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The Effect of Signal to Noise Ratio on Linear-binning and Adaptive k-means Quantification of Hyperpolarized ¹²⁹Xe Ventilation MRI

Mu He¹, Fei Tan², Wei Zha³, Leith Rankine⁴, Sean Fain^3,5,6, and Bastiaan Driehuys^4,7,8

¹Department of Electrical and Computer Engineering, Duke University, Durham, NC, United States, ²Biomedical Engineering Department, Duke University, Durham, NC, United States, ³Department of Medical Physics, University of Wisconsin-Madison, Madison, WI, United States, ⁴Department of Medical Physics, Duke University, Durham, NC, United States, ⁵Department of Biomedical Engineering, University of Wisconsin-Madison, Madison, WI, United States, ⁶Department of Radiology, University of Wisconsin-Madison, Madison, WI, United States, ⁷Department of Biomedical Engineering, Duke University, Durham, NC, United States, ⁸Department of Radiology, Duke University, Durham, NC, United States

Synopsis

¹²⁹Xe ventilation MRI lacks a reference standard. Here, we circumvent this problem in part by comparing and evaluating the robustness of two independent methods for quantifying ventilation – linear-binning and adaptive k-means - by adding MR noise to the source images until the algorithms fail. Results at different noise levels were compared to that quantified using the original high signal-to-noise ratio (SNR) ventilation image. We found that both methods provide robust quantification until SNR is less than 1.7 ± 0.8 for the linear-binning method, and 2.1 ± 1.2 for the uncorrected adaptive k-means method.

Introduction

Quantification and visualization of hyperpolarized ¹²⁹Xe MRI are critical to its accurate use in diagnosis and monitoring. To date, numerous such methods have been developed and published, with most focusing on the well-known ventilation defect percentage (VDP)^1-3. More recently, this has been extended to quantify the entire ventilation distribution, including metrics of heterogeneity and skewness^4-6. One challenge in evaluating the performance of these methods is the lack of a gold standard against which to test the veracity of their derived metrics. Here we propose an approach that overcomes the lack of gold standard, by instead testing the robustness of methods against decreasing SNR. We thus seek to use the original high-SNR image as a surrogate gold standard, and test the degree to which methods remain robust as image noise is amplified and SNR degrades. In this initial work, we compare two common techniques - linear-binning and adaptive k-means segmentation. Our objective was to identify the SNR threshold at which the resulting quantification deviated significantly from the high-SNR reference and whether one method was appreciably more robust against diminished SNR than another.

Methods

19 asthma subjects (age: 45.1±20.4 years) were retrospectively identified for analysis. All had previously undergone hyperpolarized (HP) ¹²⁹Xe at 1.5 Tesla⁷ using a 2D multi-slice GRE sequence with 3x3x12.5 mm resolution. SNR was calculated using signal within the thoracic cavity mask and noise from 4 ROIs (Figure 1), corrected to account for its Rician distribution. From each dataset 7 variants were generated, with progressively lower SNR. This was done by synthesizing complex Gaussian noise with zero mean with 7 different standard deviations. The noise sets were created in the frequency domain and then Fermi filtered identically to the original image reconstruction (radius 64, width 10 matrix units) and inverse Fourier transformed to the image domain. The resulting 7 complex image sets were then added to the original magnitude image to create complex noise-enhanced images and converted to magnitude images for analysis. All images were then analyzed using both the linear binning⁸ and the adaptive k-means⁹ methods that quantified each image into four clusters of similar signal intensities. The noise-amplified VDP was then compared for deviation from its to the corresponding original high-SNR dataset. Note that to objectively compare the two methods, an erosion-dilation denoising step that is typically included in adaptive k-means analysis⁹ was omitted. Each method was characterized by the SNR level at which they were deemed to “fail.” Failure was defined as the SNR at which the reported VDP deviated from that of the original image by >1.8%. This threshold represents the reported VDP standard deviation for a healthy reference cohort⁸.

Results

Figure 2 shows the evenly spaced SNR degradation for two representative subjects, one with normal ventilation and one with significant defects. The resulting VDP for the well-ventilated subject is shown in Figure 3 for both linear binning and adaptive k-means. Both methods show relatively similar and stable VDP at high SNR that slowly becomes larger as SNR decreases. Below an SNR of 4, both methods begin reporting significantly increased VDP. Similar analysis is shown in Figure 4 for the subject with high starting VDP. In this case, the increasing noise causes some defects to be mis-classified as ventilated regions and VDP actually decreases. This mis-classification appears to occur at slightly higher SNR for linear binning than adaptive k-means. Figure 5 shows the way in which the VDP varied as a function of SNR across the entire cohort for both the linear-binning method and the adaptive k-means. For this cohort, the original ¹²⁹Xe ventilation images had a range of 10.2±5.1, and with evenly spaced noise degradation the noisiest images had an SNR of 1.2±0.4. Using 1.8% as the tolerable difference threshold, the SNR values at which VDP deviated significantly from reference were 1.7±0.8 for the linear-binning, and 2.1±1.2 for uncorrected adaptive k-means.

