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Application of an Extended Stretched-Exponential Model for Morphometric Analysis of Accelerated Diffusion-weighted 129Xe MRI of the Rat Lung

Alexei Ouriadov¹, Matthew S Fox², Andras A Lindenmaier^3,4, Elaine Stirrat³, Grace Parraga^1,5,6, and Giles Santyr^3,4

¹Robarts Research Institute, London, ON, Canada, ²Lawson Imaging, Lawson Health Research Institute, London, ON, Canada, ³Translational Medicine Program, Peter Gilgan Centre for Research and Learning, The Hospital for Sick Children, Toronto, ON, Canada, ⁴Department of Medical Biophysics, University of Toronto, Toronto, ON, Canada, ⁵Department of Medical Biophysics, Western University, London, ON, Canada, ⁶Division of Respirology, Department of Medicine, Western University, London, ON, Canada

Synopsis

Hyperpolarized ¹²⁹Xe pulmonary MRI is poised for clinical translation due in part to the clinical-relevance of 129Xe MRI biomarkers of lung disease. A rapid multi-b diffusion-weighted ¹²⁹Xe MRI requires for clinical morphometry due to the challenges in acquiring a fully-sampled dataset during the relatively short 10-16sec breath-holds. Therefore, in this proof-of-concept evaluation, our objective was to measure morphometry estimates in a small group of control-rats as well as rats with early stage radiation-induced-lung-injury, and compare the stretched-exponential-model based morphometry estimates for three different cases: 1) fully-sampled k-space 2) 85% retrospectively under-sampled k-space, (acceleration factor (AF)=7), and 3) 90% retrospectively under-sampled (AF=10) k-space.

Introduction:

Hyperpolarized ¹²⁹Xe pulmonary MRI is poised for clinical translation due in part to the clinical relevance of ¹²⁹Xe MRI biomarkers of lung disease, a stable supply of ¹²⁹Xe gas and the commercial availability of polarizers that generate large volumes of highly polarized gas.A rapid multi-b diffusion-weighted 129Xe MRI method is required for clinical morphometry due to the challenges in acquiring fully-sampled datasets during the relatively short 10-16sec breath-holds.¹ Acquisition of whole-lung 3D multi-b diffusion-weighted data acquired in a single breath-hold has been shown to be feasible for clinical 3He lung MRI using traditional k-space sampling² and accelerated sampling with both parallel imaging³ and compressed-sensing (CS).^4-6 Recently, a stretched-exponential-model^4,7 (SEM) combined with the CS was proposed for the rapid acquisition (up to 10x faster) and evaluation of hyperpolarized gas multiple b-value diffusion-weighted ³He MRI.^8,9 SEM is not constrained to a specific range of diffusion-times (D), thus, it may be able to reveal information about the lung microstructure at different diffusion-length-scales where non-Weibel-like acinar-ducts are present, as in cases of post-irradiation-fibrosis or severe-emphysema. Unfortunately, this approach doesn’t provide clinically-relevant information about the lung parenchyma microstructure such as mean-linear-intercept (Lm).^9-11 We hypothesize that there is a correlation between the specific diffusion length scale (Lm_D)^4,6 estimated using SEM and the measurement of L_m estimated using a validated morphometry approach.^9,10 Therefore, in this proof-of-concept evaluation, our objective was to measure Lm_D/L_m estimates in a small group of control rats as well as rats with early stage radiation-induced lung injury, and compare the SEM-based Lm_D/L_m estimates for three different cases: 1) fully-sampled k-space (Figure 1a), 2) 85% retrospectively under-sampled k-space in the diffusion-weighting direction, (acceleration factor (AF)=7, Figure 1b), and 3) 90% retrospectively under-sampled (AF=10, Figure 1c) k-space in the diffusion-weighting direction.

Methods:

Four control-animals (372±37g) and five irradiated-animals (380±30g) (Sprague Dawley rats) were studied (ethics-board-approved-protocol). Animal irradiations were carried out using a Cobalt-60 source having a mean dose rate of 190cGy/min as previously described.¹² Imaging was performed at 3.0T (MR750, GEHC, WI) using a high-performance insert-gradient-coil (G=500mT/m, slew-rate=2000T/m/s)¹³ and a commercial, xenon-quadrature-rat-sized RF coil¹⁴ (Morris Instruments, Canada). In all xenon measurements the diffusion-sensitization gradient pulse ramp up/down time=500μs, constant time=2ms, Δ=5.0ms, providing eight b-values 0, 2.35, 9.39, 21.1, 37.6, 58.7, 84.5 and 115s/cm². A single breath-hold, interleaved (eight interleaves) centric 2D FGRE diffusion-weighted sequence was acquired for a coronal slice (TE/TR=10.3ms/14.5ms, BW=8kHz, matrix size=64x64, and FOV=50x50mm², variable-flip-angle, 10sec breath-hold). Hyperpolarized 129Xe (83%) gas was provided by turn-key, spin-exchange polarizer systems (Polarean 9800, polarization range: 7-15%; Xemed XeBox-E1015, polarization range: 20-35%). Four wash-in-breaths of ¹²⁹Xe were administered to the rats prior to imaging. Diffusivity (DDC), heterogeneity-index (α), LmD and morphometry maps (acinar-duct external/internal radius; (R/r), alveolar-sleeve-depth (h), L_m) were generated using the cylinder-model (CM) as previously described.^{6,10,11,16,17} Two k-space masks mimicking AF=7/AF=10 were retrospectively applied to the fully-sampled k-space data in order to obtain under-sampled k-spaces with two different AFs. The histological mean-linear-intercept (MLI) estimates were obtained as previously described.¹²

