Elastography is an imaging technique to reconstruct elasticity distributions of heterogeneous objects. Since cancerous tissues are stiffer than healthy ones, for decades, elastography has been applied to medical imaging for noninvasive cancer diagnosis. Although the conventional strain-based elastography has been deployed on ultrasound diagnostic-imaging devices, the results are prone to inaccuracies. Model-based elastography, which reconstructs elasticity distributions by solving an inverse problem in elasticity, may provide more accurate results but is often unreliable in practice due to the ill-posed nature of the inverse problem. We introduce ElastNet, a de novo elastography method combining the theory of elasticity with a deep-learning approach. With prior knowledge from the laws of physics, ElastNet can escape the performance ceiling imposed by labeled data. ElastNet uses backpropagation to learn the hidden elasticity of objects, resulting in rapid and accurate predictions. We show that ElastNet is robust when dealing with noisy or missing measurements. Moreover, it can learn probable elasticity distributions for areas even without measurements and generate elasticity images of arbitrary resolution. When both strain and elasticity distributions are given, the hidden physics in elasticity—the conditions for equilibrium—can be learned by ElastNet.

弹性成像是一种重建异质物体弹性分布的成像技术。由于癌组织比健康组织更硬，几十年来，弹性成像已应用于医学成像以进行无创癌症诊断。尽管传统的基于应变的弹性成像已部署在超声诊断成像设备上，但结果容易出现不准确的情况。基于模型的弹性成像通过解决弹性的逆问题来重建弹性分布，可以提供更准确的结果，但由于逆问题的不适定性质，在实践中通常不可靠。我们介绍了 ElastNet，这是一种将弹性理论与深度学习方法相结合的从头弹性成像方法。有了物理定律的先验知识，ElastNet 可以摆脱标记数据带来的性能上限。ElastNet 使用反向传播来学习对象的隐藏弹性，从而实现快速准确的预测。我们展示了 ElastNet 在处理嘈杂或缺失的测量时是稳健的。此外，即使没有测量，它也可以学习区域的可能弹性分布，并生成任意分辨率的弹性图像。当应变和弹性分布都给定时，弹性中隐藏的物理特性——平衡条件——可以通过 ElastNet 学习。即使没有测量，它也可以学习区域的可能弹性分布，并生成任意分辨率的弹性图像。当应变和弹性分布都给定时，弹性中隐藏的物理特性——平衡条件——可以通过 ElastNet 学习。即使没有测量，它也可以学习区域的可能弹性分布，并生成任意分辨率的弹性图像。当应变和弹性分布都给定时，弹性中隐藏的物理特性——平衡条件——可以通过 ElastNet 学习。