School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14850, USA.
IEEE Trans Med Imaging. 2010 Apr;29(4):1012-21. doi: 10.1109/TMI.2009.2039225. Epub 2010 Mar 22.
A methodology for estimating the spatial distribution of elastic moduli using the steady-state dynamic response of solids immersed in fluids is presented. The technique relies on the ensuing acoustic field from a remotely excited solid to inversely estimate the spatial distribution of Young's modulus of biological structures (e.g., breast tissue). This work proposes the use of Gaussian radial basis functions (GRBF) to represent the spatial variation of elastic moduli. GRBF are shown to possess the advantage of representing smooth functions with quasi-compact support and can efficiently represent elastic moduli distributions such as those that occur in soft biological tissue in the presence of unhealthy tissue (e.g., tumors and calcifications). The direct problem consists of a coupled acoustic-structure interaction boundary-value problem solved in the frequency domain using the finite element method. The inverse problem is cast as an optimization problem in which the error functional is defined as a measure of discrepancy between an experimentally measured response and a finite element representation of the system. Nongradient based optimization algorithms are used to solve the resulting optimization problem. The feasibility of the proposed approach is demonstrated through a series of simulations and an experiment. For comparison purposes, the surface velocity response was also used for the inverse characterization as the measured response in place of the acoustic pressure.
提出了一种利用浸没在流体中的固体的稳态动力响应来估计弹性模量空间分布的方法。该技术依赖于远程激励固体产生的后续声场，以反演生物结构（例如乳房组织）的杨氏模量的空间分布。本工作提出使用高斯径向基函数（GRBF）来表示弹性模量的空间变化。GRBF 具有表示具有准紧支集的光滑函数的优点，并且可以有效地表示弹性模量分布，例如在存在不健康组织（例如肿瘤和钙化）的情况下在软生物组织中出现的分布。正问题由频域中使用有限元方法求解的耦合声学-结构相互作用边值问题组成。逆问题被表述为优化问题，其中误差泛函定义为实验测量响应与系统的有限元表示之间差异的度量。非梯度优化算法用于求解所得的优化问题。通过一系列模拟和实验证明了所提出方法的可行性。为了进行比较，还使用表面速度响应作为测量响应来进行逆特征化，而不是使用声压。
