It has been suggested that during a hyperoxic calibration, the effect of the paramagnetic oxygen dissolved in the arterial blood plasma can be a concerning factor for the interpretation of the calibrated BOLD signal. We recently showed that dissolved oxygen in the arterial blood plasma has little effect on the susceptibility, R₂, and R₂^* of blood plasma^1,2. Nevertheless, R₁ was significantly enhanced due to the paramagnetic effect of the dissolved oxygen. Hence, the overall effect from the dissolved O₂ on the calibrated BOLD signal needs to be further investigated. In this study, we modified the detailed BOLD model (DBM)³ to incorporate dissolved O₂ related relaxation enhancement in order to predict the relative effect of dissolved O₂ on the calibrated BOLD signal.

The DBM was implemented using custom Matlab (Mathworks, Inc) functions. The DBM was then expanded in two ways to account for hyperoxic calibrated BOLD experiments: the arterial plasma R₁ changes due to dissolved O₂ were incorporated (DBM-R₁); or both the arterial plasma R₁ and R₂^* changes due to dissolved O₂ were incorporated (DBM-R₁-R₂^*). The relative BOLD signal was then given by:

$$\delta{S}=H[(1-V_{I})e^{-TE\cdot\Delta{R_{2E}^{*}}}+\eta\epsilon_{A}V_{A}e^{-TE\cdot\Delta{R_{2A}^{*}}}+\epsilon_{C}V_{C}e^{-TE\cdot\Delta{R_{2C}^{*}}}+\epsilon_{V}V_{V}e^{-TE\cdot\Delta{R_{2V}^{*}}}]-1$$

Where

$$\eta=\frac{(1-{e^{-TR\cdot{R_{1A,0}}}}{e^{-TR\cdot\Delta{R_{1A}}}})\cdot{(1-{e^{-TR\cdot{R_{1A,0}}}\cos\theta}})}{(1-{e^{-TR\cdot{R_{1A,0}}}}{e^{-TR\cdot\Delta{R_{1A}}}\cos\theta})\cdot{(1-{e^{-TR\cdot{R_{1A,0}}}}})}$$

Here is the volume fraction of each compartment. The subscripts I, A, C, and V represent intravascular, arterial, capillary, and venous compartments, respectively. The subscript “0” defines the baseline values. If not mentioned, the definitions of variables follow the same rules as described in the original DBM paper³. The parameter $$$\eta$$$ is the ratio of the signal at TE = 0 with and without a stimulus. $$$\Delta{R_{1A}}$$$ is the change of the R₁ relaxation rate in the arterial blood with a stimulus. The parameter $$$\theta$$$ represents the flip angle. To incorporate the effect of the change of the R₂^* relaxation rate of the arterial blood plasma, $$$\Delta{R_{2A}^{*}}$$$ is also separated into two components: the change of R₂^* caused by the oxygen saturation of hemoglobin ($$$\Delta{R_{2A,Hb}^{*}}$$$); and the change of R₂^* in RBC water and plasma water due to dissolved oxygen ($$$\Delta{R_{2A,O_2}^{*}}$$$).

Three simulations were performed: 1) the original DBM was simulated; 2) the DBM was expanded with the parameter $$$\eta$$$ to examine the effect of R₁; 3) the DBM was expanded to include the parameter $$$\eta$$$ and the two-compartment model of $$$\Delta{R_{2A}^{*}}$$$. Simulations were performed for 3 T with TE = 30 ms, TRs = 0.5 s (typical of simultaneous multi-slice fMRI⁴) and 3 s (traditional fMRI). In addition to the relative BOLD signal change, the hyperoxic calibration parameter M_HO was simulated as:

$$M_{HO}=\frac{\delta{S}}{1-(\frac{[dHb]}{[dHb]_0})^\beta}$$

Where [dHb]/[dHb]₀ is the fractional reduction of the deoxyhemoglobin concentration in the venous vasculature due to the hyperoxic stimulus. The parameter $$$\beta$$$ is a constant linking the blood oxygenation and the BOLD signal. $$$\beta$$$ was set to 1.3 for a field strength of 3 T⁵.

Simulations of the hyperoxia calibrated BOLD signal change using the DBM, DBM-R₁ and DBM-R₁-R₂^* are shown in Figure 1. For the range of pO₂ (210 to 610 mmHg), the simulated relative BOLD signal increase was 1-3%; these increases were nearly identical for all three simulation schemes. For TR = 3 s, the average of the calibration parameter M across all ranges of pO₂ was found to be 10.0±0.3 for the DBM, 10.1±0.3 for DBM-R₁, and 10.1±0.3 for DBM-R₁-R₂^*. Differences in M calculated from DBM-R₁ and DBM-R₁-R₂^* were negligible. When a TR of 0.5 s was used in the simulations, the R₁ effect became larger for higher pO₂ levels. For TR = 0.5 s, the average of the calibration parameter M across all ranges of pO₂ was 10.0±0.3 for the DBM, 10.3±0.4 for DBM-R₁, and 10.2±0.4 for DBM-R₁-R₂^*. Again, these differences are very small and well below the measurement precision of M. The simulation results showed very small difference in both the relative BOLD signal and the calibration parameter calculated with the effect of dissolved oxygen, indicating that the dissolved oxygen induced relaxation rate changes are negligible. The effect of R₁ and R₂^* changes will increase with shorter TRs and longer TEs. However, even for a short TR of 0.5 s, as commonly seen in the accelerated simultaneous multi-slice fMRI acquisition, there will be only a small increase in the relative BOLD signal due to the R₁ effect. Therefore, during hyperoxic conditions, the influence of the dissolved oxygen in arterial blood plasma on the measured calibrated BOLD signal at 3 T can generally be ignored.