We introduce a method for MR parameter mapping based on three concepts: 1) an inversion recovery, variable flip angle acquisition strategy designed for speed, signal, and contrast; 2) a compressed sensing reconstruction which exploits spatiotemporal correlations through low rank regularization; and 3) a model-based optimization to simultaneously estimate proton density, T1, and T2 values from the acquired measurements. Compared to MR Fingerprinting, the proposed method achieves a five-fold acceleration in acquisition time, reconstructs an unaliased series of images, and does not rely on dictionary matching for parameter estimation.
In an MRI experiment the observed signal y(t) can be described by the combination of a spatial function with a temporal signal evolution: y(t)=∫rρ(r)ft(r)e2πik(t)⋅rdr where ρ(r) is the spatial distribution of the spin density at position r, k(t) is the k-space trajectory, and ft(r) is the temporal signal, given by the recursion: f_t(\mathbf{r})=f_{t-1}(\mathbf{r})g\left( \boldsymbol{\theta}_a(t);\boldsymbol{\theta}_b(\mathbf{r})\right). The temporal signal f_t(\mathbf{r}) at time t is determined by the signal value at the previous time point modulated by g\left( \cdot \right), a function of two different parameter sets: the temporally varying acquisition parameters \boldsymbol{\theta}_a(t), e.g. flip angle \alpha (t) and repetition time T_R(t); and the spatially dependent biological parameters of interest \boldsymbol{\theta}_b(\mathbf{r}), such as T_1(\mathbf{r}) and T_2(\mathbf{r}). In MRF, the temporal signals are denoted fingerprints, where the method aims at creating unique signals for different spatial locations through pseudorandom variations of the acquisition parameters \boldsymbol{\theta}_a(t). Alternatively, we chose \boldsymbol{\theta}_a(t) to satisfy three criteria: speed, signal, and contrast. We increased the speed by minimizing T_R(t), and optimized \alpha(t) for signal and contrast using a training dataset \mathbf{x} \in \mathbb{C}^{L\times T} with L observations and T time points; wherein we experimentally attempted to increase both the orthogonality between observations, and the norm within observations[2]–[4].
Whereas the original MRF reconstructs aliased images from the measurements, recent work has shown that the acquired data can also be reconstructed in an iterative framework[5]–[10]. Based on these ideas, we implemented a compressed sensing (CS)[11] reconstruction that constrains the temporal signal evolution to a low dimensional subspace[6],[9], and regularizes the image series by promoting local low rank of spatiotemporal image patches[12],[13]. Finally, once we reconstruct an unaliased image series, we propose to replace the matching to a simulated dictionary with an optimization based on least-squares curve fitting for the simultaneous estimation of \rho (\mathbf{r}), T_1(\mathbf{r}) and T_2(\mathbf{r}).
We acquired a single slice from a healthy volunteer based on the FISP implementation of MRF[14] on a GE HDx MRI system (GE Medical Systems, Milwaukee, WI), with an eight channel receive only head RF coil. After an initial inversion, we applied a train of T=1000 pulses with \alpha(t) and T_R(t) as in[14] (T_{acq}=12.67\ s per slice). In addition, we acquired a train of T=300 variable flip angles (vFA) (Fig. 1b) with T_R=8 \ ms (T_{acq} = 2.42 \ s per slice). For both acquisitions, we used a variable density spiral designed with 22.5\times 22.5\ cm^{2} FOV, 256\times 256 matrix size, 1 \ mm in-plane resolution, 5\ mm slice thickness, and golden angle rotations between every interleave. Each acquisition was reconstructed using the nuFFT operator[15] and with the proposed CS method, and parameter maps were subsequently estimated with both dictionary matching and optimization. We simulated the dictionary using the EPG formalism[16], [17].
We found that a vFA scheme of two linear ramps yielded T_1 and T_2 sensitivity while reducing the cost (see Fig. 1). Compared to MRF, the proposed strategy reduces the number of repetitions (Fig. 1a-b), while increasing the orthogonality of the signal evolutions between training observations (Fig. 1c-d). This acquisition, coupled with the proposed CS reconstruction, allows for the recovery of a series of unaliased images (Fig. 2), which in turn facilitate a model-based optimization for parameter mapping (Figs. 3,4).
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