Magnetic resonance imaging (MRI) is the primary modality for the imaging of soft tissues (e.g. brain, muscle, liver). Therefore, it is an essential radiological tool for diagnosis and surgical planning. The contrast in MR images is due to tissues responding differently to the magnetic fields generated by the scan-ning system. This response can be de-scribed by the physical properties of the tissue (e.g. proton density, magnetic relaxation) and the magnetic fields. These physical properties are represent-ed by multiple parameters that can be estimated through quantitative MRI (qMRI) methods. The parameters are considered more reproducible than con-ventional MR images, which simplifies the comparison of MR data from differ-ent subjects or scanning systems. Esti-mating multiple parameters simultane-ously is needed to reduce error from system imperfections and deliver accu-rate estimates of the physical tissue pa-rameters...

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.