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Combined cluster analysis of time evolution and tissue type with total variation denoising (CCTV) for QQ-based oxygen extract fraction mapping

Junghun Cho¹, Pascal Spincemaille¹, 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

A Combined Cluster analysis of time evolution and tissue type with Total Variation denoising (CCTV) was developed to suppress noise propagation in oxygen extraction fraction (OEF) maps based on the QSM+qBOLD (QQ) model of multi-echo gradient echo data without vascular challenge. Compared to cluster analysis of time evolution (CAT), the developed CCTV provided more accurate OEF in simulation and greater contrast to noise ratio between lesion and its healthy contralateral side in ischemic stroke patients.

Introduction

Oxygen extraction fraction (OEF) is a crucial biomarker to assess brain tissue viability and function in various neurologic disorders^1-3. A recent integrated model of QSM and qBOLD (QSM+qBOLD or QQ) can map OEF by utilizing both the magnitude and phase of multi-echo gradient echo (mGRE) data⁴. This method does not require any vascular challenge and therefore has a great potential in clinical applications. To overcome the noise sensitivity of QQ due to its non-convex inversion, the cluster analysis of time evolution (CAT) algorithm has been introduced leading to a significant improvement of effective SNR^5-8. To further suppress noise propagation on OEF, we integrate tissue-type information with CAT for improved clustering and apply total variation regularization.

Theory and 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 (phase analysis) and qBOLD (magnitude analysis) with a priori regulation

$R$ .

${argmin}_{Y,v,R_{2},S_{0},\chi_{nb}}\left\{w||\chi-F_{QSM}\left(Y,v,\chi_{nb}\right)||^{2}_{2}+\sum_j|||S_{j}|-F_{qBOLD}\left(S_{0},Y,v,R_{2},\chi_{nt},t_{j}\right)||^{2}_{2}+R(Y)\right\}$ The first term divides voxel-wise susceptibility (

$\chi$ ) into deoxyhemoglobin in venous blood, i.e. OEF effect, and non-blood tissue susceptibility (

$\chi_{nb}$ ), referenced to fully oxygenated arterial blood

$\chi_{ba}=-108.3$ ppb⁹.

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

$\alpha = 0.77$ ¹⁰ and

$\psi_{Hb}=0.090$ assuming Hct =0.357^11-14,

$\Delta \chi_{Hb}=12522$ ppb between deoxy- and oxy- hemoglobin^15,16.
The second term applies qBOLD model to magnitude signal,

$|S_{j}|$ , at the jth echo⁴:

$F_{qBOLD}\left(S_{0},Y,v,R_{2},\chi_{nb},t_{j}\right)=S_{0}\cdot e^{-R_{2}\cdot t_{j}}\cdot F_{BOLD}\left(Y,v,\chi_{nb},t_{j}\right)\cdot G(t_{j})$ where

$F_{BOLD}$ is the deoxygenated blood effect inside the voxel:

$F_{BOLD}\left(y,v,\chi_{nb},t_{j}\right)=exp\left[-v\cdot f_{s}\left(\delta\omega\cdot t_{j}\right)\right]$ ¹⁷, where

$f_{s}$ is the signal decay by the blood vessel network¹⁸, and

$\delta\omega\left(Y,\chi_{nb}\right)=\frac{1}{3}\cdot \gamma \cdot B_{0}\cdot \left[Hct\cdot \Delta\chi_{0}\cdot \left(1-Y\right)+\chi_{ba}-\chi_{nb}\right]$ ⁴with

$\gamma$ =267.513MHz/T,

$B_{0}$ main magnetic field, Hct=0.357¹¹,

$\Delta\chi_{0}$ the susceptibility difference between fully oxygenated and deoxygenated red blood cells (

$4\pi\ \times 0.27$ ppm)¹⁹ and

$G\left(t_{j}\right)$ is a macroscopic field effect⁴. In the current cluster analysis of time evolution (CAT), the voxels with similar signal time evolution (

$\frac{F_{qBOLD}}{G}$ ) form a cluster and are assumed to have similar tissue parameters (

$Y,v,\chi_{nb}$ ) for SNR improvement and

$R\left(Y\right)=\lambda\left(\overline{OEF\left(Y\right)}-OEF_{wb}\right)^{2}$ is used for the regularization that the whole brain average OEF,

$\overline{OEF\left(Y\right)}$ , should be similar to the brain OEF value estimated from the main draining vein, the straight sinus

$OEF_{wb}$ ,

$\lambda$ is regularization weighting that was chosen using L-curve analysis²⁰.

Combined cluster analysis of time evolution and tissue-type with total variation denoising (CCTV)
Tissue type information is incorporated into clusters obtained from CAT by dividing each cluster into its gray matter, white matter, and cerebrospinal fluid sub-components, the segmentations of which were obtained by using FSL FAST²¹ on T1-weighted image, for improving clustering and subsequent optimization initial guess. In addition, the total variation regularization,

$R\left(Y\right)=\lambda ||\triangledown Y||_{1}$ , is used for effective denoising²² instead of the whole brain OEF average regularization used in CAT.

