Personalized cardiac diagnostics require accurate reconstruction of myocardial displacement fields from sparse clinical imaging data, yet current methods often demand intrusive access to computational models. In this work, we apply the non-intrusive Parametrized-Background Data-Weak (PBDW) approach to three-dimensional (3D) cardiac displacement field reconstruction from limited Magnetic Resonance Image (MRI)-like observations. Our implementation requires only solution snapshots -- no governing equations, assembly routines, or solver access -- enabling immediate deployment across commercial and research codes using different constitutive models. Additionally, we introduce two enhancements: an H-size minibatch worst-case Orthogonal Matching Pursuit (wOMP) algorithm that improves Sensor Selection (SS) computational efficiency while maintaining reconstruction accuracy, and memory optimization techniques exploiting block matrix structures in vectorial problems. We demonstrate the effectiveness of the method through validation on a 3D left ventricular model with simulated scar tissue. Starting with noise-free reconstruction, we systematically incorporate Gaussian noise and spatial sparsity mimicking realistic MRI acquisition protocols. Results show exceptional accuracy in noise-free conditions (relative L2 error of order O(1e-5)), robust performance with 10% noise (relative L2 error of order O(1e-2)), and effective reconstruction from sparse measurements (relative L2 error of order O(1e-2)). The online reconstruction achieves four-order-of-magnitude computational speed-up compared to full Finite Element (FE) simulations, with reconstruction times under one tenth of second for sparse scenarios, demonstrating significant potential for integration into clinical cardiac modeling workflows.

翻译：个性化心脏诊断需要从稀疏的临床影像数据中精确重构心肌位移场，然而现有方法通常要求侵入式访问计算模型。在本工作中，我们将非侵入式参数化背景数据弱方法应用于从有限的磁共振成像类观测中重构三维心脏位移场。我们的实现仅需解的快照——无需控制方程、组装例程或求解器访问——从而能够立即部署于使用不同本构模型的商业和研究代码中。此外，我们引入了两项改进：一种H尺寸小批量最坏情况正交匹配追踪算法，在保持重构精度的同时提高了传感器选择的计算效率；以及利用向量问题中块矩阵结构的内存优化技术。我们通过在模拟疤痕组织的三维左心室模型上进行验证，证明了该方法的有效性。从无噪声重构开始，我们系统地引入了模拟真实MRI采集协议的高斯噪声和空间稀疏性。结果显示，在无噪声条件下具有卓越的精度，在10%噪声条件下表现出稳健的性能，并能从稀疏测量中有效重构。在线重构相比完整有限元模拟实现了四个数量级的计算加速，在稀疏场景下重构时间低于十分之一秒，展现了集成到临床心脏建模工作流程中的巨大潜力。