Real-time dynamic vocal tract imaging using an accelerated spiral GRE sequence and low rank plus sparse reconstruction

Abstract

Purpose:

To develop a real-time dynamic vocal tract imaging method using an accelerated spiral GRE sequence and low rank plus sparse reconstruction.

Methods:

Spiral k-space sampling has high data acquisition efficiency and thus is suited for real-time dynamic imaging; further acceleration can be achieved by undersampling k-space and using a model-based reconstruction. Low rank plus sparse reconstruction is a promising method with fast computation and increased robustness to global signal changes and bulk motion, as the images are decomposed into low rank and sparse terms representing different dynamic components. However, the combination with spiral scanning has not been well studied. In this study an accelerated spiral GRE sequence was developed with an optimized low rank plus sparse reconstruction and compared with L1-SPIRiT and XD-GRASP methods. The off-resonance was also corrected using a Chebyshev approximation method to reduce blurring on a frame-by-frame basis.

Results:

The low rank plus sparse reconstruction method is sensitive to the weights of the low rank and sparse terms. The optimized reconstruction showed advantages over other methods with reduced aliasing and improved SNR. With the proposed method, spatial resolution of 1.3*1.3 mm² with 150 mm field-of-view (FOV) and temporal resolution of 30 frames-per-second (fps) was achieved with good image quality. Blurring was reduced using the Chebyshev approximation method.

Conclusion:

This work studies low rank plus sparse reconstruction using the spiral trajectory and demonstrates a new method for dynamic vocal tract imaging which can benefit studies of speech disorders.

INTRODUCTION

The production of human speech is a complex process and requires cooperation of multiple organs and vocal structures including the lungs, diaphragm, larynx, pharynx, vocal cords, tongue, lips and soft palate (velum). (1). A number of acquired and inherited diseases including cancer (2), cleft lip and/or palate (3), vocal cord nodules and polyps (4) and neurological conditions (5) can affect the function of certain organs to cause speech disorders. For example, during most speech sounds, elevation and posterior retraction of the velum closes the velopharyngeal port, which prevents nasal air emission and directs airflow and voice through the oral cavity. Incomplete closure of the velopharyngeal port causes abnormal nasal airflow and results in a speech impediment known as velopharyngeal insufficiency and is commonly seen in children with a cleft palate repair. Dynamic imaging during speech can be used to evaluate the movement patterns of multiple organs for accurate clinical assessment including endoscopy and X-Ray fluoroscopy (6–8). However, endoscopy is invasive and causes patient discomfort and fluoroscopy is limited by the soft-tissue contrast and leads to radiation exposure. Magnetic resonance imaging (MRI) has the advantage of good soft tissue contrast, noninvasiveness and no ionizing radiation, so that it is a more attractive imaging modality in a clinical environment. However, the relatively slow imaging speed has posed a great challenge for real-time dynamic MRI during speech, especially with the requirements of high spatial and temporal resolution and signal-to-noise ratio (SNR). In clinical practice, it is often a balance between the resolution and SNR.

