Sumi C, Nakayama K
Department of Electrical and Electronics Engineering, Faculty of Science and Technology, Sophia University, Tokyo, Japan.
IEEE Trans Med Imaging. 1998 Jun;17(3):419-28. doi: 10.1109/42.712131.
To noninvasively quantify tissue elasticity for differentiating malignancy of soft tissue, we previously proposed a two-dimensional (2-D) mechanical inverse problem in which simultaneous partial differential equations (PDE's) represented the target distribution globally of relative shear moduli with respect to reference shear moduli such that the relative values could be determined from strain distributions obtained by conventional ultrasound (US) or nuclear magnetic resonance (NMR) imaging-based analysis. Here, we further consider the analytic solution in the region of interest, subsequently demonstrating that the problem is inevitably ill-conditioned in real-world applications, i.e., noise in measurement data and improper configurations of mechanical sources/reference regions make it impossible to guarantee the existence of a stable and unique target global distribution. Next, based on clarification of the inherent problematic conditions, we describe a newly developed numerical-based implicit-integration approach that novelly incorporates a computationally efficient regularization method designed to solve this differential inverse problem using just low-pass filtered spectra derived from strain measurements. To evaluate method effectiveness, reconstructions of the global distribution are carried out using intentionally created ill-conditioned models. The resultant reconstructions indicate the robust solution is highly suitable, while also showing it has high potential to be applied in the development of an effective yet versatile diagnostic tool for quantifying the distribution of elasticity in various soft tissues.
为了非侵入性地量化组织弹性以鉴别软组织的恶性程度，我们之前提出了一个二维机械逆问题，其中联立偏微分方程全局表示相对于参考剪切模量的相对剪切模量的目标分布，以便能够从通过传统超声（US）或基于核磁共振（NMR）成像分析获得的应变分布中确定相对值。在此，我们进一步考虑感兴趣区域的解析解，随后证明在实际应用中该问题不可避免地是病态的，即测量数据中的噪声以及机械源/参考区域的不当配置使得无法保证存在稳定且唯一的目标全局分布。接下来，在明确固有问题条件的基础上，我们描述了一种新开发的基于数值的隐式积分方法，该方法创新性地结合了一种计算效率高的正则化方法，旨在仅使用从应变测量得出的低通滤波谱来求解此微分逆问题。为了评估方法的有效性，使用故意创建的病态模型进行全局分布的重建。所得重建结果表明稳健解非常合适，同时还表明它在开发用于量化各种软组织弹性分布的有效且通用的诊断工具方面具有很高的应用潜力。
