Optimization of drug controlled release from multi-laminated devices based on the modified Tikhonov regularization method

TL;DR

This paper introduces a modified Tikhonov regularization method to optimize drug release profiles from multi-laminated devices, effectively addressing the ill-posed inverse problem and improving design outcomes.

Contribution

It develops a new regularization filter based on singular value theory, enhancing the classical Tikhonov method for drug release optimization.

Findings

Modified Tikhonov method outperforms classical in simulations

Achieves better approximation of desired drug release profiles

Proves suitable for designing multi-laminated drug delivery devices

Abstract

From the viewpoint of inverse problem, the optimization of drug release based on the multi-laminated drug controlled release devices has been regarded as the solution problem of the diffusion equation initial value inverse problem. In view of the ill-posedness of the corresponding inverse problem, a modified Tikhonov regularization method is proposed by constructing a new regularizing filter function based on the singular value theory of compact operator. The convergence and the optimal asymptotic order of the regularized solution are obtained. Then the classical Tikhonov regularization method and the modified Tikhonov regularization method are applied to the optimization problem of the initial drug concentration distribution. For three various desired release profiles (constant release, linear decrease release and linear increase followed by a constant release profiles), better results can be obtained by using the modified Tikhonov regularization method. The numerical results demonstrate that the modified Tikhonov regularization method not only has the optimal asymptotic order, but also is suitable for the optimization and design of multi-laminated drug controlled release devices.