Pedro A. Gómez^{1,2}, Guido Buonincontri^{3}, Miguel Molina-Romero^{1,2}, Jonathan I. Sperl^{2}, Marion I. Menzel^{2}, and Bjoern H. Menze^{1}

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: $$y(t)=\int_{\mathbf{r}}\rho(\mathbf{r})f_t(\mathbf{r})e^{2\pi i\mathbf{k}(t)\cdot\mathbf{r}}d\mathbf{r}$$ where $$$\rho (\mathbf{r})$$$ is the spatial distribution of the spin density at position $$$\mathbf{r}$$$, $$$\mathbf{k}(t)$$$ is the k-space trajectory, and $$$f_t(\mathbf{r})$$$ 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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