A two-phase model for drug release from microparticles with combined effects of solubilisation and recrystallisation

Model-Informed Drug Development: In Silico Assessment of Drug Bioperformance following Oral and Percutaneous Administration

The pharmaceutical industry has faced significant changes in recent years, primarily influenced by regulatory standards, market competition, and the need to accelerate drug development. Model-informed drug development (MIDD) leverages quantitative computational models to facilitate decision-making processes. This approach sheds light on the complex interplay between the influence of a drug's performance and the resulting clinical outcomes. This comprehensive review aims to explain the mechanisms that control the dissolution and/or release of drugs and their subsequent permeation through biological membranes. Furthermore, the importance of simulating these processes through a variety of in silico models is emphasized. Advanced compartmental absorption models provide an analytical framework to understand the kinetics of transit, dissolution, and absorption associated with orally administered drugs. In contrast, for topical and transdermal drug delivery systems, the prediction of drug permeation is predominantly based on quantitative structure-permeation relationships and molecular dynamics simulations. This review describes a variety of modeling strategies, ranging from mechanistic to empirical equations, and highlights the growing importance of state-of-the-art tools such as artificial intelligence, as well as advanced imaging and spectroscopic techniques.

Stability analysis of drug dynamics model: A mathematical approach

In this paper, a mathematical model of drug release from polymeric matrix and consequent intracellular drug transport is proposed and analyzed. Modeling of drug release is done through solubilization dynamics of drug particles, diffusion of the solubilized drug through the polymeric matrix in addition to reversible dissociation/recrystallization process. The interaction between drug-receptor, drug-plasma proteins along with other intracellular endosomal events is modeled. This leads to a mixed system of partial and ordinary differential equations with associated pertinent set of initial and boundary conditions. Furthermore, besides the stability of the proposed model, several sub-models are also studied for their stability criteria. Prominence is provided to the reduced model system having requisite relevance to the original system where quasi steady state approximation (QSSA) theory is utilized. For the model to be potent enough to generate appropriate predictive results for drug delivery, the stability properties of equilibrium in the mathematical model are analyzed both analytically and numerically. Numerical simulation in the embodiment of graphical representations speaks about various vital characteristics of the underlying physical phenomena along with the importance and sensitized impact of the model parameters controlling significant biological functions. Probed new therapies and clinical procedures could be assessed considering the present mathematical model and its analysis as the basis framework in order to effectively enhance therapeutic efficacy and improved patient compliance. The present study confirms the necessity of stability analysis study so that advocated mathematical model can effectively complement the real physiological behavior of pharmacokinetics.

Mathematical modelling of liposomal drug release to tumour

The primary aim of liposomal drug delivery is to wisely modulate the drug delivery system in order to target diseased tissues. Temperature-sensitive liposomes function as a prospective weapon to combat toxic side effects corresponding to direct infusion of anticancer drugs. The main objective of the present study is to model liposomal drug release, subsequent drug transport in solid tumour along with integrated actions of tumour cell surface and endosomal events. Generalized mathematical model for liposomal drug delivery is proposed in which vital physical phenomena, such as kinetics of liposome-encapsulated drug, free drug release from liposomes, transport of both liposomal drug and free drug into the tumour compartment, plasma clearance, protein-drug interactions, drug-tumour cell receptor interactions, internalization of drug through endocytosis along with corresponding endosomal events. The model is expressed through a system of coupled partial differential equations along with appropriate set of initial, interface and boundary conditions which is solved numerically. Simulated results are compared with respective existing experimental data to demonstrate the potency and reliability of the proposed model. Graphical representations of time variant concentration profiles are illustrated to understand the underlying phenomena in details. Moreover, the model speaks for the sensitivity of important drug kinetic parameters, such as advection coefficients, drug release coefficient, plasma clearance rate and internalization parameters through graphical portrayals. The proposed model and the simulated results act as a tool in designing a more effective drug delivery system for cancerous tumours.

A Nonlinear Mathematical Model of Drug Delivery from Polymeric Matrix

The objective of the present study is to mathematically model the integrated kinetics of drug release in a polymeric matrix and its ensuing drug transport to the encompassing biological tissue. The model embodies drug diffusion, dissolution, solubilization, polymer degradation and dissociation/recrystallization phenomena in the polymeric matrix accompanied by diffusion, advection, reaction, internalization and specific/nonspecific binding in the biological tissue. The model is formulated through a system of nonlinear partial differential equations which are solved numerically in association with pertinent set of initial, interface and boundary conditions using suitable finite difference scheme. After spatial discretization, the system of nonlinear partial differential equations is reduced to a system of nonlinear ordinary differential equations which is subsequently solved by the fourth-order Runge-Kutta method. The model simulations deal with the comparison between a drug delivery from a biodegradable polymeric matrix and that from a biodurable polymeric matrix. Furthermore, simulated results are compared with corresponding existing experimental data to manifest the efficaciousness of the advocated model. A quantitative analysis is performed through numerical computation relied on model parameter values. The numerical results obtained reveal an estimate of the effects of biodegradable and biodurable polymeric matrices on drug release rates. Furthermore, through graphical representations, the sensitized impact of the model parameters on the drug kinetics is illustrated so as to assess the model parameters of significance.

An analytical study of drug release kinetics from a degradable polymeric matrix

In modern days, biodegradable polymeric matrix used as the kingpin of local drug delivery system is in the center of attention. This work is concentrated on the formulation of mathematical model elucidating degradation of drug-loaded polymeric matrix followed by drug release to the adjacent biological tissues. Polymeric degradation is penciled with mass conservation equations. Drug release phenomenon is modeled by considering solubilization dynamics of drug particles, diffusion of the solubilized drug through polymeric matrix along with reversible dissociation/recrystallization process. In the tissue phase, reversible dissociation/association along with internalization processes of drug are taken into account. For this, a two-phase spatio-temporal model is postulated, which has ensued to a system of partial differential equations. They are solved analytically with appropriate choice of initial, interface and boundary conditions. In order to reflect the potency of the advocated model, the simulated results are analogized with corresponding experimental data and found laudable agreement so as to validate the applicability of the model considered. This model seems to foster the delicacy of the mantle enacted by important drug kinetic parameters such as diffusion coefficients, mass transfer coefficients, particle binding and internalization parameters, which is illustrated through local sensitivity analysis.