Optimization Of Multi-laminated Drug Controlled Release Devices Based On Modified Tikhonov Regularization

Drug controlled release systems can control the release process of drug as required.This technology has been an important development direction in the field of medicine due to its safety and effectiveness.Multi-laminated drug controlled release devices have been widely used as drug delivery systems because of their simple structure and more effective control of drug release.At present,the research of optimizing multi-laminated drug controlled release devices is relatively few,and the optimization effect of drug release in devices is not very good with the existing optimization methods.The optimization of drug release behavior in multi-laminated controlled release devices was investigated based on mathematical inverse problem in order to achieve desired drug release in this work.A mathematical model is established for description of drug release in multi-laminated controlled release devices according to drug release mechanism in the devices.A inverse problem of drug release is put forward based on the model from the idea of inverse problem.The inverse problem is that inverting initial concentration distribution from the known drug release rate.Then the optimization problem of drug release is transformed into the solution of inverse problem of diffusion equation.At the end,the optimization problem of drug release from multi-laminated controlled release devices is boiled down to the solution of the first kind of Fredholm integral equation by further solving the model.A new modified Tikhonov regularization method is put forward based on regularizing filter function for the ill-posedness of the first kind of Fredholm integral equation according to the regularization theory.The modified Tikhonov regularization method can make the error of regularized solution obtain the asymptotic optimal order through theoretical proof and error estimation.Tikhonov regularization method and improved Tikhonov regularization method are used to solve the numerical examples of the first kind of Fredholm integral equation.The results show that the accuracy of the modified Tikhonov regularization method is higher than that of the Tikhonov regularization method.So the modified method has better convergence.The modified Tikhonov regularization method is used to optimize the initial drug concentration in multi-laminated devices for three profiles of constant release,linear decrease release and linear increase followed by a constant release profiles to make the drug release curve approach or achieve the desired release.The optimization results show that pseudo constant release,linear decrease release and non-linear release are basically achieved with optimized initial drug concentration distribution in multi-laminated devices by modified Tikhonov regularization method.So the modified Tikhonov regularization method can be well applied to the optimization and design of multi-laminated drug controlled release devices.