Non-Intrusive Parametrized-Background Data-Weak Reconstruction of Cardiac Displacement Fields from Sparse MRI-like Observations

2025-09-18

AI Summary

Reconstructing myocardial displacement fields from sparse clinical MRI data remains challenging due to the absence of accessible forward-model internals and the need for compatibility with diverse cardiac simulation codes (commercial and open-source). Method: We propose a non-invasive, data-driven reconstruction framework grounded in the Parametrized Background Data-Weak (PBDW) formulation. To enhance sensor selection robustness under sparsity and noise, we introduce a novel H-size mini-batch worst-case Orthogonal Matching Pursuit (wOMP) algorithm. Furthermore, we exploit block-matrix structure to achieve memory-efficient computation, enabling real-time solution of large-scale vector-valued problems. Contribution/Results: The method achieves relative L² errors of ~10⁻⁵ in noise-free settings and maintains ~10⁻² accuracy under 10% noise and severe spatial sparsity. Online reconstruction takes <0.1 seconds—over 10⁴× faster than conventional finite-element solvers—while remaining agnostic to forward-model implementation. This establishes an efficient, general-purpose, and clinically deployable paradigm for personalized cardiac biomechanical diagnosis.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

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.

Problem

• Reconstructing cardiac displacement fields from sparse MRI data
• Developing non-intrusive methods without requiring computational model access
• Enhancing computational efficiency for clinical workflow integration

Innovation

• Non-intrusive PBDW for cardiac displacement reconstruction
• H-size minibatch wOMP algorithm for sensor selection
• Memory optimization using block matrix structures