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Sparsity based machine learning algorithms for oxygen extraction fraction mapping1Biomedical Engineering, Cornell University, New York, NY, United States, 2Computer Software Engineering, Kumoh National Institute of Technology, Gumi, Republic of Korea, 3Radiology, Weill Cornell Medical College, New York, NY, United States, 4Electrical and Computer Engineering, Cornell University, New York, NY, United States, 5Computer Assisted Clinical Medince, Heidelberg University, Mannheim, Germany
Synopsis
In this work, dictionary and deep learning based algorithms are developed that take advantage of sparse signal representations to improve the accuracy and speed of oxygen extraction fraction (OEF) mapping based on the QSM+qBOLD (QQ) modeling of multi-echo gradient echo data without vascular challenge. The developed dictionary learning (QQ-DL) and deep neural network (QQ-NET) algorithms are significantly faster and provide more accurate OEF maps in simulation than a current algorithm based on cluster analysis of time evolution (CAT). In ischemic stroke patients, QQ-DL and QQ-NET show OEF maps that are consistent with DWI-defined lesions.
Introduction
Quantitative mapping of oxygen extraction fraction (OEF) provides valuable assessment of brain tissue viability and function (1-3). By modeling both magnitude and phase of multi-echo gradient echo (mGRE) data, a combined model of QSM and qBOLD (QSM+qBOLD or QQ) (4), OEF can be mapped without any vascular challenge making it suitable for clinical applications. However, the non-convexity in the inversion of QQ makes OEF dependent on optimization details such as initial guess and parameter scaling. The recent cluster analysis of time evolution (CAT) algorithm (5) suggests the presence of sparsity in the QQ model of OEF and QSM + mGRE magnitude Accordingly, we investigate sparsity based dictionary and deep learning algorithms (6) to solve QQ inversion without dependency on optimization details and with faster reconstruction speed.Theory and Methods
QSM and qBOLD formulism are combined in the QQ model to estimate $$$OEF=1-\frac{Y}{Y_{a}}$$$ where $$$Y_{a}=0.98$$$ arterial oxygenation (4). The QSM-based model divides voxel-wise susceptibility into two contributions: deoxyhemoglobin in venous blood, i.e. OEF effect, and non-blood tissue susceptibility ($$$\chi_{nb}$$$), in reference to fully oxygenated arterial blood $$$\chi_{ba} = -108.3 $$$ ppb (7), $$F_{QSM}(Y,v,\chi_{nb})=\left[\frac{\chi_{ba}}{\alpha}+\psi_{Hb}\cdot\Delta\chi_{Hb}\cdot\left(-Y+\frac{1-\left(1-\alpha\right)\cdot Y_{a}}{\alpha}\right)\right]\cdot v + \left(1-\frac{v}{\alpha}\right)\cdot \chi_{nb}$$ where $$$\alpha = 0.77$$$ (8) and $$$\psi_{Hb}=0.0909$$$ assuming $$$Hct =0.357$$$ (9-12); $$$\Delta \chi_{Hb}$$$ between deoxy- and oxy-hemoglobin (13,14). The qBOLD model of mGRE magnitude signal decay is (4):$$S_{qBOLD}\left(t\right)=S_0\cdot e^{-R_2\cdot t}\cdot F_{BOLD}\left(Y,v,\chi_{nb},t\right)\cdot G(t)$$ where $$$G(t)$$$ is a macroscopic field effect (4), $$$F_{BOLD}$$$ is the deoxygenated blood effect inside the voxel: $$$F_{BOLD}\left(Y,v,\chi_{nb},t\right)=exp\left(-v\cdot f_{s}\left(\delta\omega\cdot t\right)\right)$$$ (15), where $$$f_s$$$ is the signal decay by the blood vessel network (16), and $$$\delta \omega$$$ is (4): $$$\delta \omega\left(Y,\chi_{nb}\right)=\frac{1}{3}\cdot \gamma \cdot B_{0}\cdot \left[Hct\cdot \Delta \chi_{0}\cdot \left(1-Y\right) + \chi_{ba}-\chi_{nb}\right]$$$, with $$$\gamma =267.513 $$$MHz/T, $$$B_{0}$$$ main magnetic field, $$$Hct=0.357$$$ (9), $$$\Delta \chi_{0}$$$ the susceptibility difference between fully oxygenated and deoxygenated red blood cells (17).Dictionary learning for QQ (QQ-DL)
QQ-DL consists of 1) sparse dictionary generation and 2) dictionary matching. For the sparse dictionary generation, a list of representative outputs (simulated using Eqs. 1 and 2) and inputs (QQ-CAT parameters, e.g. OEF) were generated from a sample patient dataset (6 out of 30 patients) based on the weighted L2 norm of the output difference (WLN), and the grouping of similar magnitude time courses for sparsity (3000 atoms). Dictionary matching was performed for each voxel by selecting the two nearest components in the dictionary based on WLN and performing bilinear interpolation.
