Recently a streamlined quantitative BOLD (qBOLD) technique was described to improve the robustness of measurements of the oxygen extraction fraction (OEF) and deoxygenated blood volume (DBV) by simplifying the analysis model¹. This was achieved by removing confounding effects during data acquisition; enabling the number of model compartments to be reduced. However, measurements of DBV using this technique were larger than typically observed; potentially explaining why the measured OEF in these experiments was lower than expected. We hypothesise that this is due to the effect of diffusion, which is not accounted for in the qBOLD model where the static dephasing regime (SDR) is assumed². The SDR assumption has been challenged by the results of numerical simulations of the Gradient Echo Sampling of Spin Echo (GESSE) pulse sequence that demonstrate a diffusion dependent shift in the R₂′-weighted signal curve³ (R₂′ - reversible transverse relaxation rate). However, the streamlined qBOLD approach uses the Asymmetric Spin Echo (ASE) pulse sequence, for which the effect of diffusion has not been examined. In this work we compare the effect of diffusion on the ASE technique versus the GESSE technique using Monte Carlo simulations. We then examine the implications of this effect on measurements of R₂′, DBV and OEF using ASE.

Synthetic R₂′-weighted qBOLD signals were generated following previously described Monte Carlo simulation approaches^3,4. In brief, blood vessels were modelled as infinitely long cylinders, which were uniformly and randomly distributed in a spherical universe up to a defined volume fraction. The blood oxygenation of these vessels was modelled as an intravascular to extravascular susceptibility difference. A proton was allowed to randomly diffuse around this universe sampling the magnetic field perturbations due to the vessels. The magnetic field at the proton location manifests as a phase accrual, which was sampled every 200μs and saved every 2ms. This process of universe generation and proton phase accrual was repeated 10,000 times. Phases were added or subtracted to simulate the GESSE and ASE techniques and the sum of phases across all protons used to simulate the magnitude signal. The amount of R₂′-weighting is determined by the spin echo displacement time τ. The range of τ values was matched for GESSE and ASE. Due to the low vessel volume fraction (~2-5%), protons spend the majority of their time in the extravascular space and as such these simulations model the extravascular signal (a first-order approximation of the experimentally observed signal).

This approach was used to investigate the effect of varying vessel radius in the range 1μm to 1mm, for a fixed diffusion coefficient⁴ D=1.3μm²ms^-1. GESSE and ASE signals were compared for DBV=3%, OEF=40%, Hct=40%. The analytical qBOLD model¹ (Fig. 1, Eq. 1) was used to estimate R₂′, DBV and OEF from the simulated ASE data. Comparison was made with the SDR by setting D=0.

$$OEF=\frac{R_2^\prime}{DBV\;\gamma\frac{4}{3}\pi\;\Delta\chi_0\;Hct\;B_0}\tag{1}$$

Fig. 2 compares the signal decay for the GESSE and ASE methods. As in previous work³ a shift in the GESSE signal curve is observed with decreasing vessel radius (Fig. 2a). This effect is not observed for the ASE signal, although the short τ signal shows increasing attenuation with decreasing vessel radius (Fig. 2b). The full analytical solution for the SDR is plotted as a black line with 1mm vessels approaching this regime. Fig. 3 displays the fitted qBOLD parameters as a function of vessel radius. When D=0 (SDR) the estimated parameter values are independent of vessel radius, whereas with diffusion all parameters show vessel radius dependence. Quantitative BOLD is a promising technique for the measurement of OEF using endogenous contrast. The simulations presented here reveal that the GESSE and ASE pulse sequences are both affected by diffusion, but in different ways. As hypothesised for ASE, diffusion is shown to result in an overestimation of DBV for typical parenchymal vessel radii (5-25μm), consistent with previous ASE based qBOLD measurements^1,5. In contrast, R₂′ measurements appear to be insensitive to vessel radius above a critical value (>10μm), providing a more robust parameter albeit sensitive to the product of DBV and OEF. With this in mind, it seems likely that the underestimation of OEF is due to the overestimation of DBV. Further work is required to understand the contribution of intravascular signal and vessels with multiple radii and blood oxygenation levels.The effect of diffusion manifests as a vessel radius dependence of R₂′, DBV and OEF measured using qBOLD with an ASE acquisition. However, by incorporating the results of these simulation in a modified qBOLD model, more accurate estimates of DBV may be possible and hence more accurate measurements of OEF.