The Human Performance Laboratory, Faculty of Kinesiology, University of Calgary, Calgary, Alberta, Canada.
Med Eng Phys. 2011 Oct;33(8):893-9. doi: 10.1016/j.medengphy.2011.02.003. Epub 2011 Mar 6.
We developed and analyzed an inverse numerical model based on Fick's second law on the dynamics of drug release. In contrast to previous models which required two state descriptions of diffusion for long- and short-term release processes, our model is valid for the entire release process. The proposed model may be used for identifying and reducing experimental errors associated with measurements of diffusion based release kinetics. Knowing the initial and boundary conditions, and assuming Fick's second law to be appropriate, we use the methods of Lagrange multiplier along with least-square algorithms to define a cost function which is discretized using finite difference methods and is optimized so as to minimize errors. Our model can describe diffusion based release kinetics for static and dynamic conditions as accurately as finite element methods, but results are obtained in a fraction of CPU time. Our method can be widely used for drug release procedures and for tissue engineering/repair applications where oxygenation of cells residing within a matrix is important.
我们开发并分析了一个基于菲克第二定律的药物释放动力学逆数值模型。与之前需要对长期和短期释放过程进行两种扩散状态描述的模型不同，我们的模型适用于整个释放过程。所提出的模型可用于识别和减少与基于扩散的释放动力学测量相关的实验误差。已知初始和边界条件，并假设菲克第二定律适用，我们使用拉格朗日乘子法和最小二乘法算法来定义一个成本函数，该函数使用有限差分法离散化，并通过优化来最小化误差。我们的模型可以准确描述静态和动态条件下基于扩散的释放动力学，与有限元方法一样，但结果只需要一小部分 CPU 时间。我们的方法可以广泛应用于药物释放过程和组织工程/修复应用，其中细胞在基质内的氧合作用很重要。
