Robust Control of Repeated Drug Administration with Variable Doses Based on Uncertain Mathematical Model.

The aim of this paper was to design a repeated drug administration strategy to reach and maintain the requested drug concentration in the body. Conservative designs require an exact knowledge of pharmacokinetic parameters, which is considered an unrealistic demand. The problem is usually resolved using the trial-and-error open-loop approach; yet, this can be considered insufficient due to the parametric uncertainties as the dosing strategy may induce an undesired behavior of the drug concentrations. Therefore, the presented approach is rather based on the paradigms of system and control theory. An algorithm was designed that computes the required doses to be administered based on the blood samples. Since repeated drug dosing is essentially a discrete time process, the entire design considers the discrete time domain. We have also presented the idea of applying this methodology for the stabilization of an unstable model, for instance, a model of tumor growth. The simulation experiments demonstrated that all variants of the proposed control algorithm can reach and maintain the desired drug concentration robustly, i.e., despite the presence of parametric uncertainties, in a way that is superior to that of the traditional open-loop approach. It was shown that the closed-loop control with the integral controller and stabilizing state feedback is robust against large parametric uncertainties.

Using a State-Bounding Observer to Predict the Guaranteed Limits of Drug Amounts in Rats after Oral Administration Based on an Uncertain Pharmacokinetic Model.

In the first part of this paper, the problem of using an uncertain pharmacokinetic model is resolved to determine drug concentrations in rats after the oral administration of drug suspensions with and without added tenside. To this end, a generalized pharmacokinetic model determining the guaranteed limits of drug concentrations was designed. Based on this, the design of the so-called state-bounding observer is described in the second part. Rather than being driven by the output of the pharmacokinetic model, the observer can be driven exclusively by a concentration collected from a suitable part of the body and predict the possible risk of the drug concentration not remaining within the therapeutic range for a sufficiently long time. Specifically, the observer determines the upper and lower limits of the concentrations in all the compartments, especially those that are inaccessible for the collection of samples. The proposed approaches are demonstrated by examples.

In-Vivo Analysis and Model-Based Prediction of Tensides' Influence on Drug Absorption.

Depending on their concentrations the surface-active substances, tensides (surfactants) can positively or negatively influence the drug absorption, which is widely used in the design of the dosage forms with controlled release. A problem is that the (in-vivo) rate of absorption cannot be directly measured and for that reason, it is frequently substituted by evaluation of the (in-vitro) dissolution. On other hand, a suitably designed pharmacokinetic model can directly predict virtually all pharmacokinetic quantities including both the rate of absorption and fraction of the dose reaching the blood circulation. The paper presents a new approach to the analysis of the rate of drug absorption and shows its superiority over traditional in-vivo approaches. Both the in-vivo analysis and model-based prediction of the tenside (monolaurin of sucrose) influence on the rate of absorption of the drug (sulfathiazole) after instantaneous per-oral administration to rats are discussed. It was found that 0.001% solution of tenside can increase the rate of absorption by cca 50% and a two-fold increase in absolute bioavailability can be reached. Attention is also devoted to the formal requirements laid on the model's structure and its identifiability. The systematic design, substantiation and validation of a parsimonious predictive model that confirms in-vivo results are presented. The match between in-vivo observations and model-based predictions is demonstrated. The frequently overlooked metaphysics lying behind the compartmental modelling is briefly explained.

Effect of Molecular Composition of Head Group and Temperature on Micellar Properties of Ionic Surfactants with C12 Alkyl Chain.

