采用改进Tikhonov正则化方法优化多层平板药物控释

多层平板药物控释体系是目前最常用的药物控释体系之一.为了使药物能够按照预期的释放速率释放到人体中,对多层平板控释体系中的药物释放行为进行了优化.首先借鉴数学反问题的求解思路,将基于多层平板体系药物扩散模型的药物释放优化问题转化为扩散方程初值反问题的求解;然后基于紧算子奇异值系统理论,构造了一种新的正则化滤子函数,从而提出了一种改进的Tikhonov正则化方法,并给出了改进方法的渐进最优阶估计;最后采用改进Tikhonov正则化方法,针对恒速、线性下降和先线性增加后恒速的非线性释放这3种目标释放要求,优化了多层平板体系中的药物初始浓度分布,使药物的释放曲线接近或达到所需的目标释放.结果表明:改进的Tikhonov正则化方法不仅在理论上能够使正则解的误差具有渐进最优阶,而且在多层平板控释体系的优化中也取得了良好的效果;通过采用改进Tikhonov正则化方法优化多层平板控释体系中的药物初始浓度分布,基本实现了体系中的拟恒速、拟线性降低以及拟非线性的药物释放行为.

Applying the modified Tikhonov regularization method to the optimization of multi-laminated drug controlled release

Multi-laminated drug controlled release devices are one of the most commonly used drug controlled release devices at present. In order to release the drug into human body according to the predetermined release rate, an optimization approach to achieve desired drug release behavior using multi-laminated drug controlled release devices was proposed. First, based on the idea of inverse problem, the optimization of drug release based on the multi-laminated drug controlled release devices was transformed into an initial value inverse problem of diffusion equations. Then, a modified Tikhonov regularization method was proposed by constructing a new regularizing filter based on the singular value theory of compact operators, and the convergence and the optimal asymptotic order of the regularized solution were obtained. Finally, the modified Tikhonov regularization method was applied to the optimization of the initial drug concentration distribution. For three targeted release requirements (constant release, linear decrease release, and linear increase followed by a constant release), better results could be achieved by using the optimized initial drug concentration distributions obtained by the modified Tikhonov regularization method. Numerical results demonstrate that the modified Tikhonov regularization method not only had the optimal asymptotic order, but also had a good effect on optimizing the multi-laminated controlled release device. By using the modified Tikhonov regularization method to optimize the initial concentration of the drug in the multi-laminated controlled release device, the drug release behavior of the system was basically realized as constant velocity release behavior, quasi-linear release behavior, and non-linear release behavior.