The Intravoxel Incoherent Motion (IVIM) (1) model in combination with parallel imaging (R=2) has successfully been used clinically to map perfusion in the brain (2). Parallel imaging, however, inherently reduces the signal-to-noise ratio along with spatially dependent noise amplification and therefore undersampling factors beyond a factor of two are difficult to implement for IVIM in practice. To exploit the redundancy among the diffusion-weighted images (DWI) acquired for IVIM, constrained image reconstruction methods operating in the spatio-principal component space may be utilized.

It is the objective of the present work to implement and validate k-t PCA (3,4) for IVIM. Using in-vivo brain data, IVIM parameter maps of diffusion (D), perfusion fraction (f) and pseudo-diffusion (D*) are compared relative to maps derived from parallel imaging and fully sampled data.

Iterative k-t PCA (5) was implemented to reconstruct data obtained with optimized k-b sampling (referred to as k-b PCA). Here b denotes the dimension spanned by DWI data acquired at different b-values. In k-b PCA, data consistency is enforced along with a regularization term to incorporate information from low-resolution data acquired alongside and decomposed into spatially dependent weights and b-dependent basis functions. Accordingly, image reconstruction is performed in x-pc space (5):

$$\min_{\vec{i}} \|E\vec{i}-\vec{d}\|_{2}^{2}+\lambda\|\left(^{x-pc}M\right)^{-1}B_{f\rightarrow pc}F_{b\rightarrow f}\vec{i}\|_{2}^{2} \qquad (1)$$

here $$$E$$$ denotes the forward encoding operator, $$$d$$$ the acquired k-b space data, $$$M$$$ low resolution data, $$$F_{b\rightarrow f}$$$ and $$$F_{f\rightarrow pc}$$$ transform operators and λ a regularization parameter.

For reference, CG-SENSE reconstruction (6) was implemented and performed on each b-image separately. Coil calibration data for both k-b PCA and CG-SENSE were obtained from a separate fully sampled coil calibration scan.
Datasets from 6 healthy volunteers (female, age: 22.8±3.5 years, weight: 61.7±7.5 kg) were obtained on a 3T Philips Achieva scanner (Philips Healthcare, Best, the Netherlands) equipped with an 8-channel head coil using dedicated pads (Pearltec, Zurich, Switzerland) for head fixation. Single-shot diffusion-weighted spin-echo EPI data were collected with a FOV of 194x150x80 mm³, voxel size 1.2x1.2x4 mm³, TE=179 ms, TR=4000 ms, 20 slices and 16 b-values (7) (range: 0-1000 s/mm²) encoded along three orthogonal directions in a total scan time of 6:24 min for the fully sampled reference.

The reconstruction error in the region of the brain including CSF for net 1.8 to 4.0-fold undersampling factors was quantified for both k-b PCA and CG-SENSE using the normalized root mean square error (NRMSE) relative to the fully sampled reference. IVIM parameter maps were derived using a segmented least-squares fit of the IVIM model as described in (8). The parameter estimation error of D, f and D* is reported for images reconstructed from undersampled and fully sampled data.

Spatially dependent noise amplification in the mages reconstructed with CG-SENSE is readily apparent, while k-b PCA reconstructed images show reduced overall noise (Fig. 1). The reconstruction error (NRMSE) for a net undersampling factor of R=4 and b=0 s/mm2 was 10.2±1.0 % for CG-SENSE and 10.1±5.6 % for k-b PCA (λ=10^-9) over all volunteers. For b=1000 s/mm², the mean and standard deviation of NRMSE over all volunteers and diffusion encoding directions was 61.2±6.2 % for CG-SENSE and 27.0±6.2 % for k-b PCA. Fig. 2 displays the reconstruction error as a function of net undersampling factor R for one volunteer. An analysis of different regularization parameters λ (Fig. 3) revealed that the reconstruction error decreased with increasing λ leveling off between 10^-9 and 10^-8. While IVIM parameter maps reconstructed based on CG-SENSE data were noisy especially around the ventricles, k-b PCA resulted in improved estimates, in particular for D and f.

Example parameter maps of one volunteer are shown in Fig. 4. The absolute parameter estimation errors as for an (effective) undersampling factor of R=4 using CG-SENSE and k-b PCA were 1.8±2.0·10^-4 mm²/s and 1.3±1.9·10^-4 mm²/s for D, 0.085±0.101 and 0.068±0.083 for f and 7.6±18.3·10^-2 and 6.4±16.9·10^-2 mm²/s for D* as shown in Fig. 5.

In this work k-b PCA has been implemented to exploit redundancy among diffusion-weighted images thereby improving accelerated IVIM of the brain. In contrast to CG-SENSE reconstruction, 4-fold accelerated k-b PCA allowed reconstructing IVIM parameter maps comparable to those derived from fully sampled images. Since undersampling simultaneously allows for a shorter EPI readout and correspondingly lower echo times, the relative signal-to-noise ratio penalty due to reduced data acquisition is partly compensated for. Accelerating IVIM using k-b PCA is a promising alternative to parallel imaging to reduce scan times while maintaining the quality of diffusion and perfusion parameter maps in brain exams.