Data-driven regularized inversion (DRI) for improved QSM+qBOLD based CMRO2 Mapping: a feasibility study in healthy subjects and ischemic stroke patients
Junghun Cho1, Shun Zhang2, Youngwook Kee3, Pascal Spincemaille3, Thanh Nguyen3, Simon Hubertus4, Ajay Gupta3, and Yi Wang1,3

1Biomedical Engineering, Cornell University, Ithaca, NY, United States, 2Radiology, Tongji Hospital, Wuhan, China, 3Radiology, Weill Cornell Medical College, New York, NY, United States, 4Computer Assisted Clinical Medicine, Heidelberg University, Mannheim, Germany


We propose the use of machine-learning to improve the accuracy of a QSM+qBOLD model based Cerebral metabolic rate of oxygen (CMRO2) and oxygen extraction fraction (OEF) mapping. The proposed method, data-driven regularized inversion or DRI, significantly outperformed, in simulation, the current method at all SNR levels. In n=11 healthy subjects, uniform OEF maps were obtained as expected. In n=18 ischemic stroke patients, low OEF regions were clearly located within the lesion region as defined by DWI.


The cerebral metabolic rate of oxygen (CMRO2) and oxygen extraction fraction (OEF), important markers of brain tissue viability and function1-3, can be obtained from gradient echo (GRE) data using a combined QSM modeling of signal phase and qBOLD modeling of signal magnitude (QSM+qBOLD)4. However, qBOLD and hence QSM+qBOLD suffer from substantial errors caused by measurement noise propagation in parameter estimation or from low signal to noise ratio (SNR)5,6. Assuming sparse representation of tissue in the signal parameter space, we introduce a data-driven regularized inversion (DRI) method to obtain OEF and CMRO2 with improved SNR.


CMRO2 (μmol/100g/min) and OEF (%) can be expressed as $$CMRO2=CBF\cdot OEF\cdot [H]_a$$ $$OEF=1-\frac{Y}{Y_a}$$ where CBF is the cerebral blood flow, $$$[H]_a$$$ is the oxygenated heme molar concentration in the arteriole (7.377 μmol/ml)7, $$$Y$$$ and $$$Y_a$$$ are venous and arterial (0.98) oxygenation. The QSM+qBOLD model consists of solving $$Y^*,v^*,\chi^*_{nb},S^{0*},R^*_2=argmin_{Y,v,\chi_{nb},S^{0},R_2}|||S|-F_{qBOLD}(Y,v,\chi_{nb},S^{0},R_2)||_2^2$$ $$Y^*,v^*,\chi^*_{nb}=argmin_{Y,v,\chi_{nb}}||F_{QSM}(Y,v,\chi_{nb})-QSM||_2^2$$ where $$$S^0$$$ the GRE signal at TE=0 and $$$R_2$$$ the cellular contribution to signal decay. $$F_{qBOLD}(Y,v,\chi_{nb},S^{0},R_2)=S^0 \cdot e^{-R_2\cdot TE}\cdot F_{BOLD}(v,\delta \omega(Y,\chi_{nb}),TE)\cdot G(TE)$$ where $$$F_{BOLD}$$$ and $$$G$$$ are extravascular and macroscopic contribution to magnitude decay6,8. $$$\delta \omega(Y,\chi_{nb})$$$ is the frequency difference between deoxygenated blood and the surrounding tissue: $$\delta \omega(Y,\chi_{nb})=\frac{1}{3}\cdot \gamma \cdot B_0 \cdot [\Delta \chi\cdot (1-Y)+\chi_{ba}-\chi_{nb}]$$ $$$\gamma$$$ is the gyromagnetic ratio (267.513 MHz/T), $$$B_0$$$=3T, $$$\Delta \chi$$$ is the susceptibility difference between fully oxygenated and fully deoxygenated blood ($$$0.357\times 4\pi \times 0.27$$$ ppm)9, $$$\chi_{ba}$$$ is purely oxygenated blood susceptibility ( -108.3 ppb). $$F_{QSM}(Y,v,\chi_{nb})=\left[\frac{\chi_{ba}}{\alpha}+\psi_{Hb}\cdot \Delta \chi_{Hb}\cdot (-Y+\frac{1-(1-\alpha)\cdot Y_a}{\alpha})\right]\cdot v + \left(1-\frac{v}{\alpha}\right)\cdot \chi_{nb}$$ where $$$\alpha$$$ is the 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)7,10,11.

