Whole-body magnetic resonance diffusion-weighted imaging (WBDWI) is rapidly gaining popularity as a visual tool for diagnosis and monitoring of patients with metastatic bone disease from a range of primary malignancies [1]. WBDWI images acquired at two or more b-values provide quantification of disease status via measurement of the apparent diffusion coefficient (ADC) at each voxel location. Common radiological practice simultaneously utilizes both high b-value images and ADC maps to perform diagnosis and staging of disease. However, ADC maps are typically noisy and the degree of confidence in measured values is unknown during radiological review. Typical WBDWI measurements consist of multiple excitations (3-6) at each b-value, each of which are acquired in three orthogonal directions to account for diffusion anisotropy. Vendors typically export only the average of all acquired images at each b-value (9-18) to improve image signal-to-noise ratio and remove the effects of diffusion anisotropy. In this abstract we investigate the utility of storing all single acquisitions in WBDWI scans. We demonstrate the potential for estimating maps of ADC uncertainty from these data and discuss a new post-processing methodology for WBDWI examinations, namely, noise-corrected exponential diffusion-weighted imaging (nc-eDWI).

Patients: Three patients with metastatic disease from prostate cancer. The research study received local ethics approval.

Imaging: Images were acquired on a 1.5T MRI scanner (MAGNETOM Aera, Siemens AG, Healthcare Sector, Erlangen, Germany). Parameters for the DWI scans included: b-values = 50/900 or 50/600/900 s/mm2, orthogonal diffusion encoding directions, STIR fat suppression (TI = 180ms), Slice Thickness = 5mm, GRAPPA image acquisition (reduction factor = 2). Images were acquired on a moving table in 4 stations comprising of 40 slices each to cover the entire torso. Images at each station were acquired 3 times, each with 1 signal average (NeX), and data from the individual diffusion encoding directions were exported individually. The final data set therefore consisted of 9 images acquired at each slice location at each b-value.

Image analysis: ADC maps were generated using a weighted linear least-squares fit of the logarithm of the image intensity at each voxel location [2]. The weighting applied at each b-value was calculated as the reciprocal of the log-signal variance from repeat measurements at that b-value, that is (Fig. 1) $$w(b) = \frac{1}{\text{Var}[\ln \text{S}(b)]}$$ In such a regime the maximum-likelihood estimates for ADC and the logarithm of the signal at b = 0, $$$\ln \text{S}(0)$$$, are given by $$(\widehat{\text{ADC}}, \widehat{\ln\text{S}(0)}) = (\mathbf{b}^{T}\mathbf{W}\mathbf{b})^{-1}\mathbf{b}^{T}\mathbf{W}\mathbf{s}$$where $$$\mathbf{s}$$$ represents the N-vector of log signal intensities at each voxel location, $$$\mathbf{W} = \text{diag}(w_{1}, w_{2}, \dots, w_{N})$$$ and $$$\mathbf{b}$$$ represents a Nx2 matrix, the first column being filled with all b-values used to generate $$$\mathbf{s}$$$ and the second filled with 1’s. The 2x2 covariance matrix for these estimates is given by $$\mathbf{\Sigma} = (\mathbf{b}^{T}\mathbf{W}\mathbf{b})^{-1}$$ such that the variance in ADC estimates is obtained by $$$\sigma^{2}_{\text{ADC}} = \mathbf{\Sigma}_{11}$$$. Maps of $$$\sigma_{\text{ADC}}$$$ can be generated and viewed alongside whole-body ADC maps to inform on the confidence of estimates within certain regions. Furthermore, to combine both sources of information into a single image we define the noise-corrected exponential diffusion weighted image (nc-eDWI) as a computed image [2] with the following signal intensity (Fig. 2): $$\text{S}_{\text{nc}}(a, b_{c}) = \exp\left(-a\cdot\sigma_{\text{ADC}} \right)\exp\left(-b_{c}\cdot\widehat{\text{ADC}} \right)$$Note that the computed b-value, $$$b_{c}$$$ and ADC uncertainty weighting, $$$a$$$, are both user defined. Using in-house developed software, we provide an interactive environment such that the user may alter these parameters in real-time. We use a $$$3\times3$$$ median filter on $$$\sigma_{\text{ADC}}$$$ maps to reduce the presence of noisy outliers.

Figures 3-5 demonstrate three clinical examples of the utility of nc-eDWI in patients with metastatic prostate cancer. It is clear that it is able to remove the spurious discontinuities in signal intensity present at the inter-station interface in normal high b-value whole body DWI studies. Furthermore, it can improve the contrast between normal/metastatic bone, and removes the presence of non-DWI contrast including T2 shine-through, T1-weighting, proton density and coil sensitivity.Here we have investigated the utility of collecting and analysing all excitations from whole-body DWI and shown that, at the cost of additional data storage requirements, we are able to infer maps of confidence in the values of calculated ADC. Such maps enable clinicians to determine confidence in clinical decisions made using quantitative DWI. Furthermore, the use of noise-corrected eDWI provides diffusion-weighted contrast that is unaffected by T2 shine-through and coil sensitivity, thus enabling comparison of signal intensity in pre/post-treatment studies. These methods, when used alongside conventional DWI analysis, will provide a great deal of additional information for clinical review of patients with metastatic bone disease.