BOSS fMRI has been proposed as an alternative to GRE BOLD to alleviate its limitations¹. Nevertheless, it needs careful shimming and provides limited spatial coverage. Averaged-BOSS (A-BOSS) has been suggested to eliminate the spatial coverage problem of BOSS fMRI while utilizing its advantages by compressing the SSFP profile into the size of each voxel by adding an exact 2π extra dephasing in each TR (shown in Figure 1) ². A-BOSS can provide images free of banding artifacts with low susceptibility distortions. The feasibility of this method for functional imaging has already been shown ². Here we present a Monte Carlo simulation to investigate the A-BOSS functional contrast and its relevance with the reported values. We further compare the A-BOSS contrast with S1 and S2 SSFP fMRI.

Here the vessels were considered as infinite cylinders with random orientations. Diameter and distribution of these vessels were obtained from the model in Piechnik et al.³ with a blood volume fraction of 2 %. Susceptibility values for active (Y_act=0.75) and resting (Y_rest=0.67) states ⁴ were obtained from Spees et al.⁵. Assuming the B₀=3 T, field inhomogeneity felt by each spin was evaluated from ⁶ :

$$\triangle\bf B(r\geq R)=2\pi \gamma Hct \triangle\chi B_0 (1-Y) (R/r)^2 cos2\phi sin^2\theta$$

$$\triangle\bf B(r < R)=(2\pi/3) \gamma Hct \triangle\chi B_0 (1-Y) (3cos^2\theta-1)$$

Where Hct is hematocrit level (Hct=0.4), Δχ is the susceptibility difference between active and resting states. Y is the oxygenation level, R is the cylinder radius, r is the distance between the spin and central axis of the cylinder, θ is the angle between the cylinder axis and the main magnetic field and φ is the angle between the plane indicated by cylinder axis and B₀ direction with the vector r.

1000 spins capable of 3D Brownian random walk with d=0.001 mm²/s were placed in the extravascular space (T₁=1200 ms , T₂=90 ms as in ⁴). To model the intravascular contrast , in addition to field inhomogeneity, blood relaxation time also changes as approximated in ⁷. The sequence was then applied to all spins and complex intra and extra vascular signals were combined, after getting weighted by their volume fractions, to obtain the total signal.

A-BOSS signal can be generated by a variety of pulse sequences. Here we chose the double echo (DESS or FADE) sequence, shown in Figure 2, as it can demonstrate the difference between A-BOSS and closely related non-balanced SSFP signals, S1 and S2. To this end, the exact extra-dephasing value was first set to 2π, as required by A-BOSS theory. The simulation was then repeated with dephasing value increased to 4π, to completely destroy A-BOSS and generate distinct S1 and S2 signals instead. In all cases, simulations have been performed for a range of TRs (8-40 ms) and flip angles (5-30⁰).

Figure 3 shows the results of normalized absolute signal change for A-BOSS, S1 and S2 SSFP fMRI (/M₀) for a range of TRs and FAs. These results illustrate the superior absolute signal change for A-BOSS when it is compared to each of S1 and S2, separately. It further shows the considerable dependency of A-BOSS contrast to TR and flip angle values. The results for A-BOSS absolute signal change if converted to relative functional signal, agree well with experimental values of around 3-3.5% for TR=40 ms and 0.5-1% for TR=10 ms ⁸, justifying the simulation results. There are a couple of noteworthy observations with this method: first the simulations show that S1 and S2 echoes appear in opposed phase while A-BOSS signal is formed in between and has 90⁰ phase difference with each of these two signals. The other point is about formation of A-BOSS from 2π extra-dephasing. For stronger dephasing values we get two well-separated signals for S1 and S2. Decreasing this extra-dephasing value, proportionally decreases the time difference between these two echoes until we get close to 2π. For 2π we get the A-BOSS echo with specific characteristics (phase and functional contrast) which differentiate it from S1 and S2. It also worth noting that the approximations for intravascular relaxation changes are only a rough estimate and need to be measured in vitro for these particular sequences for a more accurate simulation (Similar to the work for Balanced-SSFP ⁹).The Monte Carlo simulation which has been presented here agrees well with the reported experiments and demonstrates the desirable acquisition parameters. These results show superior absolute functional signal change for A-BOSS compared to other non-Balanced SSFP signals.