Cluster analysis of time evolution (CAT) for quantitative susceptibility mapping (QSM) and quantitative blood oxygen level-dependent magnitude (qBOLD)-based oxygen extraction fraction (OEF) and cerebral metabolic rate of oxygen (CMRO2 ) mapping

Abstract

Purpose: To improve the accuracy of QSM plus quantitative blood oxygen level-dependent magnitude (QSM + qBOLD or QQ)-based mapping of the oxygen extraction fraction (OEF) and cerebral metabolic rate of oxygen (CMRO₂ ) using cluster analysis of time evolution (CAT).

Methods: 3D multi-echo gradient echo and arterial spin labeling images were acquired in 11 healthy subjects and 5 ischemic stroke patients. DWI was also carried out on patients. CAT was developed for analyzing signal evolution over TE. QQ-based OEF and CMRO₂ were reconstructed with and without CAT, and results were compared using region of interest analysis and a paired t-test.

Results: Simulations demonstrated that CAT substantially reduced noise error in QQ-based OEF. In healthy subjects, QQ-based OEF appeared less noisy and more uniform with CAT than without CAT; average OEF with and without CAT in cortical gray matter was 32.7 ± 4.0% and 37.9 ± 4.5%, with corresponding CMRO₂ of 148.4 ± 23.8 and 171.4 ± 22.4 μmol/100 g/min, respectively. In patients, regions of low OEF were confined within the ischemic lesions defined on DWI when using CAT, which was not observed without CAT.

Conclusion: The cluster analysis of time evolution (CAT) significantly improves the robustness of QQ-based OEF against noise.

Keywords: K-means; cerebral metabolic rate of oxygen; cluster analysis of time evolution; machine learning; oxygen extraction fraction; quantitative blood oxygenation level-dependent imaging; quantitative susceptibility mapping.

Figure 1.

Influence of SNR on the sensitivity of the estimated Y on the initial guess (Numerical Simulation 1). Shown is the relative error between the estimated Y and the ground truth (Y_T). Y₀ and v₀ are the initial guesses of Y and v, respectively. As SNR decreases, Y becomes increasingly more sensitive to the initial guess, resulting in larger errors when the initial guess is away from the ground truth value. This seems more severe in the case with smaller v: v_T = 0.03 (Case 1) vs. 0.01 (Case 2). The gray box indicates the ground truth values (Y_T and v_T).

Figure 2

Comparison between the OEF obtained by QQ without and with CAT at different SNRs in the simulated stroke brain (Numerical Simulation 2). At all SNRs, QQ with CAT captures low OEF values, whereas QQ without CAT is not sensitive to low OEF values at low SNRs. The numbers in white indicate the OEF average and standard deviation in the whole brain, and black represents the root-mean-square error (RMSE).

Figure 3.

Comparison of OEF, CMRO2, v, R₂ and χ_nb maps between QQ without and with CAT in a healthy subject. QQ with CAT shows a less noisy and more uniform OEF, and a good CMRO2 contrast between cortical gray matter and white matter without extreme values. The corresponding anatomy as depicted on a T1-weighted image, CBF map and susceptibility map are shown for reference.

Figure 4.

Comparison of OEF, CMRO2, v, R₂ and χ_nb maps between QQ without and with CAT in a stroke patient imaged 6 days post stroke onset. In the CMRO2 and OEF maps, the lesion can be distinguished more clearly with QQ with CAT. For QQ with CAT, a low OEF region is clearly visualized and contained with the lesion region as defined on DWI, but a low OEF region obtained with QQ without CAT is not as well localized nor contained within the lesion as defined on DWI. QQ with CAT generally shows lower v in the DWI-defined lesion. The contrast in v in QQ without CAT result is similar in appearance to that of CBF. QQ with CAT shows generally higher R₂ and χ_nb maps.

Figure 5.

The histogram of OEF values in the lesion and its contralateral side in a second stroke patient imaged 12 days post stroke onset. QQ with CAT shows a different distribution in the lesion as compared to mirror side. The lesion shows 8 peaks with the strongest two peaks at 0 and 17.5%, while the contralateral side has 6 peaks with dominant peaks at 35 ~ 45%. However, QQ without CAT does not have a distribution specific to low OEF values in the lesion, but there are bell-shaped distributions for both the lesion and contralateral side (broader in the contralateral side) with peaks at 47% and 49%, respectively.

Figure 6.

The segmentations and resultant OEF maps using a different number of clusters (K = 1,5,10,15,20, as well as the X-means result, 17 indicated in red) in a third stroke patient (4 days post stroke onset). In the segmentations, different colors indicate different clusters. The resulting OEF appearance is nearly constant for K ≥ 5.

Figure 7.

X-means clusering (K = 17) and the average signal evolution for each clusters in the third stroke patient (4 days post stroke onset). Different color indicates different cluster in the segmentation map. The corresponding average sigal evolution was shown in the same color as the cluster color. The width of the signal evolution is proportional to the number of voxels within clusters in the lesion and the contralateral side: The thicker the curve is, the more voxels the correspoding cluster has. For each voxel, the signal evolution was normalized by the average signal across echoes after the macroscopic field inhomogeneity contribution, G was removed. The average of these normalized signal evolutions across each cluster is shown here in different colors.

Figure 8.

Average and standard deviation of OEF, CMRO2, v, R₂, and χ_nb maps between QQ without and with CAT in cortical gray matter from healthy subjects (N=11). QQ with CAT shows smaller average CMRO2, OEF and v than the one without CAT, but QQ with CAT shows higher average R₂ and χ_nb values. * p<0.01 (paired t-test).