Introduction

The quantitative BOLD (qBOLD) technique provides the capability to non-invasively and quantitatively map the oxygen extraction fraction (OEF) on a regional level^1,2. OEF is derived from the ratio of the irreversible transverse relaxation rate (R₂′) and the deoxygenated blood volume (DBV), the latter of which has been found to be overestimated for asymmetric spin echo (ASE) based acquisitions leading to an underestimation of OEF³. Recently it was proposed⁴ that an independent measure of DBV could be acquired by using the BOLD response to administration of medical oxygen⁵ dubbed hyperoxia qBOLD (hqBOLD). In this simulation study the potential for systematic error due to physiological variability and the effect of noise were both examined for the proposed hqBOLD technique and compared with simulations of ASE based qBOLD (standard qBOLD).

Methods

Simulations of the qBOLD and hyperoxia-BOLD signal were performed using a previously reported Monte Carlo based approach⁶. Modifications were made to model the hyperoxia BOLD signal using a model of oxygen transport⁷.

Systematic error was investigated in the absence of system noise and incorporated variations in physiology by randomly generating values in a predefined range (Figure 1) using a uniform random number generator⁵. These values were used to generate ASE and BOLD signals for 1,000 different physiological states. These signals were processed to generate estimates of R₂′ and OEF.

The effect of noise was investigated by simulating signals for standard physiological values (Figure 1). Representative Gaussian noise (ASE SNR 52, BOLD SNR 87) was added to these signals before calculating R₂′, DBV and OEF and repeated 20,000 times. To account for the averaging process inherent in the experimental linear regression analysis, multiple signals with added noise were generated for normoxia and hyperoxia and averaged before calculating the BOLD signal change.

Results

Figure 2 presents the simulation of systematic error. The R₂′ estimated from the simulated qBOLD data is plotted against the true R₂′ based on the ‘true’ static dephasing qBOLD model⁸ (Fig. 2a). The DBV from standard qBOLD shows a large amount of uncertainty which increases with true OEF when compared with true DBV (Fig. 2b). Whilst the DBV from hyperoxia BOLD has a much lower uncertainty when OEF ≳ 30 % (Fig. 2c). The OEF from standard qBOLD does increase with true OEF, but has a very small dynamic range (Fig. 2d). Finally, the OEF from hyperoxia qBOLD increases monotonically with true OEF for OEF > 20 % with a dynamic range consistent with the full range of OEF (Fig. 2e).

Figure 3 presents simulations of the effect of system noise. The true R₂′ was estimated to be 2.8 s^-1, whilst the median value simulated was 2.3 s^-1 (Fig. 3a). Standard qBOLD DBV had an interquartile range (IQR) of 3.2 % (Fig. 3b), compared with the hyperoxia BOLD DBV IQR of 0.0033 % (Fig. 3c). The main difference in the standard qBOLD and hyperoxia qBOLD estimates of OEF is in their propensity for outliers, with the former having an excess kurtosis value of 5826.1 (Fig. 3d) and the latter a value of 0.1 (Fig. 3e).

Discussion

Simulations of the standard BOLD technique were consistent with previous results⁶, namely that R₂′ is linearly related to the true R₂′, that standard qBOLD DBV is a function of the OEF and this leads to a reduced dynamic range of OEF measurements with standard qBOLD.

Simulations of the new hyperoxia qBOLD technique predict a considerable improvement in estimates of both DBV and OEF compared with the standard qBOLD technique. These results also provide an independent confirmation of the heuristic model for scaling the hyperoxia BOLD signal change to DBV. This heuristic was developed using an entirely different model to the one presented here based on analytical models of three vascular compartment⁵. In this previous work a narrower range of healthy OEF values were simulated (35 – 55 %). Despite this, the heuristic model generalises well to the much larger OEF range simulated in this study (0 – 100 %) (Fig. 2d). This is emphasised by the close correspondence between hyperoxia BOLD DBV and true DBV with a slope of 0.95 for OEF > 30 % (Fig. 2c). Therefore, when combined with the simulated measurement of R₂′, the dynamic range of hyperoxia qBOLD is markedly improved.

Using representative noise levels estimated from the data, the simulations show that for a single physiological state the uncertainty in standard qBOLD DBV (Fig. 3b) is considerably larger than for hyperoxia BOLD (Fig. 3c).

Conclusions

These simulations show that introducing an independent measure of DBV into the qBOLD framework provides improved estimates of OEF.

Acknowledgements

This work was funded by EPSRC grant EP/K025716/1.

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