An Efficient Method for Multi-Parameter Mapping in Quantitative MRI Using B-Spline Interpolation

An Efficient Method for Multi-Parameter Mapping in Quantitative MRI Using B-Spline Interpolation

van Valenberg, W. (TU Delft ImPhys/Medical Imaging; TU Delft ImPhys/Computational Imaging)
Klein, S. (Erasmus MC)
Vos, F.M. (TU Delft ImPhys/Computational Imaging; TU Delft ImPhys/Medical Imaging; Amsterdam UMC)
Koolstra, Kirsten (Leiden University Medical Center)
van Vliet, L.J. (TU Delft ImPhys/Computational Imaging)
Poot, D.H.J. (TU Delft ImPhys/Computational Imaging)

2020

Quantitative MRI methods that estimate multiple physical parameters simultaneously often require the fitting of a computational complex signal model defined through the Bloch equations. Repeated Bloch simulations can be avoided by matching the measured signal with a precomputed signal dictionary on a discrete parameter grid (i.e. lookup table) as used in MR Fingerprinting. However, accurate estimation requires discretizing each parameter with a high resolution and consequently high computational and memory costs for dictionary generation, storage, and matching. Here, we reduce the required parameter resolution by approximating the signal between grid points through B-spline interpolation. The interpolant and its gradient are evaluated efficiently which enables a least-squares fitting method for parameter mapping. The resolution of each parameter was minimized while obtaining a user-specified interpolation accuracy. The method was evaluated by phantom and in-vivo experiments using fully-sampled and undersampled unbalanced (FISP) MR fingerprinting acquisitions. Bloch simulations incorporated relaxation effects $(\boldsymbol {T}_{\boldsymbol {1}},\boldsymbol {T}_{\boldsymbol {2}})$ , proton density $\left ({\boldsymbol {PD} }\right)$ , receiver phase ( $\boldsymbol {\varphi }_{\boldsymbol {0}}$ ), transmit field inhomogeneity ( $\boldsymbol {B}_{\boldsymbol {1}}^{\boldsymbol {+}}$ ), and slice profile. Parameter maps were compared with those obtained from dictionary matching, where the parameter resolution was chosen to obtain similar signal (interpolation) accuracy. For both the phantom and the in-vivo acquisition, the proposed method approximated the parameter maps obtained through dictionary matching while reducing the parameter resolution in each dimension ( $\boldsymbol {T}_{\boldsymbol {1}},\boldsymbol {T}_{\boldsymbol {2}},\boldsymbol {B}_{\boldsymbol {1}}^{\boldsymbol {+}}$ ) by - on average - an order of magnitude. In effect, the applied dictionary was reduced from .47GB$ to $464KB$. Furthermore, the proposed method was equally robust against undersampling artifacts as dictionary matching. Dictionary fitting with B-spline interpolation reduces the computational and memory costs of dictionary-based methods and is therefore a promising method for multi-parametric mapping.

B-spline interpolation
dimensionality reduction
least-squaresminimization
magnetic resonance fingerprinting
quantitative magnetic resonance imaging
singular value decomposition

http://resolver.tudelft.nl/uuid:13bcdb4e-12a7-439d-b106-f2c3a78cd1e8

https://doi.org/10.1109/TMI.2019.2954751

2020-05-19

0278-0062

IEEE Transactions on Medical Imaging, 39 (5), 1681-1689

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

journal article

© 2020 W. van Valenberg, S. Klein, F.M. Vos, Kirsten Koolstra, L.J. van Vliet, D.H.J. Poot