Temporal clustering, tissue composition, and total variation for mapping oxygen extraction fraction using QSM and quantitative BOLD

Abstract

Purpose:

To improve the accuracy of quantitative susceptibility mapping plus quantitative blood oxygen level-dependent magnitude (QSM+qBOLD or QQ) based mapping of oxygen extraction fraction (OEF) and cerebral metabolic rate of oxygen (CMRO2) using temporal clustering, tissue composition, and total variation (CCTV).

Methods:

Three-dimensional multi-echo gradient echo and arterial spin labeling images were acquired from 11 healthy subjects and 33 ischemic stroke patients. Diffusion-weighted imaging (DWI) was also obtained from patients. The CCTV mapping was developed for incorporating tissue-type information into clustering of the previous cluster analysis of time evolution (CAT) and applying total variation (TV). The QQ-based OEF and CMRO₂ were reconstructed with CAT, CAT+TV (CATV), and the proposed CCTV, and results were compared using region-of-interest analysis, Kruskal-Wallis test, and post hoc Wilcoxson rank sum test.

Results:

In simulation, CCTV provided more accurate and precise OEF than CAT or CATV. In healthy subjects, QQ-based OEF was less noisy and more uniform with CCTV than CAT. In subacute stroke patients, OEF with CCTV had a greater contrast-to-noise ratio between DWI-defined lesions and the unaffected contralateral side than with CAT or CATV: 1.9 ± 1.3 versus 1.1 ± 0.7 ($P=.01$) versus 0.7 ± 0.5 ($P<.001$).

Conclusion:

The CCTV mapping significantly improves the robustness of QQ-based OEF against noise.

1 ∣. INTRODUCTION

Oxygen extraction fraction (OEF) and cerebral metabolic rate of oxygen (CMRO₂) are valuable for assessing brain tissue viability and function in neurological disorders including stroke and neurodegeneration.^1-4 In MRI, quantitative mapping of OEF and CMRO₂ has been developed by considering the strong paramagnetic effect of blood deoxyhemoglobin on (1) the magnitude signal, including calibrated functional MRI,^5-8 T₂-based methods,^9-12 and quantitative BOLD (qBOLD)^13-17; and (2) the phase signal, such as whole-brain susceptometry-based oximetry^18-20 and quantitative susceptibility mapping (QSM)-based macrovascular^21-23 and microvascular^24-28 OEF mapping. A recent integrated model of QSM and qBOLD (QSM+qBOLD or QQ) can map OEF without vascular challenges by utilizing both magnitude and phase of multi-echo gradient-echo (mGRE) data,²⁹ a readily applicable sequence in any MRI system. Therefore, this QQ-based OEF mapping tool has great potential in clinical applications.

A major challenge in OEF mapping is its poorly conditioned nonconvex inversion nature that is sensitive to data noise.^16,30 The cluster analysis of time evolution (CAT) algorithm has improved effective SNR in the QQ approach.^31-34 To further suppress noise propagation in OEF, we integrate tissue-type information with CAT and apply total variation (TV) regularization in this study. Limited clusters using magnitude signal time evolution in CAT³¹ may be improved by additional tissue type information, particularly gray matter (GM) versus white matter (WM), which helps to determine tissue-specific QQ model parameters including venous blood volume^35,36 and R₂.¹⁷ Furthermore, TV regularization should help alleviate the propagation of measurement noise into the parameter map.³⁷ Accordingly, we propose to combine temporal clustering, tissue composition, and total variation (CCTV) for the QQ approach to OEF and CMRO₂ (with regional blood flow) mapping.

2 ∣. THEORY

The CMRO₂ (μmol/100 g/min) can be estimated with $CMR{O}_2=OEF\cdot CBF\cdot [H{]}_{\mathrm{a}}$, where CBF is regional cerebral blood flow (mL/100 g/min) and $[H{]}_{\mathrm{a}}=7.377$ μmol/mL is the oxygenated heme molar concentration in an arteriole with hematocrit (Hct) = 0.357.²⁴

The OEF can be defined as OEF = 1 – $Y∕Y_a$, where $Y$ and $Y_a$ (= 0.98²⁹) are the venous and arterial oxygenation, respectively. For OEF estimation, the QQ model combines QSM (phase analysis) and qBOLD (magnitude analysis). Regularization $R$ is imposed using a priori physiological constraints for robust parameter determination, such as suppressing noise propagation in the ill-posed CMRO₂ model inversion²⁵:

$$Y^{\ast },v^{\ast },R_2^{\ast },S_0^{\ast },{\chi }_n^{\ast }=\underset{Y,v,R_2,S_0,{\chi }_{nb}}{\text{argmin}}\left\{w{\Vert \chi -F_{QSM}\left(Y,v,{\chi }_n\right)\Vert }_2^2+\sum _j{\Vert \mid S_j\mid -F_{qBOLD}\left(S_0,Y,v,R_2,{\chi }_n,t_j\right)\Vert }_2^2+R(Y)\right\},$$ (1)

where $w$ is weighting on the first QSM term.

