A Model for Transport and Dispersion in the Circulatory System Based on the Vascular Fractal Tree

Materials are distributed throughout the body of mammals by fractal networks of branching tubes. Based on the scaling laws of the fractal structure, the vascular tree is reduced to an equivalent one-dimensional, tube model. A dispersion–convection partial differential equation with constant coefficients describes the heterogeneous concentration profile of an intravascular tracer in the vascular tree. A simple model for the mammalian circulatory system is built in entirely physiological terms consisting of a ring shaped, one-dimensional tube which corresponds to the arterial, venular, and pulmonary trees, successively. The model incorporates the blood flow heterogeneity of the mammalian circulatory system. Model predictions are fitted to published concentration-time data of indocyanine green injected in humans and dogs. Close agreement was found with parameter values within the expected physiological range. © 2003 Biomedical Engineering Society. PAC2003: 8710+e, 8719Hh, 8719Uv     

Modeling of supersaturated dissolution data.

A recursion equation which relies on the population growth model of dissolution is used for the analysis of supersaturated dissolution data. The concentration-time data of dissolution experiments are initially transformed to fractions of dose dissolved-generations by adopting an appropriate time interval as the time step of the recursion equation. A computer program is used to derive estimates for the maximum fraction of dose dissolved and the fraction of dose remaining in solution at steady state. Good fittings were observed when this equation was applied to phenytoin and nifedipine supersaturated dissolution data obtained from literature. Copyright     

Modelling and simulation in drug absorption processes

Drug absorption is a complex process dependent upon drug properties such as solubility and permeability, formulation factors, and physiological variables including regional permeability differences, pH, luminal and mucosal enzymes, and intestinal motility, among others. Despite this complexity, various qualitative and quantitative approaches have been proposed for the estimation of oral drug absorption. These approaches are reviewed in this article with particular emphasis on drug dissolution modelling, dynamic systems for oral absorption and absorption models based on structure. The regulatory aspects of oral drug absorption and in particular the biopharmaceutic classification of drugs are also discussed. Models for drug dissolution and release describe adequately the in vitro data, and models for oral drug absorption provide reasonable results. The development of in vitro-in vivo correlations based on the official compendia specifications are facilitated using commercial computer packages.     

Analytical Expressions for Combining Population Pharmacokinetic Parameters from Different Studies

We provide a set of formulas that allow the combination of separately performed analyses of population pharmacokinetic (PK) studies, without any further computational effort. More specifically, given the point estimates and uncertainties of two population PK analyses, the formulas provide the point estimates and uncertainties of the combined analysis, including the mean population values, the between-subject variability, and the residual variability. To derive the formulas we considered distributional assumptions applicable for the conjugate priors of the Bayesian problem of “unknown mean and variance.” In order to demonstrate the approach, the formulas were applied to an example involving the results of fitting two real experimental datasets. The formulas presented offer an easy-to-use method of combining different analyses particularly applicable to a combination of literature information.     

Nonlinear Dynamics and Chaos Theory: Concepts and Applications Relevant to Pharmacodynamics

The theory of nonlinear dynamical systems (chaos theory), which deals with deterministic systems that exhibit a complicated, apparently random-looking behavior, has formed an interdisciplinary area of research and has affected almost every field of science in the last 20 years. Life sciences are one of the most applicable areas for the ideas of chaos because of the complexity of biological systems. It is widely appreciated that chaotic behavior dominates physiological systems. This is suggested by experimental studies and has also been encouraged by very successful modeling. Pharmacodynamics are very tightly associated with complex physiological processes, and the implications of this relation demand that the new approach of nonlinear dynamics should be adopted in greater extent in pharmacodynamic studies. This is necessary not only for the sake of more detailed study, but mainly because nonlinear dynamics suggest a whole new rationale, fundamentally different from the classic approach. In this work the basic principles of dynamical systems are presented and applications of nonlinear dynamics in topics relevant to drug research and especially to pharmacodynamics are reviewed. Special attention is focused on three major fields of physiological systems with great importance in pharmacotherapy, namely cardiovascular, central nervous, and endocrine systems, where tools and concepts from nonlinear dynamics have been applied.     

A Population Growth Model of Dissolution

Purpose. To develop a new approach for describing drug dissolution which does not require the presuppositions of time continuity and Fick's law of diffusion and which can be applied to both homogeneous and heterogeneous media. Methods. The mass dissolved is considered to be a function of a discrete time index specifying successive 'generations' (n). The recurrence equation: _n+1 = _n + r(l – _n)(1 – _n X ₀/) was derived for the fractions of dose dissolved _n and _{n +1}, between generations n and n + 1, where r is a dimensionless proportionality constant, X ₀ is the dose and is the amount of drug corresponding to the drug's solubility in the dissolution medium. Results. The equation has two steady state solutions, _ss = 1 when (X ₀/) 1 and _ss = /X ₀ when (X ₀/) > 1 and the usual behavior encountered in dissolution studies, i.e, a monotonic exponential increase of _n reaching asymptotically the steady state when either r < /X ₀ < 1 or r < 1 < /X ₀. Good fits were obtained when the model equation was applied to danazol data after appropriate transformation of the time scale to 'generations'. The dissolution process is controlled by the two dimensionless parameters /X ₀ and r, which were found to be analogous to the fundamental parameters dose anddissolution number, respectively. The model was also used for the prediction of fraction of dose absorbed for highly permeable drugs. Conclusions. The model does not rely on diffusion principles and therefore it can be applied under both homogeneous and non-homogeneous conditions. This feature will facilitate the correlation of in vitro dissolution data obtained under homogeneous conditions and in vivo observations adhering to the heterogeneous milieu of the GI tract.