Authors
de Albuquerque, D. F., de Albuquerque, M. A. S.
Abstract
Recent models describe drug release from polymeric nanoparticles through an analogy with the quantum tunneling effect, treating the delivery system as a static rectangular potential barrier. We argue that this analogy is structurally identical to the standard solution of the Schrodinger equation for a rectangular barrier, and that the introduction of a multifractal formalism to describe time evolution - via a formal mathematical substitution of space for time - lacks direct physical justification.As an alternative, we treat the barrier height as an effective function of time that decays progressively to reflect the degradation or swelling of the polymeric matrix. Two hypotheses for this decay are examined - exponential decay and rational (Hill-type) decay. Rather than the thick-barrier approximation commonly used in such models, we employ the exact transmission formula throughout, which remains mathematically smooth even after the barrier collapses, avoiding artificial step-like transitions. Both decay hypotheses predict a finite barrier collapse time, with qualitatively different behaviors depending on the energy ratio of the drug molecule to the barrier height, offering a distinguishable criterion from experimental release data. The model was tested against ex-vivo chicken-skin permeation kinetics of 5-fluorouracil digitized from a published study, for three distinct systems. The exact formula substantially improved fit quality over the approximate version for all three systems. Fits were obtained by global optimization rather than a simple local search, which proved necessary for this class of models. For two of the three systems, the exponential decay model was well-identified, with all parameter uncertainties below 11% of their estimates and excellent correlation with the data, while the rational (Hill) model remained poorly identified for all three systems - favoring, by parsimony, the simpler exponential model throughout. One system remained non-identified when its energy ratio was left as a free parameter. A sensitivity check fixing this energy ratio at a value derived from a well-identified system resolved this issue at negligible cost in fit quality, consistent with a shared energy ratio for that particular system. However, applying the same constraint to another well-identified system degraded its fit substantially; its own energy ratio differed from the shared value by a statistically significant margin, so a single universal energy ratio is rejected for the complete set of systems studied. Reference values from the original multifractal study and candidate extensions to further drug delivery systems are also discussed. We discuss the implications of this treatment and its limits of validity, and point out paths for further empirical validation.
Preprint server:
bioRxiv
The authors list and abstract were imported from bioRxiv on 06 Aug 2026.
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