Parameter estimation in blood flow models from highly undersampled k-space magnetic resonance imaging data

Area of Science:

• Medical Imaging
• Biomedical Engineering
• Computational Fluid Dynamics

Background:

• 4D Flow Magnetic Resonance Imaging (MRI) is crucial for cardiovascular inverse problems but suffers from long scan times.
• Undersampled k-space acquisition in 4D Flow MRI necessitates assumptions for image reconstruction, leading to inaccuracies.
• The optimal k-space sampling pattern for 4D Flow MRI is often unclear.

Purpose of the Study:

• To develop a parameter estimation framework that directly utilizes highly undersampled 4D Flow MRI k-space data.
• To assess the accuracy of this framework for estimating boundary-condition parameters in cardiovascular models.
• To compare the performance of different k-space sampling strategies.

Main Methods:

• A parameter estimation framework was developed to directly process undersampled k-space measurements.
• The numerical solution was implemented using a Reduced-Order Unscented Kalman Filter.
• The framework was evaluated on a synthetic aortic blood flow model and validated with real MRI data from a mechanical phantom.

Main Results:

• The proposed framework achieved more accurate boundary-condition parameter estimates than compressed-sensing based reconstructions.
• The study identified how estimation accuracy is influenced by various k-space sampling patterns.
• Substantially higher accuracy was demonstrated compared to inverse problems relying on compressed-sensing reconstructed velocity fields.

Conclusions:

• Directly using undersampled k-space data with a Reduced-Order Unscented Kalman Filter offers a more accurate approach for cardiovascular parameter estimation from 4D Flow MRI.
• This method mitigates inaccuracies associated with traditional compressed-sensing reconstructions.
• The findings provide guidance on selecting optimal sampling strategies for improved 4D Flow MRI analysis.