The average proportion of the cortex found to be significantly correlated with a given NIRS regressor (using a two-tailed, voxel-wise t-test, p < 0.01) was 17.8 % for HbR signals and 16.8 % for HbO signals, with subject means ranging from 5–22 %. Subject 6 showed very little correlation despite there being no obvious issues with either the NIRS or fMRI recordings. shows an example of a significance map for a single, well-correlated HbO regressor. The average proportion of the cortex significantly correlated with the synthetic NIRS signals was 3.7 %.
An example of the significance map for a single subject, run and NIRS-HbO regressor. Note that significantly correlated voxels are spread throughout the cortex as well as in deeper regions of the brain.
Whole cortex variance reduction
The percentage variance reduction (PVR) was computed for the HbO, HbR, HbO & HbR, RETROICOR and synthetic NIRS models. The results of this process are shown in as a function of the number of NIRS channels (n) in each linear model.
Figure 3 The percentage variance reduction obtained by the HbO, HbR and HbO & HbR models as a function of the number of NIRS channels incorporated into each model. Values of PVR are obtained in comparison to the reference model. The corresponding results (more ...)
Each data point in corresponds to the mean PVR achieved over the whole cortex and averaged over all runs and either every possible combination of n channels or 28 random combinations of n channels, whichever is smaller. For example, the HbO data point corresponding to 1 NIRS channel is the average PVR obtained across every possible model containing a single HbO regressor (if no channels were excluded, there would be 28 possible models), for each subject and run. For the HbO data point corresponding to 2 NIRS channels, 28 pairs of non-excluded HbO regressors were randomly selected, and the average PVR achieved by those pairs of regressors is presented. The upper limit on the number of random combinations was set at 28, as it was computationally prohibitive to use every possible model in most cases (for example, 28 choose 2 = 378 possible models). This process was performed in order to minimize the sensitivity of the results to channel selection. This same process was applied to obtain the HbR model PVR results in . For the HbO & HbR models, 1 NIRS channel corresponds to 2 regressors (the HbO and HbR regressors corresponding to each single NIRS channel), 2 NIRS channels corresponds to 4 regressors and so on. This randomized selection approach was also applied for the whole-cortex HRF simulation results below.
As shown in , the PVR increases with the addition of NIRS regressors for all models until 15 NIRS channels are applied, at which point the PVR is equal to 36 % for the HbO & HbR model. The PVR is significantly larger than zero for all models (one-tail t-test, p < 0.01). The addition of the slice-specific respiration and pulse RETROICOR regressors to the reference model also produces a significant reduction in variance, averaging 6.4 %. The PVR achieved by the HbO & HbR model becomes significantly larger than that of the RETROICOR model when 2 NIRS channels are applied (one-tail, paired t-test, p < 0.01). It is worth noting that the use of 8 synthetic NIRS regressors (the same number of regressors used in the RETROICOR model) produces an average PVR of 4.7 %.
shows the corrected PVR, achieved by subtraction of the variance reduction calculated using the synthetic NIRS waveforms. This provides a lower-bound estimate of the average PVR attributable to each NIRS model. A peak value of 17.0 % is achieved for the HbO & HbR model incorporating 9 NIRS channels. The PVR remains significantly larger than zero for all models after subtraction of the synthetic NIRS results (one-tail t-test, p < 0.01).
Whole cortex HRF simulation
shows the average mean squared error (MSE) between the synthetic and recovered HRFs for HbO, HbR, HbO & HbR, RETROICOR and the synthetic HbO & HbR models (synthetic HbO and synthetic HbR models were also calculated but for simplicity are not displayed). These data are normalized to the value obtained using the reference model (i.e. that without NIRS regressors) and are shown as a function of the number of NIRS channels applied (n). For each NIRS model, either all possible combinations, or 28 combinations of n NIRS channels were randomly selected and the results provided are an average of all combinations, as described above for . The MSE decreases with the addition of NIRS regressors for HbO, HbR and HbO & HbR models. This decrease reaches significance (one-tail paired t-test, p < 0.01) with the use of a single NIRS channel for the HbO & HbR model and with the use of 2 NIRS channels for both the HbO and HbR models. The minimum, equal to reduction of 21 %, is found for the HbO & HbR model when 10 NIRS channels are applied.
Figure 4 The result of the HRF simulation applied across all cortical voxels for HbO, HbR, HbO & HbR and synthetic NIRS models as a function of the number of NIRS channels applied. The corresponding results for the pulse and respiration RETROICOR model (more ...)
