Introduction

MRI is increasingly important for prostate cancer screening¹. Diffusion-weighted images (DWI), and apparent diffusion coefficient (ADC) maps show restricted water diffusion, indicating a higher probability of cancer^2,3. DWI and ADC maps have low signal-to-noise ratios (SNR), making it difficult to identify suspicious areas and to provide correct locations for targeted biopsy⁴. The typical approach to improve SNR is to collect multiple acquisitions during the scan and use their average as the MR image. However, this results in blurring due to motion between acquisitions. In addition, small bulk motions of the prostate occurring during application of diffusion sensitizing gradients can result in loss of signal and obscure regions with restricted diffusion. For high b values, this effect is more drastic since the DWI sequence becomes more sensitive to motion artifacts with increased b values, which also provide the greatest sensitivity to restricted diffusion associated with cancer. Thus, for each group of acquisitions, the signal for cancer voxels at high b values may include some relatively high signals due to restricted diffusion, and some lower signals that are likely to be artifacts due to local motion. In this case, conventional signal averaging is not appropriate since it combines acquisitions that show cancer signals with acquisitions that do not. The extent and adverse effects of this inter-acquisition variation have recently been quantitatively studied⁵. Although there are some studies aiming to address the signal variation via post-filtering and image enhancement techniques⁶, pre-selection of fruitful acquisitions on voxel-level remails an unsolved problem.

Methods

In this study, we propose to address this issue via an unsupervised approach that rejects the potentially motion-corrupted acquisitions prior to image generation. Therefore, we assign more weight to the higher signals versus lower signals. The method we propose objectively filters the set of acquisitions to be used in image generation, as opposed to taking the mean of all acquisitions. Specifically, we apply hierarchical agglomerative clustering algorithm (HAC) over the set of acquisitions for each voxel and calculate the similarity ‘tree’ reflecting a measure of the coherence of acquisitions⁷. HAC pairs two most similar observations into a larger cluster at each step, potentially representing the true restricted diffusion in the voxel-of-interest. This pairing step continues until the whole set of acquisitions are segmented into two clusters. For merging clusters, we used the Ward’s minimum variance criterion⁸ so that minimum increase in the total within-cluster variance is obtained after merging. In the end, the cardinalities and the means of the resulting two clusters are compared to determine the acquisitions to be rejected. We hypothesize that higher signals among the set of acquisitions for a given voxel on DWI are likely to correctly represent restricted diffusion, while lower signals in the same voxel are more likely to be due to motion. Therefore, if the mean difference between the clusters is larger than the noise range, then this variation is more likely to be originating from a motion-induced signal loss, and accordingly, all acquisitions of the cluster with a smaller mean are rejected if it is not constituting at least 80% of the acquisitions. This method is based on the hypothesis that artifacts (predominantly local motion) in DWI are more likely to decrease signal than to increase signal. The resulting diffusion-weighted image is produced from the mean of the remaining acquisitions for each voxel. Figure 1 shows dendrogram trees from the HAC algorithm, calculated for a cancer voxel and the contralateral benign tissue.

Results

The proposed algorithm was applied to DWI data from ten patients with biopsy verified prostate cancers. 12 or 24 acquisitions were obtained for each patient and the HAC algorithm was applied to discard corrupted acquisitions and reduce signal variability. HAC filtered out an average of 49% of the acquisitions. The ADC map with HAC-based filtering shows biopsy-verified cancer regions. Figure 2 compares the ADC maps from HAC-filtered images to the original mean image. HAC detects voxels with cancer that the mean image misses. Comparison of the standard deviation maps of the mean images with all acquisitions to the HAC-processed images shows that the undesired variation on the prostate region was mostly removed, and the signal standard deviation was reduced by an average of 42%. Standard deviation maps of two patients are given in Figure 3, with and without HAC-based filtering. The noise remaining in the image is close to the level expected from SENSE reconstruction of electronic white noise.

Discussion

Inter-acquisition variability in DWI is large relative to differences between prostate cancer and normal tissue⁵. Taking the conventional mean of multiple acquisitions to improve SNR disregards the effects of this variation and can obscure cancers. Here, we propose a new approach to filtering diffusion-weighted images to reduce the effects of motion-induced signal loss via unsupervised clustering. This decreases signal variability and increases cancer conspicuity.

Conclusion

We propose an unsupervised method of addressing the motion-induced inter-acquisition variability in DWI. We show that hierarchical clustering of acquisitions increases cancer conspicuity. In the future, this method will be extended to include information from neighboring voxels in the clustering algorithm and used as input to multi-image super-resolution methods.

Acknowledgements

This work was supported by the Sanford J. Grossman Charitable Trust (Sanford J. Grossman Center of Excellence in Prostate Imaging and Image-Guided Therapy)