Institute of Mechanics, Ruhr-University Bochum, Bochum, Germany.
Phys Med Biol. 2010 Apr 7;55(7):2035-56. doi: 10.1088/0031-9155/55/7/016. Epub 2010 Mar 19.
This paper is concerned with an efficient implementation suitable for the elastography inverse problem. More precisely, the novel algorithm allows us to compute the unknown stiffness distribution in soft tissue by means of the measured displacement field by considerably reducing the numerical cost compared to previous approaches. This is realized by combining and further elaborating variational mesh adaption with a clustering technique similar to those known from digital image compression. Within the variational mesh adaption, the underlying finite element discretization is only locally refined if this leads to a considerable improvement of the numerical solution. Additionally, the numerical complexity is reduced by the aforementioned clustering technique, in which the parameters describing the stiffness of the respective soft tissue are sorted according to a predefined number of intervals. By doing so, the number of unknowns associated with the elastography inverse problem can be chosen explicitly. A positive side effect of this method is the reduction of artificial noise in the data (smoothing of the solution). The performance and the rate of convergence of the resulting numerical formulation are critically analyzed by numerical examples.
本文关注的是一种适用于弹性反向问题的高效实现方法。更确切地说，与以前的方法相比，新算法通过结合和进一步扩展变分网格自适应与类似于数字图像压缩中已知的聚类技术，允许我们通过测量的位移场来计算软组织中的未知刚度分布，从而大大降低了数值成本。在变分网格自适应中，只有在局部细化会导致数值解的显著改善的情况下，才会对基础有限元离散化进行细化。此外，上述聚类技术降低了数值复杂度，其中描述各软组织刚度的参数根据预定义的区间数进行排序。通过这样做，可以明确选择与弹性反向问题相关的未知数的数量。该方法的一个积极影响是减少数据中的人为噪声（平滑解）。通过数值示例对所得到的数值公式的性能和收敛速度进行了严格分析。
