The perfusion-weighted imaging (PWI) offers a good indicator to measure the metabolism of the biologic tissues. So it has various applications for the clinical diagnosis and for the neuroscience. There are two typical methods for PWI. One is the dynamic susceptibility contrast-MRI (DSC-MRI) and the other is arterial spin labeling (ASL). While the DSC-MRI method offers the high contrast-to-noise ratio (CNR), it is used reluctantly because it requires an invasively exogenous tracer (1). Alternatively, the non-invasive ASL technique can be more widely applied, but it still has the major drawback of a poor signal-to-noise ratio (SNR) (2). In this abstract, a new high-resolution PWI technique without the exogenous is proposed.

The proposed method obtains perfusion information by separating diffusion and perfusion information based on the concept of IVIM (3) using the radial spin-echo sequence. When a single bi-polar gradient is applied, as shown in Fig. 1(a), the MR signal of a voxel is modeled by the exponential decay for diffusion and the decay of a sine integral function for perfusion, which considers the laminar flow in the capillary (4). However, the double bi-polar gradients in Fig. 1(a) can compensate the perfusion effects, but not the diffusion effects. Thus, the signal intensity from the single (S ^single) and double (S ^double) bi-polar gradients can be respectively described as follows,

\[S^{\tt single}=S_{0}\exp(-bD){\tt Si}(2\alpha v)/(2\alpha v)\\ S^{\tt double}=S_{0}\exp(-bD),\\{\tt where}~{\tt Si}(x)=\int_{0}^{x}\frac{\sin\tau}{\tau}d\tau,{\tt and}~\alpha=|\int_{t}^{}G(\tau)d\tau|.\tag1\]

The S₀ is the MR signal independent of diffusion and perfusion terms, D is the apparent diffusion coefficients (ADC), and v is voxel-averaged velocity of the capillaries, which is directly proportional to cerebral blood flow (CBF) and cerebral blood volume (CBV). Since the cerebral perfusion is anisotropic (5), the signal decay from perfusion is affected by the direction of the bi-polar gradients. So the direction of bi-polar gradients is changed for each projection view (radial spoke) to obtain an averaged perfusion weighting (6, 7).

\[S^{\tt single}=\frac{S_{0}}{N}\sum_{n=1}^N\exp(-bD_{n}){\tt Si} (2\alpha v_{n})/(2\alpha v_{n})\\S^{\tt double}=\frac{S_{0}}{N}\sum_{n=1}^N\exp(-bD_{n})\tag2\]

Eq. [2] means the arithmetic averaged signal due to changing the direction of bi-polar gradient along the radial spoke, where N is the total number of bi-polar gradient directions, D_n and v_n are the ADC and voxel-averaged capillary velocity, respectively, of the n^th bi-polar gradient direction. Then, Eq. [2] is approximated as Eq. [3] with error rates of ε1 and ε2.

\[S^{\tt single}=S_{0}\exp(-b\frac{1}{N}\sum_{n=1}^ND_{n}){\tt si}(2\alpha\frac{1}{N}\sum_{n=1}^Nv_{n})/(2\alpha\frac{1}{N}\sum_{n=1}^Nv_{n})+S_{0}\cdot\epsilon1\\S^{\tt double}=S_{0}\exp(-b\frac{1}{N}\sum_{n=1}^ND_{n})+S_{0}\cdot\epsilon2\tag3\]

It was already proven that ε2 is negligible (7). ε1 can be estimated with the Taylor series expansion of exponential function and the series expression of sine integral function (8) with in-vivo imaging parameters. If ε1 is also negligible, the voxel-averaged velocity of capillaries, which considers the perfusion anisotropy (i.e., mean of v_ns), can be calculated by the inverse process of (S ^single / S ^double). In-vivo experiments were performed using a 3 T MRI scanner (Siemens Magnetom Verio, Erlangen, Germany) to validate the proposed method. Imaging parameters are given as field of view (FOV) = 256×256 mm², matrix size = 328×328, TR/TE = 2000/52 ms, number of averages = 1, b-values = 52 s/mm², and number of sampling points for each projection view = 328. A total of 328 projection views with 328 different bi-polar gradient directions were used.

Figure 2 shows that the proposed signal model has the error rate (ε1) less than 1.2 %, when fractional anisotropies (FAs) of diffusion and perfusion do not have extreme value (i.e., FA < 0.6). Therefore, the error term in the approximated S ^single can be ignored. The proposed method offers the voxel-averaged capillary velocity map with an in-plane resolution of 0.78 × 0.78 mm², as shown in Fig. 3. Figure 4 shows a fusion image that the voxel-averaged capillary velocity map is overlaid on the anatomical T₂-weighted image. The proposed method reflects the general characteristic that perfusion information between the gray matter and white matter is different.As demonstrated by the simulations based on the formula and the in-vivo experiments, the proposed method offers the high-resolution quantitative perfusion map. Thus, the proposed method can be a useful PWI tool.