Simon Hubertus^{1}, Sebastian Thomas^{1}, Junghun Cho^{2}, Shun Zhang^{3,4}, Yi Wang^{2,3}, and Lothar R. Schad^{1}

The oxygen extraction fraction (OEF) is a promising biomarker for cerebral tissue vitality. Combining quantitative blood oxygenation level-dependent (qBOLD) modelling and quantitative susceptibility mapping (QSM) from gradient echo (GRE) data revealed promising results but still suffered from biases in white matter and required good parameter initialization. We showed that using an additional gradient echo sampling of spin echo (GESSE) sequence enables OEF reconstruction with higher accuracy, precision and robustness to parameter initialization in simulation. Yet, this increased robustness did still not allow for parameter initialization without prior knowledge of local distributions in vivo, which lead to a non-physiological gray-white matter contrast in the OEF.

2D-GESSE, 3D-GRE and 2D-EPI pseudo-continuous arterial spin labeling (pCASL) data were acquired
from 7 healthy volunteers on
a clinical 3T Magnetom TRIO scanner (Siemens
Healthineers, Erlangen, Germany). GESSE parameters were: TR$$$\,=\,$$$2780$$$\,$$$ms; TE_{1}$$$\,=\,$$$29$$$\,$$$ms; ΔTE$$$\,=\,$$$2$$$\,$$$ms; 32 echoes; spin echo$$$\,=\,$$$#10; matrix size$$$\,=\,$$$128$$$\,$$$x$$$\,$$$96;
20 slices; voxel size$$$\,=\,$$$2$$$\,$$$x$$$\,$$$2$$$\,$$$x$$$\,$$$2$$$\,$$$mm³; acquisition time$$$\,=\,$$$10:00$$$\,$$$min. GRE parameters
were: TR$$$\,=\,$$$61$$$\,$$$ms; TE1$$$\,=\,$$$4.5$$$\,$$$ms; ΔTE$$$\,=\,$$$5.5$$$\,$$$ms; 8 echoes; matrix size$$$\,=\,$$$256$$$\,$$$x$$$\,$$$192$$$\,$$$x$$$\,$$$72; voxel size$$$\,=\,$$$0.9$$$\,$$$x$$$\,$$$0.9$$$\,$$$x$$$\,$$$1.4$$$\,$$$mm³; acquisition time$$$\,=\,$$$7:51$$$\,$$$min. Cerebral blood flow (CBF) was calculated from pCASL data.^{2} QSM was applied to the GRE data and employed as a
regularization for the single-compartment quantitative BOLD fit following
the approach of Cho et al.^{1}
to the GESSE and GRE data respectively to quantify OEF, deoxygenated blood volume *ν*, *R*_{2}, non-blood
susceptibility *χ*_{nb} and signal intensity *S*_{0}: $$\text{argmin}_{\text{OEF},\nu,R_2,S_0,\chi_\text{nb}}\left[\sum_\text{TE} ||S_\text{GESSE/GRE}(\text{TE}))-F_\text{qBOLD}(\text{OEF},\nu,R_2,S_0,\chi_\text{nb},\text{TE})\}||_2^2\\+w||\text{QSM}-F_\text{QSM}(\text{OEF},\nu,\chi_\text{nb}))||_2^2\right] .$$ *F*_{QSM} calculates magnetic susceptibility according to Cho et al.^{1}. *F*_{qBOLD} is
the single-compartment qBOLD model for GESSE^{3,4}:$$F_\text{qBOLD}(\text{OEF},\nu,R_2,S_0,\chi_\text{nb},t)=S_0\cdot\text{exp}(-\nu\cdot f(\delta\omega\cdot t)-R_2\cdot(t+\text{SE}))$$ with *t* being referenced to the time of spin echo SE and GRE (5):$$F_\text{qBOLD}(\text{OEF},\nu,R_2,S_0,\chi_\text{nb},t)=S_0\cdot\text{exp}(-R_2\cdot t)\cdot\left(1-\frac{\nu}{1-\nu}\cdot f(\delta\omega\cdot t)+\frac{1}{1-\nu}\cdot f(\nu\cdot \delta\omega\cdot t)\right)$$ respectively with the hypergeometric function (6):$$f(\delta\omega\cdot t)=~_1F_2\left(\{-0.5\};\{0.75,1.25\};-\frac{9}{16}(\delta\omega\cdot t)^2\right)-1$$ and frequency shift:$$\delta\omega(\text{OEF},\chi_\text{nb})=\frac{1}{3}\cdot\gamma\cdot B_0\cdot\left[\text{Hct}\cdot\Delta\chi_0\cdot(1-\text{SaO2}\cdot(1-\text{OEF}))+\chi_\text{ba}-\chi_\text{nb}\right]\,.$$ The
constants are hematocrit^{7} Hct$$$\,=\,$$$0.357, susceptibility difference between fully de-
and oxygenated red blood cells^{8} Δ*χ*_{0}$$$\,=\,$$$3.481$$$\,$$$ppm, arterial oxygen saturation SaO2$$$\,=\,$$$0.98 and fully oxygenated blood susceptibility^{9} *χ*_{ba}$$$\,=\,$$$-0.1082$$$\,$$$ppm. The parameters were initialized
with a fit to low resolution data for GESSE and by estimating OEF from straight
sinus and *ν* from CBF^{10} and using those values to fit for
an initial estimate of* S*_{0} and *R*_{2} for GRE. The
weighting factor was determined with an L-curve approach.^{11} Intersubject means of the parameters were compared (Student’s
t) between sequences within the same tissue type and between tissue types
within the same sequence. An 8$$$\,$$$x$$$\,$$$8$$$\,$$$x$$$\,$$$8 voxel single- and multi-compartment
simulation representing the three compartments of white matter^{12} with SNR$$$\,=\,$$$190 was also utilized. The former was
performed with optimal and biased ($$$\pm$$$20% OEF and *ν*), the latter
only with optimal initialization. Accuracy and precision were determined as
relative bias of the reconstructed mean and relative standard deviation over
all voxels respectively.

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