The QSM term decomposes voxel-wise susceptibility ($\chi$) into (1) blood susceptibility consisting of venous deoxyhemoglobin (i.e., OEF effect and fully oxygenated blood, ${\chi }_{ba}=-108.3$ ppb)²⁵ and (2) nonblood neural tissue susceptibility (${\chi }_n$) as follows:

$$\begin{gathered} F_{QSM}\left(Y,v,{\chi }_n\right) \\ =\left[{\psi }_{Hb}\cdot \Delta {\chi }_{Hb}\cdot \left(-Y+\frac{1-(1-\alpha )\cdot Y_a}{\alpha }\right)+\frac{{\chi }_{ba}}{\alpha }\right]\cdot v+\left(1-\frac{v}{\alpha }\right)\cdot {\chi }_n \end{gathered}$$ (2)

where ${\psi }_{Hb}=0.0909$ is the hemoglobin volume fraction assuming Hct = 0.357^26,38-40; $\Delta {\chi }_{Hb}=12522$ ppb is the susceptibility difference between deoxyhemoglobin and oxyhemoglobin^24,41; $\alpha =0.77$ is the ratio between the venous and total blood volumes⁴²; and $v$ is the venous blood volume fraction.

The second qBOLD term models magnitude signal, $\mid S_j\mid$, at the $j$th echo²⁹ as follows:

$$F_{qBOLD}\left(S_0,Y,v,R_2,{\chi }_n,t_j\right)=S_0\cdot e^{-R_2\cdot t_j}\cdot F_{BOLD}\left(Y,v,{\chi }_n,t_j\right)\cdot G\left(t_j\right)$$ (3)

where $S_0$ is signal intensity at $t_j=0;R_2$ is the transverse relaxation rate; $F_{BOLD}(Y,v,{\chi }_n,t_j)=\text{exp}[-v\cdot f_s(\delta \omega \cdot t_j)]$¹⁶; $f_s$ is the signal decay due to the presence of blood vessel network whose asymptotic behavior is $f_s(\delta \omega \cdot t_j)\approx \frac{3}{10}(\delta \omega \cdot t_j{)}^2$ for $t_j\ll 1∕\delta \omega$ and $f_s(\delta \omega \cdot t_j)\approx \delta \omega \cdot t_j$ for $t_j\gg 1∕\delta \omega$¹⁷; and $\delta \omega (Y,{\chi }_n)=\frac{1}{3}\cdot \gamma \cdot B_0\cdot \left[{\psi }_{Hb}\cdot \Delta {\chi }_{Hb}\cdot (1-Y)+{\chi }_{ba}-{\chi }_n\right]$ is the characteristic frequency by the susceptibility difference between deoxygenated blood and the surrounding tissue,²⁹ in which $\gamma =267.513$ (rad/s)/T; B₀ is the main magnetic field strength; and $G(t_j)$ is the macroscopic field inhomogeneity contribution to the mGRE signal estimated using the voxel spread function (see Appendix of Cho et al²⁹).

In the previously introduced CAT method,³¹ voxels with similar signal time evolution ($F_{qBOLD}∕G$) form a cluster and are assumed to have similar tissue parameters ($Y,v,R_2$) for SNR improvement. In the proposed CCTV, tissue-type information is incorporated into the clusters obtained from CAT by dividing each cluster into its GM, WM, and cerebrospinal fluid (CSF) subcomponents, which can lead to comprehensive clustering using both temporal signal pattern and tissue-type information and to improved subsequent optimization initialization. In addition, as OEF is a linear function of $Y$ ($OEF=1-Y∕Y_a$ where $Y_a=0.98$), the TV regularization, $R(Y)=\lambda \Vert \nabla Y{\Vert }_1$, is expected to suppress noise propagation into the OEF map by imposing spatial smoothness.³⁷

