Optimal experimental design with k-space data: application to inverse hemodynamics
Miriam Löcke, Ahmed Attia, Dariusz Ucínski, Cristóbal Bertoglio
TL;DR
The paper tackles the challenge of lengthy 4D Flow MRI acquisitions by introducing an Optimal Experimental Design framework to tailor k-space sampling masks for parameter inference in inverse hemodynamics. By constructing a Fisher information-based design criterion from measurement sensitivities and solving a combinatorial mask-selection problem with greedy and exchange algorithms, the authors demonstrate that OED-designed masks outperform conventional undersampling patterns and can achieve up to a 10x reduction in acquisition time without sacrificing accuracy. Analytic and aortic test cases show reduced parameter error and variance with OED masks, and the exchange algorithm provides robustness at low sampling budgets. This approach promises faster, patient-specific hemodynamic inference and indicates clear directions for extending to real MRI data, coil sensitivity maps, and uncertainty-aware design.
Abstract
Subject-specific cardiovascular models rely on parameter estimation using measurements such as 4D Flow MRI data. However, acquiring high-resolution, high-fidelity functional flow data is costly and taxing for the patient. As a result, there is growing interest in using highly undersampled MRI data to reduce acquisition time and thus the cost, while maximizing the information gain from the data. Examples of such recent work include inverse problems to estimate boundary conditions of aortic blood flow from highly undersampled k-space data. The undersampled data is selected based on a predefined sampling mask which can significantly influences the performance and the quality of the solution of the inverse problem. While there are many established sampling patterns to collect undersampled data, it remains unclear how to select the best sampling pattern for a given set of inference parameters. In this paper we propose an Optimal Experimental Design (OED) framework for MRI measurements in k-space, aiming to find optimal masks for estimating specific parameters directly from k-space. As OED is typically applied to sensor placement problems in spatial locations, this is, to our knowledge, the first time the technique is used in this context. We demonstrate that the masks optimized by employing OED consistently outperform conventional sampling patterns in terms of parameter estimation accuracy and variance, facilitating a speed-up of 10x of the acquisition time while maintaining accuracy.