Can  the  Stretched  Exponential  Model  of  Gas  Diffusion  Provide Clinically -Relevant Parenchyma  Measurements of Lung Disease?
Alexei Ouriadov1, Eric Lessard1, David G McCormack2, and Grace Parraga1

1Robarts Research Institute, The University of Western Ontario, London, ON, Canada, 2Department of Medicine, The University of Western Ontario, London, ON, Canada

Synopsis

We hypothesized that using inhaled noble gas MRI diffusion-weighted imaging, the diffusion scale estimated using the stretched exponential model would be strongly related to MRI estimates of the mean linear intercept of the lung parenchyma. In this proof-of-concept evaluation, we evaluated 34 never- and ex-smokers and compared parenchyma morphological estimates acquired using two different MRI approaches ad as well with CT and pulmonary function test measurements of acinar duct structure and function. This is important because in obstructive lung disease, the non-invasive measurement of parenchyma tissue destruction or maldevelopment may serve as a therapeutic target.

Purpose

Inhaled noble gas magnetic resonance imaging (MRI) has emerged as a research tool for the quantitative evaluation of parenchymal abnormalities in a variety of lung pulmonary diseases including emphysema, bronchopulmonary dysplasia, congenital lobar emphysema and alpha 1 antitrypsin deficiency. Recently, a stretched exponential model (SEM) was proposed for the evaluation of hyperpolarized gas multiple b-value diffusion-weighted MRI1 as a more straightforward alternative to existing approaches.2,3 The stretched exponential model is not constrained to a specific range of diffusion times, thus, it may be able to reveal information about the lung microstructure at different length scales. Another major advantage is the possibility of simple and straightforward analyses of multiple b-value data. On the other hand, until now, this simplified approach has not been shown to provide clinically-relevant information about the lung parenchyma microstructure such as mean linear intercept (Lm), which is a drawback. However, we hypothesize that there is a correlation between the diffusion scale (LD) estimated using SEM and the measurement of Lm estimated using the morphometry approach. Therefore, in this proof-of-concept evaluation, our objective was to evaluate LD and Lm estimates in a small group of never-smokers (NS) as well as ex-smokers with (ESE) and without (ESnE) emphysema (ESnE).

Methods

As shown in Table 1, 34 subjects including 14 never-smokers, 12 ex-smokers without emphysema and eight ex-smokers with emphysema provided written informed consent to an ethics-board approved study protocol and underwent spirometry, plethysmography, CT and 3He MRI. Imaging was performed at 3.0T (MR750, GEHC, Waukesha WI) using whole-body gradients (5G/cm maximum) and a commercial, rigid linear human RF coil (Rapid Biomedical, Germany). In a single breath-hold, five interleaved acquisitions (TE=3msec, TR=5.0msec, matrix size=128x128, number of slices=7; slice thickness=30mm, and FOV=40x40cm) with and without diffusion sensitization were acquired for a given line of k-space to ensure that RF depolarization (4o constant flip angle was used) and T1 relaxation effects (scan time was 2sec per slice) were minimal. The diffusion-sensitization gradient pulse ramp up/down time=500μs, constant time=460μs and diffusion time (Δ)=1.46ms and this resulted in images acquired at five different b values: 0, 1.6, 3.2, 4.8 and 6.4s/cm2. A diffusion time of 1.46 ms was used in order to provide 3He diffusion sensitivity to alveolar length scales as previously described3. As previously described1,4, maps of Lm, diffusivity (DDC) and heterogeneity index (α) along with two b-value (0 and 1.6 s/cm2) ADC, were computed from diffusion-weighted images on a pixel-by-pixel basis.4

Results

Figure 1 shows representative centre slice ADC, Lm, DDC and α maps for a single NS, ESnE and ESE subject each while Table 1 shows mean estimates of Lm, DDC and α. Figure 2 shows the experimental non-linear (the second order polynomial) dependencies between the diffusion scale ([2ΔDo]1/2) and the mean linear intercept observed for NS (R=0.90), ESnE (R=0.74) and ESE (R=0.94). Figure 2 also shows the experimental dependencies between DDC and α for NS (R=0.95, linear dependence), ESnE (R2=0.81, single exponential dependence) and ESE (R2=0.95, single exponential dependence). There were strong correlations for estimates of mean LD and Lm in the three different subject subgroups.

Discussion and Conclusion

These findings suggest that the stretched exponential model may be used to estimate clinically-relevant parenchyma microstructure measurements such as the mean linear intercept. However, the nature of the experimentally-observed dependencies is not well-understood and require further mathematical modeling and theory development. In addition, the strongest correlations for mean LD and Lm estimates were observed in subjects with a narrow distribution of morphometric parameters and this also requires further investigation. Regardless, the application of diffusion-weighted inhaled gas MRI to provide estimates of subvoxel acinar duct morphology is an important breakthrough in our understanding of the wide variety of parenchyma abnormalities that accompany smoking-related emphysema, congenital emphysema and bronchopulmonary dysplasia. Perhaps the greatest impact can be derived from the longitudinal evaluation of emphysema related to alpha-one antitrypsin deficiency, where lung biomarkers of disease progression and treatment efficacy are lacking. We are developing these diffusion-weighted MRI measurements for a better understanding of the differences in these parenchyma diseases and these proof-of concept results provide a foundation to build these modelling approaches.

Acknowledgements

No acknowledgement found.

References

1 Parra-Robles, J., Marshall, H. & Wild, J. M. [abstract]. ISMRM 21st Annual Meeting (2013).

2 Parra-Robles, J. & Wild, J. M. J Magn Reson 225, 102-113 (2012).

3 Sukstanskii, A. L. & Yablonskiy, D. A.. J Magn Reson 190, 200-210 (2008).

4 Paulin, G. A. et al. Physiological Reports 3, doi:10.14814/phy2.12583 (2015).

Figures

Figure 1. Representative MRI ventilation, ADC, morphometry and SEM maps. TOP panel: Elderly never-smoker (FEV1%pred=91%, DLCO=148%pred) MIDDLE panel: Ex-smoker without emphysema (FEV1%pred=133%, DLCO=78%pred) BOTTOM panel: Ex-smoker with emphysema (FEV1%pred=126%, DLCO=62%pred) ADC= MRI apparent-diffusion-coefficient; Lm= MRI mean-linear-intercept estimate; DDC= MRI-derived diffusivity estimate; Alpha = MRI heterogeneity-index estimate.

Figure 2. Correlations for diffusion scale ([2ΔDo]1/2) and Lm Relationships for never-smokers (NS, top panel), Ex-smokers without emphysema (ESnE=middle panel) and Ex-smokers with emphysema (ESE=bottom panel). Solid lines show fit for LD vs Lm and DDC vs α where LD=diffusion-scale, Lm= MRI mean-linear-intercept estimate and DDC= MRI-derived diffusivity estimate.

BMI=body mass index; FEV1=forced-expiratory-volume-1-sec; %pred= percent-predicted; FVC=forced-vital-capacity; RV=residual-volume; TLC=total-lung-capacity; DLCO=diffusing capacity of the lung for carbon monoxide; VDP=ventilation defect percent; RA950=relative area of the CT density histogram<-950 Hounsfield units; DDC=MRI diffusivity estimate; Lm= MRI mean linear intercept estimate; Alpha = MRI-derived heterogeneity index



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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