Ramped Hybrid Encoding for Improved Ultrashort Echo Time Imaging

Ramped Hybrid Encoding

We propose RHE as a technique to allow the greatest flexibility compared to currently available methods in controlling unwanted slice selectivity while optimizing overall encoding time for UTE imaging. Figure 2-a shows the pulse sequence diagram for RHE. In RHE, an initial gradient during RF excitation, G_RF, is chosen to be small enough to minimize slice selectivity (by considering the limitations of the frequency profile of the RF pulse). After application of the RF pulse, the gradient is ramped to the maximum encoding amplitude, G_max, at the highest slew rate possible to minimize overall sampling duration. Data are acquired after RF deadtime until the desired spatial resolution is achieved.

As in PETRA, RHE utilizes SPI to measure data in central k-space regions that frequency encoding omits during RF deadtime. Central k-space is encoded by Cartesian SPI, and the outer k-space is acquired by frequency encoding as shown in Figure 2-b. Note that in Figure 2-a the solid line in the pulse sequence diagram (PSD) shows the gradient amplitude along the readout direction used to scan half radial spokes (blue arrows in Figure 2-b). The readout gradient is then rotated at each TR to frequency-encode k-space. In Cartesian SPI sampling (red dots in Figure 2-b), the maximum gradient amplitude is linearly scaled as dotted lines in Figure 2-a shows to encode different k-space point at the constant encoding time over TRs. Note that the same maximum gradient is applied to both SPI and frequency encoding to prevent discontinuity in encoding times at the interface between the two different encoding schemes. This acquisition can also be extended to multi-echo acquisitions, where Figure 2-c shows the pulse sequence used to obtain multi-echo RHE images with 5 half-echoes obtained within a single acquisition. Note that SPI encoding is used to fill the central region of k-space in each half-echo.

In RHE, the diameter of the SPI-encoded region in k-space, N_SPI, is determined by the following equation.

where γ̄ is the gyromagnetic ratio in unit of HzT^-1, g_S denotes gradient slew rate in units of Tm^-1s^-1, fov_D denotes the desired FOV, and t_D is the desired echo time chosen after deadtime. Due to eddy currents that effectively derate the gradients in ramping, SPI data are prone to be slightly oversampled and hence result in a larger FOV than the desired FOV (fov_D) at the desired TE (t_D). The FOV can be corrected in the reconstruction stage using conventional convolution gridding methods. In practice, larger N_SPI can be intentionally used to obtain oversampled SPI data allowing some flexibility in selecting TE when RF deadtime is not known a priori.

The maximum gradient amplitude during RF excitation, G_RF, can be selected by considering both slice selectivity and N_SPI. An upper bound for G_RF can be analytically determined using the expected RF pulse shape and its frequency profile. However, large G_RF amplitudes may result in impractical scan times due to the large required N_SPI. In that case, G_RF needs to be reduced to allow reasonable scan times. The maximum readout gradient, G_max, can be as large as possible within the constraints of the readout bandwidth and safety factors such as gradient heating and peripheral nerve stimulation.

Gradient calibration

In RHE, data is acquired during ramping gradients. Therefore, timing errors and eddy current effects may distort the k-space sampling trajectory, and hence naïve reconstruction based on the prescribed gradient parameters is generally not suitable. In this study, we developed a rapid new calibration method that benefits from the well-known zoom-in effect (decreasing FOV with increasing phase encoding time delay) in SPI(15,16,29), based on a similar concept to previous work by Balcom et. al(30). For calibration, three sets of 1D projection images are acquired using an SPI scheme in each gradient axis. Note that 1D SPI imaging can be easily implemented in any pulse sequence by scaling the gradients to enable pure phase encoding. Typically this calibration data can be acquired very rapidly, within several seconds for all gradient axes.

