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Multi-echo Complex QSM+qBOLD (mcQQ) for Oxygen Extraction Fraction (OEF) mapping

Junghun Cho¹, Jinwei Zhang², Pascal Spincemaille¹, Hang Zhang², Thanh D. Nguyen¹, Ajay Gupta¹, and Yi Wang^1,2
¹Radiology, Weill Cornell Medicine, New York, NY, United States, ²Biomedical Engineering, Cornell University, Ithaca, NY, United States

Synopsis

Quantitative mapping of oxygen extraction fraction (OEF) is critical to evaluate brain tissue viability and function in neurologic disorders. An integrated model of QSM and qBOLD (QSM+qBOLD or QQ) has been developed to map OEF from a routine gradient echo MRI without the need for vascular challenges, and QQ inversion can be obtained using deep learning. This study proposes a multi-echo complex QQ (mcQQ) that improves fidelity to data noise characteristics using complex domain. The proposed mcQQ provided more accurate OEF in simulation and an improved sensitivity to OEF abnormalities in ischemic stroke patients, compared to the current QQ method.

Introduction

Quantitative mapping of oxygen extraction fraction (OEF) is critical to evaluate brain tissue viability and function in stroke^1-3. An integrated model of quantitative susceptibility mapping and quantitative blood oxygen level dependent magnitude (QSM+qBOLD or QQ) has been developed to consider the OEF effect on both magnitude and phase of a widely available multi-echo gradient echo (mGRE) data^4-8, and validated against calibrated fMRI⁴ and ¹⁵O-PET⁷. With removing clinically impractical vascular challenges, its clinical feasibility has already been shown in ischemic stroke^{9, 10}, multiple sclerosis¹¹, and brain cancer¹². Recently, deep learning allowed to further improve the robustness of QQ against noise and the reconstruction speed¹³. The current QQ optimization assumes Gaussian noise for both QSM and mGRE magnitude^{5, 6, 8, 13}, which may not be valid especially in low SNR regions, e.g., stroke lesions, due to QSM estimation by multi nonlinear steps from mGRE phase signal with non-Gaussian noise^14-16 and Rician noise in mGRE magnitude¹⁷. We formulated a novel QQ using the assumption of Gaussian noise in multi-echo complex mGRE data with a deep learning solver (mcQQ-NET) and compared it with the current deep learning based QQ (QQ-NET)¹³ in simulation and ischemic stroke patients.

Theory and Methods

Multi-echo complex QQ (mcQQ)
The mcQQ model combines the QSM-based and qBOLD based OEF mapping methods using a nonlinear complex formulation to estimate OEF$$$=1-Y/Y_{a}$$$ with venous oxygenation ($$$Y$$$) and arterial oxygenation ($$$Y_{a}$$$= 0.98)⁸. $$Y^{*},v^{*},R_{2}^{*},S_{0}^*,\chi_{n}^{*}=\begin{array}{c}argmin\\Y,v,R_{2},S_0,\chi_{nb}\end{array}\left\{ \begin{array}{c}\begin{array}{c}||S_{j}-F_{qBOLD}\left(S_{0,},Y,v,R_{2,}\chi_{n},t_{j}\right)e^{i\omega_{0}t_{j}d*F_{QSM}\left(Y,v,R_{2,}\chi_{n}\right)}||_{2}^{2}+R\end{array}\end{array}\right\}$$ Here, $$$S_{j}$$$ is the complex signal at the j’th echo with removal of the initial phase and background phase^{18, 19}, $$$\omega_{0}$$$ Larmor frequency, $$$d$$$ the dipole kernel, $$$*$$$ the convolution operator. For robust parameter determination, we imposed total variation on $$$Y$$$($$$R$$$). The QSM-based model separates voxel-wise susceptibility into the contribution of deoxy-hemoglobin in venous blood, i.e., OEF effect, and non-blood neural tissue susceptibility ($$$\chi_{n}$$$). $$F_{QSM}(Y,v,\chi_{n})=\left[\frac{\chi_{ba}}{\alpha}+\psi_{Hb}\cdot\Delta\chi_{Hb}\cdot\left(-Y+\frac{1-\left(1-\alpha\right)\cdot Y_{a}}{\alpha}\right)\right]\cdot v + \left(1-\frac{v}{\alpha}\right)\cdot \chi_{n}$$ where $$$\chi_{ba}=-0.108 ppb$$$ the fully oxygenated blood susceptibility assuming tissue hematocrit $$$Hct =0.357$$$²⁰, $$$\alpha=0.77$$$ the ratio between the venous blood volume ($$$v$$$) and total blood volume²¹, $$$\psi_{Hb}=0.0909$$$ the hemoglobin volume fraction with $$$Hct=0.357$$$^22-25, $$$\Delta\chi_{Hb}=12522 ppb$$$ the susceptibility difference between deoxy- and oxyhemoglobin^{26, 27}. The qBOLD model describes the OEF effect on the mGRE magnitude⁸: $$F_{qBOLD}\left(S_{0,},Y,v,R_{2,}\chi_{n},t_{j}\right)=S_0\cdot e^{-R_2\cdot t_{j}}\cdot F_{BOLD}\left(Y,v,\chi_{n},t_{j}\right)\cdot G(t_{j})$$ where $$$S_{0}$$$ is signal intensity at $$$t=0$$$, $$$R_{2}$$$ is the transverse relaxation rate, $$$F_{BOLD}\left(Y,v,\chi_{n},t\right)=exp\left(-v\cdot f_{s}\left(\delta\omega\cdot t\right)\right)$$$²⁸ where $$$f_s$$$ is the signal decay by the presence of the blood vessel network²⁹ and $$$\delta\omega$$$ is the characteristic frequency due to the susceptibility difference between deoxygenated blood and the surrounding tissue⁸: $$$\delta \omega\left(Y,\chi_{n}\right)=\frac{1}{3}\cdot \gamma \cdot B_{0}\cdot \left[Hct\cdot \Delta \chi_{0}\cdot \left(1-Y\right) + \chi_{ba}-\chi_{n}\right]$$$ with $$$\gamma =267.51 rad s^{-1}T^{-1}$$$ the gyromagnetic ratio, and $$$B_{0}$$$ the main magnetic field strength. $$$G(t_{j})$$$ is the macroscopic field inhomogeneity contribution to mGRE signal decay⁸.
mcQQ is solved using a deep neural network, mcQQ-NET, consisting of 2 fully 4D (3D with multiple channels corresponding to the model parameters) convolutional subnetworks based on U-net^30,
31, each for mGRE phase and magnitude input, respectively (Figure 1). mcQQ-NET was trained with simulated data based on the QQ solution5 as ground truth after adding gaussian noise to the simulated complex mGRE. The loss function was weighted sum of 1) L1 difference between the truth and output of mcQQ, 2) model loss (Eq. 1), and 3) L1 difference of Y spatial gradient. mcQQ-NET was implemented using Pytorch 1.4.032 with performing optimization by ADAM³³, and training was stopped at 240 epochs as the validation loss became stable.
Validation
mcQQ was compared with the prior QQ solved using deep neural network¹³ in 1) simulated stroke brains (Figure 2) and 2) 30 real ischemic stroke patients in which 3D mGRE (0.47x0.47x2.0 mm³ voxel size, TE₁/ΔTE/TE₈ = 4.5/5/39.5 ms, TR= 42.8 ms) and DWI (0.94x0.94x3.2 mm³ voxel size, 0, 1000 s/mm² b-values) was acquired. The stroke patients were classified into 2 groups based on the time interval between stroke onset and MRI scan³⁴: acute (6-24 hours, N=5) and subacute (1-14 days, N=25) phase (Figures 3 and 4). Five-fold cross-validation was performed in all experiments to ensure no overlap between training and test data¹³.

