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

Willem Van Valenberg*, Stefan Klein, Frans M. Vos, Kirsten Koolstra, Lucas J. Van Vliet, Dirk H.J. Poot

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

6 Citations (Scopus)
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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.

Original languageEnglish
Article number8908815
Pages (from-to)1681-1689
JournalIEEE Transactions on Medical Imaging
Issue number5
Publication statusPublished - 2020

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project 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.


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

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