The paper analyses influences of the temperature and hydrophilic groups on micellar properties of ionic surfactants with 12-carbonic hydrophobic chains. The aim is to assess the impact of hydrophilic groups and temperature on thermodynamic parameters and micellization. This knowledge is indispensable for the formulation of new dosage forms. The method uses conductometric measurements. The following hydrophilic groups are analyzed: trimethylammonium bromide, trimethylammonium chloride, ethyldimethylammonium bromide, didodecyldimethylammonium bromide, pyridinium chloride, benzyldimethyl-ammonium chloride, methylephedrinium bromide, cis and trans-[(2-benzyloxy)-cyclohexyl-methyl]-N, N-dimethylammonium bromide, sodium sulphate and lithium sulphate. Except for a few cases, there is a good agreement between values of critical micellar concentrations (CMC) and critical vesicle concentration (CVC) obtained here and those which were obtained by other authors and/or by other physicochemical methods. Values of the CMC are compared with respect to the molar masses of hydrophilic groups. It was found that CMC values increased non-linearly with increasing system temperature. The degrees of counterion binding and thermodynamic parameters, like the standard molar Gibbs energy, enthalpy and entropy of micellization are determined and discussed in detail. The results obtained will be incorporated into in silico processes of modeling and design of optimal dosage forms, a current interdisciplinary research focus of the team.

Association, Distribution, Liberation, and Rheological Balances of Alkyldimethylbenzylammonium Chlorides (C12-C16).

It is known that cationic surfactants have an antimicrobial effect and act as enhancers. This paper studies three cationic surfactants from the group of alkyldimethylbenzylammonium chlorides (dodecyl-, tetradecyl-, and hexadecyl). Interest is focused on the association of the surfactants with respect to temperature, partition balances and their influence on drug release, rheological properties, and the pH of hydrogels. The critical micelle concentrations (CMC) of the surfactants were estimated from dependencies of conductivity, density, spectrofluorimetry, and UV-VIS spectrophotometry on molarity in the temperature range of 25-50 °C. It was found that the temperature dependence of a CMC is U-shaped, with its minimum at 30 °C, and the CMC value decreases as the length of the chain increases. The pseudo-phase separation model was used for the calculation of various thermodynamic parameters, such as the Gibbs free energies (spontaneous process), enthalpies (exothermic process), and entropies of the micelles' formation, CMCs, and the degree of counterion binding. All thermodynamic parameters, as functions of the temperature, were estimated. It was found that partition coefficients increase as the length of the alkyl chain and the pH = (5.0-7.0) increase. The influences of surfactants, below and above the CMC, on drug (chlorhexidine dihydrochloride) release from hydrogels, rheological properties, and pH at 30 °C were studied. Also, the amounts of the released drug increase as the alkyl chains of the surfactants prolongate. The amounts of the released drug with the surfactant below the CMC are greater than that above the CMC. All hydrogels (regardless of the length of the alkyl chain) exhibit a non-Newtonian pseudo-plastic flow. The results obtained will be used in the formulation of the drug and surfactants into dosage forms.

Alternative and generalized approach to in vitro-in vivo correlation.

Evaluation of in vitro-in vivo correlation (IVIVC) plays important role in securing therapeutic effect if a dosage form undergoes technological modifications. Similarity (closeness) of dissolution profiles of the original and modified dosage forms has been traditionally considered to be sufficient for similar in vivo responses. This may be true if the IVIVC model (dependence between the dissolution and corresponding absorption profiles) is given by a linear straight line with the unit slope. The paper presents an alternative and generalized approach to IVIVC evaluation. Influences of pre-systemic processes (disintegration, dissolution, absorption) on the system response (concentration time profile C(t), bioavailability BD and other) are analyzed and evaluated. Both the magnitude and sign of IVIVC are then derived from the magnitudes and signs of these influences. The underlining idea is that pre-systemic processes do not correlate with the system response, (e.g., plasmatic concentration) if small modifications of the former do not induce significant changes of the later. If this is so, the therapeutic effects of the modified and original dosage forms may be considered equal or at least similar. In this way the problem of IVIVC is not only exactly mathematically founded but modifications of pre-systemic processes are directly projected to the system output-- the time profile of plasmatic concentration. Moreover, the approach is applicable to virtually any dosage form. Its feasibility was validated in vivo.