3 ∣. METHODS

3.1 ∣. Numerical simulation

To compare the accuracy of QQ among CAT, CAT+TV (CATV), and CCTV, a simulation was performed similar to “Numerical Simulation 2” in Cho et al.³¹ The average of the CAT, CATV, and CCTV results (a set of 3D $Y$, $v$, $R_2$, $S_0$, ${\chi }_n$ maps) from 1 real stroke patient (6 days following onset) was used as the ground truth. The mGRE and QSM values were then simulated using Equations 2 and 3 using this ground truth, with Gaussian noise added to obtain an SNR of 20. The noisy simulated data were processed using CAT,³¹ CATV, and CCTV, with the same optimization parameters and settings as in the experimental data. This was repeated 5 times for different instances of Gaussian noise to allow accuracy and precision measurement.

Additionally, to investigate the effect of the choice of ground truth on algorithm performance, the simulation was performed with four different ground truths (Supporting Information Table S1): case 1, CAT result; case 2, CATV result; case 3, CCTV result; and case 4, the average of the CAT, CATV, and CCTV results.

3.2 ∣. Data acquisition

3.2.1 ∣. Healthy subjects

This study was approved by the local institutional review board, and all subjects provided written consent. Without caffeine or alcohol intake 24 hours before MRI, 11 healthy adults (1 female, age 34 ± 12 years) underwent an MRI on a 3T scanner (HDxt; GE Healthcare, Waukesha, WI) in the resting state using (1) a 3D fast spin-echo arterial spin labeling (FSE ASL) sequence^43-45 (20-cm FOV, 1.56 × 1.56 × 3.5 mm³ voxel size, 1500-ms labeling period, 1525-ms postlabel delay, 976.6-Hz/pixel bandwidth, spiral sampling of eight interleaves and 512 readout points per leaf, 35 axial slices, TE = 10.1 ms, TR = 4533 ms, and three signal averages), (2) a 3D spoiled mGRE sequence^46-48 with flow compensation in all three directions⁴⁸ (0.78 × 0.78 × 1.2 mm³ voxel size, identical FOV to the 3D FSE ASL sequence, and seven equally spaced echoes: TE₁/ΔTE/TE₇ = 2.3/3.9/25.8 ms, TR = 30.5 ms, bandwidth = 488.3 Hz/pixel, and flip angle = 15°), and (3) an inversion-prepared T₁-weighted spoiled gradient-echo sequence (BRAVO)⁴⁹ (0.78 × 0.78 × 1.2 mm³, identical FOV to the 3D FSE ASL sequence, TE = 2.92 ms, TR = 7.69 ms, 450-ms prep time, bandwidth = Hz/pixel, and flip angle = 15°).

3.2.2 ∣. Stroke patients

This retrospective image analysis was approved by the local institutional review board. Thirty-three ischemic stroke patients all with lesions in unilateral cerebral artery territory were classified into two groups based on the time interval between stroke onset and MRI scan⁵⁰: acute (6-24 hours, $N=6$) and subacute (1-14 days, $N=27$) phase. They underwent MRI on a clinical 3T scanner (GE MR Discovery 750) using (1) 3D FSE ASL (24-cm FOV, 1.9 × 1.9 × 2.0 mm³ voxel size, 1500-ms labeling period, 1525-ms postlabel delay, 976.6-Hz/pixel bandwidth, 68 axial slices, TE = 14.6 ms, TR = 4787 ms, and three signal averages), (2) 3D mGRE (0.47 × 0.47 × 2.0 mm³ voxel size, identical FOV to the 3D FSE ASL sequence, and eight equally spaced echoes: TE₁/ΔTE/TE₈ = 4.5/5/39.5 ms, TR = 42.8 ms, bandwidth = 244.1 Hz/pixel, and flip angle 20°), and (3) DWI (24-cm FOV; 0.94 × 0.94 × 3.2 mm³ voxel size; 1953.1-Hz/pixel bandwidth; 0, 1000 s/mm² b-values; TE = 71 ms; TR = 3000 ms; and four signal averages), and (4) a T₁-weighted fluid attenuated inversion recovery sequence⁵¹ (24-cm FOV, 0.5 × 0.5 × 5 mm³ voxel size, TE = 23.4 ms, and TR = 1750 ms).