Data-driven Regularized Inversion

The idea behind DRI is that voxels with similar GRE signal curves should have similar parameters ($$$Y,v,R_2$$$). To identify clusters of similar signal, k-means clustering was applied. Once clusters are obtained, the parameters ($$$Y,v,R_2$$$) are assumed to be uniform within each cluster, thereby effectively increasing SNR for inversion significantly.


An initial guess for $$$Y_0$$$ was obtained from the sagittal sinus, $$$\chi_{nb,0}$$$ set to $$$\chi_{ba}$$$, and $$$R_{2,0}$$$ obtained from a mono-exponential fit against Eq. 5 with $$$Y_0,v_0,\chi_{nb,0}$$$.Three initial values for $$$v$$$ were selected (1, 2, and 3 %). The $$$Y,v,R_2$$$ were scaled by their initial guess: $$$x\mapsto \frac{x}{avg(x_0)+4\cdot std(x_0)}$$$. The L-BFGS-B algorithm12,13 was used for constrained optimization. At each iteration, $$$\chi_{nb}$$$ was updated from Eq. 4 and the other unknowns were updated from Eq. 3. The solution with the smallest residual across the three $$$v_0$$$ values was selected. After performing the optimization with ($$$Y,v,R_2$$$) constant within each cluster, the $$$Y,v,R_2$$$ values were updated voxel-to-voxel using the cluster-based result as initial guess.


The proposed DRI-based QSM+qBOLD was compared with voxel-wise QSM+qBOLD in a numerical simulation (Fig. 1) and with the previous QSM+qBOLD with the constant OEF initial guess4 in n=11 healthy subjects at 3T: 3D ASL (20 cm FOV, 1.56x1.56x3.5 mm3 voxel size, 1500 ms labeling period, 1525 ms post-label delay) and 3D spoiled Gradient Echo (SPGR, 0.78x0.78x1.2 mm3 voxel size, 7 echoes, TE1=2.3ms, 3.9 ms, 30.5 ms), and n=18 ischemic stroke patients at 3T: 3D ASL (24 cm FOV, 1.9x1.9x2.0 mm3 voxel size, 1500 ms labeling period, 1525 ms post-label delay) and 3D spoiled Gradient Echo (SPGR, 0.47x0.47x2 mm3 voxel size, 8 echoes, TE1=4.5ms, 4.9 ms, 42.8 ms).


DRI-based QSM+qBOLD provides a more accurate OEF map than voxel-wise QSM+qBOLD in simulation especially at low SNRs (Fig. 1). In healthy volunteers, the DRI-based QSM+qBOLD shows uniform OEF, whereas the previous method provides higher OEF with extreme values in Globus pallidus (Figs. 2 and 3). In ischemic stroke patients, low OEF regions by DRI-based QSM+qBOLD are well within DWI defined lesions, which is not the case for the previous QSM+qBOLD method (Fig. 4). DRI-based QSM+qBOLD is sensitive to low OEF values in the lesion (Fig. 5).


Uniform OEF in healthy subjects (Fig. 2) and low lesion OEF values in the chronic stroke patients and large inter-subject OEF variation among the acute stroke patients (Figs. 4 and 5) from DRI-based QSM+qBOLD are consistent with prior PET studies14-16. More accurate OEF seems to result from increasing SNR effectively with DRI (Fig. 1). Both DRI-based QSM+qBOLD and previous QSM+qBOLD provided reasonable OEF values in healthy subjects (Fig. 3)17,18.


