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Dissolution research started to develop about 100 years ago as a field of physical chemistry and since then important progress has been made. However, explicit interest in drug related dissolution has grown only since the realisation that dissolution is an important factor of drug bioavailability in the 1950s. This review attempts to account the most important developments in the field, from a historical point of view. It is structured in a chronological order, from the theoretical foundations of dissolution, developed in the first half of the 20th century, and the development of a relationship between dissolution and bioavailability in the 1950s, going to the more recent developments in the framework of the Biopharmaceutics Classification System (BCS). Research on relevant fields of pharmaceutical technology, like sustained release formulations, where drug dissolution plays an important role, is reviewed. The review concludes with the modern trends on drug dissolution research and their regulatory implications.

The QBCS provides a basis for compound classification into four explicitly defined drug categories using the fundamental biopharmaceutical properties, permeability, and dose/solubility ratio. Semiquantitative predictions for the extent of absorption are essentially based on these drug properties, which either determine or are strongly related to the in vivo kinetics of drug dissolution and intestinal wall permeation.

We explore the use of fractional order differential equations for the analysis of datasets of various drug processes that present anomalous kinetics, i.e. kinetics that are non-exponential and are typically described by power-laws. A fractional differential equation corresponds to a differential equation with a derivative of fractional order. The fractional equivalents of the "zero-" and "first-order" processes are derived. The fractional zero-order process is a power-law while the fractional first-order process is a Mittag-Leffler function. The latter behaves as a stretched exponential for early times and as a power-law for later times. Applications of these two basic results for drug dissolution/release and drug disposition are presented. The fractional model of dissolution is fitted successfully to datasets taken from literature of in vivo dissolution curves. Also, the proposed pharmacokinetic model is fitted to a dataset which exhibits power-law terminal phase. The Mittag-Leffler function describes well the data for small and large time scales and presents an advantage over empirical power-laws which go to infinity as time approaches zero. The proposed approach is compared conceptually with fractal kinetics, an alternative approach to describe datasets with non exponential kinetics. Fractional kinetics offers an elegant description of anomalous kinetics, with a valid scientific basis, since it has already been applied in problems of diffusion in other fields, and describes well the data.

We have re-examined the random release of particles from fractal polymer matrices using Monte Carlo simulations, a problem originally studied by Bunde et al. [J. Chem. Phys. 83, 5909 (1985)]. A certain population of particles diffuses on a fractal structure, and as particles reach the boundaries of the structure they are removed from the system. We find that the number of particles that escape from the matrix as a function of time can be approximated by a Weibull (stretched exponential) function, similar to the case of release from Euclidean matrices. The earlier result that fractal release rates are described by power laws is correct only at the initial stage of the release, but it has to be modified if one is to describe in one picture the entire process for a finite system. These results pertain to the release of drugs, chemicals, agrochemicals, etc., from delivery systems.

Drug release from a matrix, as a result of a diffusion process assuming excluded volume interactions between the drug molecules, can be described using a Weibull function. This model, although approximate and semiempirical, has the benefit of providing a simple physical connection between the model parameters and the system geometry, which was something missing from other semiempirical models.

Fractional calculus, the branch of calculus dealing with derivatives of non-integer order (e.g., the half-derivative) allows the formulation of fractional differential equations (FDEs), which have recently been applied to pharmacokinetics (PK) for one-compartment models. In this work we extend that theory to multi-compartmental models. Unlike systems defined by a single ordinary differential equation (ODE), considering fractional multi-compartmental models is not as simple as changing the order of the ordinary derivatives of the left-hand side of the ODEs to fractional orders. The latter may produce inconsistent systems which violate mass balance. We present a rationale for fractionalization of ODEs, which produces consistent systems and allows processes of different fractional orders in the same system. We also apply a method of solving such systems based on a numerical inverse Laplace transform algorithm, which we demonstrate that is consistent with analytical solutions when these are available. As examples of our approach, we consider two cases of a basic two-compartment PK model with a single IV dose and multiple oral dosing, where the transfer from the peripheral to the central compartment is of fractional order α < 1, accounting for anomalous kinetics and deep tissue trapping, while all other processes are of the usual order 1. Simulations with the studied systems are performed using the numerical inverse Laplace transform method. It is shown that the presence of a transfer rate of fractional order produces a non-exponential terminal phase, while multiple dose and constant infusion systems never reach steady state and drug accumulation carries on indefinitely. The IV fractional system is also fitted to PK data and parameter values are estimated. In conclusion, our approach allows the formulation of systems of FDEs, mixing different fractional orders, in a consistent manner and also provides a method for the numerical solution of these systems.

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