The quantitative mapping of cerebral metabolic rate of oxygen (CMRO2) and oxygen extraction fraction (OEF) are important indicators for neural viability. Since blood oxygen saturation is linearly related to its magnetic susceptibility¹, CMRO2 and OEF maps can be computed using quantitative susceptibility mapping (QSM) and cerebral blood flow (CBF) acquired in two brain states, such as before and after a caffeine challenge in healthy subjects². However, there are two limitations regarding this approach: 1) noisy CMRO2 and OEF maps with extreme, physiologically impossible OEF values (>1 or <0) due to error propagation. 2) ~30 minutes of waiting time for caffeine to exert its vaso-constrictive effects; To overcome these limitations we propose a new constrained optimization algorithm and to use hyperventilation (HV) as an efficient vasoconstrictive for quantitative CMRO2 mapping.

OEF maps can express as a function of CBF and susceptibility χ²:

$$$CMRO2=4SaO_2[Hb]CBF\cdot OEF$$$

$$$OEF=\frac{1}{SaO_2}\left(\frac{\chi-\chi_{nb}-\chi_{a}}{CBV_v\psi_{hb}\left(\chi_{dHb}-\chi_{oHb}\right)}-\left(1-SaO_{2}\right)\right)$$$

Here, χ_nb is susceptibility contributions from non-blood tissue sources. Other parameters are constant: SaO₂ is arterial oxygen saturation; χ_a is susceptibility contributions from arterial blood; CBV_v is the volume fraction of venous blood in a voxel; Ψ_Hb is the volume fraction of Hemoglobin (Hb) within blood; χ_dHb and χ_oHb are the volume susceptibilities of pure deoxyHb (dHb) and oxyHb (oHb), respectively.

The OEFs at baseline (OEF_base), at challenge state (OEF_chal), and χ_nb were organized into a vector of unknowns in a linear system Ax=b format. To reduce error propagation in the solution, the system of equations were redefined as A* x*=b, where A*=AP and x*=P^-1 x. P is a right preconditioner which scales the elements of x* to the same order of magnitude. In addition a global physiological constraint was imposed based on the expectation that the global CMRO2 calculated from the CMRO2 map should be similar to that calculated from global OEF estimated from susceptibility of venous blood in straight sinus. The constrained solution x* was obtained by minimizing the following cost function using a limited-memory Broyden–Fletcher–Goldfarb–Shanno-Bound (L-BFGS-B) algorithm with physiological bounds on OEF between 0 and 1 over the whole brain. Summation index i is over brain voxels.$$$x^{*}=argmin_{x^{*}}\left\{\parallel A^{*}x^{*}-b\parallel _2^2+\lambda \left(\left(\sum_iCBF_{base,i}OEF_{base,i}\right)-OEF_{base,vein}\sum_i CBF_{base,i}\right)^2+\lambda \left(\left(\sum_iCBF_{chal,i}OEF_{chal,i}\right)-OEF_{chal,vein}\sum_i CBF_{chal,i}\right)^2\right\}$$$

MRI was performed on healthy volunteers (n=11) before and during hyperventilation using a 3T scanner and a protocol consisting of a 3D ASL and a 3D spoiled Gradient Echo (SPGR) sequence. Total scan time was 15 minutes. The 3D ASL parameters were: 22cm FOV, 1500 ms labeling period, 1525 ms post-label delay, 3.5 mm isotropic resolution. CBF maps (ml/100g/min) were generated from the ASL data using GE functool. The 3D SPGR parameters were: identical coverage as the ASL scan, 7 equally spaced echoes, 2.2 ms first TE, 30.8ms TR, 1.2 mm isotropic resolution. QSM generated from magnitude and phase images using Morphology Enabled Dipole Inversion (MEDI)^3,4. All images were co-registered to the first QSM acquisition. The protocol was repeated 30 min later for reproducibility study (HV2). Within a week volunteers returned for an additional scan using caffeine as challenge with similar protocol².

The GM mask was generated from T1 BRAVO images and further segmented into vascular territories (VT) for ROI analysis. Paired t-test and bland-Altman was performed to analysis the reproducibility of the method.

Fig.1 compares maps generated by unconstrained and constrained methods. Reduction in extreme values can be appreciated. Fig.2 compares maps generated with constraint method using caffeine and HV challenges. The maps are visually comparable. Fig. 3 shows bland-Altman plots comparing VT ROIs across all subjects between the two challenges, and between the two HV scans. The comparisons show small (<10%) or statistically insignificant bias. In this work, we formulated a baysian approach to estimate CMRO2, which allows the use of prior knowledge such as physiological constraints to find a reasonable solution. Compared to unconstrained method, the proposed method eliminated physiologically impossible values and showed good reproducibility with small or statistically insignificant bias. Exam time for QSM CMRO2 also reduced by 4 folds (15 vs 60 minutes) when hyperventilation was used compared to caffeine while yielding visually comparable image.The proposed algorithm eliminated physiologically impossible OEF values and showed good reproducibility. The study also suggests that hyperventilation is a more efficient vasoconstrictive challenge for QSM based CMRO2. Further investigation is warrant in patient cohort.