Mathematical Model Construction And Computer Simulation Of Transdermal Absorption

Transdermal drug delivery which drugs are absorbed through the skin into the blood circulation to play a therapeutic role.As a new type of drug delivery,this kind of drug delivery method has the advantages of good adaptability to patients,no first pass effect,and long-term stability of blood drug concentration,so it has attracted more and more attention.To master the process of percutaneous absorption and the influence of various factors is helpful to optimize the effective and safe skin drug delivery system.In this paper,I constructed a mathematical model to describe the percutaneous absorption process of drugs reasonably,it can quantify the process of percutaneous drug delivery in detail.Based on the Fick mass transfer and diffusion model,and considering the process of drug binding and metabolism in the skin,the mathematical process of drug mass transfer in the skin is solved by various methods.The computer is used as an auxiliary tool to simulate the process of drug skin delivery,and the reasonable simulation results of drug transdermal absorption process are obtained.This can not only evaluate the transdermal / transmucosal drug delivery,optimize the formulation and process,predict the percutaneous absorption of drugs,but also evaluate the bioequivalence risk of generic drugs.Firstly,the law of transdermal absorption process is summarized and abstracted into a model of mass transfer and diffusion,and the diffusion process conforms to the Fick diffusion law.Using the Fick diffusion equation as the control equation,and substituting the general initial conditions of percutaneous absorption,the mathematical model of percutaneous absorption was constructed.The model is composed of partial differential equations.In order to predict the law of drug administration,it is necessary to solve the analytical solution of partial differential equations.According to different situations of transdermal drug delivery,the mathematical model was refined and improved,and different partial differential equations were constructed and solved.Secondly,in the process of solving partial differential equations,we find the limitations of analytical solutions in solving complex partial differential equations,and then use the finite difference method to solve the numerical solutions of partial differential equations.I write the calculation program by using the finite difference method in MATLAB.According to the penetration and diffusion of a variety of drugs into the skin,different calculation programs were written for numerical simulation.The feasibility and accuracy of the program are verified by numerical simulation and in vitro experiments.Then,the partial differential equations of the mathematical model of percutaneous absorption were solved by the finite element method and COMSOL software.Through the in vitro experiment of long-term drug delivery patch to verify the feasibility of finite element method numerical verification,explore and analyze the possible problems of in vitro experiment and the limitations of the method,through the simulation experiment,on the premise of proving the rationality of the simulation procedure,design and optimize the prescription,reduce the trial and error experiment in the prescription design,and improve the efficiency of the experiment.At the same time,in view of the possible reaction with enzyme or protein in the process of drug transdermal,some specific models were established,and the experimental results were verified by experiments in vitro.Finally,a pharmacokinetic model of percutaneous drug delivery in vitro was constructed by combining the model of multilayer diffusion of percutaneous absorption with the model of atrioventricular kinetics.Using Fourth-order Runge-Kutta method and finite element method solve the ordinary differential equations,and clinical data were used to further verify the feasibility and accuracy of the model and numerical simulation.