$$$\hspace{1cm}$$$Abnormalities in brain oxygen metabolism are found in tumors, cerebrovascular and neurodegenerative diseases. A useful biomarker of metabolic brain activity is the cerebral metabolic rate of oxygen consumption (CMRO₂). CMRO₂ can be quantified with direct ¹⁷O-MRI [2-6] by fitting a pharmacokinetic model to the signal dynamics seen during and after the administration of ¹⁷O-enriched gas. So far, ¹⁷O-MRI was applied mainly at ultra-high fields (B₀≥7T) to overcome the low SNR at clinical field strengths (B≤3T) [4]. Recently, preliminary results showed that ¹⁷O-MRI is feasible at clinical field strengths [5,6].

$$$\hspace{1cm}$$$The aim of this work is to enable of 3D CMRO₂ quantification at clinical field strengths by using prior information from co-registered ¹H-MR data in combination with iterative, constrained image reconstructions. For that purpose, Anisotropic Diffusion as non-Homogeneous Constraint (ADHOC) using ¹H MPRAGE data [5] were further expanded to T₂-weighted images, the constraint weighting factors and the width of the AD operators were optimized, best values are reported and compared to binary mask (BM) constraint.

$$$\hspace{1cm}$$$4D ¹⁷O data sets were acquired in two in-vivo ¹⁷O-MR experiments [3-6] on the same volunteer with inhalation of 2.5L of 70%-enriched ¹⁷O gas (NUKEM Isotopes), at a nominal resolution Δx=10/8mm and a temporal resolution of 1min. For ¹⁷O-MRI, a clinical 3T MR system (Tim Trio, Siemens) and 3D ultrashort TE (UTE) density-adapted projection sequence (DAPR) [7] were used. Kaiser-Bessel (KB) gridding without/with Hanning filtering was used to reconstruct ¹⁷O MR images. After gridding, an iterative reconstruction was applied that minimizes the objective function:

$$J(\textbf{x})=\mid\mid{}\textbf{A}\cdot{}\textbf{x}-\textbf{y}\mid\mid_2^{2},$$

where A denotes the system matrix that maps the image x to the corresponding raw data y, λ is the weighting factor of the regularization term R, which is initially chosen to be BM of the brain:

$$\textbf{R}_{\textbf{BM}}=\mid\mid{}\textbf{BM}\cdot\textbf{x}\mid\mid_2^{2}.$$

$$$\hspace{1cm}$$$ To include more anatomical information, ADHOC method with a high resolution proton prior, co-registered to the ¹⁷O-MRI data, was used for an edge-preserving reconstruction. Here, the regularization term contains a gradient operator 𝒈 which is applied to either T₁- or T₂-weighted ¹H images:

$$\textbf{R}_{D}=\int{}\textbf{x}\triangledown{}(\textbf{D}\triangledown{}\textbf{x})\hspace{1cm}and\hspace{1cm}\textbf{D}=(1-\frac{\textbf{g}\cdot\textbf{g}^{T}}{\mid\textbf{g}\mid^2}\diagup\sqrt{1+\frac{\textbf{g}^{2}}{a^{2}}})$$

$$$\hspace{1cm}$$$After image reconstruction, CMRO₂ values were calculated from the signal time curves using a model fit [3]. The factor λ for both BM and ADHOC constraints and for ADHOC were tested over the range 𝜆∈[10…10⁵] and a∈[10^-3…10³] to find the best correspondence with ¹⁵O-PET CMRO₂ values [1] without image distortions. For comparison, theoretical CMRO₂ maps (Fig.1f) were calculated based on tissue segmentation from ¹H MPRAGE data and PET values [1]. All reconstructed images and maps were interpolated to 64³.

$$$\hspace{1cm}$$$3D CMRO₂ maps of different reconstruction techniques are shown in Fig.1. ¹⁷O-MR images reconstructed with KB gridding without filtering have low SNR=7 (Fig.1a) prohibiting pixel-wise fitting of CMRO₂ (Fig.1g). Usage of BM information (Fig.1c) does not improve pixel-wise CMRO₂ quantification (Fig.1i), whereas CMRO₂ maps obtained with either Hanning filter (Fig.1b,h) or ADHOC (Fig.1j,k) show some anatomical features. Reconstruction with ADHOC, however, has highest amount of pixels with successfully fitted CMRO₂ values (Fit_%) compared to any other reconstruction (Tab.1).

$$$\hspace{1cm}$$$Weighting factors λ for penalty terms are optimized for highest Fit_% and lowest root-mean-square deviation (RMSD) to the theoretical value. For BM it was λ=1000/10000, and λ=4000/10000 with a=10^-3 for both T₁/T₂-based ADHOC for Δx=10/8mm. Both CMRO₂ maps with T₁-and T₂-based ADHOC reconstructions are similar (Fig. 1j,k), with a better quality and best Fit_% (99%) and higher precision compared to Hanning-filtered KB gridding. Figure 2 shows a model fit to the signal-time curve in a representative GM pixel with the ADHOC based on ¹H MPRAGE image. For Δx=8mm which has a two-fold lower SNR than Δx=10mm data, Fit_% is 20-40% smaller and RMSD for ADHOC is 17% higher (Tab.2).

$$$\hspace{1cm}$$$Filtering among the neighboring pixels was beneficial: ADHOC smoothes data among pixels with similar intensity (mostly within one brain tissue component) and preserves borders within different tissue compartments (edge-preservation), which is favorable compared to isotropic homogeneous Hanning filtering. The BM constraint suppresses noise outside the head, but barely increases SNR within the head. CMRO₂ maps from ADHOC differ from the theoretical CMRO₂ map due to the partial volume effects (PVEs). PVEs are only partly corrected by AD reconstruction and mainly caused by fast T₂^*=2ms relaxation of ¹⁷O nucleus, which leads to blurring.

$$$\hspace{1cm}$$$The results show that smoothing among neighboring pixels enables quantification of 3D CMRO₂ maps in dynamic ¹⁷O-MR experiments. Iterative reconstructions with Anisotropic Diffusion as non-Homogeneous Constraint (ADHOC) applied to either T₁-or T₂-based ¹H images are favorable. The reconstruction techniques will be applied for data analysis of further dynamic ¹⁷O-MR experiments on glioblastoma patients to investigate the metabolism of different tumor regions