without significant changes with time. The final prevalence in Dutch children under 15 years of ESRD was 38.7 p.m.c.p. The most frequent primary renal disease leading to ESRD was urethral valves, with a significant increase vs. the previous observation period (14% vs. 6%). The distribution of primary renal diseases was similar in patients of non-Dutch origin and in Dutch patients. Peritoneal dialysis was the most frequent dialysis procedure initially applied (62% vs. 26% in the earlier observation period). Thirteen percent of all first transplantations (n=278) were pre-emptive and 19% from living donors. Five-year graft survival after a living-donor and a cadaver graft was 80% and 73%, respectively. Overall patient survival after 10 years on RRT was 94%.

OEs represent a promising new additive therapy in multiple myeloma which will be further evaluated in a randomized phase III trial in the USA.