Various techniques have been developed to accelerate real-time dynamic MRI during speech including sequence design, k-space sampling and image reconstruction. Radiofrequency (RF) spoiled gradient echo (GRE) and steady-state free precession (SSFP) sequences can be optimized to have minimal repetition time (TR) for fast imaging. Although SSFP, especially balanced SSFP, has higher SNR in theory, the air-tissue boundary in the upper airway can cause severe off-resonance to affect the steady state and thus reduce SNR, and may even lead to more severe banding artifacts with balanced SSFP. Therefore, a GRE sequence is usually preferred in this application. In order to reduce scan time using the GRE sequence, the field-of-view (FOV) can be reduced to only focus on the region-of-interest (ROI) by applying spatial saturation bands to suppress signals outside the ROI. In k-space sampling, non-Cartesian trajectories such as radial and spiral (9) trajectories have higher acquisition efficiency and thus are preferred. The spiral trajectory is also more robust to motion as the gradient moments are not accumulated (10) and have been shown to be superior to the radial trajectory in non-accelerated real-time cardiac MRI (11). However, one important issue with the spiral trajectory is the sensitivity to B0 inhomogeneity as the images will be blurred with off-resonance, which can be even worse near air-tissue boundaries. This can be addressed using various correction methods such as linear correction (12) and model-based correction with Chebyshev approximation (13). A new method was recently proposed using the phase of single-TE dynamic images and showed improved sharpness (14). In image reconstruction, acceleration can be achieved by undersampling the k-space of every frame and utilizing the combination of parallel imaging with multiple surface coils (15–17) and compressed sensing with spatial and temporal sparsity (18–20) in model-based reconstruction using various spatial-temporal models. With the spiral trajectory, the SPIRiT method (17) has advantages over other non-Cartesian parallel imaging methods and has been combined with compressed sensing relying on the sparsity in the image differences between consecutive frames in dynamic velopharyngeal imaging using the l1-SPIRiT framework (20). However, one disadvantage of this method is that each coil image needs to be reconstructed separately so that the reconstruction time is very long. Even with coil compression, the final number of compressed coils is often larger than 4 in practice without losing too much information. Low rank plus sparse matrix decomposition is a new method with the advantages of improved reconstruction quality due to the separation of low rank and sparse components and faster computation as the final coil-combined image is the direct reconstruction target (21). However, the combination of this reconstruction method with the spiral trajectory has not been well studied, as well as the effects of different hyper-parameters on the reconstructed images.

The goal of this study is to develop an accelerated imaging method using a spiral GRE sequence and low rank plus sparse reconstruction for real-time vocal tract imaging and evaluate it during speech. Sequence details including spiral trajectory design, spatial saturation for reduced FOV, acceleration factors and spatial and temporal resolution will be optimized for this specific application. Low rank plus sparse reconstruction, followed by the Chebyshev approximation off-resonance correction method, will be evaluated. The following sections describe these methods in detail.

METHODS

K-space Trajectory

In dynamic MRI using a non-Cartesian k-space trajectory, a golden-angle based acquisition strategy by rotating each radial/spiral interleaf with 137.5° for every TR was used, because it can reduce temporal blurring by maximally de-correlating the temporal sampling pattern (22–23). For each interleaf, as the center k-space carries more energy than the edge k-space, a linear variable-density design (24) in which the sampling density linearly decreased from 3.5x to 0.1x of the Nyquist sampling limit was used. The ratio is with respect to a fully sampled k-space trajectory containing 18 interleaves in our design. Note that we ignored the actual angle of each interleaf as it was rotated following the golden-angle method. We targeted 6x acceleration to reconstruct one frame per 3 interleaves so that the effective sampling density at the k-space center was 0.58x. For each interleaf, 1800 samples with 2 us sampling time were acquired resulting in a readout time of 3.6 ms.

Sequence Implementation and Reduced FOV

A real-time 2D spiral GRE sequence with RF spoiling was developed and used in this study. A mid-sagittal slice with 8 mm slice thickness was selected for visualization of the movement patterns of multiple organs and structures during speech. To increase spatial resolution without increasing sampling time, the FOV was reduced to 150×150 mm² and focused on a region-of-interest (ROI) around the upper airway. Two spatial saturation bands with 5 ms each were used to suppress signals outside of the ROI. Instead of applying the saturation bands every TR, which may significantly length the acquisition time, the bands were applied every 3 TRs, or every frame with the accelerated trajectory. Other sequence parameters were: TR: 6.96 ms, TE: 0.78 ms, flip angle: 20°. The resulting spatial resolution calculated from the maximum extent of the spiral k-space was 1.3×1.3 mm² and temporal resolution was 30 frames-per-second (fps). To increase the robustness of the Chebyshev approximation based off-resonance correction, a low-resolution field map was obtained using two single-shot spiral interleaves covering the center of k-space with different TEs at the beginning of data acquisition as the baseline in subsequent automatic per-frame field map estimation. This low-resolution dataset was also used for obtaining calibration information to estimate coil sensitivities, as will be discussed later.

