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Robust Bias Correction and Segmentation of 7 Tesla Structural Brain Images with an iterative Bias-Corrected Fuzzy C-means and N4 Bias Correction (iBCFCM+N4)
Andrew Palmera Leynes1, Melanie Morrison1, Angela Jakary1, Peder Larson1, and Janine Lupo1

1Radiology and Biomedical Imaging, University of California San Francisco, San Francisco, CA, United States

### Synopsis

To introduce and evaluate a novel strategy for iterative combination of bias-corrected fuzzy c-means (BCFCM) and N4 bias correction for robust bias correction and segmentation in 7 Tesla brain imaging studies.

### Introduction

One major challenge faced by 7 Tesla imaging is the presence of strong intensity inhomogeneity due to B0 and B1 fields. Common intensity-based segmentation methods misclassify tissues due to the large shift in intensity that often result from residual errors in bias field estimation with N3 or N4 bias correction.

N4 bias correction is an improvement over the popular and robust N3 bias correction method1. Both methods, however, are sensitive to the segmentation mask over which the bias field would be computed. Bias-corrected fuzzy c-means (BCFCM) is a bias correction and segmentation method that produces soft segmentation maps and simultaneously estimates the bias field2.

We propose the iterative combination of BCFCM and N4 bias correction (iBCFCM+N4) for improved simultaneous bias correction and segmentation. BCFCM provides a preliminary estimation of the bias field for robust segmentation of tissues to weight the bias correction for robust estimation of the bias field.

### Methodology

A 7 Tesla bias field was obtained using a head phantom with a 32-channel receive coil (NOVA Medical Inc., Wilmington, MA) and 2-channel transmit with a proton-density weighted zero echo-time (ZTE) pulse sequence (FOV=256mm×256mm×182mm, resolution = 1mm×1mm×1mm, BW=±62.5kHz, FA=2°). This measured bias field was applied to twenty simulated T1-weighted images provided by the BrainWeb database3,4. The synthetic images were processed with the iterative combination of BCFCM and N4 bias correction method as shown in Figure 1, with the same set of parameters applied to all patients. The relative root-mean-square error (RMSE) was measured as

$$RMSE=\sqrt{\frac{1}{N}\sum_N(\frac{x_n-y_n}{y_n})}$$

with the scaled images having a white matter intensity normalized to 1. The original image, bias corrupted image, and bias corrected images were then segmented using k-means clustering. A Jaccard index was measured from resulting segmentation maps. The segmentation results of the bias corrupted image and bias corrected image were compared using a Wilcoxon signed-rank test. The method was then tested on in vivo images in order to qualitatively examine its performance in terms of the effect on brain tissue segmentation with FSL’s automated segmentation tool (FAST)5.

### Results

The measured bias field, synthetic images, synthetic images with bias field, and corrected images are shown in Figure 2. The measured bias field has a range of 0.61 to 1.41. The overall relative RMSE is 0.15±0.05, after excluding one outlier having an RMSE of 1.66. The segmentation of the corrected images yields a significantly different (p<0.001) white matter Jaccard index of 0.69±0.04 from 0.56±0.015 and a significantly different (p<0.001) gray matter Jaccard index of 0.67±0.05 from 0.60±0.014 between corrected and uncorrected images. Representative images and segmented maps of grey matter, white matter, and CSF maps are shown in Figure 3.

The results of segmentation using FAST are shown in Figure 4. The segmentation using FAST demonstrates that proper bias correction is necessary in order to have accurate cortical segmentation. Comparing with other masking methods (Otsu thresholding, whole-volume mask) for the N4 bias correction, the combination of BCFCM and N4 bias correction yields the most accurate definition of the grey-white matter boundary.

### Discussion

The strong intensity inhomogeneity in 7 Tesla imaging can lead to errors in later processing. With the use of the iterative combination of BCFCM and N4 bias correction, this intensity inhomogeneity can be corrected, which improves image-processing results. A major advantage of retrospective bias correction methods is that it is not limited to the type of contrast that is present in the image, making these methods applicable to any image with inhomogenous image intensity.

### Conclusion

We introduced an iterative combination of BCFCM and N4 bias correction for improved simultaneous bias correction and segmentation. We demonstrated its success with synthetic data applied with a realistic 7 Tesla bias field and showed improved segmentation results for in vivo data using FAST. Since this method is built upon previously evaluated, robust, and freely available tools, it is easily accessible and potentially applicable to a wide range of structural MR imaging sequences.

### Acknowledgements

This study was supported by R01HD079568 and an investigator initiated grant with GE Healthcare.

### References

1. Tustison NJ, Avants BB, Cook PA, et al. N4ITK: Improved N3 Bias Correction. IEEE Trans Med Imaging. 2010;29(6):1310-1320. doi:10.1109/TMI.2010.2046908.

2. Ahmed MN, Yamany SM, Mohamed N, Farag AA, Moriarty T. A modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data. IEEE Trans Med Imaging. 2002;21(3):193-199. doi:10.1109/42.996338.

3. BrainWeb: Simulated Brain Database. http://brainweb.bic.mni.mcgill.ca/brainweb/. Accessed November 9, 2016.

4. Collins DL, Zijdenbos AP, Kollokian V, et al. Design and construction of a realistic digital brain phantom. IEEE Trans Med Imaging. 1998;17(3):463-468. doi:10.1109/42.712135.

5. Zhang Y, Brady M, Smith S. Segmentation of brain MR images through a hidden Markov random field model and the expectation-maximization algorithm. IEEE Trans Med Imaging. 2001;20(1):45-57. doi:10.1109/42.906424.

### Figures

Flowchart for the iterative combination of bias-corrected fuzzy c-means and N4 bias correction (iBCFCM+N4). The segmentation maps from BCFCM and partially corrected images are used as inputs to the N4 bias correction. This process is repeated iteratively to generate the final bias-corrected image.

Head phantom image (a), the measured bias field (b), and bias-corrected head phantom image (c). The synthetic 7 Tesla image (e) is generated by multiplying the simulated T1-weighted image from the BrainWeb database (d) with the measured bias field (b). The synthetic 7 Tesla image is corrected using the method described to yield the bias-corrected image (f).

Synthetic 7 Tesla brain images (left column) and the results of segmentation using k-means clustering (right column). The bias-corrected images (b,d,e) provide significantly improved cortical segmentation compared to the uncorrected images (a,c,e).

An in vivo 7 Tesla MPRAGE image (a) was corrected using N4 bias correction with different segmentation maps used as input. Corrected images using an Otsu thresholding mask (c), whole-volume mask (e), and BCFCM segmentation maps (g) are segmented using the FSL automated segmentation tool (FAST) to get the respective segmentation maps (b,d,f,h). The zoomed in images (i,j,k,l,m,n,o,p) correspond to yellow dotted box as shown in the original image (a). The orange arrow indicates an area of over segmentation of white matter that is corrected by using BCFCM in conjunction with N4 bias correction.

Proc. Intl. Soc. Mag. Reson. Med. 25 (2017)
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