Validation
QQ-CAT and QQ-CCTV were compared with 1) a simulated stroke brain constructed in the same way as Numerical Simulation 2 in 23 with SNR 20 (5 trials at the same noise level) and QQ-CCTV result as ground truth, and 2) 30 real ischemic stroke patient data used in 8 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), DWI (0.94x0.94x3.2 mm³ voxel size, 0, 1000 s/mm² b-values), and T1-weighted image (0.5x0.5x2 mm³ voxel size, TE=23.4 ms, TR=2992.3 ms, TI= 869.1 ms) was acquired. In simulation, the accuracy and precision was measured by mean absolute error (

$MAE\equiv \frac{1}{N_{v}}\sum_{i=1}^{N_{v}}\left|OEF_{truth}-OEF_{avg}\right|$ ) and mean standard deviation (

$MSD\equiv \frac{1}{N_{v}}\sum_{i=1}^{N_v}OEF_{std}$ ) where

$OEF_{avg}\equiv \frac{1}{N_t}\sum_{j=1}^{N_{t}}OEF_{i,j}$ ,

$OEF_{std}\equiv \sqrt{\frac{1}{N_{t}}\sum_{j=1}^{N_{t}}\left(OEF_{i,j}-\frac{1}{N_{t}}\sum_{j=}^{N_{t}}OEF_{i,j}\right)^{2}}$ ,

$i$ : the voxel index,

$j$ : the trial index,

$N_{v}$ : the number of voxels,

$N_{t}$ : the number of trials. In the stroke cases, the lesion OEF values are referenced to the one in the contralateral side (

$\overline{OEF_{lesion}}-\overline{OEF_{mirror}}$ ) and the detectability of lesion OEF abnormality was measured by the contrast to noise ratio between lesion and contralateral side (

$CNR\equiv\frac{|\overline{OEF_{lesion}}-\overline{OEF_{mirror}}|}{\sigma\left(OEF_{mirror}\right)}$ ) assuming the OEF variation within the contralateral side is originated from the noise.

Result

Compared to QQ-CAT, QQ-CCTV showed more accurate OEF results in simulation (Figure 1) with smaller MAE (4.5% vs. 3.5%) and smaller MSD (5.1% vs. 1.7%): QQ-CCTV provided 1)

$OEF_{avg}$ map which better depicted the spatial OEF variation and 2) smaller

$OEF_{std}$ map (Figure 2). In the 30 stroke patients, QQ-CCTV generally showed less noisy and more uniform OEF maps than QQ-CAT (Figure 2). In the 7 and 9 day post-onset cases, low OEF regions from QQ-CCTV agreed better with DWI-defined lesion. QQ-CCTV provided significantly greater CNR: 1.9±1.8 vs. 1.2±0.9 (p=0.04, paired t-test) (Figure 3).

Discussion

QQ-CCTV shows generally more uniform OEF except in stroke lesions (Figure 2), which agrees with previous PET studies^24,25. The higher OEF CNR in QQ-CCTV, which may be caused by noise reduction in OEF maps, suggests better lesion OEF abnormality detection (Figure 3).

Conclusion

With the improved accuracy by the integrated temporal and tissue-type clustering and total variation denoising, the proposed QQ-CCTV can be readily applied to study tissue viability in various neurologic disorders, such as Alzheimer’s disease^26,
27, multiple sclerosis²⁸, tumor²⁹, and ischemic stroke³⁰.

Acknowledgements

No acknowledgement found.

References

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Figures

Figure 1. Comparison between the OEF obtained by QQ-CAT and QQ-CCTV in a simulated stroke dataset. The numbers indicate RMSE (yellow) and MSD (white). On average, QQ-CCTV provide greater accuracy (MAE: 4.5 and 3.5%) and precision (MSD: 5.1 vs 1.7%). The OEF^_avg and OEF_std indicates the average and standard deviation OEF map among 5 trials, respectively.

Comparison between the OEF obtained by QQ-CAT and QQ-CCTV in 6 stroke patients imaged between 6hrs and 10 days post stroke onset. QQ-CCTV generally shows more uniform OEF maps compared to QQ-CAT. In 7 and 9 days post-onset patients, low OEF areas in QQ-CCTV agree better with DWI-defined lesions.

Figure 3. Box plot of contrast to noise ratio (CNR) between lesion and contralateral side in 30 stroke patients. On average, QQ-CCTV provided significantly greater CNR, 1.9±1.8 vs. 1.2±0.9 (p=0.04, paired t-test). The number indicates average ± standard deviation.

Proc. Intl. Soc. Mag. Reson. Med. 29 (2021)

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