3.3 ∣. Data processing: QSM and CBF

The QSM reconstruction comprised the total field estimation using an adaptive, quadratic fit of the mGRE phase,⁴⁸ local field calculation with the projection onto dipole fields (PDF) method,⁴⁷ and susceptibility estimation using the morphology-enabled dipole inversion with automatic uniform CSF zero-reference algorithm.^46,52-54 In stroke patients, the total field was estimated using a linearfit of the mGRE phase,⁵⁵ as 3D flow compensation was not available on the clinical scanner. The CBF maps (mL/100 g/min) were generated from the ASL data using FuncTool (GE Healthcare). All images were co-registered and interpolated to the resolution of the QSM maps using the FSL FLIRT algorithm.^56,57

3.4 ∣. Data processing: OEF

The OEF map was estimated by QQ-CAT, QQ-CATV (QQ-CAT + TV), and the proposed QQ-CCTV. For CAT, the same OEF reconstruction as in the original CAT paper³¹ was used, including clustering and optimization, except: (1) The regularization that average OEF for the whole brain should be similar to the brain OEF value estimated from the straight sinus vein was excluded, because this estimation is not based on a biophysics principle such as mass conservation; and (2) the v initial guess was set to 4/2/1% for GM/WM/CSF instead of 3/1.5/1%, to be consistent with the values from a similar mGRE-based method.¹⁷ First, x-means clustering, a modified k-means with automatic optimal cluster number selection, was used on voxel-wise $F_{qBOLD}∕G$. Cluster-based and voxel-wise optimization were performed consecutively to estimate the model parameters ($Y$, $v$, ${\chi }_n$, $R_2$, $S_0$). For CATV, TV regularization ($\lambda \Vert \nabla Y{\Vert }_1$) was added to CAT with $\lambda =2\times {10}^{-5}$ by L-curve analysis.⁵⁸

For CCTV, each cluster from CAT was further separated into GM/WM/CSF subclusters using segmentation that was performed with T₁-weighting using the FSL FAST algorithm.⁵⁹ The same optimization procedure as CAT was used except setting the $R_2$ scaling factor to $avg(R_{2,0})+6.5\cdot SD(R_{2,0})$ instead of $avg(R_{2,0})+4\cdot SD(R_{2,0})$ to consider the decreased $SD(R_{2,0})$ due to the reduced cluster-wise number of voxels, where $avg(R_{2,0})$ and $SD(R_{2,0})$ denote the average and standard deviation (SD) of the $R_2$ initial guess in each cluster, respectively. The weights on QSM ($w$) and regularization ($\lambda$) were chosen by consecutive L-curve analysis⁵⁸: $w=2.5\times {10}^{-2}$ and $\lambda =1\times {10}^{-5}$.

3.5 ∣. Statistical analysis

In the numerical simulation, accuracy and precision were measured by mean absolute error ($\text{MAE}\equiv \frac{1}{{\mathrm{N}}_{\mathrm{v}}}{\sum }_{\mathrm{i}=1}^{{\mathrm{N}}_{\mathrm{v}}}\mid OE{F}_{truth}-OE{F}_{avg}\mid$) and mean SD ($\text{MSD}\equiv \frac{1}{{\mathrm{N}}_{\mathrm{v}}}{\sum }_{\mathrm{i}=1}^{{\mathrm{N}}_{\mathrm{v}}}OE{F}_{std}$), where $OE{F}_{avg}\equiv \frac{1}{{\mathrm{N}}_{\mathrm{t}}}{\sum }_{\mathrm{j}=1}^{{\mathrm{N}}_{\mathrm{t}}}OE{F}_{\mathrm{i},\mathrm{j}}$; $OE{F}_{std}\equiv \sqrt{\frac{1}{{\mathrm{N}}_{\mathrm{t}}}{\sum }_{\mathrm{j}=1}^{{\mathrm{N}}_{\mathrm{t}}}{\left(OE{F}_{\mathrm{i},\mathrm{j}}-\frac{1}{{\mathrm{N}}_{\mathrm{t}}}{\sum }_{\mathrm{j}=1}^{{\mathrm{N}}_{\mathrm{t}}}OE{F}_{\mathrm{i},\mathrm{j}}\right)}^2}$; is the voxel index; j is the trial index; N_v is the number of voxels; and N_t is the number of trials.