Results:

Table 1 shows the CM-based morphometry estimates for all rats. Mean R/r/h/L_m estimates for control rats were significantly different from corresponding mean R/r/h/L_m estimates for irradiated rats (p<.03; for all, AF=1). Table 2 shows Lm_D estimates obtained for all rats at three different AF. Mean Lm_D estimates for the control rats were significantly different from corresponding mean Lm_D estimates for the irradiated rats (p<.01; for all AF). Figure 2B shows the Lm_D values correlated with L_m (histological MLI estimates) and the empirical relationship. This relationship was used to calculate the L_m estimates for three different AF (Table 2). Figure 3 shows representative DDC/α/Lm_D/L_m maps for the Control-4 reconstructed from the AF=1/AF=7/AF=10 k-spaces. The mean differences of 7.0%/(9.0%), 2.0%/(2.0%), 2.0%/(2.0%) and 6.0%/(5.0%) were observed between AF=1 and AF=7/(AF=10) for the DDC/α/LmD/Lm values, respectively. Figure 4 shows representative DDC/α/Lm_D/L_m maps for the Irradiated-1 reconstructed from the AF=1/AF=7/AF=10 k-spaces. The mean differences of 3.0%/(2.0%), 1.0%/(2.0%), <1.0%/(<1.0%) and <1.0%/(<1.0%) were observed between AF=1 and AF=7/(AF=10) for the DDC/α/Lm_D/L_m values, respectively.

Discussion and Conclusion:

In this proof-of-concept study we showed that the SEM can be extended to provide clinically-relevant morphometry estimates. We also show that the differences in ¹²⁹Xe MRI-based Lm_D/L_m estimates from fully-sampled and under-sampled (AF=7/AF=10) k-space were similar to those observed with accelerated ¹²⁹Xe multi-b diffusion-weighted MRI.⁴ Figures 2 and 3 suggest that morphometry estimates were reasonably close between AF=1/AF=7/AF=10 acquisitions. This, supported by the measured histological MLI estimates (Figure 2B) suggests that the accelerated SEM may be used as an alternative to the cylinder-model. Moreover, by utilizing AF=10, within a single 1sec breath-hold, whole lung projection ¹²⁹Xe MRI-based morphometry estimates can potentially be generated.

Acknowledgements

The authors wish to acknowledge the following sources of funding: Canadian Institutes for Health Research (Operating grant MOP-123431), Ontario Research Fund (Ontario Preclinical Imaging Consortium) and the Natural Sciences and Engineering Research Council. The authors would also like to thank Adam Farag, Paula Pflugfelder and Zack Zytner for assistance with MRI experiments and data analysis.

Authors thank Abascal, et all for providing Matlab code for the image reconstruction.

References

1 Ouriadov, A. et al. Lung morphometry using hyperpolarized (129) Xe apparent diffusion coefficient anisotropy in chronic obstructive pulmonary disease. Magn Reson Med 70, 1699-1706, doi:10.1002/mrm.24595 (2013).
2 Paulin, G. A. et al. Noninvasive quantification of alveolar morphometry in elderly never- and ex-smokers. Physiol Rep 3, doi:10.14814/phy2.12583 (2015).

3 Chang, Y. V., Quirk, J. D. & Yablonskiy, D. A. In vivo lung morphometry with accelerated hyperpolarized (3) He diffusion MRI: a preliminary study. Magn Reson Med 73, 1609-1614, doi:10.1002/mrm.25284 (2015).

4 Chan, H. F., Stewart, N. J., Norquay, G., Collier, G. J. & Wild, J. M. 3D diffusion-weighted (129) Xe MRI for whole lung morphometry. Magn Reson Med 79, 2986-2995, doi:10.1002/mrm.26960 (2018).

5 Zhang, H. et al. Lung morphometry using hyperpolarized (129) Xe multi-b diffusion MRI with compressed sensing in healthy subjects and patients with COPD. Med Phys 45, 3097-3108, doi:10.1002/mp.12944 (2018).

