$$$\hspace{1cm}$$$In healthy brain tissue, oxidative metabolization of glucose fulfills most of cellular energy demand, whereas in tumor tissue the energy production is usually shifted towards less efficient anaerobic glycolysis[1]. To quantify energy metabolism, an imaging method would be desirable to map the local cerebral metabolic rate of oxygen consumption (CMRO₂).

$$$\hspace{1cm}$$$CMRO₂ can be quantified with ¹⁵O-PET[2,3] or with direct ¹⁷O-MRI[4-8], where the ¹⁷O signal change is detected after the administration of ¹⁷O-enriched gas. Recently, ¹⁷O-MRI results in humans at 3T were presented[7,8]; however, acquisition parameters need to be optimized for clinical routine application, but the costly and rare ¹⁷O₂ gas allows only for limited imaging studies. Thus, in this work a flexible simulation framework and two phantoms: analytical tumor and numerical, are presented to analyze the influence of various protocol parameters on CMRO₂ quantification by simulation.

$$$\hspace{1cm}$$$¹⁷O-MR signal in k-space was either analytically expressed or numerically estimated to simulate a dynamic ¹⁷O-MRI experiment, which consists of 4 phases: baseline, inhalation of ¹⁷O-enriched gas, re-breathing and wash-out[6-8]. Signal intensity in different brain regions was simulated separately: the modulation of the ¹⁷O signal was calculated on the k-space sampling time scale (i.e., the TR). Expected signal changes over time for the different tissues ρ_i(t) were retrieved and calculated according to CMRO₂ ¹⁵O-PET studies[2,3]. After reconstruction of the dynamic datasets, input CMRO₂ values were compared to the simulation results from fitting.

$$$\hspace{1cm}$$$At first, simulations were performed on an AnalytiCally Represented Oxygen-17 BrAin Tumor (ACROBAT) with the following substructures (Fig.1e): white (WM) and gray brain matter (GM), cerebral spinal fluid (CSF), and the tumor regions contrast-enhancing rim (CE), necrotic tumor center (NE) and perifocal edema (PE).

$$$\hspace{1cm}$$$Making use of linearity of the FT, the Fourier domain signal Sk of a ACROBAT phantom was calculated as a combination of multiple 3D objects, that have an analytic representation in k-space (ellipsoids[9] and spheres):

$$Sk(\rho(t),G,\textbf{k})=\sum_{i}^{N}Sk_i(\rho_i(t),G_i,\textbf{k})\cdot{}e^{\frac{-(TE+\widetilde{t})}{T_2^*}}+A_N\cdot(randn+j\cdot{}randn).$$

G_i: shape of i_th object, $$$\widetilde{t}$$$ indicates the sampling time for a certain position in k-space. The last term represents Gaussian noise, which was added to the complex k-space signal Sk using experimental SNR values (amplitude $$$A_N\sim{1/}\sqrt{BW}$$$,BW-readout bandwidth). Measured at 3T MR system in human brain T₂^*=2ms decay was assumed[4]. K-space simulation was done for a radial image acquisition with density adapted sampling using parameters of a ¹⁷O-MRI experiment at 3T[7,8].

$$$\hspace{1cm}$$$Secondly, a numerical ¹⁷O-MRI phantom was created from the segmented ¹H MPRAGE data, where ¹⁷O concentrations were assigned to each brain tissue: GM, WM and CSF (Fig.1d). An operator A, representing dynamic ¹⁷O-MR measurement (sampling k-space trajectory), was than applied to calculate k-space signals. Finally, the framework for signal dynamics described above was applied.

$$$\hspace{1cm}$$$Figure 2 shows CMRO₂ differences in GM, WM and CE as a function of spatial resolution and BW. For WM small deviations of 2% are seen at Δx≥8mm and at all BWs, since the simulated WM region is large (Fig.1e). For Δx<8mm CMRO₂ is underestimated due to nonlinear signal behavior at low SNR. If only 8 or less out of 10 simulation runs for the parameter pair were successful, then they are not plotted,otherwise blue/black error bar is shown for 9/10 successful runs. As seen in Fig.2, BW≤250Hz/px and Δx≥8mm are required for reproducible CMRO₂ quantification in CE tumor region. Results for different temporal and spatial re­solution (Fig.3) are more heterogeneous: CMRO₂ values change smoothly for a temporal re­solution 75≤Δt≤240sec, whereas they vary strongly otherwise. Thus, intermediate parameter settings seem unfavorable. For CMRO₂ quantification in the CE region 150≤BW≤250Hz/px, and Δx>7mm are required.

$$$\hspace{1cm}$$$Results of the numerical phantom (Fig.4) show that GM CMRO₂ (1.12±0.11µmol/g_tissue/min) is always underestimated by about 30%, but does neither depend on BW nor on spatial resolution, whereas for WM CMRO₂ values are overestimated. The best values are found at BW=150Hz/px and 7≤Δx≤9mm, and for BW=250Hz/px and Δx≥7mm, with the mean CMRO₂=0.74±0.03 µmol/g_tissue/min and 20% overestimation.

$$$\hspace{1cm}$$$Calculated underestimation of the CMRO₂ values is different in two presented phantoms since the ACROBAT phantom has simpler structure than the numerical phantom. However, the regions of most precise CMRO₂ values are similar: 150≤BW≤250Hz/px and 8≤Δx≤9mm for brain and tumor regions.

$$$\hspace{1cm}$$$A framework with an analytical tumor ACROBAT and numerical phantoms are presented for the simulation of the dynamic ¹⁷O-MRI experiments which can be used for flexible and fast evaluation of optimal acquisition schemes. Based on the proposed framework, other phan­toms are currently implemented to investigate the effect of different object sizes on the precision of CMRO₂ quantification. The influence of the MR system,T₁ relaxation time and other data ac­quisition scheme can also be included in the framework.