提出新方法检测弹性成像中模型失效,定位错误假设区域。
The Illusion of Fit: Spatially Resolved Assessment of Constitutive Model Validity in Elastography and Physics-Based Inverse Problems
- 将应力场设为独立潜变量,直接比对平衡方程与本构模型预测
- 在合成数据中识别出5个数量级精度差异的异常区域
- 无需正向模型,适用于噪声大、采样稀疏场景,适合医学影像分析
从测量形变反推软组织力学属性是弹性成像的核心挑战。现有方法常隐含假设本构模型准确描述组织,但当该假设不成立时,反演仍产生看似合理的参数估计——即“拟合幻觉”,无法揭示局部模型失效,可能误导临床判断。本文提出一种概率框架,将本构模型有效性从隐含假设转变为显式、空间分辨的推断目标。核心是将应力场视为独立潜变量,而非由本构模型导出,从而实现机械平衡所需应力与模型预测应力的逐点比较。两个控制方程作为虚拟观测纳入概率学习目标,分别设置精度超参数:平衡定律精度预设为小值以反映其绝对可靠性,而本构精度在稀疏性促进先验下推断。由此获得的本构精度场可提供不确定性感知图谱,标识模型被数据支持或不支持的区域。通过随机变分推断实现无正向模型的推理。在脑切片几何的合成谐波弹性成像实验中验证,该方法在25–35 dB噪声和四倍稀疏观测下,均能稳健识别出包含物与有效区域之间五阶数量级的精度对比。在超声测量线弹性体的仿真实验中,未出现假阳性失效判定,并成功恢复真实刚度对比。
原文摘要 · Abstract (English)
Inferring the mechanical properties of soft tissues from measured deformations is a fundamental challenge in elastography. A rarely examined assumption underlying existing approaches is that the assumed constitutive law correctly describes the imaged material. When it fails, inversion still yields plausible-looking estimates - an illusion of fit with no indication of local model invalidity, which can mislead clinical interpretation. We propose a probabilistic framework that transforms constitutive model validity from an implicit assumption into an explicit, spatially resolved inference target. The key is to treat the stress field as an independent latent variable rather than deriving it from the constitutive law. This enables a pointwise comparison between the stress required by mechanical equilibrium and the stress predicted by the assumed constitutive model. Both governing equations enter the probabilistic learning objective as virtual observables with separate precision hyperparameters: the conservation law precision is set a priori to a small value reflecting its undisputed validity, while the constitutive precision is inferred under a sparsity-promoting prior. The resulting constitutive precision field provides an uncertainty-aware map of where the assumed model is supported by the data and where it is not. Inference is carried out via stochastic variational inference and is forward-model-free. We validate the framework on synthetic harmonic elastography experiments on a brain-slice geometry with an anisotropic inclusion. The inferred precision field identifies the inclusion with a five-order-of-magnitude precision contrast against the valid domain, robustly across 25-35 dB noise and four-fold sparser observations. A phantom experiment with ultrasound measurements on a linear elastic material yields no false-positive violations and recovers the true stiffness contrast.
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