6 Chan, H. F., Stewart, N. J., Parra-Robles, J., Collier, G. J. & Wild, J. M. Whole lung morphometry with 3D multiple b-value hyperpolarized gas MRI and compressed sensing. Magn Reson Med 77, 1916-1925, doi:10.1002/mrm.26279 (2017).

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8 Abascal, J. F. P. J., Desco, M. & Parra-Robles, J. Incorporation of prior knowledge of the signal behavior into the reconstruction to accelerate the acquisition of MR diffusion data. ArXiv e-prints 1702 (2017). <http://adsabs.harvard.edu/abs/2017arXiv170202743A>.

9 Westcott, A., Guo, F., Parraga, G. & Ouriadov, A. Rapid Single-breath Hyperpolarized Noble Gas MRI Based Biomarkers of Airspace Enlargement. J Magn Reson Imaging, doi:10.1002/jmri.26574 (2018).

10 Ouriadov, A., Lessard, E., Sheikh, K., Parraga, G. & Canadian Respiratory Research, N. Pulmonary MRI morphometry modeling of airspace enlargement in chronic obstructive pulmonary disease and alpha-1 antitrypsin deficiency. Magn Reson Med 79, 439-448, doi:10.1002/mrm.26642 (2018).

11 Yablonskiy, D. A. et al. Quantification of lung microstructure with hyperpolarized 3He diffusion MRI. J Appl Physiol (1985) 107, 1258-1265, doi:10.1152/japplphysiol.00386.2009 (2009).

12 Ouriadov, A. et al. Early stage radiation-induced lung injury detected using hyperpolarized (129) Xe Morphometry: Proof-of-concept demonstration in a rat model. Magn Reson Med 75, 2421-2431, doi:10.1002/mrm.25825 (2016).

13 Foster-Gareau, P., Heyn, C., Alejski, A. & Rutt, B. K. Imaging single mammalian cells with a 1.5 T clinical MRI scanner. Magn Reson Med 49, 968-971, doi:10.1002/mrm.10417 (2003).

14 Kaushik, S. S. et al. Single-breath clinical imaging of hyperpolarized (129)Xe in the airspaces, barrier, and red blood cells using an interleaved 3D radial 1-point Dixon acquisition. Magn Reson Med 75, 1434-1443, doi:10.1002/mrm.25675 (2016).

15 Hersman, F. W. et al. Large production system for hyperpolarized 129Xe for human lung imaging studies. Acad Radiol 15, 683-692, doi:10.1016/j.acra.2007.09.020 (2008).

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Figures

Figure 1. Representative ¹²⁹Xe MRI rat lung images obtained for eight different b-values with full k-space sampling (AF=1, (A)); Sparsity Pattern for AF=7 (B) and 10 (C). K-space under-sampling scheme, ensuring a variety of sparsity patterns for each b-value (AF=7 and AF=10) was retrospectively applied in diffusion direction.

*ANOVA between control and irradiated rats; R = acinar duct external radius; r = acinar duct internal radius; h = alveolar sleeve depth; L_m = mean linear intercept estimate.

(A) *ANOVA between control and irradiated rats; SEM =stretched exponential model; AF = Acceleration Factor; Lm_D = specific to acinar duct mean diffusion length; L_m = mean linear intercept estimate.

(B) Figure 2B. Relationships for mean linear intercept (cylinder-model) with diffusion-scales (stretched-exponential-model). Relationship for Lm_D = mean-diffusion-length-scale with L_m and MLI for irradiated (solid squares) and control (solid circles) (R = 0.94; y = 1.8x – 150µm; p < 0.0006) rats. Histological data (MRI-based Lm_D vs MLI) are shown for demonstration purposes only. MLI = histological mean-linear-intercept.

Figure 3. Representative ¹²⁹Xe MRI maps obtained with the SEM for the Control Rat (C4) with acceleration of 1, 7 and 10.

DDC = MRI-derived apparent diffusivity estimate; Alpha (α) = MRI-derived heterogeneity index; Lm_D = MRI specific to acinar duct mean-diffusion-length; L_m = MRI mean-linear-intercept estimate; AF = Acceleration Factor.

AF=1: DDC = .013cm²s^-1, α = .80, Lm_D = 160µm, L_m = 130µm;

AF=7: DDC = .020cm²s^-1, α = .80, Lm_D = 140µm, L_m = 110µm;

AF=10: DDC = .020cm²s^-1, α = .80, Lm_D = 140µm, L_m = 110µm.

Figure 4. Representative ¹²⁹Xe MRI maps obtained with the SEM for the Irradiated Rat (I-1) with acceleration of 1, 7 and 10.

AF=1: DDC = .013cm²s^-1, α = .80, Lm_D = 130µm, L_m = 90µm;

AF=7: DDC = .013cm²s^-1, α = .80, Lm_D = 135µm, L_m = 90µm;

AF=10: DDC = .013cm²s^-1, α = .80, Lm_D = 135µm, L_m = 95µm.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)

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