Yongwan Lim^{1}, Sajan Goud Lingala^{1}, Shrikanth Narayanan ^{1}, and Krishna Nayak^{1}

Spiral real-time MRI (RT-MRI) is a valuable tool in speech production research. A key drawback is off-resonance blurring artifact that appears at the boundaries of important articulators. In this work, we demonstrate dynamic off-resonance estimation that is directly captured from phase of single echo-time dynamic images after coil phase compensation. Multi-frequency reconstruction then provides deblurring and improved depiction of articulator boundaries including the tongue, hard palate, and soft palate.

Dynamic Field Map Estimation

Consider spiral RT-MRI, where the phase of the image time series (${I}_{c}(\mathbf{\text{r}},t)$) for *c*-th coil is:

$${\phi}_{c}(\mathbf{\text{r}},t)=\mathrm{\angle}{S}_{c}(\mathbf{\text{r}})-2\pi \mathrm{\Delta}f(\mathbf{\text{r}},t)TE$$

where $\mathbf{\text{r}}\in (x,y)$ is image domain spatial coordinates, $\mathrm{\angle}{S}_{c}(\mathbf{\text{r}})$ is coil-phase that is spatially smooth and independent of time, and $\mathrm{\Delta}f(\mathbf{\text{r}},t)$ is dynamic off-resonance. Phase accrual during the spiral readout is ignored. We estimate the coil sensitivity map $\hat{{S}_{c}}(\mathbf{\text{r}})$ and the coil-phase $\mathrm{\angle}\hat{{S}_{c}}(\mathbf{\text{r}})$ using the sum-of-square method^{13} from a temporally-averaged and spatially-low-pass-filtered image ${I}_{avg,c}(\mathbf{\text{r}})=LP{F}_{x,y}\{(1/N)\sum _{t=1}^{N}{I}_{c}(\mathbf{\text{r}},t)\}$. We then combine the individual coil images ${I}_{c}(\mathbf{\text{r}},t)$ into a single image, $I(\mathbf{\text{r}},t)$ using optimal B1 combination^{13}. We compute a dynamic field map estimate $\hat{\mathrm{\Delta}f}(\mathbf{\text{r}},t)$ from $I(\mathbf{\text{r}},t)$ as follows:

$$\hat{\mathrm{\Delta}f}(\mathbf{\text{r}},t)=\mathrm{\angle}I(\mathbf{\text{r}},t)/(-2\pi TE)$$

Note that this approach only captures the dynamic field map, i.e. there will be a residue ($f(\mathbf{\text{r}},t)-\hat{\mathrm{\Delta}f}(\mathbf{\text{r}},t)$) that equals $LP{F}_{x,y}\{(1/N)\sum _{t=1}^{N}\mathrm{\Delta}f(\mathbf{\text{r}},t)\}$, a spatially low-pass filtered version of the time-averaged field map, where $LP{F}_{x,y}\{\cdot \}$ is the same one used to generate ${I}_{avg,c}(\mathbf{\text{r}})$.

Figure 1 contains reconstructed image frames without and with the proposed correction, and the corresponding estimated dynamic field map. Near air-tissue interfaces, we observed rapid temporal variations.

Figure 2 contains representative image frames without and with the proposed correction. The proposed correction improved the depiction of air-tissue boundaries, especially the hard palate, soft palate, and tongue boundaries (see red arrows).

Figure 3 contains intensity
vs. time profiles from different image locations (dotted lines in Fig. 2). The
profiles allow one to easily appreciate the sharper air-tongue boundary.
Correction also results in more temporally consistent signal intensity in the
hard and soft palate (red arrows). This result agrees with the fact that the
hard palate, which is a bony structure covered by a thin layer of tissue, does
not change its shape during speech production^{14}.

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Figure 1. Long
spiral readout (readout duration = 4.016 ms) images (without and with the
proposed correction). The left column shows an image frame with no correction,
the middle column shows an image frame after the proposed correction, and the
right column shows the estimated field map corresponding to the image frame. The
estimated field map,
$\hat{\mathrm{\Delta}f}(\mathbf{\text{r}},t)$ only
captures the
time-varying off-resonance frequency ($f(\mathbf{\text{r}},t)-LP{F}_{x,y}\{(1/N)\sum _{t=1}^{N}\mathrm{\Delta}f(\mathbf{\text{r}},t)\}$). The
field map here is masked based on image intensity such that noise area has zero
frequency value.

Figure 2. Representative
mid-sagittal image frames of vocal tract in 2D RT-MRI of speech. The top row
shows images reconstructed with no correction and the bottom row shows images
reconstructed using the proposed correction. Red arrows point out the regions
that are most obviously affected by off-resonance. Image after correction
provides improved image depiction of the air-tissue boundaries such as the tongue,
hard palate, and soft palate as shown with red arrows.

Figure 3.
Comparison of image quality of articulator boundaries. The images show
intensity vs. time profiles from cut-views lines that are extracted from three
different locations marked by the white dotted lines in Figure 2. The profile
after correction exhibits the sharper boundary between tongue and air than those
with no correction. In addition, correction results in more temporally
consistent signal intensity in the hard palate and soft palate (red arrows in
the middle and right columns).