Département de génie mécanique, Université de Sherbrooke, Québec, Canada.
Laboratoire de Mécanique des Solides, Institut Polytechnique de Paris, Paris, France.
Int J Numer Method Biomed Eng. 2023 Aug;39(8):e3741. doi: 10.1002/cnm.3741. Epub 2023 Jun 14.
Identification of the mechanical properties of a viscoelastic material depends on characteristics of the observed motion field within the object in question. For certain physical and experimental configurations and certain resolutions and variance within the measurement data, the viscoelastic properties of an object may become non-identifiable. Elastographic imaging methods seek to provide maps of these viscoelastic properties based on displacement data measured by traditional imaging techniques, such as magnetic resonance and ultrasound. Here, 1D analytic solutions of the viscoelastic wave equation are used to generate displacement fields over wave conditions representative of diverse time-harmonic elastography applications. These solutions are tested through the minimization of a least squares objective function suitable for framing the elastography inverse calculation. Analysis shows that the damping ratio and the ratio of the viscoelastic wavelength to the size of the domain play critical roles in the form of this least squares objective function. In addition, it can be shown analytically that this objective function will contain local minima, which hinder discovery of the global minima via gradient descent methods.
粘弹性材料的力学性能的识别取决于所研究物体内部观察到的运动场的特征。对于某些物理和实验配置以及测量数据中的某些分辨率和方差，物体的粘弹性性质可能无法识别。弹性成象方法试图基于传统成象技术（如磁共振和超声）测量的位移数据提供这些粘弹性性质的图谱。这里，使用粘弹性波动方程的一维解析解在代表各种时谐弹性成像应用的波动条件下生成位移场。这些解通过最适合弹性成像逆计算的最小二乘目标函数的最小化来进行测试。分析表明，阻尼比和粘弹性波长与域大小的比值在这个最小二乘目标函数的形式中起着关键作用。此外，可以分析证明，这个目标函数将包含局部最小值，这通过梯度下降方法阻碍了全局最小值的发现。
