Nan Wang^{1,2}, Anthony Christodoulou^{1}, Yibin Xie^{1}, Zixin Deng^{1,2}, Zhaoyang Fan^{1,3}, and Debiao Li^{1,2}

We recently proposed two techniques, qMATCH and DCE, based on Low Rank Tensor (LRT) framework. qMATCH is a single 8-min scan for carotid T1 T2 mapping and LRT DCE is a 10-min scan evaluating inflammatory status of carotid atherosclerosis. The LRT DCE has many advantages over conventional DCE protocols, but has a scan time longer than typical 5-6 minutes. In this work, we proposed a new protocol combining qMATCH and 5-min DCE. In vivo studies have demonstrated the feasibility of the joint reconstruction. Results of joint reconstruction showed improved image quality with shortened scan time.

Sequence design and
sampling pattern: As described
previously^{5,6}, qMATCH part employed 3D flow-compensated spoiled
gradient echo readout (FLASH) with
variable-duration T2-IR preparations to generate T1 and T2 contrast. The DCE sequence implemented
the same FLASH readout following SR preparations. Cartesian acquisition with randomized
reordering in ky and kz directions was implemented according to a
variable-density Gaussian distribution. The center k-space line was collected every eighth readout to serve as
LRT training data^{4}.

Joint reconstruction: qMATCH images form a 3-way tensor
$$$\mathscr{A}_1$$$ with spatial dimension
$$$\mathbf{r}=(x,y,z)$$$, an IR dimension $$$T_I$$$, and a T2prep-duration dimension $$$T_E$$$. DCE images form a 3-way tensor $$$\mathscr{A}_2$$$ with a spatial dimension $$$\mathbf{r}$$$, an SR dimension $$$\tau$$$, and a DCE dimension *t*. Due to the strong correlation between
images with different contrasts, each tensor is low-rank with a shared spatial subspace and can be factorized as
$$$\mathbf{A}_{1,(1)}=\mathbf{U\Phi}_1$$$ and
$$$\mathbf{A}_{2,(1)}=\mathbf{U\Phi}_2$$$, where the rows of $$$\mathbf{\Phi}_1$$$ and $$$\mathbf{\Phi}_2$$$ span temporal tensor subspaces
for qMATCH and DCE, respectively. In the joint recon, $$$\mathbf{\Phi}=[\mathbf{\Phi}_1,\mathbf{\Phi}_2]$$$ are determined together from subspace
training data $$$\mathbf{D}_{\rm{tr}}=[\mathbf{D}_{\rm{tr,1}},\mathbf{D}_{\rm{tr,2}}]$$$.
$$$\mathbf{U}$$$, the spatial coefficients for both qMATCH
and DCE, is then recovered by fitting $$$\mathbf{\Phi}$$$ to the remainder of the sparsely sampled data.

Motion removal: Abrupt patient motion is a major
challenge for vessel wall scan due to the
small anatomical structure. In the LRT framework, abrupt-motion frames are less correlation to the remainder of
the images, corresponding to a higher residual after LRT estimation. The residual
$$$\boldsymbol{r}_{res}$$$ is calculated by:
$$\boldsymbol{r}_{res}=\sum\nolimits_{i}|(\mathbf{D}_{\rm{tr}}-\mathbf{D}_{\rm{tr}}\mathbf{\Phi}^\dagger\mathbf{\Phi})_{ij}|^2,$$Where
$$$\mathbf{D}_{\rm{tr}}\in\mathbb{C}^{N_r\times N_t}$$$ is the matrix form of subspace training data. $$$N_r$$$ and $$$N_t$$$ represent the total number of voxels and time points, respectively. High-residual time points were removed and recovered by LRT framework during the recovery of
subspace training data inherently^{4}.

Imaging protocol: All data were acquired
on a 3T commercial MR scanner (MAGNETOM Verio, Siemens Healthineers, Erlangen, Germany).
Healthy subjects (n=2) were scanned with the following parameters: coronal orientation, spatial resolution=0.7mm
isotropic, FOV=150x150x26mm^{3},
$$$\alpha =8^\circ$$$, echo spacing=11ms. For qMATCH part, TR=2360ms, T2-prep duration=20/30/40/50/60/70ms, scan duration=8min. For DCE part, TR/temporal resolution=590ms,
scan duration = 5min.

Data
analysis: We reconstructed the acquired data in two
ways. One is the described joint reconstruction, the other is solo reconstruction
of the 5-min DCE data only^{6}. In the analysis, we compared the SNR
and sharpness of DCE images from these two reconstruction methods.

1 Kerwin, W. S., Oikawa, M., Yuan, C., Jarvik, G. P. & Hatsukami, T. S. MR imaging of adventitial vasa vasorum in carotid atherosclerosis. Magn Reson Med 59, 507-514, doi:10.1002/mrm.21532 (2008).

2 Yuan, C., Oikawa, M., Miller, Z. & Hatsukami, T. MRI of carotid atherosclerosis. Journal of nuclear cardiology 15, 266-275 (2008).

3 Cai, J.-M. et al. Classification of human carotid atherosclerotic lesions with in vivo multicontrast magnetic resonance imaging. Circulation 106, 1368-1373 (2002).

4 Christodoulou, A.G., Shaw, J.L., Sharif, B., Li, D. A general low-rank tensor framework for high-dimensional cardiac imaging: application to time-resolved T1 mapping. 24th Annual Meeting of ISMRM, Singapore, 2016. Abstract 3032.

5 Xie, Y., Christodoulou, AG., Wang, N., Li, D. Quantitative Multi-Contrast Atherosclerosis Characterization (qMATCH): Comprehensive Quantitative Evaluation of Atherosclerosis in a Single-Scan. 25th Annual Meeting of ISMRM, Honolulu, HI, USA, 2017. Abstract 5148.

6 Wang, N., Christodoulou, AG., Xie, Y., Li, D. Quantitative 3D Dynamic Contrast Enhanced (DCE) Imaging of Carotid Vessel Wall by Fast T1 Mapping. 25th Annual Meeting of ISMRM, Honolulu, HI, USA, 2017. Abstract 7331.

Fig
1: Example images for joint reconstruction and DCE-only reconstruction at peak
enhancement. (A) is the images of DCE-only reconstruction. Yellow arrows on the images point out some areas with severe artifacts. (B) is the images of joint reconstruction.
The upper images are displayed in coronal orientation, while the lower in
transversal orientation. With joint reconstruction, the images were sharper
with alleviated artifacts.

Fig 2: Another example of images
comparing joint reconstruction and DCE-only
reconstruction at peak enhancement.

Table 1: SNR and sharpness of images for
joint reconstruction and DCE-only reconstruction. For both cases, the SNR of
images with joint reconstructions were
more than 2 times higher comparing the result with DCE-only reconstruction.
Images with joint reconstruction also had better sharpness.