Characterizing gradient echo signal decays in gynecologic cancers at 3T using a Gaussian augmentation of the monoexponential (GAME) model

Abstract

Purpose: To assess whether R2* mapping with a standard Monoexponential (ME) or a Gaussian Augmentation of the Monoexponential (GAME) decay model better characterizes gradient-echo signal decays in gynecological cancers after external beam radiation therapy at 3T, and evaluate implications of modeling for noninvasive identification of intratumoral hypoxia.

Materials and methods: Multi-gradient-echo signals were acquired on 25 consecutive patients with gynecologic cancers and three healthy participants during inhalation of different oxygen concentrations at 3T. Data were fitted with both ME and GAME models. Models were compared using F-tests in tumors and muscles in patients, muscles, cervix, and uterus in healthy participants, and across oxygenation levels.

Results: GAME significantly improved fitting over ME (P < 0.05): Improvements with GAME covered 34% of tumor regions-of-interest on average, ranging from 6% (of a vaginal tumor) to 68% (of a cervical tumor) in individual tumors. Improvements with GAME were more prominent in areas that would be assumed hypoxic based on ME alone, reaching 90% as ME R2* approached 100 Hz. Gradient echo decay parameters at different oxygenation levels were not significantly different (P = 0.81).

Conclusion: R2* may prove sensitive to hypoxia; however, inaccurate representations of underlying data may limit the success of quantitative assessments. Although the degree to which R2 or σ values correlate with hypoxia remains unknown, improved characterization with GAME increases the potential for determining any correlates of fit parameters with biomarkers, such as oxygenation status. J. MAGN. RESON. IMAGING 2016;44:1020-1030.

Keywords: Gaussian; Lorentzian; biophysical modeling; blood oxygenation; gynecologic cancers; transverse relaxation.

Figure 1

Summary of patient and healthy participant protocols: (a) N-P = Normal in patients (n=5), (b) HL-P = High-Low in patients (n=18), (c) HIL-P = High-Intermediate-Low in patients (n=2); and (d) HIL-H: High-Intermediate-Low in healthy participants (n=3) (“…” denotes other imaging, unused in this study, of 5–7 minute duration).

Figure 2

Sample fits and parameters (a) Anatomy (T2W TSE) with tumor contour, on Patient X (b–e) Semi log plots of multi-echo GRE signal (arbitrary units) over time (TE: 3, 8.96, 17.92, 26.88, 35.84, and 44.80 ms) at the red voxel locations (b–d) log(Signal) vs. TE shows significant curvature (P < 0.05), and GAME outperforms ME improving SSEs by over 400-fold to over 3000-fold (e) As σ → 0, log(Signal) vs. TE becomes linear, and the models become equivalent. (f) Anatomy (T2W TSE) with tumor (red) and muscle (green, yellow) contours, on Patient Y (g) ME ${\mathit{R}}_{\mathbf{2}}^{*}$ (h) GAME R₂, and (i) GAME σ, parameter maps (black-white checkered regions in (g) demonstrate areas within the tumor with complete signal loss where fitting was not performed; white arrows point to areas of low ${\mathit{R}}_{\mathbf{2}}^{*}$, R₂ and σ; gray arrows point to areas of high ${\mathit{R}}_{\mathbf{2}}^{*}$ and R₂, with low σ; black arrows point to areas of high ${\mathit{R}}_{\mathbf{2}}^{*}$, and σ, with low R₂).

Figure 3

(a–b) Highly significant improvements are seen with GAME over ME in tumors (P <0.05), P-values are shown for Patients X and Y (of Figure 2) (c) The physical extent of improvements with GAME over ME, for all patient and healthy participant ROIs (as a percentage of the entire ROI volume, Eq. [4]). Improvements with GAME cover 34% of tumor ROIs on average at P < 0.05 (based on clustering), and persist at increasing levels of statistical significance (Pc: P value based on clustering; Pb: P value based on Bonferroni correction) (d) The extent of statistically significant improvements with GAME over ME increases in areas that would be assumed indicative of hypoxia based on ME fits alone (areas of high ${\mathit{R}}_{\mathbf{2}}^{*}$ according to the ME model). ME ${\mathit{R}}_{\mathbf{2}}^{*}$ cutoff = 0 corresponds to calculating the extent of improvements with GAME as a percentage of the entire ROI volume (irrespective of the ME ${\mathit{R}}_{\mathbf{2}}^{*}$ estimates within the ROI, Eq. [4], as in Figure 3c). ME ${\mathit{R}}_{\mathbf{2}}^{*}$ cutoff > 0 corresponds to selecting high ${\mathit{R}}_{\mathbf{2}}^{*}$ sub-ROIs within each ROI, where using the ME model alone would have indicated hypoxia, and calculating the extent of improvements with GAME as a percentage of these smaller ROIs (Eq. [5]) (shown for muscle and tumor ROIs at P <0.05, combined across all patients; circles depict ROIs of decreasing size with increasing ME ${\mathit{R}}_{\mathbf{2}}^{*}$ cutoff; red-blue stripes indicate part of these ROIs that improve significantly with GAME).

Figure 4

ME and GAME fit parameters (mean ± SD, Hz) in tumors and muscles of patients, in regions where GAME significantly improved fitting (P < 0.05, ROI_GAME) versus where GAME did not significantly improve fitting and simply reduced to the ME model (ROI_ME) (Eqs. [6]). ME ${\mathit{R}}_{\mathbf{2}}^{*}$ was lower in ROI_ME, while GAME R₂ was lower and GAME σ was higher in ROI_GAME.

Figure 5

Macroscopic background inhomogeneities estimated from multi-echo GRE data helped identify regions where high σ did or did not overlap with high TPGs (a, b) Consecutive slices (T2w TSE with tumor outlined); (c, d) Multi-echo GRE field map estimates (Eq. [7], Hz); (e, f) Magnitude of the TPG across each slice (Eq. [8], Hz/mm); (g, h) GAME σ (Hz), shown in areas where GAME statistically significantly improved blue color coded portions within each circle indicate the approximate fraction of each ROI that improves significantly with GAME and where σ values were calculated, for tumors and muscles, respectively).

Figure 6

σ and TPG (a) Scatter plots, regression lines and adjusted coefficients of determination, (for each subject with a fieldmap). σ increases with TPG in most tumors, but in few muscles (b) The extent of improvements with GAME over ME as a function of TPG (P < 0.05, across all patients with fieldmaps): increases then decreased in tumors, but is stable in muscles (c) Mean σ increases with increasing TPG cutoffs. TPG cutoff = 0 corresponds to using the entire ROI volume (irrespective of the field inhomogeneity within the ROI, Eq. [4]). TPG cutoff > 0 corresponds to selecting high TPG sub-ROIs within each ROI, and calculating the extent of improvements with GAME as a percentage of (Eq. [9]) and mean σ values within (Eq. [10]) these smaller ROIs (Sizes of the circles within each graph indicate the approximate sizes of the ROIs under consideration: ROIs of decreasing size with increasing TPG cutoff. Sizes of the red and blue color coded portions within each circle indicate the approximate fraction of each ROI that improves significantly with GAME and where σ values were calculated, for tumors and muscles, respectively).