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

Abstract

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.

Reducing the Risk in Controlled Drug Release by Using Tannic Acid in Liposomal Formulations

“…It is worth mentioning that even the phenomena that occur simultaneously are numerous, the release kinetics reveals a smooth evolution towars a stable state; we can affirm that the system (drug delivery polymeric matrix in the release environment) is a complex system which behaves like a self-organized structure, in which the release paths find their own equilibrium [20][21][22][23][24][25][26].…”

Possible Dynamics of Polymer Chains by Means of a Ricatti s Procedure - an Exploitation for Drug Release at Large Time Intervals

“…Through such a procedure, the probability distribution (for example (14)) for the polymer amplitudes of a free harmonic oscillator can be found (equivalent procedures can be found in [3] and also, in its references). Moreover, new methodologies can be intuited, such as the fractal one [12][13][14][15][16] in order to analyze the polymer chains dynamics [17][18].…”

Bupivacaine‐loaded chitosan hydrogels for topical anesthesia in dentistry

“…where M t represents the amount of drug released at time t, M ∞ the amount of drug released as time approaches infinity that can be approximated as the drug amount loaded, cn is Jacobi's elliptic function of s modulus, which is the rate of evolution towards an unstable and disordered state, s is the initial system nonlinearity and K(s) and E(s) are the complete elliptic integrals. [29][30][31] In vitro cytotoxicity assays on human dermal fibroblasts In vitro cytotoxic effects of bupivacaine-loaded hydrogels were assessed using the HDFa cell line. HDFa cells were cultured in Dulbecco's modified Eagle medium, supplemented with 10% fetal bovine serum, an antibiotic cocktail consisting of 1% (v/v) penicillin-streptomycin and 1% (v/v) non-essentials amino acids.…”