1D single point images can be reconstructed without calibration. The three sets of 1D projection images across a range of encoding time are reconstructed at native FOVs (exploiting the zoom-in effect), as depicted in Figure 3. The image matrix shown in Figure 3-a contains 1D projection images (y-axis) versus phase encoding time delay (x-axis) for a gradient direction encoded by 1D single point imaging. The size of the object (bright region in center of FOV) increases with encoding time (zoom-in effect). The speed of the FOV change in Figure 3-a is directly proportional to the gradient strength shown in Figure 3-b, exhibiting acceleration in ramping up, constant change in plateau, and deceleration in ramping down. Therefore, the gradient waveform can be calibrated by directly computing the scaling factors between neighboring phase encoding time delays within the 1D images.

The FOV scaling factors between images are found automatically using unconstrained nonlinear optimization (Nelder-Mead Simplex). A reference image is first selected as the latest time delay, t_ref, and the relative scaling factors between t_ref and other time delays are found by minimizing the L2-norm of the error function as shown in the following equation.

, where I(t,x) denotes magnitude of 1D image at encoding time t and spatial position x, N is 1D matrix size, s is a scaling factor between images, and N_c is index for the center of image (e.g., for matrix size=N, N_c=[N/2]). Images are transformed based on the scaling factor, s, to find the best scaling factor. This scaling transformation can be performed in the either image or k-space domain by using an affine transform or convolution gridding, respectively. In this study, the transform was performed in the image domain using bilinear interpolation because it provided reliable results that could be computed much faster than using a gridding approach.

Once proper FOV scaling factors are found across all phase encoding time delays, relative k-space position can be recovered. Note that the FOV scaling factors only describe the relative scaling difference between encoding times. To obtain the absolute FOV, we examine the RHE data acquired during constant gradient. First, the slope of FOV scaling factors is calculated at a time (t_ref) when the gradient is constant (and known) G_max. Then, the slope can be used to calculate the true FOV at the reference encoding time, t_ref, using following equation.

, where c is slope of FOV scaling factor found at constant gradient. Now, the FOV for the entire encoding time, FOV(t), can be recovered by simply using equation 2 with the given FOVscale(t) and FOV(t_ref).

Image reconstruction

After the k-space trajectories are estimated via the above gradient calibration method, the acquired SPI and radial data are combined together. 3D convolution gridding is applied to obtain the k-space with desired FOV(31–33). To control variable density sampling within k-space, iterative density compensation(34) is applied. Note that the sampling density along a half radial spoke in frequency encoding sampling density is dependent upon the readout bandwidth and the shape of the encoding gradient, while within the SPI region it is determined by TE and the shape of the encoding gradient. In Figure 4, a block diagram shows how raw data are processed to obtain a final RHE image.

Computer simulation

To compare encoding times and the resultant image quality between RHE and other UTE imaging schemes, a 1D computer simulation was performed. Note that a conventional point spread function (PSF) simulation is not possible because the PSF is spatially-variant at each encoding position in k-space, as described above. Therefore, each point in k-space was independently simulated with different slice selectivity resultant from the differing encoding gradient amplitude, as described above. To generate the 1D digital phantom, 11 tubes were generated with different proton densities, 0.7, 1.0, 0.7, 0.3, 0.7, 1.0, 0.7, 0.3, 0.7, 1.0 and 0.7 in arbitrary units from left to right. The diameter of each tube was 40mm. A mono-exponential T₂* decay model (T₂* = 100μs or 500μs) was simulated for all tubes.

System parameters included a TE of 80μs, a slewrate of 118 mTm^-1ms^-1, and a maximum gradient of 35 mTm^-1. For PETRA G_max = 7 or 20 mTm^-1 was used. For RHE, G_RF = 3.5 or 7 mTm^-1 and G_max = 35 mTm^-1 was used. For RHE and FE-UTE, the gradients were ramped immediately after the RF pulse or after deadtime, respectively. 1D sampling was simulated using frequency encoding or PETRA/RHE encoding to acquire a 500x1 k-space with FOV=500mm, which achieves approximately 1mm resolution. For PETRA and RHE, the slice selectivity effect was simulated using the spatial profiles of the 24μs hard pulse shown in Figure 1-b. N_SPI was set to the minimum value according to the prescribed gradient shape (N_SPI=24, 69, 29, and 40 respectively for PETRA with G_max=7mTm^-1, PETRA with G_max=20mTm^-1, RHE with G_RF=3.5mTm^-1, and RHE with G_RF=7mTm^-1). No eddy current effects were applied in the computer simulation.

