用解剖先验约束神经网络,实现更真实、少数据的血管变形预测。
Anatomy-Informed Neural Networks: Encoding Anatomic Priors in Loss and Architecture, with an SE(3) Formulation of Guidewire-Induced Aortoiliac Deformation

- 在损失函数和网络结构中嵌入解剖约束,防止不合理的解剖结构出现
- 基于SE(3)空间建模血管与导丝,通过接触力耦合实现弹性变形最小化
- 仅用2D造影图就能训练3D变形预测,适合数据稀缺的临床场景
深度学习模型虽数值合理却可能违背解剖事实,且在数据稀缺时泛化能力差。本文提出解剖先验神经网络(AINN),将软解剖先验作为损失项中的惩罚项(如将肾移植动脉误置于髂外而非主动脉视为异常而非不可能),硬解剖先验(如血管连续性)则直接嵌入网络架构与状态表示,使无效预测在可实现处被禁止。研究聚焦临床难题:导丝置入后腹主动脉-髂动脉树的变形,对现代主动脉手术及自主内血管导航至关重要。将血管中心线与导丝路径从R^3提升至SE(3)群中帧曲线,通过单边腔内接触不等式耦合柯西杆导丝与挠曲调制、解剖锚定的血管。预测为耦合弹性能量的约束极小值,接触力为拉格朗日乘子。监督使用基于C臂几何投影的Wasserstein-2最优传输损失,实现由2D造影图训练3D预测。运动学、损失与投影经已知真值验证;力学求解器仅验证自身最优性条件,预测位移尚未网格收敛。当前无需训练网络。未来工作将此仿真模型迁移到真实CT扫描,检验其是否提升预测精度并减少训练数据需求。
原文摘要 · Abstract (English)
Deep-learning models of anatomy can be numerically plausible yet anatomically impossible, and they generalize poorly when data are scarce. We introduce Anatomy-Informed Neural Networks (AINN), in which soft anatomic priors enter as penalty terms in the loss (e.g., a branching penalty that treats a renal transplant artery off the iliac instead of the aorta as unexpected rather than impossible), in direct analogy to a physics-informed neural network, and hard anatomic priors (e.g., continuity of the vessel) are built into the architecture and state representation, making such invalid predictions impossible by construction wherever the prior admits architectural enforcement. We develop it on a clinical test case with limited data: how the aortoiliac tree deforms when a stiff wire is introduced endoluminally. This is important to contemporary aortic surgery and will matter to autonomous endovascular navigation. We lift the vessel centerline and the wire path from R^3 to curves of frames in the Lie group SE(3), and couple a Cosserat-rod wire to a tortuosity-modulated, anatomically anchored vessel through a unilateral lumen-contact inequality. The prediction is a constrained minimizer of the coupled elastic energy, with contact forces as its Lagrange multipliers. Supervision is a Wasserstein-2 optimal-transport loss between the predicted projection through the C-arm geometry and the observed angiogram, so a 2D angiogram can train a 3D prediction. The kinematics, loss and projection are verified against known ground truth; the mechanics solver only against its own optimality conditions, and predicted displacement is not yet mesh-converged. Here, no network is trained. Future work will transfer this in silico model to real CT scans and test whether it improves predictive accuracy and reduces the training data required.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。