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

Quantitative Transient-state Imaging (QTI) is a non-random, dictionary-less MR Fingerprinting alternative. Through iterative reconstructions, QTI recovers a series of contrast-weighted images from transient-state acquisitions and subsequently estimates the parameters that best describe the resulting dynamic signal evolutions. Here, we extend the QTI framework by incorporating a simple velocity model that accounts for blood flowing into and out of the imaging slice. The model, however wrong, can be very useful: it predicts signal hyperintensities in the presence of flow, allowing for the simultaneous reconstruction of MR Angiography images, hundreds of dynamic contrast-weighted images, and their corresponding parametric maps.

Multiparametric mapping methods, such as Quantitative Transient-state Imaging (QTI)[1] and MR Fingerprinting (MRF)[2], enable the estimation of several parametric maps with a single acquisition by enforcing consistency with a model. If such model is assumed to be perfect, the estimated parametric maps contain all the relevant information. However, commonly used models have limitations, and by consequence the maps can disregard useful information.

Here, we propose to simultaneously reconstruct images and compute parametric maps, and demonstrate that simple models, however wrong, can be very useful in the context of contrast-weighted imaging. For example, by accounting for blood flowing through an imaging slice with a mean velocity scalar, we can predict a signal hyperintensity throughout the course of the acquisition. Thus, the reconstructed signals can be taken advantage of to obtain MR Angiography (MRA) images.

Methods

In the transient-state, the observed signal over time $$$y(t)\in\mathbb{C}^T$$$ with $$$T$$$ measurements can be described as a spatial function modulated by a temporal signal:

$$y(t)=\int_\mathbf{r}\rho(\mathbf{r})f_t(\mathbf{r})e^{-2\pi i\mathbf{k}(t)\cdot\mathbf{r}}d\mathbf{r};$$ where $$$\rho(\mathbf{r})$$$ is the 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: $$f_t(\mathbf{r})=\sum_{i=0}^Tf_{i-1}f_t(\mathbf{r})g\left(\eta_i;\theta(\mathbf{r})\right)\ast h_i(t).$$ The signal $$$f_t (\mathbf{r})$$$ is determined at sample time $$$i$$$ by an operation $$$g\left(\cdot \right)$$$ on the signal from the previous sample $$$f_{i-1}(\mathbf{r})$$$, where the operator $$$g\left(\cdot \right)$$$ is a function of two parameter sets: the temporally varying acquisition parameters $$$\eta_i$$$, and the spatially dependent biophysical parameters of interest, such as T1$$$(\mathbf{r})$$$ and T2$$$(\mathbf{r})$$$. Finally, $$$h_i(t)$$$ gives the fraction of spins tagged with RF pulse $$$i$$$ that will remain in the imaging slice after time $$$t$$$. We have chosen $$$h(t)$$$ as plug flow (Fig. 1), i.e. a constant velocity scalar over time[3].

Although flow is not constant in time or across the lumen of a vessel, modeling it as a constant scalar predicts the presence of unsaturated spins with every RF pulse. These spins will cause signal hyperintensities in the transient-state, whereas stationary spins will become saturated and follow the dynamics dictated by the choice of acquisition parameters $$$\eta_i$$$ (Fig. 2).

We acquired 112, 2 mm thick slices of a healthy volunteer on a GE 3T MR750w scanner with a 12 channel receive only head RF coil (GE Medical Systems, Milwaukee, WI). For every slice, we inverted the magnetization locally and then applied a train of 350 RF pulses with a flip angle ramp described in Fig. 2a and TR/TE = 18/2 ms. In every repetition, we acquired data with a variable density spiral with 1 mm in-plane resolution. We reconstructed the entire four-dimensional dataset using the reconstruction proposed in[1], where we projected the data onto a lower dimensional temporal subspace[4] and regularized the reconstruction with a local low-rank operation on 4D spatiotemporal image patches. We created the subspace by sampling a prior distribution of tissue classes for both stationary and non-stationary tissues (Fig. 3 and Fig. 2f), and simulated the signal over time using the EPG formalism[5]. After reconstruction, we estimated T1, T2, and proton density (PD) from the temporal dynamics and summed all temporal frames into one volume to create MRA images.

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