Synopsis

Current two CMRO2 mapping methods, QSM-based method and qBOLD, suffer from the issues in their own model assumptions, such as blood flow challenge and linear relationship assumption between cerebral blood volume (CBV) and flow (CBF) in QSM-based method and the high sensitivity to noise and recent one-compartment assumption in qBOLD. We combined these two models with regularization based on that vein blood volume fraction and vein oxygenation are shared, which removes the challenge and linear assumption in QSM method and alleviates the high noise sensitivity and one-compartment assumption issue in qBOLD. The proposed model provided more uniform OEF and CMRO2.

Purpose

Theory and Methods

CMRO2 and OEF can be expressed.

$$CMRO2 = CBF×OEF×CaO_2$$ $$OEF=1-\frac{Y}{SaO_2}$$ where $$$CaO_2$$$ is arterial oxygen concentration (7.377 μmol/ml), $$$SaO_2$$$ is arterial oxygen saturation (0.98), and $$$Y$$$ is oxygenation in vein.

QSM-based CMRO2 had two unknowns in previous studies7,8, $$$Y$$$ and non-blood susceptibility ($$$\chi_{nb}$$$), assuming vein blood volume fraction ($$$v$$$) is constant. In this study, we removed the assumption and treated $$$v$$$ as a fitting parameter. The magnitude part of qBOLD has four unknowns, signal intensity at TE=0 ($$$S_0$$$), cellular contribution to signal decay ($$$R_2$$$), $$$v$$$ and $$$Y$$$. As the two models share $$$v$$$ and $$$Y$$$, we combined them and solve the following optimization.

$$minimize_{v,Y,\chi_{nb},S_0,R_2}\left\{||F_{QSM}(v,Y,\chi_{nb})-QSM||^2_2+\lambda_1\left[|||S|-F_{qBOLD}(S_0,R_2,v,Y)||_F^2+\lambda_2||\triangledown Y||_2^2\right]\right\}$$ Where $$$||\cdot||_F$$$ is Frobenius norm, $$$\lambda_1$$$ is relative weight between two models, and $$$\lambda_2$$$ is a regularization factor on $$$Y$$$ smoothness.

1) First term-QSM-based method⁸.

$$F_{QSM}(v,Y,\chi_{nb})=\left[\frac{\chi_{ba}}{\alpha}+\psi_{Hb}×\Delta\chi_{Hb}×\left(-Y+SaO_2-\frac{1+SaO_2}{\alpha}\right)\right]×v+\left(1-\frac{v}{\alpha}\right)×\chi_{nb}$$

where $$$\chi_{ba}$$$ is purely oxygenated blood susceptibility, $$$\psi_{Hb}$$$ is hemoglobin volume franction, $$$\Delta\chi_{Hb}$$$ is susceptibility difference between deoxy- and oxy-hemoglobin, and $$$\alpha$$$ is vein volume fraction (0.77)

2) Second term-Magnitude part of qBOLD model⁴.

$$F_{qBOLD}(S_0,R_2,v,Y) = S_0×e^{-R_2×TE}×F_{BOLD}(v,Y,TE)×G(TE)$$

where $$$F_{BOLD}$$$ and $$$G$$$ are extracvascular and macroscopic contributions to the GRE signal decay respectively.

3) Optimization

The five unknowns, $$$v,Y,\chi_{nb},S_0,R_2$$$, were scaled with initial guess as $$$x'=\frac{x-avg(x_0)}{max(x_0)-min(x_0)}$$$. The lower and upper bound then was set to -5 and 5. For initial guesses, $$$Y$$$ was estimated from Straight Sinus vein (0.65). $$$v$$$ was set by the linear relationship between CBV and CBF². $$$\chi_{nb}$$$ is estimated via $$$F_{QSM}$$$ with the $$$Y$$$ and $$$v$$$ initials. The $$$S_0$$$ and $$$R_2$$$ initials were obtained by mono-exponential fitting with the consideration of $$$G$$$⁶ in $$$F_{qBOLD}$$$. For tuning parameters, $$$\lambda_2$$$ was first chosen without the QSM term. The maximum value was selected before qBOLD term increases dramatically (1.8×10⁵). With the $$$\lambda_2$$$ value, $$$\lambda_1$$$ was set to 5.7×10^-8 for visible QSM contribution. The limited-memory Broyden-Fletcher-Goldfarb-Shanno-Bound (L-BFGS-B) algorithm was used for the constrained optimization, and performed on 2D slice for speed.

4) Validation

We compared our QSM+qBOLD model with the sole QSM-based method⁸ and qBOLD. MRI was performed on a healthy volunteer after hyperventilation using a 3T scanner and a protocol consisting of a 3D ASL and a 3D spoiled Gradient Echo (SPGR) sequence⁸. The 3D ASL parameters were: 22cm FOV, 3 mm isotropic resolution, 1500 ms labeling period, 1525 ms post-label delay. 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 by morphology enable dipole inversion⁵. All images were co-registered to QSM. T1 weighted images were used to ROI segmentation.

Result

Discussion

Conclusion

Acknowledgements

References

1. J-C Baron, 'Mapping the Ischaemic Penumbra with Pet: Implications for Acute Stroke Treatment', Cerebrovascular diseases, 9 (1999), 193-201.

2. K. L. Leenders, D. Perani, A. A. Lammertsma, J. D. Heather, P. Buckingham, M. J. Healy, J. M. Gibbs, R. J. Wise, J. Hatazawa, S. Herold, and et al., 'Cerebral Blood Flow, Blood Volume and Oxygen Utilization. Normal Values and Effect of Age', Brain, 113 ( Pt 1) (1990), 27-47.

3. M. A. Mintun, M. E. Raichle, W. R. Martin, and P. Herscovitch, 'Brain Oxygen Utilization Measured with O-15 Radiotracers and Positron Emission Tomography', J Nucl Med, 25 (1984), 177-87.

4. Xialing Ulrich, and Dmitriy A Yablonskiy, 'Separation of Cellular and Bold Contributions to T2* Signal Relaxation', Magnetic resonance in medicine, 75 (2016), 606-15.

5. Y. Wang, and T. Liu, 'Quantitative Susceptibility Mapping (Qsm): Decoding Mri Data for a Tissue Magnetic Biomarker', Magn Reson Med, 73 (2015), 82-101.

6. Dmitriy A Yablonskiy, Alexander L Sukstanskii, Jie Luo, and Xiaoqi Wang, 'Voxel Spread Function Method for Correction of Magnetic Field Inhomogeneity Effects in Quantitative Gradient-Echo-Based Mri', Magnetic resonance in medicine, 70 (2013), 1283-92.

7. Jingwei Zhang, Tian Liu, Ajay Gupta, Pascal Spincemaille, Thanh D Nguyen, and Yi Wang, 'Quantitative Mapping of Cerebral Metabolic Rate of Oxygen (Cmro2) Using Quantitative Susceptibility Mapping (Qsm)', Magnetic resonance in medicine, 74 (2015), 945-52.

8. Jingwei Zhang, Dong Zhou, Thanh D Nguyen, Pascal Spincemaille, Ajay Gupta, and Yi Wang, 'Cerebral Metabolic Rate of Oxygen (Cmro2) Mapping with Hyperventilation Challenge Using Quantitative Susceptibility Mapping (Qsm)', Magnetic resonance in medicine (2016).