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A deep neural network for Oxygen Extraction Fraction (OEF) mapping based on No Training1Department of Biomedical Engineering, University at Buffalo, Buffalo, NY, United States
Synopsis
Keywords: Oxygenation, Oxygenation, Contrast Mechanism
Motivation: Quantitative mapping of oxygen extraction fraction (OEF) is critical to evaluate brain tissue viability and function in neurologic disorders. A recent deep learning-based OEF technique, namely QQ-NET, provided OEF maps sensitive to disease-related abnormalities. However, QQ-NET suffers from training data dependency and requires extensive amount of training data.
Goal(s): Our goal is to resolve the training data dependency issue.
Approach: We developed a novel deep learning scheme, namely QQ-NTD, which minimizes the biophysics model fidelity on each single dataset.
Results: The proposed QQ-NTD provided a more accurate OEF than QQ-NET.
Impact: With no need for extensive training and independence from input imaging parameters, our novel deep learning approach, QQ-NTD, can be used readily used to obtain OEF maps in clinical setting.
Introduction
Quantitative mapping of oxygen extraction fraction (OEF) provides critical insights about the brain’s response to changes in oxygen supply and demand across various neurologic disorders including stroke1, 2. Recently, a combined model of quantitative susceptibility mapping 3-6and quantitative blood oxygen level dependent magnitude 7-9(QSM+qBOLD=QQ)3, 10-12 a deep neural network QQ-NET has been developed to map OEF. This QQ accounts for the OEF effect on both magnitude (using qBOLD) and phase (using QSM) of a widely available multi-echo gradient echo (mGRE) data. Furthermore, a deep learning-based QQ approach, QQ-NET, was introduced and provided reliable OEF maps that show decreased OEF in chronic stroke lesions12. However, QQ-NET relies on an extensive combination of parameters in the training dataset, necessitating a lengthy training (approximately 5 days). Moreover, it requires a re-training to test data with different imaging parameters, e.g., different echo times (TEs). In this study, we propose a novel deep learning approach, QQ-NTD, which minimizes model fidelity loss in a single dataset, thereby removing the need for the extensive training and re-training.Method
The QQ model combines the QSM-based and qBOLD-based OEF mapping methods to estimate$$$ OEF=1-Y⁄Y_a$$$ with venous oxygenation ($$$ Y$$$ ) and arterial oxygenation ($$$ Y_{a}=0.98$$$) 10. 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$$$ \chi_{ba}=-108.3$$$ ppb the fully oxygenated blood susceptibility assuming tissue hematocrit Hct =0.3576,$$$\alpha=0.77$$$ the ratio between the venous blood volume ($$$v$$$ ) and total blood volume13, $$$\psi_{Hb}= 0.0909$$$ the hemoglobin volume fraction with Hct=0.3514-17, $$$\Delta\chi_{Hb}=12522$$$ the susceptibility difference between deoxy- and oxyhemoglobin18, 19. The qBOLD model describes the OEF effect on the mGRE magnitude10:
$$ F_{qBOLD}\left(S_{0},R_{2}Y,v,\chi_{n},t_{j}\right)=S_0\cdot e^{-R_2\cdot t_{j}}\cdot F_{BOLD}\left(Y,v,\chi_{n},t_{j}\right)\cdot G(t_{j})$$
where $$$S_{0}$$$ is signal intensity at $$$ t=0$$$ ,$$$ R_{2}$$$ is the transverse relaxation rate,$$$ F_{BOLD}\left(Y,v,\chi_{n},t\right)=exp\left[-v\cdot f_{s}\left(\delta\omega\cdot t\right)\right]$$$ 9 where$$$ f_{s}$$$is the signal decay by the presence of the blood vessel network20 and $$$ \delta\omega$$$ is the characteristic frequency due to the susceptibility difference between deoxygenated blood and the surrounding tissue: $$$ \delta \omega\left(Y,\chi_{n}\right)=\frac{1}{3}\cdot \gamma \cdot B_{0}\cdot \left[\psi_{Hb}\cdot \Delta \chi_{Hb}\cdot \left(1-Y\right) + \chi_{ba}-\chi_{n}\right]$$$ with $$$ \gamma=267.51$$$ rad s-1T-1 the gyromagnetic ratio, and $$$ B_{0}$$$ the main magnetic field strength. $$$ G(t_{j})$$$ is the macroscopic field inhomogeneity contribution to mGRE signal decay 10.
Deep neural network for QQ with no training (QQ-NTD)
A recent study shows that deep neural network (DNN) weights for solving model inversion can be updated using a single test dataset21. Inspired by this idea, we updated the DNN weights ($$$\theta^*$$$) for our QQ model to minimize the model fidelity $$$E_{model}$$$ in a single dataset , which is a concatenated set of mGRE magnitude ($$$ S_{mag}$$$) and QSM.
$$ E_{model}= ||S_{mag}-F_{qBOLD}(\psi(S;\theta^*))|| + ||QSM - F_{QSM}(\psi(S;\theta^*))||$$
The results network weights ($$$ \theta^*$$$) are specific to the dataset $$$S$$$, and the resulting output ($$$ \psi(S;\theta^*$$$) are the five parameters of QQ ($$$ S_{0},R_{2},Y,v,\chi_{n}$$$). Unlike conventional deep learning training, no training is required in this scheme (no-training DNN or NTD).
Validation
We compared QQ-NTD with the previous QQ-NET12 in a simulated stroke brain dataset using 3D mGRE imaging parameters (0.47x0.47x2.0 mm3 voxel size, TE1/ΔTE/TE8 = 4.5/5/39.5 ms).
Results
QQ-NTD showed more accurate OEF compared to QQ-NET in simulation, e.g., a smaller mean error in whole brain (-0.01 vs -0.03) and lesion (0.176 vs. 0.189) (Figure 2). Moreover, QQ-NTD better depicted low lesion OEF, showing improved spatial overlap of low OEF regions compared to the ground truth, a dice score 0.66 vs. 0.97 (Figure).Discussion
This study demonstrates the feasibility of NTD approach for QQ-based OEF mapping. The new approach led to improved OEF accuracy in simulation (Figure 2), in both presumably healthy tissue and abnormal low OEF lesion. This suggests that NTD approach may learn the underlying biophysics model of QQ by minimizing the model fidelity term. Unlike the conventional deep learning approaches, including QQ-NET, the proposed QQ-NTD does not require 1) training on extensive datasets and 2) re-training when there are differences in imaging parameters between training and test data. With improved sensitivity to OEF abnormality and a significantly faster and simplified training scheme (e.g., QQ-NTD vs QQ-NET, 2 days vs. 4~ days), QQ-NTD has high potential for clinical use in investigating tissue variability in neurologic disorders.Acknowledgements
No acknowledgement found.References
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