, , and show typical temporal traces for the SEP and hemoglobin responses to four conditions in three animals, for the duration, amplitude, and frequency experiments. The left panels in the figures report the average SEP responses during the different stimulation trains. In the middle panels we overlap all of the SEP responses from within a train to emphasize the differences in amplitude and response shape between the first and subsequent stimuli within the train (the response to the first stimulus is shown in black). The right panels report the hemoglobin response for the given stimulus train.
When increasing train duration () the SEP amplitude remains almost constant (left panels); the P1 responses are similar in amplitude and duration during the first and the other stimuli in the train (middle panels); N1 and P2 amplitudes are largest for the first stimulus (black curve) and decrease for the other stimuli in the train. The hemoglobin response (right panel) quickly saturates in amplitude: i.e., hemoglobin amplitude for the 3 s train is the same as the amplitude for 5 or 7 s trains, but continues to grow in duration for longer trains.
Both the SEP and the hemoglobin response amplitudes increase with increasing stimulation amplitude (). Below the motor threshold, there are no amplitude differences for the P1, N1 and P2 responses to the first and the other stimuli in the train (middle panels), while there are differences for the N1 and P2 amplitudes for stimulation above the MT. Increasing stimulation amplitude broadens the three SEP components for all stimuli presented after the first stimulus in the train.
When increasing the stimulation frequency (), the SEP amplitudes decrease and the hemoglobin response amplitude has a maximum between 2-3 Hz. At low frequencies the three SEP components are the same for the first and the other stimuli in the train. In contrast, at higher frequencies (>2Hz) for all stimuli presented after the first stimulus in the train, the onset of P1 is delayed and the peak broadened, the N1 component is delayed and its amplitude largely reduced especially for the even stimuli, and the amplitude of P2 is strongly reduced. The behavior of P1 at high frequencies closely matches the responses measured with intracellular recording in layer IV of the rat barrel cortex (Higley and Contreras, 2006
). The hemoglobin response at higher frequencies decreases in both amplitude and duration.
The trends shown in , , and are consistent with the results in all of the rats measured. The varying behaviors of the three SEP components in the three experiments enables analysis to determine which component covaries best with the hemodynamic response.
The results of the relationship between integrated SEP or hemodynamic responses versus stimulus condition for the three experiments averaged over all of the animals are shown in (Figure 1osm in the online supplemental material
is the same as but includes error bars calculated as standard errors). Panels a, b and c report the integrated SEP responses; panels d, e and f report the squared SEP responses Σ(SEP2
). In the duration experiment ( panels a and d), the integrated SEP and hemoglobin responses are linear with the input stimuli. The correlation coefficients (R) are ≥0.98 for all SEP components and hemoglobin concentrations. In the amplitude experiment ( panel b), the correlation coefficients between S and integrated SEP P1 or Hb are slightly lower than for duration (R 0.97 and 0.98, respectively). More important, while the P1 SEP component tends to saturate for higher stimulation amplitudes, the hemoglobin response begins to rise only at higher stimulation amplitudes and, in our range of amplitudes, does not saturate for higher amplitudes. ΣN1 and ΣP2 in the range of amplitudes used are linear with S. By considering Σ(SEP2
) the dependence of N1 and P2 with the input stimuli becomes very similar to the hemoglobin concentration dependence with S. For the frequency experiment, there is a strong non-linearity of both integrated SEP and hemodynamic responses with S. Moreover N1, P2, T and Hb are anticorrelated with input stimuli, while for P1 the correlation coefficient is positive (P 0.82). The integrated hemodynamic response decreases rapidly with frequency; ΣN1 and ΣP2 decrease more slowly, while ΣP1 does not decrease with frequency. Similar to the amplitude experiment, by considering Σ(SEP2
) the dependence of N1 and P2 with S becomes very similar to the dependence of the hemoglobin concentrations with S.
Figure 5 ΣHbO, ΣHbR, ΣHbT (HbT = total hemoglobin concentration = HbO+HbR) (both left and right panels), ΣSEP (left panels) and Σ(SEP2) (right panels) vs. stimulus conditions for the grand average of all rats. Panels a and (more ...)
In general, when using the square of the integrated signals, N1, P2 and T have a similar dependence with input stimuli as the hemoglobin responses, while the P1 dependence with S still differs from the Hb dependence with S. From these figures it can also be noted that oxy-, deoxy- and total hemoglobin concentrations have a very similar dependence on input stimuli and in the following figures only HbO is reported for brevity. Using the peak amplitude (max) instead of the area of the SEP components produces similar results for the duration and amplitude experiments (see Fig. 2osm in the online supplemental material
). For the frequency experiment N1 and P2 max decrease more slowly with stimulation frequency and when squared do not overlap as well with the hemodynamic response as when considering the area.
shows scatter plots of the integrated oxy-hemoglobin response vs. the integrated SEP responses (Figure 3osm in the online supplemental material
is the same as but includes error bars calculated as standard errors). As for , panels a, b and c report ΣSEP; panels d, e and f report Σ(SEP2
). In the duration experiment (panels a and d), the integrated SEP responses are linear with the integrated hemoglobin responses (R~0.98). In the amplitude experiment (panels b and e) the correlation coefficient between the integrated SEP and the hemodynamic response improves by using Σ(SEP2
). For the frequency experiment (panel c), the integrated SEP responses are not linear with the hemodynamic responses (R~0.84-0.94 for N1, P2 and T, and R=-0.52 for P1). By squaring the SEP responses, N1, P2 and T become more linear with the hemodynamic response (R~0.96-0.98, panel f), while P1 remains nonlinear with HbO (R= 0.18). Using the SEP max instead of the area (Fig. 4osm in the online supplemental material
) we obtain similar results for the duration and amplitude experiments but worse linearity between N1 or P2 and HbO for the frequency experiment. P1 linearity with the hemoglobin responses improves by using the max, but the correlation coefficients for P1 are still significantly lower than those for N1 and P2.