Deep learning for QQ (QQ-NET)
A fully convolutional neural network (QQ-NET), processing 4-dimentional inputs (3D and model parameter), was based on an established architecture, U-net (27 layers) (18). QQ-NET was trained with simulated data based on the QQ-CAT results as ground truth using Eqs. 1 and 2 at SNR 100. The loss function was the L1 difference between the truth and the output of QQ-NET. QQ-NET was implemented using Pytorch 1.0.1 (19) on an NVIDIA TITAN Xp GPU. The minimization was performed with ADAM (20) with learning rate 10-4, 27 epochs (~ 18 hours) as the performance (validation loss) was shown to be stable.
Validation
QQ-DL and QQ-NET were compared with QQ-CAT in 1) simulated stroke brain datasets constructed in the same way as the dictionary with additional Gaussian noise (SNR 100), 2) 30 real ischemic stroke patient data in which 3D ASL (24 cm FOV, 1.9x1.9x2.0 mm3 voxel size, 1500 ms labeling period, 1525 ms post-label delay), 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. For comparison, QQ-CAT was also performed on the testing datasets (5).
Results
QQ-DL and QQ-NET (20 and 30 sec recon time) showed more accurate OEF results in simulation (Figure 1) with smaller RMSE values compared to QQ-CAT (30 min recon time), with average RMSE: 6.1, 6.1, 7.4 %, respectively. In the 30 stroke patients, QQ-DL and QQ-NET generally showed similar OEF maps compared to QQ-CAT (Figure 2). In the 1.5 days and 7 days post-onset cases, low OEF regions from QQ-DL and QQ-NET agreed better with DWI-defined lesion. In the 7 days post-onset, the relative volume with OEF<20% in the lesion is 26%, 33%, and 57% for QQ-CAT, QQ-DL, and QQ-NET. Figure 3 shows the post-onset time vs. the ratio of average OEF between lesion and contralateral side. Here, QQ-DL and QQ-NET showed a greater difference among different phases compared to QQ-CAT. Also, QQ-NET showed a ratio > 100% in the acute phase.Discussion
QQ-CAT, QQ-DL, and QQ-NET show generally uniform OEF except in stroke lesions (Figure 2), which is in agreement with previous PET studies (21,22). The stronger decreasing pattern of QQ-DL and QQ-NET with stroke phase progression compared to QQ-CAT may suggest better agreement with disease progression, which is exemplified in better concordance between low OEF regions and DWI-defined lesions in some cases (Figure 3). The greater ratio than 100% from QQ-NET in the acute phase is consistent with expected OEF elevation (23). With the improved accuracy and speed allowed by the use of sparsity based machine learning, QQ-DL and QQ-NET can be readily applied to investigate tissue viability in various diseases, such as Alzheimer’s disease (24,25), multiple sclerosis (26), tumor (27), and ischemic stroke (28).Acknowledgements
No acknowledgement found.References
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