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 ...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.展开更多
This study is about an analytical attempt that explores the two-dimensional concentration distribution of a solute in an open channel flow.The solute undergoes reversible sorption at the channel bed.The method of mult...This study is about an analytical attempt that explores the two-dimensional concentration distribution of a solute in an open channel flow.The solute undergoes reversible sorption at the channel bed.The method of multiple scales is used to find the two-dimensional concentration distribution,which is important for modem day application in industry,environmental risk assessment,etc.Study deduces an analytic expression of two-dimensional concentration distribution for an open channel flow with sorptive channel bed.Effects of retention parameter,Darnkohler number on the solute dispersion are also discussed in this paper.Results reveal that slow or strong kinetics(small value of Darnkohler number)increases solute dispersion.It is also observed.that for slow phase exchange kinetics between bulk flow and small retentive channel bed,solute concentration distribution will uniform faster than their inert counterpart.展开更多
文摘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.
文摘This study is about an analytical attempt that explores the two-dimensional concentration distribution of a solute in an open channel flow.The solute undergoes reversible sorption at the channel bed.The method of multiple scales is used to find the two-dimensional concentration distribution,which is important for modem day application in industry,environmental risk assessment,etc.Study deduces an analytic expression of two-dimensional concentration distribution for an open channel flow with sorptive channel bed.Effects of retention parameter,Darnkohler number on the solute dispersion are also discussed in this paper.Results reveal that slow or strong kinetics(small value of Darnkohler number)increases solute dispersion.It is also observed.that for slow phase exchange kinetics between bulk flow and small retentive channel bed,solute concentration distribution will uniform faster than their inert counterpart.