This study shows the feasibility of the data-driven regularized inversion in QSM+qBOLD based CMRO2 mapping in both healthy subjects and stroke patients. With highly improved accuracy in simulation, DRI-based QSM+qBOLD may be readily applied to investigate tissue viability in various diseases, such as Alzheimer’s disease19,20, multiple sclerosis21, tumor22, and ischemic stroke23.


This work was supported by NIH grant R01 NS095562, R01 NS060464, R01 CA181566, R21 EB024366, S10 OD021782.


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Numerical simulation of the accuracy comparison between voxel-wise and DRI-based QSM+qBOLD at different SNRs. The brain mask of the 6 days onset stroke patient was divided into the two: lesion (OEF 10%) and normal (OEF 35%). The GRE signals and the QSM values were simulated using $$$F_{qBOLD}$$$ and $$$F_{QSM}$$$. Then, gaussian noise was added to simulated data: no noise, SNR 1000, 100, and 50. As SNR decreases, the DRI-based QSM+qBOLD provides highly more accurate OEF values than voxel-wise QSM+qBOLD, e.g. 39.2 % and 13.4% vs. 31.0% 26.8% for ground truth 35% and 10% at SNR 50.

The comparison of CMRO2, OEF, $$$v$$$, $$$R_2$$$, and $$$\chi_{nb}$$$ map between previous QSM+qBOLD and DRI-based QSM+qBOLD in a healthy subject. DRI-based QSM+qBOLD shows a good CMRO2 contrast between CGM and WM without extremely high values (>400 μmol/100g/min), uniform OEF, higher $$$R_2$$$vales, and less noisy $$$\chi_{nb}$$$ than previous QSM+qBOLD.

The ROI analysis of CMRO2, OEF, $$$v$$$, $$$R_2$$$, and $$$\chi_{nb}$$$ map between previous QSM+qBOLD and DRI-based QSM+qBOLD in cortical gray matter of the healthy subjects (N=11). CMRO2 was 184.2 ± 17.6 and 127.5 ± 23.5 μmol/100g/min, OEF was 40.8 ± 2.3 and 28.0 ± 3.9 %, $$$v$$$ was 4.48 ± 0.41 and 2.93 ± 0.0%, $$$R_2$$$ was 12.9 ± 0.5 and 15.6 ± 0.8 Hz, and $$$\chi_{nb}$$$ was -19.8 ± 3.5 and -13.3 ± 3.8 ppb for previous QSM+qBOLD and DRI-based QSM+qBOLD, respectively.

The OEF comparison between previous QSM+qBOLD and DRI-based QSM+qBOLD in the 5 stroke patients (18hour, 4, 6, 7, and 12day onset). DRI-based QSM+qBOLD shows a good agreement between low OEF area and the lesion in DWI. On the other hand, previous QSM+qBOLD does not show a clear low OEF lesion which coincides with the lesion in DWI.

The ratio of the average OEF between the lesion and its mirror side in 18 stroke patients: previous QSM+qBOLD (black) vs. DRI-based QSM+qBOLD (red). $$$\frac{\overline{OEF_{low,lesion}}}{\overline{OEF_{mirror}}}$$$ and $$$\frac{\overline{OEF_{high,lesion}}}{\overline{OEF_{mirror}}}$$$ is the ratio between the average of the ‘low’ and ‘high’ OEF group in the lesion (2-means) and the average of the mirror side, respectively. Each dot on the left indicates each patient. DRI-based QSM+qBOLD (red) show smaller $$$\frac{\overline{OEF_{low,lesion}}}{\overline{OEF_{mirror}}}$$$. For $$$\frac{\overline{OEF_{high,lesion}}}{\overline{OEF_{mirror}}}$$$, both previous QSM+qBOLD and DRI-based QSM+qBOLD show almost 100%. More distinctive difference between acute and sub-acute phase with DRI-based QSM+qBOLD is shown in the low OEF lesion group.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)