Experimental setup

To evaluate the proposed encoding scheme, MR experiments were performed on a 3.0T MR scanner (MR750, GE Healthcare, Waukesha, WI). A phantom experiment was performed to compare UTE imaging schemes (PETRA, FE-UTE, and RHE) with an object that only has short T₂* components. Human brain imaging was performed with 2 different RF pulses (8μs, 24μs) with flip angle 2^° and 6^° respectively) and gradient settings. A multi-echo RHE experiment to generate a short T₂* image was performed in the human knee.

For phantom experiments, a phantom made of Acrylonitrile Butadiene Styrene (ABS) plastic (Big Ben, item # 21013, a cowboy minifigure from Palace Cinema, item # 10232, and a white horse made by LEGO, Billund, Denmark) with T₂* approximately 400-500μs. An 8-ch receive-only head coil (High Resolution Brain Coil, GE Healthcare) was used for the phantom experiment. For in vivo experiments, a human subject was imaged in accordance with local IRB protocols. The 8-ch receive-only head coil was used for in vivo brain imaging, and an 8-ch transmit-receive knee coil (GE Precision Eight Knee Array Coil, Invivo, Gainsville, Florida) was used for in vivo knee imaging.

All parameters used for the phantom, knee, and brain imaging are shown in Table 1. A single echo acquisition (as shown in Figure 2-a) was performed in phantom and brain imaging, while multi-echo imaging (as shown in Figure 2-c) was performed in the knee. For all datasets, the TE was 90μs, which is defined as the first encoding time after which the receiver is fully recovered from RF deadtime (as shown in Figure 3-a). Deadtime was determined empirically by observing the signal magnitude at the center of k-space. A sampling period of 2μs was used. In the phantom and knee imaging experiment comparing PETRA, FE-UTE, and RHE, N_SPI and TR were set identically to allow reasonable comparisons between imaging schemes. N_SPI was set to 33, the largest N_SPI required by PETRA with largest G_max (=20mTm^-1), while TR was set to 3.3ms, is the minimum TR of PETRA with lowest encoding gradient (G_max=7mTm^-1). Due to the reduced encoding duration, the minimum possible TR for RHE can be significantly shorter (approximately 2ms).

To perform gradient calibration, three 1D 401×1 SPI images were acquired along each physical gradient axis by linearly scaling the encoding gradient over TRs (401 equispaced steps between -1.0× and 1.0× of gradient shape to calibrate). The additional scan time required for the calibration was 401(encodings/axis) × 3(axis) × TR, which was 4 sec for the single echo acquisition and 6.7 sec for the multi-echo acquisition. For a more reliable calibration, SPI-based calibration was first performed using a spherical phantom (in a separate imaging session on a separate day and only once for all experiments), which was then used as the initial guess during calibration. The proposed SPI-based calibration was applied to both FE-UTE and RHE imaging.

During image reconstruction, convolution gridding was performed using a Kaiser-Bessel kernel with grid width=5 (for phantom and head imaging) or 7 (for knee imaging) and oversampling ratio=2. Phantom data were gridded to achieve FOV=200mm and matrix size of 201×201×201, and brain data were gridded to achieve FOV=240mm and matrix size of 241×241×241, which is equivalent to 1mm resolution. In the knee experiment five 3D knee images were reconstructed at TE=90μs, 1502μs, 1550μs, 2900μs, and 2950μs with FOV=200mm and a matrix size of 401×401×401, which is equivalent to 0.5 mm resolution. Separate fat and water images were computed using Iterative Decomposition of water and fat with Echo Asymmetry and Least-squares estimation (IDEAL)(35). Because we do not expect the short T₂* species to have different image phase, all five images were used for the IDEAL reconstruction using a non-R₂* corrected model. The image representative of short T₂* species was obtained by subtracting the computed water and fat images from the RHE image at TE=90μs.

