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An improved data acquisition for robust oxygen extraction fraction (OEF) mapping using an integrative model of QSM and qBOLD (QSM+qBOLD=QQ)1Biomedical Engineering, SUNY Buffalo, Buffalo, NY, United States, 2Weill Cornell Medicine, New York, NY, United States
Synopsis
Keywords: Oxygenation, Quantitative Imaging
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 utilizing a routine multi-echo gradient echo (mGRE) acquisition without impractical vascular challenges. This study proposes a novel mGRE acquisition with logarithmic echo spacing that acquires more data points in short echo time regime, which is critical to decouple the model parameters in QQ. The proposed novel mGRE provided more accurate OEF in two simulations, compared to the conventional mGRE.Introduction
Oxygen extraction fraction (OEF) mapping is critical to assess brain tissue viability and function in neurologic diseases1-3. Recently, a integrative 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 routinely available multi-echo gradient echo (mGRE) data4-8. QQ has been validated against calibrated fMRI9 and 15O-PET10, and its clinical feasibility has been demonstrated in ischemic stroke11, 12, multiple sclerosis13, brain cancer14, dementia15, and pre-eclampsia16.QQ has multiple model parameters with the coupling among the parameters4, 17, 18. For robust parameter decoupling, i.e., accurate OEF estimation, QQ requires data in a wide range of echo times with very high signal-to-noise ratio (SNR) as qBOLD in QQ estimates OEF by distinguishing its quadratic and linear effect in short (<15ms) and long echo times (TEs), respectively18. However, conventional mGRE with evenly spaced echoes does not provide enough data points in the short TEs, which can hinder the accurate OEF estimation. We developed a novel data acquisition scheme in mGRE, logarithmic TE sampling, to obtain sufficient data points in short TEs and compared it with the conventional evenly distributed echo sampling in simulations.
Methods
For OEF estimation, $$$OEF= 1-Y/Y_{a}$$$ where $$$Y$$$ and $$$Y_{a}$$$(=0.984) are the venous and arterial oxygenation, QQ model combines QSM of phase modeling and qBOLD of magnitude modeling with a priori regulation $$$R$$$ on $$$Y$$$7. $${argmin}_{Y,v,R_{2},S_{0},\chi_{n}}\left\{w||\chi-F_{QSM}\left(Y,v,\chi_{n}\right)||^{2}_{2}+\sum_j|||S_{j}|-F_{qBOLD}\left(S_{0},Y,v,R_{2},\chi_{n},t_{j}\right)||^{2}_{2}+R(Y)\right\}$$ The first term divides voxel-wise susceptibility ($$$\chi$$$) into deoxyhemoglobin in venous blood, i.e. OEF effect, referenced to fully oxygenated arterial blood $$$\chi_{ba}=-0.108.3 ppb$$$19, and non-blood 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 $$$\alpha = 0.77$$$ the ratio between the venous blood volume ($$$v$$$) and total blood volume20, $$$\psi_{Hb}=0.0909$$$ the hemoglobin volume fraction with Hct=0.35721-24, $$$\Delta\chi_{Hb}=12522 ppb$$$ the susceptibility difference between deoxy- and oxyhemoglobin25, 26.The qBOLD model considers the OEF effect on the mGRE magnitude4: $$F_{qBOLD}\left(S_{0,},Y,v,R_{2,}\chi_{n},t_{j}\right)=S_0\cdot e^{-R_2\cdot t_{j}}\cdot F_{BOLD}\left(Y,v,\chi_{n},t_{j}\right)\cdot G(t_{j})$$ where $$$S_0$$$ is signal intensity at $$$t=0$$$, $$$R_2$$$ is the transverse relaxation rate, $$$F_{BOLD}\left(Y,v,\chi_{n},t\right)=exp\left(-v\cdot f_{s}\left(\delta\omega\cdot t\right)\right)$$$18 where $$$f_s$$$ is the signal decay by the presence of the blood vessel network27 and $$$\delta\omega$$$ is the characteristic frequency due to the susceptibility difference between deoxygenated blood and the surrounding tissue4: $$$\delta \omega\left(Y,\chi_{n}\right)=\frac{1}{3}\cdot \gamma \cdot B_{0}\cdot \left[Hct\cdot \Delta \chi_{0}\cdot \left(1-Y\right) + \chi_{ba}-\chi_{n}\right]$$$ with $$$\gamma=$$$267.51 rad s-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 decay4.
Validation
To investigate the effect of TE sampling schemes on the OEF accuracy, QQ was compared between two TE sets that have the same number of echoes and the same last echo time (Figure 1): 1) 7 evenly spaced echoes (7 linear TE, [5, 10, 15, 20, 25, 30, 35] ms) and 2) 7 logarithmically spaced echoes (7 logarithmic TE, [1, 1.8, 3.3, 5.9, 10.7, 19.4, 35] ms) in two numerical simulations.
Simulation 1: Healthy brain tissue scenario
The QSM and mGRE magnitude values were simulated using the equations of $$$F_{QSM}$$$ and $$$F_{qBOLD}$$$ with two TE sets: 7 linear TE and 7 logarithmic TE. The input (ground truth) was chosen based on normal brain tissue values in literature7: $$$Y=60%$$$, $$$v=3%$$$, $$$S_{0}=1000 au$$$, $$$R_2=15 Hz$$$, and $$$\chi_{n}=-0.1 ppm$$$. Gaussian noise was added to the mGRE and QSM to obtain SNR 50, 100, 200, and 500. For each SNR, the optimization was subsequently performed to estimate $$$Y$$$7.This was repeated 500 times for each SNR. A relative error was computed as $$$\frac{\overline{OEF}-OEF_{true}}{OEF_{true}}$$$.
Simulation 2: Detection of OEF abnormality
To compare the OEF accuracy between the two TE sets in OEF abnormalities, a stroke brain with low OEF abnormality was used to simulate QSM and mGRE with the two TE sets at SNR 100 (0.94x0.94x3.2 mm3 voxel size, FOV=24 cm), and the optimization was performed using cluster analysis of time evolution algorithm7. Root-mean-square-error (RMSE) was calculated for the error measurement.
Results
A novel mGRE acquisition (7 logarithmic TE) provided a more accurate OEF value with smaller relative errors in all the SNRs in a healthy brain tissue scenario (Simulation 1), compared to a conventional mGRE acquisition, 7 linear TE (Figure 2). The novel mGRE also better identified OEF abnormality (Figure 3), e.g., the conventional mGRE (7 linear TE) provided problematic high OEF values at the periphery of the abnormality (black arrows), whereas the novel mGRE (7 logarithmic TE) correctly identified low OEF regional variation (yellow arrow).Discussion
This study demonstrated the feasibility of a novel mGRE acquisition for accurate OEF estimation in QQ model. More accurate OEF by the novel GRE than conventional mGRE may be driven by better decoupling between $$$Y$$$ and $$$v$$$. More data points in short echo regime, e.g., 2 more echoes within 15 ms in the novel mGRE, may lead to better separation of two distinctive signal behaviors (quadratic and linear behavior in short and long TEs) of qBOLD in QQ, which may result in the improved decoupling. With a straightforward setting in routine mGRE, the novel mGRE can be readily utilized to investigate tissue variability in neurologic disorders including Alzheimer’s disease28, 29 and multiple sclerosis30.Acknowledgements
No acknowledgement found.References
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