In healthy subjects, cortical GM (CGM) masks were constructed based on the inversion-prepared T₁-weighted spoiled gradient-echo image by an experienced neuroradiologist (A.G., 11 years of experience). To compare OEF and CMRO₂ values from QQ among CAT, CATV, and CCTV, region-of-interest analyses (mean and SD) were performed and, to assess statistical significance, Kruskal-Wallis (KW) tests and post hoc Wilcoxon rank sum (WRS) tests were performed. In the post hoc WRS tests, multiple-comparison correction was performed using the false discovery rate.⁶⁰ For stroke patients, regions of interest for the lesion and its corresponding contralateral side were drawn based on DWI by the same neuroradiologist. The detectability of lesion OEF abnormality was measured by the contrast-to-noise ratio (CNR) between the lesion and the contralateral side ($CNR\equiv \frac{\mid \overline{OE{F}_{lesion}}-\overline{OE{F}_{contralateralside}}\mid }{\sigma (OE{F}_{contralateralside})}$), assuming that OEF variation within the contralateral side originated from noise. The CNR was compared among CAT, CATV, and CCTV using KW tests and post hoc WRS tests. A $p$-value less than .05 was considered significant.

4 ∣. RESULTS

Figure 1 shows the OEF comparison between QQ-CAT, QQ-CATV, and QQ-CCTV in the simulated stroke brain (numerical simulation). The QQ-CCTV provided the most accurate OEF map (smallest MAE: 5.3 vs 5.4 vs 4.3%) with the highest precision (smallest MSD: 3.1 vs 2.4, and 1.8%). The $OE{F}_{avg}$ map from QQ-CCTV best captured low OEF values in the lesion (smallest MAE in the lesion: 3.4 vs 3.5 vs 2.8%). In the investigation of the effect of the choice of ground truth on algorithm performance, QQ-CCTV provided the highest accuracy for cases 1, 3, and 4 and highest precision for all cases (Supporting Information Table S1).

FIGURE 1.

Comparison between the oxygen extraction fraction (OEF) obtained by QQ (QSM + qBOLD) CAT (cluster analysis of time evolution), QQ-CATV (CAT + total variation), and the proposed QQ-CCTV (temporal clustering, tissue composition, and total variation) in a simulated stroke data set. The numbers indicate mean absolute error (MAE; black) and mean SD (MSD; white). On average, QQ-CCTV provides the greatest accuracy (smallest MAE 4.3%) and precision (smallest MSD 1.8%). OEF_avg and OEF_std indicate the average and SD OEF maps among five trials, respectively

Figure 2 shows a comparison of QQ among CAT, CATV, and CCTV in a healthy subject. Compared with QQ-CAT, QQ-CCTV showed a less noisy and more uniform OEF map and subsequently a less noisy CMRO₂ map. The $v$ map from QQ-CCTV showed a clear CGM/WM difference. In the CGM of healthy subjects, QQ-CCTV provided greater $v$ than QQ-CAT and QQ-CATV (Supporting Information Figure S1). For QQ-CAT, QQ-CATV, and QQ-CCTV, the OEF value was 34.2 ± 5.5, 34.5 ± 7.1, and 30.6 ± 3.1% ($P=.17$, KW test); CMRO₂ was 154.5 ± 25.6, 156.6 ± 33.2, and 139.2 ± 23.9 μmol/100 g/min ($P=.24$, KW test); $v$ was 1.4 ± 0.3 ($P=.002$, WRS test), 1.4 ± 0.4 ($P=.002$, WRS test), and 2.7 ± 0.5%; R₂ was 16.2 ± 0.6, 16.2 ± 0.6, and 15.8 ± 0.6 Hz ($P=.23$, KW test); and ${\chi }_n$ was −21.3 ± 7.8, −21.3 ± 7.7, and −24.0 ± 7.8 ppb ($P=.41$, KW test).

FIGURE 2.

Comparison of OEF, cerebral metabolic rate of oxygen (CMRO₂), $v$, $R_2$, and ${\chi }_n$ maps among QQ-CAT, QQ-CATV, and QQ-CCTV in a healthy subject. The QQ-CCTV map shows a less noisy OEF and a clearer $v$ contrast between cortical gray matter and white matter. The corresponding anatomy as depicted on a T₁-weighted image, cerebral blood flow (CBF) map, and susceptibility map are shown for reference

Figure 3 shows representative OEF maps from QQ-CAT, QQ-CATV, and QQ-CCTV in ischemic stroke patients. Compared with QQ-CAT and QQ-CATV, QQ-CCTV showed an improved spatial overlap between low OEF regions and a DWI-defined lesion in the subacute phase with less noisy OEF maps (Figure 4).