Gradient calibration, gridding, and IDEAL reconstruction were performed using MATLAB (The Mathworks, Natick, MA) on a Linux computer with an Opteron 6134 processor (64 bit, 16 core).

Simulation results

Figure 5 shows the simulated curves for the per-excitation encoding time in three different UTE encoding schemes, conventional FE-UTE, PETRA, and RHE, (Figure 5-a) and the corresponding reconstructed images (Figure 5-b,c). As seen in Figure 5-a, RHE with G_RF=7mTm^-1 allows the shortest per-excitation encoding time (=429μs) between the three methods (1669μs for PETRA with G_max=7mTm^-1, 584μs for PETRA with G_max=20mTm^-1, 562μs for FE-UTE, and 454μs for RHE with G_RF=3.5mTm^-1) while controlling for blurring caused by T₂* or the finite RF pulse duration. The reconstructed images with normalized scales are shown in Figure 5-b,c. Root Mean Squared Error (RMSE) was calculated to compare the simulated images (with normalized scales) to the 1D digital phantom.

When T₂* is extremely short (100μs), RHE with G_RF=3.5mTm^-1 provides the most accurate reconstruction (RMSE=0.061) owing to its optimized encoding time and controlled slice selectivity. PETRA images show good fidelity at the center of the FOV, but exhibit loss of detail toward the edges due to the unwanted slice selectivity imposed by high encoding gradients applied during RF excitation. Note that PETRA with G_max = 20mTm^-1 provides good reconstruction at the center of the FOV owing to the large N_SPI(=69) where encoding time is constant (=TE), resulting in less intra-readout T₂* decay. However, a larger N_SPI significantly increases the total image acquisition time and is not clinically feasible. FE-UTE shows uniformly reasonable results over the entire FOV as expected. When T₂* is moderately short (=500μs), FE-UTE shows the overall best reconstruction (RMSE=0.025), while RHE with G_RF=3.5mTm^-1 shows a comparably accurate reconstruction (RMSE=0.046), particularly in the central region of the FOV.

Gradient calibration

Figure 6-a shows 1D projections from the x-axis of a calibration dataset reconstructed at the native FOVs and exhibiting the zoom-in effect (decreasing FOV with increasing phase encoding time delay). Figure 6-b shows the FOV scaling factors found between images in x-direction where ‘x’ shows five FOV scaling factors corresponding to the five images in Figure 6-a. Figure 6-c shows the calibrated trajectory along 3 gradient orientations. Note that the estimated trajectories are different between gradient axes. Figure 6-d shows the measured trajectory, the prescribed trajectory, and delay-corrected trajectory obtained in the physical z-gradient direction. The delay-corrected trajectory was obtained by matching the linear part of the prescribed k-space trajectory with the measured trajectory. The two superimposed curves for measured trajectory and the delay-corrected trajectory show little difference in the ramping portion of the encoding gradient. As seen in the images reconstructed with the three different k-space trajectories in Figure 6-e, small errors result in significant and obvious reconstruction error as shown in the region yellow arrow indicates, which shows misalignment between low and high frequency component in image due to the erroneous gradient calibration.

Estimation of the k-space trajectory could be computed rapidly. The proposed method required approximately 2 sec to process one image, which equates to 2 (sec/image) × 230 (images) / 12 (# of parallel computation) ≈ 38 sec for single echo imaging and 2 (sec/image) × 1,630 (image) / 12 (# of parallel computation) ≈ 272 sec for multi-echo imaging.

Phantom experiment

Figure 7 shows the results of the phantom experiment. Note that in the reconstructed images, RHE (Figure 7-e) preserves the high frequency details of the phantom much better than PETRA (Figure 7-a,b,c) and FE-UTE (Figure 7-d).