The slice-specific RETROICOR results are highly variable but on average the RETROICOR model fails to reduce the MSE between the synthetic and recovered HRFs, and results in an average increase in MSE of 0.1 % (standard deviation of 14 %) compared to the reference model.
shows the corresponding results for the correlation coefficient (R2) between the synthetic and recovered HRFs. Again, the data are normalized to the reference model. The value of R2 between the synthetic and recovered HRFs follows a similar pattern to that observed in the MSE results; an improvement is observed with the number of NIRS channels applied for all models up to 10 NIRS channels, at which point the HbO & HbR model produced an increase in R2 of 2.0 %. This increase in R2 above the reference model achieves significance for all NIRS models when a single NIRS channel is applied (one-tail paired t-test, p < 0.01). The RETROICOR model also fails, on average, to produce an improvement in R2, producing a mean decrease of 0.04% (standard deviation 0.4 %).
The equivalent results calculated using the synthetic NIRS data show an approximately exponential increase in MSE and decrease in R2 as synthetic regressors are added. This detrimental effect reaches significance for both MSE and R2 metrics for all synthetic NIRS models using a single NIRS channel.
Selected voxels and optimized time-lag
show scatter plots of the MSE for single-regressor HbO and HbR models plotted against the corresponding MSE of the reference model. Data points on the 45° line correspond to instances where the NIRS regressor model has had no effect on the MSE. These simulations were performed in 100 voxels specific to each subject, run and HbO or HbR regressor such that
lies between 0–0.1, 0.1–0.2 and 0.2–0.3 for respectively. This process was not repeated for the synthetic NIRS signals because their correlation with the fMRI data was insufficient.
Figure 5 The single-regressor NIRS model MSE plotted against the reference model MSE for 100 voxels selected using the value of the baseline NIRS-fMRI correlation for each voxel. The data is separated into three bands on the basis of
. The average reduction in (more ...)
For voxels in the 0–0.1 baseline correlation band (), NIRS regression provides no significant change in MSE for either the HbO or HbR models when compared to the baseline model (two-tailed t-test, p = 0.53). Both the 0.1–0.2 and 0.2–0.3 baseline correlation bands () show a significant decrease in MSE for both HbO and HbR models (p < 0.01). shows the mean percentage change in MSE for each of these three bands. are equivalent to but present the value of the correlation coefficient (R2
) between the synthetic and recovered HRF instead of the MSE. shows that the mean value of R2
increases as a function of the baseline correlation
. provides one example of the effect of HbO () and HbR () regressors in well-correlated voxels (
), for a single run and subject.
Figure 6 The single-regressor NIRS model R2 plotted against the reference model R2 for 100 voxels selected using the value of the baseline NIRS-fMRI correlation for each voxel. The data is separated into three bands on the basis of
. The average increase in R (more ...)
Figure 7 An example of the HRFs recovered using the reference model, pulse and respiration RETROICOR model and by single-regressor HbO (figure 7a) and HbR (figure 7b) models for a single subject, run and NIRS channel for voxels well correlated each NIRS regressor (more ...)
shows the results of the HRF simulation where the optimum time lag has been introduced between each NIRS HbO or HbR signal and the fMRI time series of each voxel. respectively show the MSE and R2 between the synthetic and recovered HRFs, normalized to the values obtained by the reference model. In each case the result of the comparable zero-time lag models (equivalent to the first data points of ) are provided for comparison. The use of the optimum time lag causes a significant reduction in MSE (one-tailed paired t-test, p < 0.01) for all models compared to the zero-time lag equivalent, including the synthetic NIRS model. The reduction in MSE obtained for the optimum time-lag HbO & HbR model is 13.6 % compared to 6.3 % for zero time lag. Correspondingly, there is an increase in R2 when the optimum time lag regressors are applied, but this does not quite reach significance for the HbO (p = 0.011), HbR (p = 0.014) or HbO & HbR (p = 0.10) models. The improvement is very significant for the synthetic NIRS data (p < 10−6). For both metrics, the use of optimum time lag produces a greater improvement for HbO regressors than for HbR regressors.
Figure 8 The values of the MSE and R2 between the synthetic and recovered HRFs for the zero time-lag and optimum time-lag, single-channel HbO, HbR, HbO & HbR and synthetic NIRS models, normalized to the equivalent values of the reference model. A significant (more ...)