FIGURE 3.

Comparison between the OEF obtained by QQ-CAT, QQ-CATV, and QQ-CCTV in 6 stroke patients imaged between 18 hours and 10 days post stroke onset. The QQ-CCTV shows more uniform OEF maps except for DWI-defined lesions compared with QQ-CAT and QQ-CATV. In the subacute phase patients, low OEF areas in QQ-CCTV agree better with DWI-defined lesions. The CBF maps are shown for reference in units of mL/100 g/min

FIGURE 4.

Comparison of OEF, CMRO₂, $v$, $R_2$, and ${\chi }_n$ maps from QQ-CAT, QQ-CATV, and QQ-CCTV in a stroke subject (9 days following onset). The QQ-CCTV map shows a low OEF area that agrees better with the DWI-defined lesion than QQ-CAT and QQ-CATV

Figure 5 shows a boxplot of OEF CNR between the lesion and contralateral side in ischemic stroke patients. Compared with QQ-CAT and QQ-CATV, QQ-CCTV provided significantly greater OEF CNR in the subacute phase (1.9 ± 1.3 vs 1.1 ± 0.7 [$P=.01$, WRS test] vs 0.7 ± 0.5 [$P<.001$, WRS test]), but showed similar CNR in the acute phase (0.5 ± 0.4 vs 0.7 ± 0.4 vs 0.6 ± 0.5 [$P=.83$, KW test]).

FIGURE 5.

Boxplots of OEF contrast-to-noise ratio (CNR) between the lesion and contralateral side in acute (6-24 hours post onset, $N=6$) and subacute (1-14 days post onset, $N=27$) ischemic stroke patients. The number indicates average ± SD. Asterisk (*) indicates a significant difference ($P<.05$). Compared with QQ-CAT and QQ-CATV, QQ-CCTV provided significantly greater CNR in the subacute phase, whereas the CNR was not significantly different in the acute phase

5 ∣. DISCUSSION

Our results indicate that CCTV substantially suppresses noise propagation into QQ-based OEF mapping. Compared with the previous CAT algorithm, the OEF map estimated by CCTV demonstrates greater accuracy and precision in simulation, appears less noisy and more uniform in healthy subjects, and detects OEF abnormalities better in stroke patients. Hence, CCTV provides robust QQ-based OEF mapping without vascular challenges from widely available mGRE data.

Complementary to the magnitude mGRE modeling,¹³ OEF content from phase data through QSM processing²⁴ is valuable due to QSM sensitivity to tissue iron.^61,62 The QQ approach represents a full use of mGRE data,²⁹ but denoising is still critical³¹ because its poor-conditioned nonconvex inversion is prone to data noise. Compared with CAT, CATV and CCTV show less noisy and more uniform OEF maps (Figures 2 and 3), which agree with the reference standard ¹⁵O PET-OEF.^63,64 The OEF noise suppression may result from using TV regularization, which reduces Gaussian noise³⁷ and MRI artifacts including streaking⁶⁵ and Gibbs ringing.⁶⁶ It also agrees with the suppressed Gaussian noise propagation on OEF in numerical simulation using TV (Figure 1). Additionally, in CCTV, the incorporation of tissue-type information may lead to more robust inversion with improved initialization and inversion condition.

The QQ-CCTV technique shows smaller OEF values than QQ-CAT and QQ-CATV (Figure 2 and Supporting Figure S1), 34.5 ± 7.1% vs 30.6 ± 3.1% in CGM (although the difference was not significant [uncorrected $P=.09$, WRS test]), which are accompanied by higher $v$ (1.4 ± 0.4% and 2.7 ± 0.5% [$P<.001$, WRS test]). This can be explained because, for the same measured magnitude signal decay and susceptibility, OEF decreases if $v$ increases (Equations 2 and 3). The OEF values with CAT, CATV, and CCTV are consistent with MRI OEF values reported in the literature (e.g., 26 ± 2%,⁹ 29 ± 3%,⁶⁷ 31.7 ± 6.1%,⁶⁸ and 35 ± 4%).⁶ Furthermore, the $v$ from QQ-CCTV falls into previously reported MRI-based $v$ values (e.g., 2.46 ± 0.28%,⁴² 2.68 ± 0.47%,⁶⁹ and 3.6 ± 0.4%).⁷⁰ Also, the clear CGM/WM contrast from QQ-CCTV is in line with the v contrast in MRI literature^35,36 and may be caused by tissue-type (GM/WM) integration into clustering, which leads to a more realistic $v$ initialization in optimization. The R₂ in CGM estimated with CAT, CATV, and CCTV (16.2 ± 0.6 Hz, 16.2 ± 0.6 Hz, and 15.8 ± 0.6 Hz) agree with the values from other MR techniques (15.1 ± 0.6 Hz¹⁷ and 17.1 ± 2 Hz).⁷¹

