James A Rioux^{1,2,3}, Nathan Murtha^{4}, Chris V Bowen^{1,2,3,5}, Sharon E Clarke^{1,2,3}, and Steven D Beyea^{1,2,3,5}

Golden-angle sampling allows arbitrary retrospective selection of temporal resolution in dynamic MRI scans. To select the fastest temporal resolution that preserves time course fidelity, we propose the use of image quality metrics (IQMs). We demonstrate multiple IQMs that correlate strongly with the accuracy of fitted pharmacokinetic parameters up to at least an acceleration factor of R=12. For a fixed undersampling factor, these metrics can also inform the selection of reconstruction parameters such as regularization weights for compressed sensing. This approach may enable rational, individual-level tuning of temporal resolution following a prospectively accelerated DCE-MRI scan.

Techniques
such as GRASP^{1} and CIRCUS^{2,3} combine rays or other golden-angle sampling
patterns in arbitrary arrangements, allowing the temporal resolution of
a dynamic MRI study to be selected retrospectively, and potentially on an
individual basis. However, the choice of
temporal resolution must be informed by some rational criteria such that the
quality of the resulting time series can be assessed and maximized. Recent work^{4} has indicated that image quality
metrics (IQMs) of individual volumes within a simulated DCE-MRI series correlate with the fidelity of the overall time series, as quantified by the accuracy of parameters extracted from model fits. In this work, we present further evidence for
correlation between IQMs and pharmacokinetic (PK) parameter map accuracy in clinical DCE-MRI data,
which may lead to a framework for automated individual-level selection of
temporal resolution to maximize data quality.

To demonstrate correlations between
IQMs and temporal fidelity, retrospective undersampling of clinical DCE-MRI
data was performed. Reference data were drawn from DISCO series obtained
in N=3 patients indicated for prostate MRI and scanned under an REB-approved
protocol. Data were acquired using a GE MR750 3T scanner and an 8-channel
receive coil, with 60 phases at 3.8s temporal resolution. Any k-space
samples omitted due to parallel imaging or partial-Fourier acquisition were
synthesized to create a fully-sampled reference series, which was resampled
with quantized CIRCUS^{3} to achieve acceleration factors of R=2 to 12
(see Figure 1). Different sampling patterns were generated for each time
point, with resampled data retaining the temporal resolution of the original
series. Undersampled time series were reconstructed using Blind CS^{5},
with 30 dictionary entries, regularization weight λ=0.01, images scaled to a
peak intensity of 50. Several
alternate reconstruction parameters were evaluated at R=10 to assess discrimination
of reconstruction quality at the same undersampling factor.

Each volume of each reconstructed time series
was compared to the corresponding volume in the original DISCO series, and the
following IQMs were computed: root mean square error (RMSE), structural
similarity index (SSIM^{6}) and gradient magnitude similarity deviation
(GMSD^{7}). Since the DISCO series were acquired with two echoes
for Dixon fat separation, IQMs were computed for the in-phase, out-of-phase,
and water images. PK maps were generated using in-house code written in
Matlab using an extended Tofts model, with arterial input functions from a
manually selected voxel. ROIs were drawn around the prostate, and PK maps
from undersampled data were compared with the original DISCO PK maps by
computing the normalized RMSE of the K^{trans} maps over the ROI.
Correlations between IQMs and the RMSE of the Ktrans maps were
assessed via the coefficient of determination (R^{2}) of a linear
regression model (see e.g. Figure 2).

Figure 2 shows correlations between IQMs and PK map fidelity at 7 undersampling factors in each of 3 patients. The IQMs shown are the RMSE and SSIM of the undersampled water image at the first time point, while PK map fidelity is measured by the RMSE of the Ktrans maps. Regression lines at both the individual and group level demonstrate that the precise relationship between IQM and temporal fidelity changes somewhat between patients.

Figure 3 compares several potential
IQMs evaluated on (a) the first image of the time series, or (b) all images and
averaged over the series. The behavior of the first image is representative of
the entire series; IQMs computed for the first volume and for the entire series
correlate well with each other, with R^{2} = 0.91 to 0.99. This
is critical since a framework for rapid assessment of reconstruction quality
should ideally operate on a subset of the entire series, and proceed to the
lengthier time course reconstruction only once a candidate temporal resolution
is identified. These results indicate that such an approach is feasible. In both cases the SSIM has the best overall
performance, though RMSE and GMSD of the water image also show strong correlation.

