Shore Spencer W, Barbone Paul E, Oberai Assad A, Morgan Elise F
Department of Mechanical Engineering, Boston University, 110 Cummington Street, Boston, MA 02215, USA.
J Biomech Eng. 2011 Jun;133(6):061002. doi: 10.1115/1.4004231.
To measure spatial variations in mechanical properties of biological materials, prior studies have typically performed mechanical tests on excised specimens of tissue. Less invasive measurements, however, are preferable in many applications, such as patient-specific modeling, disease diagnosis, and tracking of age- or damage-related degradation of mechanical properties. Elasticity imaging (elastography) is a nondestructive imaging method in which the distribution of elastic properties throughout a specimen can be reconstructed from measured strain or displacement fields. To date, most work in elasticity imaging has concerned incompressible, isotropic materials. This study presents an extension of elasticity imaging to three-dimensional, compressible, transversely isotropic materials. The formulation and solution of an inverse problem for an anisotropic tissue subjected to a combination of quasi-static loads is described, and an optimization and regularization strategy that indirectly obtains the solution to the inverse problem is presented. Several applications of transversely isotropic elasticity imaging to cancellous bone from the human vertebra are then considered. The feasibility of using isotropic elasticity imaging to obtain meaningful reconstructions of the distribution of material properties for vertebral cancellous bone from experiment is established. However, using simulation, it is shown that an isotropic reconstruction is not appropriate for anisotropic materials. It is further shown that the transversely isotropic method identifies a solution that predicts the measured displacements, reveals regions of low stiffness, and recovers all five elastic parameters with approximately 10% error. The recovery of a given elastic parameter is found to require the presence of its corresponding strain (e.g., a deformation that generates ɛ₁₂ is necessary to reconstruct C₁₂₁₂), and the application of regularization is shown to improve accuracy. Finally, the effects of noise on reconstruction quality is demonstrated and a signal-to-noise ratio (SNR) of 40 dB is identified as a reasonable threshold for obtaining accurate reconstructions from experimental data. This study demonstrates that given an appropriate set of displacement fields, level of regularization, and signal strength, the transversely isotropic method can recover the relative magnitudes of all five elastic parameters without an independent measurement of stress. The quality of the reconstructions improves with increasing contrast, magnitude of deformation, and asymmetry in the distributions of material properties, indicating that elasticity imaging of cancellous bone could be a useful tool in laboratory studies to monitor the progression of damage and disease in this tissue.
为了测量生物材料力学性能的空间变化，先前的研究通常对切除的组织标本进行力学测试。然而，在许多应用中，如患者特异性建模、疾病诊断以及追踪与年龄或损伤相关的力学性能退化，侵入性较小的测量方法更为可取。弹性成像（弹性图）是一种无损成像方法，通过测量应变或位移场可以重建整个标本的弹性特性分布。迄今为止，弹性成像的大部分工作都涉及不可压缩、各向同性材料。本研究将弹性成像扩展到三维、可压缩、横向各向同性材料。描述了受准静态载荷组合作用的各向异性组织反问题的公式和求解方法，并提出了一种间接获得反问题解的优化和正则化策略。随后考虑了横向各向同性弹性成像在人椎体松质骨上的几种应用。通过实验确定了使用各向同性弹性成像来获得椎体松质骨材料特性分布有意义重建的可行性。然而，通过模拟表明，各向同性重建不适用于各向异性材料。进一步表明，横向各向同性方法识别出的解能够预测测量位移，揭示低刚度区域，并以约10%的误差恢复所有五个弹性参数。发现恢复给定的弹性参数需要其相应应变的存在（例如，产生ɛ₁₂的变形对于重建C₁₂₁₂是必要的），并且正则化的应用显示可提高精度。最后，证明了噪声对重建质量的影响，并确定40 dB的信噪比作为从实验数据获得准确重建的合理阈值。本研究表明，给定一组合适的位移场、正则化水平和信号强度，横向各向同性方法可以在不独立测量应力的情况下恢复所有五个弹性参数的相对大小。重建质量随着对比度、变形大小和材料特性分布不对称性的增加而提高，表明松质骨弹性成像可能是实验室研究中监测该组织损伤和疾病进展的有用工具。
