Dynamic contrast-enhanced (DCE) 3D MRA has been widely used for diagnostic assessment of vascular morphology and hemodynamics in a clinical routine.¹ It acquires a series of time-resolved images, revealing details on contrast dynamics. To extract angiograms while eliminating unwanted background tissues, subtraction between the reference (pre-contrast) and DCE images in each time frame is typically employed. However, in the presence of non-stationary background signal transition such as subject motion and time-varying magnetic field, subtraction results in incomplete background suppression and noise amplification. Due to the inherent, subtraction sparsity in either between the reference and each dynamic image or between neighboring time frames, compressed sensing (CS) is well suited to DCE MRA to enhance spatial and temporal resolution.² Nevertheless, these approaches remain suboptimal due to the inherent limitation of subtraction. In this work, we propose a new, DCE MRA method called “concentration time-course Model-based Angiogram SEparation (MASE)”, in which DCE signals in the temporal direction are directly modeled and reconstructed with sparsity priors while background signals are attenuated.

Concentration Time-Course Model-based DCE Signal Model: It is assumed that concentration time-course can be described by a single compartment recirculation (SCR) model consisting of exponential transient phases and steady state phase,³ while stationary tissues remain nearly identical over the entire dynamic phases. Additionally, since subject motion is sporadic and incoherent, motion-induced signals with changing time tend to be much less correlated than the concentration time-course in blood vessels. Although the concentration time-course is non-linear, we hypothesize that it can be delineated by linear superposition of the temporal basis that is found by performing singular value decomposition of the SCR model-based, simulation data: $$$D=UΣV^H$$$ where $$$D$$$ is the row-vectorized (concentration time-course), stacked (row-wise) simulation data, $$$U$$$ is the basis of the column vectors, $$$V$$$ is the basis of the row vectors and becomes the temporal basis of the concentration time-course, $$$Σ$$$ is the singular value matrix. Figure 1 represents the variation of eigenvalues in $$$Σ$$$ and its corresponding eigenvectors in the temporal basis $$$V$$$. Since most of singular values are close to zero, the concentration time-course can be synthesized using only a few principal eigenvectors in $$$V$$$. Given the considerations above, the proposed DCE signal model can be written by: $$$X = X_0 + X_{\mathrm{DCE}} + N ⋍ X_0 + UV_r + N$$$ where $$$X$$$ is the Casorati matrix that an image column vector in each time frame is stacked column-wise over the entire dynamic phases, $$$X_0$$$ is the reference matrix consisting of the mean column vector by averaging the pre-contrast images, $$$X_{\mathrm{DCE}}$$$ is the dynamic angiograms of interest, $$$V_r$$$ is the truncated temporal basis, and $$$N$$$ is the additive noise matrix.

Model-based Angiogram Separation (MASE): The proposed angiogram reconstruction from undersampled k-t space is performed by solving the following constrained optimization problem with sparsity prior: $$ U=\underset{U}{\mathrm{argmin}} ||U||_1 \qquad s.t\quad d_r=F_{\mathrm{u}}(UV_r)$$ where $$$d_r$$$ is the measured, residual (k-t space) between the reference and DCE data, and $$$F_{\mathrm{u}}$$$ is the Fourier undersampling operator. Then, DCE angiograms are reconstructed by a product of $$$U$$$ and $$$V_r$$$.

DCE MRA data was acquired at 3T wole-body MR scanner (MAGNETOM Verio, Siemens Medical solutions). Informed written consent was obtained from volunteers with the approval of our institutional review board. A 3D spoiled gradient echo sequence was used for the MRA acquisitions. The imaging parameters were: TR/TE=2.5ms/0.94ms, in-plane matrix=320x240, number of partition=144, Thickness= 1.2mm, Field Of View(FOV)=400x300mm in coronal orientation, pixel bandwidth=868Hz, and flip angle=25°.

Figure 2 shows MIP images and their corresponding error maps obtained using the proposed MASE with R = 1, 20, 30, 40, and 50. Normalized-root-mean-square-error (NRMSE) at R = 50 is about 40% higher than that with R = 20. Figure 3 compares the proposed MASE with conventional dynamic CS and k-t RPCA at R = 40.2,4 Among the competing methods, the proposed MASE clearly delineates time-varying DCE angiograms (Figs. 3a-c) with the lowest level of background artifacts and noise.

We successfully demonstrated the feasibility of the proposed MASE in DCE MRA with increasing reduction factors. In this work, DCE angiogram signals are directly modeled and reconstructed, while the other signals that do not lie in the subspace of DCE angiogram tend to be neglected. It is expected that the proposed MASE would enable a rapid, robust DCE MRA and widen its applications in a clinical routine.