The sequence was implemented on a Siemens Avanto 1.5 T scanner equipped with a 4-channel head coil and a 2-channel neck coil, of which the channels close to the ROI were turned on during experiments. Healthy volunteers with informed consent were scanned while being asked to pronounce specific phonetic sounds and sentences.

Low Rank plus Sparse Reconstruction

With 6x acceleration, only 1/6 of k-space was covered in each frame. To eliminate the severe aliasing artifacts using the direct non-uniform FFT (NUFFT) reconstruction, a model-based reconstruction was used that simultaneously takes advantage of the multiple receiver coils and temporal sparsity. With multiple receiver coils, if an accurate coil sensitivity can be acquired, the SENSE reconstruction method can give a SNR-optimal solution, given as

$$z_i=F{S}_{i}m$$ [1]

in which m is the image to be reconstructed, S_i is the sensitivity of the i^th coil, F is the acquisition matrix and Z_i is the acquired data. S_i is usually estimated from a low-resolution acquisition by dividing the reconstructed coil images with the coil-combined image. However, the robustness of this method is limited, especially with aliasing from movement. An eigenvalue approach was recently proposed to improve the sensitivity estimation from the k-space data itself (25); specifically, the sensitivity map S_i can be obtained as the main eigenvector of a reconstruction operator computed from the null space of a calibration matrix formed by full-sampled k-space data. In this study, as the fully sampled low frequency data was acquired for field map estimation, it was also used for estimating S_i.

The low rank plus sparse reconstruction model with multiple surface coils and the corresponding sensitivity map S_i can be expressed as:

$$mi{n}_{L,S}\frac{1}{2}{\sum }_i{\Vert E_i(L+S)-z_i\Vert }_2^2+{\lambda }_L\Vert L{\Vert }_{*}+{\lambda }_S\Vert TS{\Vert }_1$$ [2]

in which E_i = FS_i is the encoding matrix, represents the low-rank component (few non-zero singular values) and S represents the sparse component (few non-zero entries) of the dynamic image series to be reconstructed; ||L||_∗ is the nuclear norm or sum of singular values of L, ||TS||₁ is the l1-norm or sum of absolute values of the S after temporal difference transformation; λ_L and λ_S trade off data consistency versus the complexity of the solution. In this study, because the differences between consecutive frames are considered to be sparse as many regions remain static during speech, these temporal changes were used as the transformation T. Iterative soft thresholding of the singular values of L and of the entries of TS was used for solving Eq. [2]. In implementation, for the proposed spiral trajectory, the update step size t was reduced to 0.1 to avoid divergence, as compared with t = 1 in (21) for undersampled Cartesian and radial trajectories. The images reconstructed using zero-filling were used as the initial values and the iteration number was set to 40.

As shown in Eq. [2], the parameters λ_L and λ_S will affect the reconstructed images. Although λ_L and λ_S have been optimized for Cartesian and radial trajectory in cardiac applications (21), their effect in spiral trajectory and dynamic vocal tract imaging has not been studied. Specifically, in (21), the chosen values are: λ_L = 0.01 and λ_S = 0.01, which yielded the lowest root mean square error (RMSE) in a retrospective undersampling experiment using the radial k-space trajectory. Using this as a starting point, we compared the images using different λ_L and λ_S values around 0.01. Furthermore, the resulting decomposed L and S terms were calculated as well as the ratios of their norms to learn more about the decomposition.