PETRA with G_max = 7 mTm^-1 (Figure 7-a) exhibits severe blurriness across the image, due to the long encoding time. PETRA with G_max = 14 mTm^-1 (Figure 7-b) shows an improved depiction of the object, but exhibits blurriness along the radial direction at the edge of the FOV, which is due to unwanted slice selectivity. PETRA with G_max = 20 mTm^-1 (Figure 7-c) shows the best spatial resolution in the center of the FOV and the worst slice selectivity artifact at the corners of the FOV due to the large gradient applied during RF excitation. FE-UTE (Figure 7-d) shows a good depiction of the object with no slice selectivity artifact. RHE (Figure 7-e) shows higher detail owing to the shorter per-excitation encoding time and the central k-space encoded by SPI (with TE equal to 90μs). The SNR of RHE (measured SNR=10.3) is higher than FE-UTE (measured SNR=8.7).

In vivo - knee imaging

Figure 8 shows coronal or sagittal slices of knee images at five different TEs obtained using RHE with multi echo imaging capability (Figure 8-a,b,c,d,e,i,j,k,l,m), water images (Figure 8-f,n) and fat images (Figure 8-g,o) obtained using IDEAL, and the resultant short T₂* images (Figure 8-h,p). Note that short T₂* images, tissues such as bone, tendon, and ligament are visible with positive contrast. In the coronal plane short T₂* image (Figure 8-h), the medial collateral ligament and lateral collateral ligament (white arrow) and the medial meniscus (yellow arrow) are visible. In the sagittal plane short T₂* image (Figure 8-p), the quadriceps femoris tendon (blue arrow), patellar ligament (green arrow), and anterior cruciate ligament (red arrow) are seen clearly.

In vivo - Brain imaging

Figure 9 shows brain images obtained by PETRA, FE-UTE, and RHE with two different RF pulse lengths and for PETRA, three different readout gradient amplitudes. The left 4×5 image matrix shows 2D slices selected from the reconstructed 3D images, and the right 4×5 image matrix shows corresponding zoomed-in images. Figure 9-a to Figure 9-j show images at a mid-sagittal plane, while Figure 9-k to Figure 9-t show images at an axial plane. Figure 9-a,b,c,k,l,m and Figure 9-f,g,h,p,q,r show PETRA images obtained with 8μs and 24μs respectively. In PETRA with a short RF pulse (8μs), slice selectivity is suppressed owing to the relatively broad excitation bandwidth, but SNR is reduced due to the smaller attainable flip angle. Note that with an 8μs RF pulse, images are more proton density weighted, while with a longer RF pulse (24μs) increased T₁ weighting can be achieved. With the 24μs RF pulse, the slice selectivity artifact is more noticeable in PETRA, substantially deteriorating with higher G_max (Figure 9-g,h,q,r), while the chemical shift artifact is aggravated as encoding time decreases with lower G_max (Figure 9-a,f,k,p).

Compared with PETRA, both FE-UTE (Figure 9-d,i,n,s) and RHE (Figure 9-e,j,o,t) show much better image quality with higher spatial resolution and no or minimal slice selectivity artifact respectively. However, as shown in the zoomed-in sagittal images of FE-UTE in Figure 9-d,i and RHE in Figure 9-e,j, RHE exhibits higher signal intensity than FE-UTE in occipital bone indicated by the yellow arrow. In addition, RHE shows higher signal in a tooth as indicated by the green arrow in Figure 9-i,j. In axial images, both RHE and FE-UTE show detailed views of the tissues in the sinuses as shown in zoomed-in images of Figure 9-s,t. Note that the red arrow indicates in Figure 9-s,t RHE shows higher signal intensity than FE-UTE in the region where the meninges are visible.

Overall, among the UTE imaging schemes presented here, RHE shows the highest spatial resolution, best short T₂* contrast, no apparent chemical shift artifact owing to the shortest per-excitation encoding time, and well-controlled slice selectivity with a 8μs or 24μs RF pulse.