Junghun Cho^{1}, Youngwook Kee^{2}, Pascal Spincemaille^{2}, Thanh Nguyen^{2}, Jingwei Zhang^{1}, Ajay Gupta^{2}, Shun Zhang^{2,3}, and Yi Wang^{1,2}

In this work, we propose a gradient echo (GRE) based measurement of oxygen extraction fraction (OEF) based on a simultaneous modeling of the magnitude (using quantitative BOLD corrected for non-blood tissue susceptibility) and phase (based on QSM), without additional vascular challenges and empirical assumptions. Compared to methods based on QSM only and on qBOLD only, the proposed model provided better CMRO2 contrast between gray and white matter, and more uniform OEF in healthy subjects.

**Purpose**

**Theory and Methods**

CMRO2 and OEF can be expressed.$$CMRO2=CBF\cdot OEF\cdot CaO_2$$ $$OEF=1-\frac{Y}{Y_a}$$

where $$$CaO_2$$$ is arterial oxygen concentration (7.377 μmol/ml), $$$Y_a$$$ is arterial oxygen saturation (0.98), and $$$Y$$$ is venous oxygenation. The proposed QSM+qBOLD method consists of solving $$Y^*,v^*,\chi_{nb}^*,S^{0*},R_2^*=argmin_{Y,v,\chi_{nb},S^0,R_2}\left\{|||S|-F_{qBOLD}(Y,v,\chi_{nb},S^0,R_2)||^2_2 + w\cdot ||F_{QSM}(Y,v,\chi_{nb})-QSM||^2_2\right\}$$

where $$$w$$$ is weight factor, $$$S^0$$$ the GRE signal at TE=0, and $$$R_2$$$ the cellular contribution to signal decay. Furthermore,

$$F_{qBOLD}(Y,v,\chi_{nb},S^0,R_2)=S^0\cdot e^{-R_2\cdot TE}\cdot F_{BOLD}(v,\delta\omega(Y,\chi_{nb}),TE)\cdot G(TE)$$

where $$$F_{BOLD}$$$ and $$$G$$$ are extravascular and macroscopic contribution to magnitude decay^{7}. $$$\delta\omega$$$ is the frequency difference between deoxygenated blood
and the surrounding tissue: $$\delta\omega(Y,\chi_{nb})=\frac{1}{3}\cdot \gamma \cdot B_0 \cdot \left[ \Delta\chi\cdot(1-Y)+\chi_{ba}-\chi_{nb}\right] $$

$$$\gamma$$$ is the gyromagnetic ratio (267.513 MHz/T), $$$B_0=3T$$$, $$$\Delta\chi$$$ is the susceptibility difference between fully
oxygenated and fully deoxygenated blood ($$$0.357\times4\pi\times0.27$$$ ppm)^{6}, $$$\chi_{ba}$$$ is purely oxygenated blood susceptibility (-108.3 ppb). Note that the qBOLD assumption of $$$\chi_{nb}=\chi_{ba}$$$ is not made here. Finally, $$F_{QSM}(Y,v,\chi_{nb})=\left[\frac{\chi_{ba}}{\alpha}+\psi_{Hb}\cdot \Delta\chi_{Hb}\cdot \left(-Y+\frac{1-(1-\alpha)\cdot Y_a}{\alpha}\right)\right]\cdot v + \left(1-\frac{v}{\alpha}\right)\cdot\chi_{nb}$$

where $$$\alpha$$$ is ratio between vein and total blood volume assumed (0.77), $$$\psi_{Hb}$$$ the hemoglobin volume fraction (0.0909 for tissue and
0.1197 for vein), $$$\Delta\chi_{Hb}$$$ the susceptibility difference between deoxy-
and oxy-hemoglobin (12522 ppb)^{2-4}.
Note that $$$v$$$, which was
estimated from CBF in QSM-based methods, is now an unknown to be determined by
data.

Optimization

The
five unknowns $$$Y,v,\chi_{nb},S^0,R_2$$$ were scaled by their
initial guess: $$$x\mapsto\frac{x}{|x_0|}$$$. The initial guesses were: $$$Y_0$$$ estimated from the sagittal sinus^{2,4}, $$$v$$$ based on CBF^{8}, $$$\chi_{nb,0}=\chi_{ba}$$$^{5,6}, and $$$S^0_0$$$ and $$$R_{2,0}$$$ obtained from a
mono-exponential fit against Eq. 4 with the initial values $$$Y_0$$$, $$$v_0$$$, and $$$\chi_{nb,0}$$$. $$$w$$$ was selected using the L-curve method^{9}.
L-BFGS-M was used for constrained optimization^{10,11}.

Validation

The QSM+qBOLD model was compared with a QSM-based method^{2} and qBOLD^{6} in 11 healthy volunteers at 3T. 3D
ASL (20 cm FOV,
1.56x1.56x3.5 mm^{3} voxel size, 1500 ms labeling period, 1525 ms
post-label delay). 3D
spoiled Gradient Echo (SPGR, 0.78x0.78x1.2 mm^{3} voxel size, 7 echoes,TE_{1} =2.3 ms, ΔTE = 3.9 ms, TR=30.5 ms). QSM was generated by
morphology enable dipole inversion^{12}. All images were
co-registered to QSM. T1 weighted images were used for ROI segmentation.

**Conclusion**

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Figure
1. CMRO2 map in axial, sagittal, and coronal sections from a
subject reconstructed using QSM, qBOLD, and QSM+qBOLD methods. The
corresponding T1-weighted anatomical images are shown on the right. QSM+qBOLD
shows higher contrast between gray and white matter than QSM or qBOLD.

Figure
2. OEF, vein volume ($$$v$$$),
non-blood tissue susceptibility ($$$\chi_{nb}$$$),
and CMRO2 maps in a second subject reconstructed using QSM, qBOLD, and
QSM+qBOLD models. The OEF obtained using QSM+qBOLD is more uniform than that of
QSM, and is less noisy than that of qBOLD. QSM+qBOLD and QSM show similar $$$\chi_{nb}$$$ contrast between cortical gray (CGM) and white (WM) matter, higher in CGM than in nearby WM.

Figure
3. ROI comparison of CMRO2 and OEF in anterior (ACA), middle (MCA),
and posterior (PCA) cortical artery in cortical gray matter (CGM), WM, and
whole brain among QSM (black), qBOLD (red), and QSM+qBOLD (blue). All three
methods showed lower CMRO2 values in WM. In all ROIs, QSM+qBOLD provides higher
CMRO2 and OEF values than QSM or qBOLD (p<0.01). The purple dashed line in whole brain OEF is the average OEF value from four different PET studies, 35
± 7 %^{20},
42.6 ± 5.1 %^{21}, 41 ± 6 %^{22}, and 40 ± 9 %^{23},
which agrees better with QSM+qBOLD.