For comparison, the L1-SPIRiT method was developed to reconstruct each individual coil image m_i by minimizing the following equation:

$$mi{n}_{m_i}\left\{{\Vert F{m}_i-z_i\Vert }_2^2+\lambda {\Vert (G-I)m_i\Vert }_2^2+\alpha {\Vert T{m}_i\Vert }_1^1\right\}$$ [3]

in which F is the acquisition matrix, G represents the SPIRiT kernel function and I is the identity matrix. The same temporal changes were used as the sparsity transformation T except it was applied to individual coil image. Note that the individual coil image is weighted by the coil sensitivity. In addition, we also implemented a method based on XD-GRASP (26) for the spiral trajectory, described as follows:

$$mi{n}_m\frac{1}{2}{\sum }_i{\Vert E_{i}m-z_i\Vert }_2^2+{\lambda }_S\Vert Tm{\Vert }_1$$ [4]

Compared with the low rank plus sparse reconstruction, the sparsity transformation is directly applied to the target image m. In implementation, it can be achieved by setting the low rank term set to 0 and only using the sparsity constraint. The same coil sensitivity was used. In solving for the optimal solution, the iterative soft thresholding method was used with the same parameter set such as step size and maximum number of iterations. Reconstruction was performed offline using MATLAB.

Off-Resonance Correction

Traditionally, for spiral k-space trajectory, a linear field map is estimated from a low-resolution pre-acquisition scan using two single-shot spirals at different echoes, followed by center frequency and linear gradient corrections (12). However, in this application, severe local off-resonance can happen near the air-tissue boundary and the off-resonance frequencies can change with the tongue and velum movements. Thus, an additional deblurring method, after correcting for the estimated linear field map, is needed to estimate and correct for the residual off-resonance frequencies on a frame-by-frame basis. Compared with estimating the original off-resonance frequencies, estimating the residual frequencies can reduce the possible range to avoid being trapped in local minima. A deblurring algorithm based on a Chebyshev approximation (26) can accurately estimate the residual off-resonance frequency and efficiently compensate for it. Furthermore, as demonstrated in (20), the deblurring method is compatible with any model-based reconstruction as the resulting image can serve as the 0^th order Chebyshev demodulated image the same way as the reconstructed image from a fully sampled spiral k-space, and the higher order demodulated images can then be obtained from inverse gridding. In this study, this deblurring method was implemented by first estimating and correcting for a constant linear field map, and then estimating and correcting for the residual off-resonance frequencies frame-by-frame to account for varied local off-resonance. The final images were compared with images reconstructed with no additional deblurring other than compensating for the linear terms.

RESULTS

Low Rank plus Sparse Reconstruction

Fig. 1 shows the reconstructed images of a given frame using different parameter sets. It is noted that other than for a few combinations of λ_L and λ_S, significant aliasing still exists in the final images. Table 1 shows the ratios between the norms of the low rank (L) and sparse (S) terms at the same set of parameter combinations. The ratio can vary significantly with different λ_L and can range from >200 to very close to 0. Furthermore, the larger the weight of the low rank term, the smaller the norm will be, or the more dominant the sparse term becomes. From Fig. 1, λ_L = 0.01 and λ_S = 0.1 yields the image with the least aliasing and best SNR and it corresponds to the L/S ratio of 1.43, indicating the norms of the low rank and sparse terms are comparable.

Figure 1.

Reconstructed images of a given frame using different values of λ_L and λ_S. The resulting images are very sensitive to the parameter selection. At λ_L = 0.01 and λ_S = 0.1, the image has the least aliasing and highest SNR.

Table 1.