In the subacute ischemic stroke patients (Figure 3), low OEF regions from QQ-CCTV agree better with DWI-defined lesions without severe artifacts compared with CAT or CATV. For instance, in a 9-day post-onset case (Figure 4), the low OEF region with CCTV largely coincided with the DWI-defined lesion, whereas CAT and CATV did not depict low OEF values clearly in the lesion and showed noise and artifacts in OEF maps. This is consistent with the significantly greater OEF CNR from CCTV compared with CAT and CATV in the subacute phase (1.9 ± 1.3 vs 1.1 ± 0.7 [$P=.01$, WRS test] and 0.7 ± 0.5 [$P<.001$, WRS test]) (Figure 5), which suggests better detection of OEF abnormalities. The improved OEF CNR may result from improved decoupling between OEF and $v$, a crucial issue in qBOLD-based OEF modeling without very high SNR.¹⁶ The improved decoupling may result from noise propagation suppression into OEF, using TV regularization and proper v initialization by integrating tissue-type information into clustering (Figure 4). In the acute phase (Figure 3), lesion OEF values appear similar to those on the contralateral side, which suggests that an acute lesion tissue may be salvageable.

Compared to CAT with whole-brain average OEF regularization as in the original CAT paper,³¹ CATV provided greater precision (smaller MSD: 2.8 vs 2.4%) in the simulation, lower OEF SD within the CGM of healthy subjects (5.9 ± 1.8 vs 3.2 ± 1.4%; $P=.02$; WRS test), and contralateral side in the subacute phase stroke patients (6.7 ± 3.2 vs 4.8 ± 2.7%; $P<.001$; WRS test). This suggests that TV is more effective to suppress noise propagation into OEF than the whole-brain average OEF regularization.

Among 6 acute ischemic stroke patients, 3 showed the diffusion/perfusion (DWI/CBF) mismatch region, potentially salvageable tissue or penumbra^72-74 (Supporting Information Figure S2). In the OEF maps obtained by QQ-CCTV, the hemisphere containing the lesion showed a higher average OEF than the contralateral hemisphere when the CBF deficit volume was substantially larger than the DWI-defined lesion volume; for example, the average OEF ratio between ipsilateral and contralateral hemisphere was 1.1 when the volume fraction of the DWI/CBF mismatched region relative to the DWI-defined lesion was 19.8 (24 hours post-onset case in Supporting Information Figure S2). This is consistent with previous acute ischemic stroke studies where, as blood flow decreases, OEF in the ipsilateral hemisphere may be elevated pathologically to maintain normal oxygen metabolism when autoregulatory capacity is exceeded.^75-77 However, the sample size ($N=3$) was too small to make any meaningful inferences. In addition, low lesion OEF values in the subacute stroke patients (Figure 3) may indicate irreversibly damaged tissue.

