A multiscale mechanism of drug release from polymeric matrices: confirmation through a nonlinear theoretical model

In this paper, we propose a new approach for the dynamics of drug delivery systems, assimilated to complex systems, an approach based on concepts like fractality, non-differentiability, and multiscale evolution. The main advantage of using these concepts is the possibility of eliminating the approximations used in the standard approach by replacing complexity with fractality, that imposes, in mathematical terms, the mandatory use of the non-differential character of defined physical quantities. The theoretical model presented, validated for other physical systems, demonstrates its functionality also for drug delivery systems, highlighting, in addition, new insights into the complexity of this system. The spatio-temporal scales of system evolution are characterized through the fractality degree, as a measure of the complexity of the phenomena occurring at each scale. Numerical analysis of the experiment showed that the overall drug release kinetics can be obtained by composing "smaller release kinetics" occurring at scales appropriate for each phase of the drug release mechanism, phases whose expansion depends on the system density. Moreover, the uncertainties in establishing the exact limits of the phases were removed by applying the principle of scale superposition, resulting in a global fractality degree corresponding to the entire release kinetics. Even if the theoretical model is perfectible by identifying constants specific to each delivery system, this paper is intended to be the beginning of an alternative approach to drug delivery mechanisms. The overall release kinetics are obtained by composing "smaller kinetics" at scales appropriate for each phase of the release mechanism.