In evaluating the sensitivity and accuracy of BOLD based fMRI experiments, it appears evident that these parameters are ultimately conditioned by the functional contrast-to-noise ratio (CNR=AS/N) between the activation-induced signal fluctuation and a „noise" term (N) including random noise, instrument instabilities and physiological fluctuations.
Because of the origin of the BOLD effect, the maximum available CNR at different magnetic field strengths is not univocal, but appears inhomogeneous in space due to different S values depending on the proportion of vessels and brain tissue in the voxel and on the vessel diameter.
Specifically, as stated above, voxels containing vessels larger than the voxel itself present a signal change which varies less than linearly with field strength, while voxels containing capillaries and veins/venules with a diameter less than that of the voxel itself vary greater than linearly .
Nonetheless, the contribution of noise and particularly of physiological signal sources within the noise term is also crucial for the CNR. The physical nature and temporal behaviour of physiological signal sources can be very similar in targeting functional source signals and are thus similarly affected by an increase in the magnetic field strength . This means that a substantial increase in the noise arising from physiological sources can be determined by increasing B0, potentially paralleling the increase in BOLD signal and, thus, reducing the convenience of using high magnetic field strengths.
As a consequence, while several researchers observed a large (three- to fivefold) increase in BOLD signal changes in single slice (2D) fMRI experiments performed at 4.0 T compared to 1.5 T, the ultimate benefit of high-field strength for fMRI will be dependent on the contrast-to-noise ratio and is likely to be much smaller . A study on field strength dependence of CNR (taking into account the background signal fluctuations related to scanner noise and physiologic fluctuations) has demonstrated a smaller (around 40%) improvement when the field strength is increased from 1.5 to 3.0 T . Confounding factors in these studies are a lack of information regarding the level of the physiological background noise and the effects of inflow .
With advanced understanding of the sources of physiological noise it is conceivable that the physiological noise contributions that are temporally different from signal will be reduced, so that the ratio of signal to total noise will scale at least linearly with B0.
Other studies compared CNR values for fMRI experiments performed at 1.5 and 4.0 T, suppressing inflow effects by performing 3D acquisitions and using spiral readout gradients in order to minimize instabilities related to physiologic fluctuations. When comparing fMRI experiments with the same total scan time, performed on six subjects, and with acquisition parameters optimized for each field strength, the 4.0 T scanner proved to give superior results, with a 70% greater number of activated voxels and a 20 % higher average t score for the activated voxels.
However, there are also noise-related problems that are specific for high-field applications. fMRI time-series recorded at high fields may become more sensitive to motion effects . Moreover, parametric statistical analyses of BOLD fMRI data often assume that the data are normally distributed, the variance is independent of the mean, and the effects are additive. BOLD fMRI data acquired at high-field strengths (4 T) showed a strong departure from normality with the consequence that high-field BOLD fMRI data may need to be suitably transformed before classical parametric statistical analyses are applied .
Multivariate data analysis techniques can help to separate the physiological noise from the signal sources, allowing definitely higher CNRs. This is evident for the application of independent component analysis (ICA) to fMRI data-sets . For example, Esposito et al.  showed how improvements in CNR are helpful for an ICA-based separation of functional signals from other sources ofsignal fluctuation. Hence, it is to be expected, although not yet shown by a direct comparison, that, at higher magnetic field strengths, despite the increased contribution to variance of signal and physiological noise components, the capability of ICA algorithms to separate them will be improved.
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