There are limitations in this study that warrant further investigation. First, clustering assumes that voxels with similar signal decay patterns would have similar model parameter values, including OEF. As an extreme case, voxels with identical QSM and mGRE magnitude would have the same model parameter value based on Equations 2 and 3. Clustering is critical, as very high SNR, (e.g., 500) is required for reasonable parameter estimation,¹⁶ and clustering improves the effective SNR substantially.³¹ As different tissue types show different mGRE signal decay patterns (e.g., different R₂ between GM/WM),¹⁷ clustering may be a realistic and reasonable assumption. However, its validity has not been thoroughly investigated, which remains a topic for future study. Even if the clustering assumption is valid, the resultant OEF accuracy may depend on clustering performance. For clustering in this study, x-means was used to choose the optimal number of clusters based on Bayesian information criteria.⁷⁸ The clustering result may vary with the used metric, (e.g., Akaike information criterion) or method (e.g., hierarchical clustering).^79,80 Voxel-wise optimization can be performed after cluster-wise optimization to alleviate the consequences of imperfect clustering, and the resultant OEF maps are not sensitive to the number of clusters in K-means clustering.³¹ Second, as large veins are treated identical to brain tissue, their OEF and $v$ estimations may be inaccurate. This could be alleviated by imposing $v=1$ for large veins. Third, as flow compensation was not available in the stroke patients, the oxygenation in large veins may be overestimated without considering phase errors caused by flow motion.⁴⁸ This may lead to underestimation in the whole-brain average OEF, because OEF was initialized using venous oxygenation in a main draining vein, such as the straight sinus. Fourth, a fixed Hct value due to the lack of its measurement in this study may lead to errors in OEF estimation. Tissue Hct was set to 0.357 for all subjects, which corresponds to large-vessel Hct of 0.49,³⁸ although large-vessel Hct values vary among subjects and are higher in males (0.42~0.52) than females (0.37~0.47).^81,82 Therefore, the fixed Hct assumption may result in an inaccurate OEF estimation, as the hemoglobin volume fraction, ${\psi }_{Hb}$, determined by Hct, is coupled with venous oxygenation, $Y$ (Equations 2 and 3). Fifth, in numerical simulation, the algorithm’s performance (CAT, CATV, and CCTV) may be different if a different ground truth is used, because all three algorithms may still depend on optimization details such as the initial guess. To minimize this bias, the average of CAT, CATV, and CCTV results was used as the ground truth in this study. Additionally, the effect of the choice of ground truth on algorithm performance was investigated by performing the simulation with four different sets of ground truth (Supporting Information Table S1): case 1, CAT result; case 2, CATV result; case 3, CCTV result; and case 4, the average of CCTV, CAT, and CATV results (shown in Figure 1). CCTV generally outperformed the other two algorithms by providing the highest accuracy (smallest MAE) for cases 1, 3, and 4 and the highest precision (smallest MSD) for all cases. Finally, QQ-CCTV optimization is still nonconvex, so convergence may be influenced by solver implementation, parameter scaling, initial guess, and stopping criterion. As in most machine-learning techniques that involve empirical parameters, an implemented QQ-CCTV needs to be not only verified with simulation data as done here, but also validated against a reference standard such as ¹⁵O PET³² and evaluated with respect to repeatability and reproducibility⁸³ for clinical applications such as studies over all age groups.⁸⁴

6 ∣. CONCLUSIONS

With the significantly improved accuracy by integrated temporal and tissue-type clustering and total variation denoising, the proposed QQ-CCTV method can be readily applied to study tissue viability in neurologic disorders including ischemic stroke,²³, Alzheimer’s disease,^85,86 multiple sclerosis,⁸⁷ and tumor.⁸⁸

Supplementary Material

2

FIGURE S1 Box plots of oxygen extraction fraction (OEF), cerebral metabolic rate of oxygen (CMRO₂), $\mathit{v}$, R₂, and ${\chi }_n$ between cluster analysis of time evolution (CAT), CAT+TV (CATV), and temporal clustering, tissue composition, and TV (CCTV) in healthy adults ($N=11$). Red line, blue box, black whisker, red cross, and black circle indicate the median value, interquartile range (IQR), the range extending to 1.5 of the IQR, outlier beyond the whisker range, and individual subject value, respectively. ${}^{\ast }P<.05$

FIGURE S2 The DWI, cerebral blood flow (CBF), region of interest (ROI), and OEF maps in 3 acute stroke patients with DWI/CBF mismatch. The OEF is reconstructed by QSM + quantitative BOLD (QQ)–CCTV. The CBF and OEF maps are shown in units of mL/100 g/min and %. In the ROI, green and red masks indicate the DWI-defined lesion and DWI/CBF mismatch. In OEF, the white and pink number indicates the volume ratio of the DWI/CBF mismatched region relative to the DWI-defined lesion and the average OEF ratio between ipsilateral and contralateral hemisphere

TABLE S1 Effect of the choice of ground truth on algorithm performance (CAT, CATV, and CCTV) in numerical simulation: (A) mean absolute error for accuracy measurement and (B) mean SD for precision measurement. Note: Both MAE and MSD are represented as a percentage. “Avg” indicates that the average of the CAT, CATV, and CCTV results was used as the ground truth of 3D parameter ($Y$, $v$, $R_2$, $S_0$, ${\chi }_n$) maps (case 4). The CCTV mapping provided the highest accuracy (smallest mean absolute error) in cases 1, 3, and 4, and the highest precision (smallest mean SD) in all of the cases. The OEF maps in case 4 are shown in Figure 1.