The ratios between the norms of the low rank (L) and sparse (S) terms

λs╲ λL	0.0001	0.001	0.01	0.1	1.0
0.0001	76.84	4.06	0.55	0.004	0
0.001	220.69	6.74	0.64	0.004	0
0.01	224.89	19.23	1.37	0.003	0
0.1	224.89	19.55	1.43	0.006	0
1.0	224.89	19.55	1.42	0.01	0

Using the optimal parameter set, Fig. 2 shows the resulting images at 6 time points with an interval of 6 frames using the low rank plus sparse reconstruction method for a healthy volunteer on the 1.5 T scanner as well as the corresponding low rank and sparse terms. The low rank term (top) captures the global contrast changes since the images were acquired before arriving at the complete steady state and the first few frames were brighter than later frames. The sparse term focuses more on local changes, as shown in the middle row with much brighter regions reflecting tongue movements. Noise was also contained in the sparse term. The final images accurately captured tongue movements with minimal aliasing and reduced temporal smoothing, enabling accurate analysis of the movement patterns of the associated organs and structures for various applications.

Figure 2.

Reconstructed images using the optimal λ_L and λ_S at 6 frames and the corresponding low rank (L) and sparse (S) terms. The low rank term captures the global signal changes and the sparse term captures the detailed movements of the tongue and velum. Noise is also contained in the sparse term.

Fig. 3 shows the comparison using the low rank plus sparse reconstruction, the XD-GRASP and L1-SPIRiT of one frame (left) and the time curve at two lines (red: mid, blue: right). The low rank plus sparse images have higher SNR and less blurring near the air-tissue boundaries, indicating that this reconstruction can recover more fine details during tongue movements. The reconstruction time for low rank plus sparse is also significantly shorter than L1-SPIRiT as it solves for the final image instead of image of each coil. Using MATLAB installed on a laptop with 2.9 GHz CPU, the low rank plus sparse reconstruction takes about 20 seconds while the L1-SPIRiT takes over 10 minutes even after the coil is compressed.

Figure 3.

Reconstructed images using L1-SPIRiT (top), XD-GRASP (middle) and low rank plus sparse reconstruction (bottom). The temporal changes at red and blue are shown on the middle and right columns, respectively. Low rank plus sparse has the sharpest boundaries along the temporal direction, enabling accurate tracking of the tongue and velum movements.

Off-Resonance Correction

Fig. 4 shows the images without (left) and with (right) the Chebyshev approximation based off-resonance correction. The Chebyshev method shows its effectiveness in improving local sharpness, especially around the lip as indicated by the arrows. The airway between tongue and the palate is also much sharper with the Chebyshev method, which can facilitate a more accurate quantitative analysis when contours need to be drawn to calculate variables of interest such as the length between tongue and velum. One advantage of the Chebyshev method is its efficient computation. Because only a few (~15) gridding and FFT operations are needed for each frame, it can be run very rapidly.

Figure 4.

Images after off-resonance correction. Left: Image reconstructed correcting only for linear terms with a fixed field map. Right: Image reconstructed by estimating the residual off-resonance frequencies and correcting for them on a frame-by-frame basis with the proposed Chebyshev method. Local sharpness is improved with the Chebyshev method.

DISCUSSION

We have developed a real-time dynamic vocal track imaging method during speech using an accelerated spiral GRE sequence with low rank plus sparse reconstruction. A Chebyshev approximation based off-resonance correction method was used to reduce blurring related with the spiral trajectory, especially around the air-tissue boundary. Spatial resolution of 1.3×1.3 mm² and temporal resolution of 30 fps were achieved with good image quality at a reduced FOV of 150 mm.

The spiral k-space trajectory has the advantages of high data acquisition speed due to a more efficient sampling pattern and increased robustness to motion due to the non-accumulating gradient moments. When further acceleration is needed, such as in dynamic imaging applications, the trajectory is undersampled by acquiring a fraction of the interleaves every frame. To achieve maximum acceleration, parallel imaging with multiple coils was combined with compressed sensing-based methods with a temporal sparsity constraint. However, the temporal sparsity assumption can break or be weakened with global motion or contrast changes. The low rank plus sparse reconstruction is advantageous in that the low rank term can capture such global changes so that the sparse term can have an enhanced sparsity level. We demonstrated this property in real-time vocal tract imaging with the spiral trajectory. When the sparsity transformation is applied to the whole image, as in the XD-GRASP method, the SNR and temporal sharpness are reduced. Compared with L1-SPIRiT, which uses a SPIRiT kernel to utilize multiple coils and temporal differences as the sparsity transformation, another advantage of the low rank plus sparse reconstruction is that it uses the coil sensitivity and aims to directly reconstruct the final image so that it is much more efficient.

