Quantitative diffusion-weighted MRI (DW-MRI) has been increasingly used for the detection and characterization of abdominal abnormalities in liver, spleen and bowel¹. One of the challenges in abdominal DW-MRI is respiratory, cardiac and peristalsis motion, which deteriorates robustness and reproducibility of parameter estimation and reduces clinical utility of quantitative DW-MRI parameters. Techniques such as breath-holding, gating, respiratory or cardiac triggering have been used for motion compensation. These techniques have disadvantages such as increased scan time, cooperation requirement of patient, and they do not entirely correct for motion. In this work, we introduce a simultaneous image registration and model estimation (SIR-ME) framework for motion-compensated parameter estimation. SIR-ME solver jointly estimates transformations for non-rigid alignment of images, reconstructs high SNR registered diffusion images and estimates signal decay model parameters.

In abdominal DW-MRI, multiple images (S^’_i,j, j =1..M) are acquired at the same b-value (b_i) to improve the signal-to-noise ratio (SNR). An improved SNR image (S_i) is estimated from these multiple acquisitions at each b-value. A signal decay model is then fitted to the improved SNR signal, and the model parameters are estimated. However, in the presence of motion, acquired images are not spatially aligned and therefore cannot be directly used. One solution is independent registration of each low SNR image (S^’_i,j) to a reference b=0s/mm² image. However, registration of high b-value images to a b=0 image is challenging due to contrast differences and lower SNR of high b-value images. Instead, we introduce a motion-compensated parameter estimation framework that simultaneously solves image registration and model estimation (SIR-ME) problems by utilizing the interdependence of acquired volumes along the fourth parametric dimension, i.e. diffusion weighting dimension as an additional term in the cost function. Our joint formulation is then given by:

$$$ [\hat{S},\hat{\theta},\hat{T^{'}},\hat{T}]=\operatorname*{arg\,min}_{S,\theta,T,T^{'}}\sum_{i=1}^{N}\sum_{j=1}^{M}(S_{i}-T^{'}_{i,j} \circ S^{'}_{i,j})^{2}+\sum_{i=1}^{N}(T_i \circ S_{i}-g(\theta,i))^2$$$

The first term is used to reconstruct high SNR images from registered low SNR images and the second term is the signal decay model-fitting prior. When solving this equation, the expected signal (g(θ,i)) is dependent on both the parameters of the signal decay model (i.e. θ) and the transformations (T^’_i,j,T_i), which are all unknown. Therefore, we cannot optimize this equation directly. Instead, we solve it as a simultaneous optimization problem, where registration, reconstruction of the high SNR DW-MRI images and estimation of the signal decay model parameters are iteratively performed (Table 1). We used the recently proposed spatially-constrained probability distribution model of diffusion² as the signal decay model (g(θ,i)) and the non-rigid block-matching algorithm by Commowick et al.³ for registration.

We have tested the performance of the proposed model in DW-MRI data of 16 Crohn's Disease patients, acquired with a 1.5T scanner (Avanto, Siemens) using free-breathing single-shot echo-planar imaging with parameters: (TR/TE)=7500/77ms; matrix size=192x156; field of view=300x260mm; slice thickness/gap=5mm/0mm; 40 axial slices; 7 b-values=0,50,100,200,400,600,800 s/mm2 with 1 excitation; 6 directions; acquisition time=5.5min. We computed the average RMSE between the measured signal (S_i) and the signal of fitted model (g(θ,i)) to evaluate the effect of motion-correction on goodness-of-fit. Figure-1 compares the RMSE a) in normal and b) inflamed bowel regions using no registration, independent registration and SIR-ME. The mean RMSE of inflamed bowel reduced from 12.39±8.01 to 6.66±2.91 with registration, and further reduced to 5.63±2.57 with SIR-ME. The RMSE in normal-looking bowel walls reduced from 12.23±5.54 to 7.77±3.17 with registration and further reduced to 6.27±2.42 with SIR-ME. While the independent registration decreased the RMSE on average, it increased the RMSE for some cases. SIR-ME performed either equally well or better in all cases. A representative signal decay curve in Figure-2 shows the reduction in error using the SIR-ME model. Figure-3 b) shows an image region plotted for increasing b-values. The image intensity decays smoothly due to motion correction when SIR-ME model is used. We also compared the performance of estimated parameters in differentiating normal and inflamed bowel regions. We trained Naive Bayes classifiers using D and f parameters, and obtained classification errors of 0.41 w/o registration, 0.28 with registration and 0.15 with SIR-ME using D parameter; 0.28 w/o registration, 0.28 with registration and 0.15 with SIRME using f parameter. SIR-ME achieved the best classification accuracy for both f and D parameters.Results showed that the SIR-ME method corrected for the effect of motion and reduced the model fitting error by more than 50% compared to the errors obtained from non-registered original DW-MRI images. The quantitative parameters obtained using the SIR-ME model achieved improved group differences and better discrimination between normal and inflamed bowel loops, which will potentially impact clinical utilization.