Results

mcQQ showed more accurate OEF in simulation with a smaller mean error compared to QQ (Figure 2) with better depicting low lesion OEF abnormalities (orange arrows). In the stroke patients, mcQQ showed improved spatial overlap between low OEF regions and DWI-defined lesions in the subacute phase (Figure 3). In Figure 4, mcQQ provided significantly lower OEF ratio between lesion and its contralateral normal tissue than QQ in the subacute phase, 0.71 ± 0.15 vs. 0.61 ± 0.18 (p<0.001, Wilcoxon signed rank test), but similar OEF ratio in the acute phase, 0.96 ± 0.08 vs. 0.96 ± 0.09 (p=1.000).

Discussion

This study demonstrated the feasibility of a multi-echo complex signal modeling approach for QQ (mcQQ). The improved physics model led to 1) improved OEF accuracy in simulation (Figure 2), especially in the low OEF lesions, and 2) better depiction of OEF abnormalities in subacute stroke patients (Figures 3 and 4). The more realistic data noise consideration in mcQQ is particularly beneficial in low SNR regions. With improved sensitivity to OEF abnormality, mcQQ can be readily applied to investigate tissue variability in neurologic disorders including Alzheimer’s disease^{35, 36} and multiple sclerosis³⁷.

Acknowledgements

No acknowledgement found.

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Figures

Figure 1. Network structure of mcQQ-NET. mcQQ-NET consisnts of 2 4D Unet, one for mGRE phase and the other for mGRE magnitude input. Each Unet consists of an encoding and decoding path with 18 convolutional layers with 3×3×3 kernel (blue), 4 max pooling layers with 2×2×2 kernel (green), 4 deconvolution layers with 2×2×2 kernel (red), 4 feature concatenations (purple), 1 convolutional layer with 1×1×1 kernel (yellow). Linear combination on the $$$Y, v, \chi_{n}$$$ channels of output of the 2 Unet (gray) and element-wise Tanh function were applied for parameter boundary setting (cyan).

Figure 2. Comparison between the OEFs obtained by QQ and mcQQ in 2 simulated brains: Case 1. Small subtle low lesion OEF and Case 2. With Large low lesion OEF. The numbers in black indicates mean error. Compared to QQ, mcQQ provides greater accuracy (mean error: 0.39 vs. -0.03% in Case 1 and 0.46 vs. -0.09% in Case 2) with better depiction of low OEF values (orange arrows).

Figure 3. Comparison between the OEFs obtained by QQ and mcQQ in 6 real ischemic stroke patients. Compared to QQ, mcQQ shows improved spatial overlap between low OEF regions and DWI-defined lesions in the subacute phase.

Figure 3. Box plots of OEF ration between the lesion and its contralateral normal tissue in acute (6-24 hours post onset, N=5) and subacute (1-14 days post onset, N=25) ischemic stroke patients. Red line, blue box, black whisker, and red cross indicate median, interquartile range, the range extending to 1.5 of the interquartile range, and outliers beyond the whisker range, respectively. Asterisk (*) indicates a significant difference (P<0.05, Wilcoxon signed rank test). Compared to QQ, mcQQ provided significantly lower OEF ratio in the subacute phase.

Proc. Intl. Soc. Mag. Reson. Med. 30 (2022)

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DOI: https://doi.org/10.58530/2022/0181