One possible issue of the low rank plus sparse reconstruction is that it is sensitive to the selection of the hyper-parameters, especially the weights of the low rank and sparse terms in the objective function. On many cases the reconstruction almost failed completely, which are due to imbalanced weights of the data consistency, low rank and sparse terms. In this study, a wide range of the parameters for each term were tested and most combinations yielded failed reconstruction with severe aliasing. We picked the optimal parameters from the experimental values. Although we did not conduct a rigorous search around the optimal values due to the difficulty in quantitatively comparing and evaluating the images, we found that within a small range of the optimal parameters, the performance is largely unaffected. We also studied the impact of each parameter on the decomposed terms. Interestingly, the larger the weights of the low rank term, the smaller this term will become in the final decomposition. We hypothesize that this is because with the higher weights, the norm of the whole low rank term is reduced as it is difficult to just reduce the sum of a few non-zero eigenvalues. However, doing this can reduce the sparsity level of the sparse term so that it can diminish the advantage of the decomposition. Empirically, we found that the decomposition that yields comparable terms leads to optimal results. When the λ_L is determined using this rule, the λ_S can be selected to balance between spatial aliasing and temporal sharpness. Similar to XD-GRASP and L1-SPIRiT, we found that the higher λ_s, the less spatial aliasing but more temporal blurring. With respect to the sparsifying transform, in this application, we choose the temporal difference as there is not a clear frequency pattern for the tongue and velum movements, and they may even be static when the subjects are not speaking. In either scenario, the movements, if any, are temporally continuous and the dynamic parts only account for a small portion of all voxels; therefore, the sparsity assumption will still hold. When there is little or no movements, as the proposed reconstruction utilizes the data consistency, low rank constraint and sparse constraint to get the final images, the sparse term will act similar as an averaging filter to increase the SNR of each frame. Once we obtained the optimal parameters, an encouraging news is that the proposed model works well on all subjects for this specific application. However, more validation is needed to evaluate whether these optimal parameters vary across different applications, such as in dynamic cardiac MRI.

For off-resonance correction, we used the Chebyshev approximation-based method to refine the field map obtained in the beginning of the scan on a frame-by-frame basis. Although the field map can be estimated without an acquired one, the estimation can suffer from local minima and thus lead to incorrect off-resonance correction. As center k-space data is also required in estimating the coil sensitivities and the acquisition is very short, we applied the field map acquisition in this study.

One potential limitation of this study is the lack of an objective and quantitative evaluation of the proposed data acquisition and reconstruction method as there is no ground-truth for comparison. Although retrospective undersampling is often used in such comparisons, for this application, due to the application of saturation bands every frame and the golden-angle rotation, it is very difficult to emulate the actual scenario at a desired spatial and temporal resolution. In addition, the commonly used evaluation criteria against the ground truth such as root mean square error and structure similarity index cannot fully reflect the image quality; therefore, no retrospective experiments were conducted but the comparison was mainly qualitative from the actual experiments. Future studies will be performed on more healthy volunteers and patients to quantitatively compare the proposed technology with other methods, for example, via blind ratings from radiologists, and explore novel applications.

In conclusion, a new imaging method was developed using an accelerated real-time spiral GRE sequence and the low rank plus sparse reconstruction method. The Chebyshev based off-resonance correction method was applied to reduce blurring from the spiral trajectory. This method can benefit the studies on speech disorders using dynamic MRI. In addition, the investigation of the low rank plus sparse reconstruction using a spiral trajectory is not limited to speech imaging but can be easily extended to other dynamic applications.