基于时间分数阶扩散方程的药物控释初始浓度优化

The Initial Concentration Optimization of Drug Controlled ReleaseSystem Based on the Time Fractional Order Diffusion Equation

药物控释系统是指通过调控内部某些设计参数,以达到特定药物释放目标的一种可控释体系。针对基于时间分数阶扩散方程的药物控释体系初始浓度优化问题,采用B样条小波方法求解正问题,采用结合了小生境策略和布谷鸟搜索算法的小生境布谷鸟算法优化不同分数阶下的药物初始浓度,从而近似达到三种预期药物释放目标。对于正问题求解,主要结合Caputo导数和三次B样条尺度函数,建立了一种B样条小波方法的迭代求解格式;对于初始浓度优化问题,引入了反问题研究思路,将药物控释体系的优化设计问题归结为基于分数阶扩散方程的参数辨识问题。为了实现参数反演控制,引入了小生境布谷鸟智能优化算法,反演计算控释体系中的初始浓度,有效地解决了布谷鸟算法易陷入局部极值的问题。针对恒速释放,线性降低释放和非线性释放三种释放目标,给出了最优控制参数设计,数值算例验证了所提方法的有效性。

Drug controlled release system is a kind of controlled release system which can achieve specific drug release target by adjusting some design parameters.In order to optimize the initial concentration of drug controlled release system based on time-fractional order diff-usion equation,B-spline wavelet method is used to solve the forward problem.The niche cuckoo search algorithm,which combines the niche strategy with the cuckoo search strategy,is applied to optimize the initial drug concentrations at different fractions,thus approximately achieving the three expected drug release targets.For the solution of the forward problem,an iterative solution scheme of B-spline wavelet method is established by combining the definition of the Caputo derivative and the cubic B-spline scaling function.The problem of optimal design of drug controlled release system is reduced to the problem of parameter identification of fractional diffusion equation based on the inverse problem solution scheme.In order to realize parameter inversion control,the niche cuckoo search optimization algorithm is introduced to inverse the initial concentration in the controlled release system,which effectively solves the problem.The niche cuckoo search algorithm is easily trapped in local extremum.The optimal control parameters are given based on the proposed algorithm for three kinds of release targets:constant velocity release,linear reduced release and nonlinear release.Numerical results show the effectiveness of the proposed method.