Figure 6 Panels a, b and c show the scatter plots of normalized ΣHbO and ΣSEP components for the grand averages of all rats. Panels d, e and f, the r scatter plots of normalized ΣHbO and Σ(SEP2) components. Panels a and d: duration, (more ...)
shows the measured and predicted HbO results for the grand average over all animals for each condition, for the three experiments for the linear (panels a, b and c) and quadratic (panels d, e and f) convolution models using the SEP area. The measured and predicted HbR and HbT responses behave similarly (not shown). Figure 5osm in the online supplemental material
reports the hHbO
for the linear convolution model for the three experiments. The coefficients of determination (R2
) between the measured and predicted hemoglobin responses are reported in and the color coded * above some bars indicates statistically significant higher R2
than obtained with the component labeled with the same color as the * (P<0.05, multifactor ANOVA). The predictions by the input stimuli (S) are generally worse than those using most SEP features, indicating that the vascular response is more tightly coupled to the neuronal response.
Figure 7 Grand average of the measured oxy-hemoglobin (HbO=red) response with predicted hemodynamic response using the input stimuli (S=gray), the SEP components P1 (green), N1 (black), P2 (orange), and the total SEP response (T=purple) using linear (panels a, (more ...)
Figure 8 Coefficients of determination between simulated and measured oxy-hemoglobin response across animals for the linear and quadratic convolution models for the three protocols: duration (a), amplitude (b), and frequency (c). P1 (green), N1 (black), P2 (orange), (more ...)
N1 and P2 are able to predict the hemoglobin response quite well across the different experiments, especially with the quadratic convolution model, and generally better than P1. This is best seen during the frequency experiment where the coefficients of determination of the predicted hemodynamic responses have a large magnitude and significant variation from 0.29 for P1 to 0.77-0.71 for N1 and P2 respectively in the linear case, from 0.33 to 0.87-0.84 for the quadratic case. Similarly, with the amplitude experiment P1 R2 is significantly smaller than the R2 of the other SEP components (0.56 vs. 0.88-0.89 linear, 0.60 vs. 0.91-0.92 quadratic). In the duration experiment because of the strong linearity of hemoglobin concentration with input stimuli we are not able to differentiate between the predictions using different components. In this case, measurement noise reduces the correlations and results in S having a slightly better prediction than the SEP components.
In general we found little difference in predicting the hemodynamic response by using N1, P2 and T. This is because, as previously shown, the amplitude of the P2 component strongly covaries with N1 (Kulics, 1982
) and because T strongly covaries with N1 and P2 as ~87% of its signal is derived from these two components. In fact, averaging across animals, experiments, and conditions, we found N1 contributes 47% and P2 contributes 40%, while P1 contributes only 13% to T.
reports the coefficients of determination using the peak amplitude (max) to predict the hemodynamic response (dashed bars) compared with the results using the area (solid bars). The * above the bars indicates significantly better prediction between area and max for each component. In most cases results are similar. In the duration experiment there is no broadening of the peaks and max and area produce very similar results. In the amplitude and, to a larger extent, in the frequency experiments the broadening of the components plays a role and differences between the analysis using area and max are more evident. In general N1, P2 and T predictions are better using the area, and P1 predictions are better using the max. However, the max P1 does not predict the hemodynamic response as well as the other components. Using the max, the results for P2 predictions are significantly worse than when using the area, probably because P2 is a broad component with a not well-defined peak.
Figure 9 Comparison of the coefficients of determination between simulated and measured oxy-hemoglobin responses using the SEP area or the SEP peak amplitude (max) as inputs for the linear (panel a) and quadratic (panel b) convolution models. P1 (green), N1 (black), (more ...)
Using the peak amplitudes the relative contributions to T are 42% for N1, 34% for P1 and 24% for P2. In this case, for the frequency experiment, the prediction using N1 is significantly better than that using T (P value = 0.002) because of the larger weight of P1 on T and the worse ability of P1 and P2 max to predict the hemodynamic response.
Finally, in addition to the linear and quadratic convolution models, for the SEP area we tested a cubic model and a threshold model with the threshold value set at 10, 20 and 30% of the maximum SEP signal (see Fig. 6osm in the online supplemental material
). In all cases, the P1 prediction was not as good as N1, P2, and T (p<0.05 for the amplitude and frequency experiments). The linear convolution model works best for all components in the duration experiment (statistically significantly better than quadratic, cubic and threshold 30% models). For the amplitude and frequency experiments, the quadratic and threshold 20% convolution models work best for N1, P2 and T (statistically significantly better than linear, cubic, and threshold 30% models).