Cerebral metabolic rate of oxygen (CMRO2) and oxygen extraction fraction (OEF) maps are valuable in ischemic stroke assessment, and can be computed using quantitative susceptibility mapping (QSM) and cerebral blood flow (CBF) acquired in two brain states, such as before and after caffeine¹. However, the clinical utility of these techniques is limited by the need for a physiologic challenge agent, because there is a time cost between challenge and maximal vasoconstriction (~30 min for caffeine). To overcome these limitations we propose to map CMRO2 and OEF from a single set of QSM and cerebral blood flow (CBF) measurements without challenge using minimal local variance (MLV), which is suggested as a reasonable constraint².

CMRO2 and OEF can be expressed as a function of CBF and susceptibility χ¹:

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

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

Here χ_nb is susceptibility contributions from non-blood tissue sources. Other parameters are constants: SaO₂ is arterial oxygen saturation; [Hb] is the blood hemoglobin (Hb) concentration; χ_a is susceptibility contributions from arterial blood; CBV_v is the volume fraction of venous blood in a voxel; Ψ_Hb is Hb volume fraction in blood; Х_dHb and Х_oHb are the volume susceptibilities of pure deoxyHb (dHb) and oxyHb (oHb), respectively. The OEFs and χnb are organized into a vector of unknowns ‘x’ in a linear system Ax=b format, which can be solved using numerical optimization in the following manner: 1) the MLV regularization is imposed over gray matter (GM) and white matter (WM) separately within a cubic block of 7mm size; 2) a preconditioner is used to accelerate convergence, and 3) the total CMRO2 calculated from the CMRO2 map is equal to that calculated from OEF in straight sinus and the total CBF. One χnb is fitted per tissue type per block.$$$x^{*}=argmin_{x^{*}}\left\{\parallel A^{*}x^{*}-b\parallel _2^2+\alpha\sum_{g\in b}\sum_{i\in g}\left(CMRO2_i-\overline{CMRO2}^g\right)^2+\beta\sum_{w\in b}\sum_{i\in w}\left(CMRO2_i-\overline{CMRO2}^w\right)^2+\gamma\left(\left(\sum_iCBF_iOEF_i\right)-OEF_{vein}\sum_i CBF_i\right)^2\right\}$$$Here A* and x* contains preconditioning. Summation index i is over brain voxels, b is over voxels in a block, g and w is over gray and white matter in a block respectively. Regularization parameters α, β, γ are chosen to generate similar cost weighting for all terms. The constrained solution x can be obtained using a limited-memory Broyden–Fletcher–Goldfarb–Shanno-Bound (L-BFGS-B) algorithm with physiological bounds on OEF between 0 and 1. The blocks grids were moved 6mm diagonally in 1mm steps. The maps were recalculated and averaged to obtain the final results.

To validate this MLV CMRO2, we compared it with CMRO2 obtained using caffeine reconstructed with the same solver, preconditioning, and global constraint yet without MLV. MRI was performed on healthy volunteers (n=11) before and 30 minutes after 200mg caffeine intake using a 3T scanner and a protocol consisting of a 3D ASL and a 3D spoiled Gradient Echo (SPGR) sequence. Total scan time was 60 minutes. The 3D ASL parameters were: 22cm FOV, 3 mm isotropic resolution, 1500 ms labeling period, 1525 ms post-label delay. CBF maps (ml/100g/min) were generated from the ASL data. The 3D SPGR sequence parameters were: identical coverage as the ASL scan, 0.52 mm in-plane resolution, 2mm slice thickness, 7 echoes, 4.3 ms first TE, 56.6 ms TR. QSM generated from magnitude and phase images using the Bayesian approach³. All images were co-registered to first QSM. T1 weighted images were used to generate GM and WM segmentation. The GM mask was further segmented into vascular territories (VT) for ROI analysis. Paired t-test and bland-Altman was performed to compare the two methods.

Fig.1 comparing MLV with caffeine demonstrates similar CMRO2 and OEF maps. Fig. 2 shows bland-Altman plots comparing VT ROIs across all subjects between the two methods, demonstrating no significant bias (P>0.05).Our results demonstrate that the proposed MLV CMRO2 and OEF method yields visually comparable images and quantitatively no significant bias when compared to the previous coffee challenging method. Getting rid of administration of challenging in CMRO2 and OEF mapping can vastly improve their clinical utility by reducing scan time (15 vs 60 minutes), patients’ discomfort, and complication in challenge implementation. A previous attempt simply spread venous OEF over a local block, generating poor resolution but good correlation with the gold standard 15O PET OEF². Since brain functions often involve one or multiple regional groups of neurons such as primary visual cortex⁴, we introduce structural knowledge (GW and WM) and physiological information (CMRO2 smoothness) into the local block, as well as fidelity in signal processing, which lead to much improved spatial resolution.The proposed MLV method removes the need of challenge while yielding comparable CMRO2 and OEF maps. Further investigation is warranted in patient cohorts with known or suspected hemodynamic abnormalities.