Figure 4 demonstrates the evaluation
of IQMs over a range of reconstruction choices at the same undersampling factor
(R=10). The correlations here are less than with varying undersampling
factor, though still strong (R^{2}=0.6 to 0.8 across all varied parameters for most
IQMs tested).

1. Feng L, Grimm R, Block KT, Chandarana H, Kim S, Xu J, Axel L, Sodickson DK, and Otazo R.. Golden-angle radial sparse parallel MRI: combination of compressed sensing, parallel imaging, and golden-angle radial sampling for fast and flexible dynamic volumetric MRI. Magnetic Resonance in Medicine 2014;72(3):707-717.

2. Liu J and Saloner D. Accelerated MRI with CIRcular Cartesian UnderSampling (CIRCUS): a variable density Cartesian sampling strategy for compressed sensing and parallel imaging. Quantitative Imaging in Medicine and Surgery 2014;4(1):57-67

3. Rioux JA, Murtha N, Mason A, Bowen CV, Clarke SE, and Beyea SD. Flexible Prospective Compressed Sensing Acceleration of Prostate DCE-MRI with Quantized CIRCUS. Proc. ISMRM 2017, no.1426.

4. Murtha N, Rioux JA, Marriott O, Bowen CV, Clarke SE, and Beyea SD. Simulation Reveals Evidence for Bias in Parameter Estimates for Compressed Sensing of Temporally Dynamic Systems. Proc. ISMRM 2017, no.3810.

5. Bhave S, Lingala SG, Johnson C, Magnotta V, and Jacob M. Accelerated whole brain multi-parameter mapping using Blind compressed sensing. Magnetic Resonance in Medicine, 2016;75(3);1175-86.

6. Wang Z, Bovik AC, Sheikh HR, and Simoncelli EP. Image quality assessment: from error visibility to structural similarity.. IEEE Transactions on Image Processing, 2004;13(4):600-612.

7. Xue W, Zhang L, Mou X, and Bovik AC. Gradient magnitude similarity deviation: A highly efficient perceptual image quality index. IEEE Transactions on Image Processing, 2014;23(2):684-695.

Images, DCE time courses
and K^{trans} maps from original and undersampled (R=4,8,12) DISCO
data. First column: Out-of-phase image;
the normalized RMSE compared to the original image is shown below each image. Second column: Water image after Dixon fat
separation; the yellow box denotes the ROI for PK mapping. Third column: Arterial input function (black)
and time course from a prostate voxel (blue), scale adjusted for display. Fourth column: K^{trans} map of the
prostate ROI, with normalized RMSE compared to the original K^{trans}
map shown beneath. All images of the
same type are plotted using the same color scale.

Examples of linear regression of an
IQM versus PK map fidelity for 3 patients and 7 undersampling factors from R=2
to R=12. (a) IQM is the RMSE of the
first accelerated water volume compared to original. The R^{2} of the regression lines are
0.98 for patient 1 (blue), 0.91 for patient 2 (red), 0.96 for patient 3 (green)
and 0.79 at the group level (black). (b)
IQM is the SSIM of the first water volume compared to original. Regression lines for the 3 patients and group
aggregate have R^{2} = 0.99, 0.92, 0.95 and 0.85 respectively.

Correlations of all tested IQMs
(root mean square error RMSE, structural similarity index SSIM, and gradient
magnitude similarity deviation GMSD) with PK map fidelity, as measured by
normalized RMSE of the Ktrans map. (a) IQMs computed on the first volume of the
time series only. (b) IQMs computed for all volumes and averaged over the
entire series. Correlations are shown
within each patient and across the group; performance degrades at the group
level due to individual variations in the slope of IQM vs. PK fidelity as shown
in Figure 2. In both plots, W=water
image, IP=in-phase image, OP=out-of-phase image.

Use of IQMs to evaluate
reconstruction choices within an undersampling factor (R=10). (a) SSIM of first accelerated water volume
compared to original as the reconstruction parameters controlling the peak
image intensity (scale, blue points) and regularization weight (lambda, red
points) are varied over an order of magnitude.
R^{2} values for the regression lines are 0.69 for varying
scale, 0.87 for varying lambda, 0.75 for both combined. (b) Correlations of all tested IQMs with PK
map fidelity with same notation as Figure 3.