Discussion

This study shows that both methods provide robust quantification until SNR is remarkably low. Taking the mean plus two standard deviations for k-means suggests an SNR threshold 4.5. Given this SNR threshold, it becomes possible to now propose the minimum hyperpolarized ¹²⁹Xe dose required to obtain reliable quantitative ventilation MRI¹⁰. Using the previously reported normalized SNR of 1.9 ml^-2but scaling down √(2-π/2) to correct for Rician background noise distribution, yields a required ¹²⁹Xe dose equivalent of 30.1ml for the 0.12 ml voxel resolution the images used for this analysis. Note that further improvement to the robustness of these methods could be realized by reincorporating the adaptive k-means morphometric correction.

Acknowledgements

R01HL105643, R01HL126771, P41 EB015897, Gilead Sciences

References

1. Woodhouse N, Wild JM, Paley MN, et al. Combined helium-3/proton magnetic resonance imaging measurement of ventilated lung volumes in smokers compared to never-smokers. J Magn Reson Imaging. 2005;21(4):365-369.

2. Kirby M, Heydarian M, Svenningsen S, et al. Hyperpolarized 3He magnetic resonance functional imaging semiautomated segmentation. Acad Radiol. 2012;19(2):141-152.

3. M, Kaushik SS, Robertson SH, et al. Extending semiautomatic ventilation defect analysis for hyperpolarized (129)Xe ventilation MRI. Acad Radiol. 2014;21(12):1530-1541.

4. Tzeng YS, Lutchen K, Albert M. The difference in ventilation heterogeneity between asthmatic and healthy subjects quantified using hyperpolarized 3He MRI. J Appl Physiol (1985). 2009;106(3):813-822. 5. Svenningsen S, Kirby M, Starr D, et al. Hyperpolarized (3) He and (129) Xe MRI: differences in asthma before bronchodilation. J Magn Reson Imaging. 2013;38(6):1521-1530.

6. Virgincar RS, Cleveland ZI, Kaushik SS, et al. Quantitative analysis of hyperpolarized 129Xe ventilation imaging in healthy volunteers and subjects with chronic obstructive pulmonary disease. NMR Biomed. 2013;26(4):424-435.

7. Ebner L, He M, Virgincar RS, et al. Hyperpolarized 129Xenon Magnetic Resonance Imaging to Quantify Regional Ventilation Differences in Mild to Moderate Asthma: A Prospective Comparison Between Semiautomated Ventilation Defect Percentage Calculation and Pulmonary Function Tests. Invest Radiol. 2017;52(2):120-127.

8. He M, Driehuys B, Que L, Huang Y-CT. Using Hyperpolarized 129Xe MRI to Quantify the Pulmonary Ventilation Distribution. Acad Radiol. 2016.

9. Zha W, Niles DJ, Kruger SJ, et al. Semiautomated Ventilation Defect Quantification in Exercise-induced Bronchoconstriction Using Hyperpolarized Helium-3 Magnetic Resonance Imaging: A Repeatability Study. Acad Radiol. 2016;23(9):1104-1114.

10. He M, Robertson SH, Kaushik SS, et al. Dose and pulse sequence considerations for hyperpolarized (129)Xe ventilation MRI. Magn Reson Imaging. 2015;33(7):877-885.

Figures

Figure 1. Image background noise was calculated by selecting four regions of interest (ROI) in the image corners away from the region affected by gradwrap. The standard deviation of the noise was computed by the median of the SD of each ROI, which was further corrected for its Rician distribution resulting from magnitude image reconstruction. The signal mean was calculated within the thoracic mask.

Figure 2. Illustration of image degradation induced by adding Fermi-filtered zero-mean complex Gaussian noise. The first row shows a young, well-controlled asthmatic subject with no perceptible defects in the original image. The bottom row shows an older asthmatic subject with significant defects.

Figure 3. Representative ¹²⁹Xe ventilation MRI and associated linear-binning and adaptive k-means maps for the young asthmatic subject with low VDP. Both linear binning and adaptive k-means report a stable, but slowly increasing VDP as SNR decreases.

Figure 4. Representative ¹²⁹Xe ventilation MRI and associated linear-binning and adaptive k-means maps for the older asthmatic subject with high VDP. As SNR decreases, linear-binning reports a continuously decreasing VDP due to noise in regions of ventilation defects being classified into low-ventilated regions. The adaptive k-means method appears more stable against such misclassification in this case and reports relatively stable VDP across the SNR range.

Figure 5. VDP difference plots with respect to original ¹²⁹Xe ventilation MRI using the linear-binning method and the uncorrected adaptive k-means method. Using 1.8% as a tolerated difference threshold, the SNR values at which VDP deviated significantly from reference were 1.7 ± 0.8 for linear-binning, and 2.1 ± 1.2 for uncorrected adaptive k-means.

Proc. Intl. Soc. Mag. Reson. Med. 26 (2018)

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