Eun Ji Lim^{1}, Joon Sik Park^{1}, Eung Yeop Kim^{2}, Chul-Ho Sohn^{3}, and Jaeseok Park^{1}

In this work we develop a high spatiotemporal resolution (spatial ~ 1.0 mm3, temporal ~ 1.6 sec) simultaneous DCE MRA and perfusion within a single 4D acquisition exploiting kinetic model based signal priors. It is demonstrated that the proposed, high spatiotemporal resolution DCE MRI, which enables rapid sampling of AIF, depicts microvascular permeability in pathological tissues (e.g., tumor) much more accurately than conventional DCE MRI (temporal resolution: 5.0 sec).

**DCE Data Acquisition: **Simultaneous acquisition of DCE MRA and perfusion data were performed in patients on a 3.0 T
whole body MR scanner (Skyra, Siemens Healthcare) using multi-phase spoiled 3D
GRE with high spatiotemporal resolution (spatial ~ 1.0mm3, temporal ~ 1.6 sec). Data were
vastly under-sampled in a radial-like pattern on cartesian grid (R = 50) and
then shared in the peripheral k-space over two or three neighboring phases for
reconstruction. The imaging parameters were: TR/TE = 3.05/1.3ms, flip
angle=15◦, matrix size = 92×192×144, spatial resolution = 1.1×1.1×1.1mm3, temporal resolution= 1.65sec,
number of phases = 180, bandwidth/pixel = 650Hz/pixel, asymmteric Echo = 70% in
the readout direction. For accurate quantitative analysis of perfusion, B1 maps and reference T10 maps were acquired using AFI (TRs
=7ms, 35ms) [1] and variable-flip-angle imaging (3°,15°) [2], respectively.

**DCE Signal Model:** Concentration time-course in DCE MRI can be described by
using either Patlak [3] or extended Tofts-Ketty model [3]. Given the
concentration time-course, temporal signal profiles in DCE MRI are then
simulated, row-vectorized, and stacked into a signal library: $$$D=UΣV^H$$$ where $$$D$$$ consists of
simulated temporal signal profile vectors, $$$U$$$ is the basis of
the column vectors in $$$D$$$, $$$V$$$ is the basis of
the row vectors in $$$D$$$ and is used as the temporal basis for the signal
time-course, and $$$Σ$$$ is the singular
value matrix. **Figure 1** represents the variation of eigenvalues in and its
corresponding eigenvectors in the temporal basis . 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 discrepancy of modeled signals and measured
signals, the proposed DCE signal model can be written by: $$X=X_0 + X_D + X_M + N $$
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, $$$X_D$$$ is the signal of interest, and $$$X_M$$$ is the leakages of signals
(residual artifacts).

**DCE Reconstruction with Kinetic Model Based Signal
Priors: **The proposed DCE reconstruction from incomplete measurements is
performed by solving the following constrained optimization problem with kinetic model
based signal priors:

$$(\hat{X_{D}},\hat{U},\hat{X_{M}})= \arg \underset{X_{D},U,X_{M}}{min}\left \| D_{t}X_{D} \right \|_{1}+\lambda_{U}\left \|D_{s}U \right \|_{1}+\lambda _{M}\left \| \Psi X_{M} \right \|_{1} $$$$ s.t. d_{r}=E(X_{D}+X_{M}), X_{D}=UV_{r} $$

Fig. 2 shows the sampling pattern in k-t
space. View-sharing was performed in the corresponding space. Fig. 3 shows MIP images obtained using the proposed reconstruction algorithm with R=50. Fig. 4 shows perfusion parameters
derived permeability parameters for discriminating brain tumor between
different temporal resolution. Compared
with the low temporal resolution, high temporal resolution shows superior result of K_{trans} .The proposed
method can lead to capture both macroscopic arterial and microscopic vascular
information simultaneously.

1.Vasily L, Yarnykh. Actual Flip-Angle Imaging in the Pulsed steady state : A Method for Rapid Three-Dimensional Mapping of the Transmitted Radiofrequency

2.FieldSean C.L Deoni, PhD :High-Resolution T1 Mapping of the Brain at 3T with Driven Equilibrium Single Pulse Observation of T1 with High speed Incorporation of RF Field Inhomogeneities

3.Anna K. Heye, Ross D. Culling, Maria del C. Valdés Hernández, Michael J. Thrippleton, Joanna M.Wardlaw : Assessment of blood-brain barrier disruption using dynamic contrast-enhanced MRI. A systematic review

4.Marios Spanakis , Eleftherios Kontopodis , Sophie Van Cauter , Vangelis Sakkalis , Kostas Marias : Assessment of DCE–MRI parameters for brain tumors through implementation of physiologically–based pharmacokinetic model approaches for Gd-DOTA