Under both normal and hypercapnic conditions, we observed that the whisker deflection stimulation evoked increases in blood flow and volume and a decrease in the oxygen extraction fraction (decrease in deoxyhemoglobin and increase in oxyhemoglobin) typical of a “positive BOLD” response. As shown in for the group average of the seven rats, the experimental results confirmed a trend between the amplitude of the whisker deflection and the magnitude of the experimentally measured evoked blood flow, hemoglobin, and electrophysiological signals. This linear trend was observed under both normal and hypercapnic conditions. A further comparison of the magnitudes of the evoked responses under the normal and hypercapnic states revealed that the hypercapnic responses were statistically lower in amplitude than the normal responses for all three hemoglobin variables; oxy-, deoxy-, and total-hemoglobin changes based on three-way ANOVA testing (p < 0.05; see using the individual rat and stimulus condition as the independent variables and the normal/hypercapnia condition as the dependent variable). In addition, the time-to-peak of the total-, oxy-, and deoxyhemodynamic responses were qualitatively observed to be earlier during hypercapnia, although this difference was not statistically significant by this same analysis. This empirical finding is consistent with similar observations made in previous rat model studies,8
but is opposite from previous observations that the BOLD signal becomes slower in the human brain.7
Fig. 2 Evoked hemodynamic and neuronal response. Columns (a) and (b) show the evoked hemodynamic changes, MUA, and LFP responses to whisker stimulation (conditions 3, 6, and 9) under normal and hypercapnic conditions. These responses show the ΔCBF, ΔHbO, (more ...)
Table 2 ANOVA comparisons of normal and hypercapnic response profiles. This table shows the probability of the null hypothesis testing for differences between normocapnia and hypercapnia in the response amplitudes of the hemodynamic and electrophysiological responses. (more ...)
Furthermore, we found that the peak magnitude of both the flow and hemoglobin responses were approximately linear with the amplitude of the stimulus deflection under both normal and hypercapnic conditions. We used a two degree of freedom linear model (slope and intercept) to describe this relationship. The linear goodness-of-fit (R2) statistic between deflection magnitude and the experimentally measured peak response were determined to be 0.96*, 0.97*, 0.93*, and 0.97* for the flow, and oxy-, deoxy-, and total-hemoglobin response under normocapnia respectively ( * indicates p < 0.05). The hypercapnic responses were generally less robust than the normocapnia responses, and the goodness-of-fit statistics for the linear model were 0.97**, 0.45*, 0.50*, and 0.43 for the flow, and oxy-, deoxy-, and total-hemoglobin response under hypercapnia, respectively.
In comparison to the evoked hemodynamic signals, no statistical differences in the average magnitudes of evoked local field potentials (Σ LFPs) or multiunit activity (Σ MUA) was observed between the normal and hypercapnic conditions (see ). However, we did observe that the peak LFP response was significantly elevated under hypercapnia [see and ]. We found that, like the hemodynamic variables, the magnitudes of the LFP and MUA responses increased with stimulus condition. Both the peak and mean LFP responses followed an approximately linear relation to the stimulus condition under both normal and hypercapnia (for the peak response, R2=0.85* for normocapnia and R2 =0.88* for hypercapnia; for the mean LFP response, R2 =0.23 for normocapnia and R2=0.55* for hypercapnia; * indicates p < 0.05). To further examine if this relationship was better described by a linear or nonlinear model, we also tested a nonlinear relationship between whisker deflection and response amplitudes [f(x) =a·xb with two model degrees of freedom]. We found that only the peak LFP response could be statistically (p < 0.05) better approximated with the nonlinear model in comparison to the linear model using a paired T-test of the Z-transformed R values (adjusted for degrees of freedom). In contrast to the LFP results, MUA and hemodynamic responses were not significantly improved by the nonlinear model and could be sufficiently modeled by the linear model. Note that this result indicates that any potential nonlinearity was not pronounced enough to significantly justify the higher order model, but that we cannot rule out the possibility of a nonlinear relationship by this analysis.
4.1 Vascular and Metabolic Responses
Once we had examined the correlations between the measured neural and hemodynamic signals, our multicompartment vascular model was used to further investigate the underlying neurovascular and neurometabolic changes by fitting the parametric hemodynamic and flow responses measured during normal and hypercapnic levels of cerebral perfusion (see ). Our vascular model was simultaneously fit to the multimodal measurements (oxy/deoxyhemoglobin and blood flow) from all nine stimulus conditions (27 total time courses each characterized by at least two timing (e.g., peak and width) and one magnitude degree of freedom). The model was applied independently to the normal and hypercapnic states. By fitting the model to this data, we were provided with an estimate of the nine levels of evoked CMRO2 and arterial resistance changes, as well as estimates of the biomechanical and baseline-related parameters for the normal and hypercapnic states. These results are shown in for the group-averaged dataset. Since we considered the normal and hypercapnic responses independently, no restrictions are explicitly imposed about the relationships of parameters from the normal and hypercapnic estimates, for example, baseline flow was not necessarily assumed to be higher in the hypercapnic state. This provided a further physiological check on results of our model.
Fig. 3 Model fits of evoked hemodynamic changes. This figure shows the group-averaged hemodynamic responses (dotted lines; error bars indicate StdErr) under normal and hypercapnic conditions for stimulus conditions 3,6, and 9. The solid lines show the best fit (more ...)
Table 3 Estimated vascular parameters. The vascular model parameters related to the biomechanical and baseline properties of the vascular network were estimated from the nonlinear fit of the model to the experimental data. This table shows the values of the model (more ...)
In , we show the timecourses of the estimated changes in arterial diameter and relative CMRO2 changes. We note that the magnitudes of both of these states increased with stimulus condition, as did the hemodynamic measurements from which they were derived. In , we show the magnitude of peak response of the relative CMRO2 changes estimated from the model for the normal and hypercapnic conditions. No statistical differences were noted for the magnitude of the relative CMRO2 response under normal and hypercapnic conditions (see ).
Fig. 4 Model estimates of arterial diameter and CMRO2 changes. In column (a), the temporal dynamics of the evoked CMRO2 (top row) and arterial diameter changes estimated by the model are plotted for the nine stimulus conditions (hypercapnic time courses are (more ...)
We found that the mean vascular transit time was slightly decreased under hypercapnia from 0.63 to 0.57 sec, although this difference was not statistically significant for the given level of uncertainty in the measurements. This is in agreement with the experimental observations that hypercapnic increases in flow are larger than volume changes. We also found that estimate of baseline total hemoglobin concentration also increased from 103 to 108 µM, and that the oxygen saturation levels of the three vascular compartments also increased (). Based on the values of the estimated model parameters and baseline physiology, we are able to determine the magnitudes of absolute blood flow and CMRO2 changes. The parametric changes in absolute CMRO2 and blood flow are shown in . We found no statistical differences in the parametric responses in absolute CMRO2 changes between normal and hypercapnic states (p > 0.3), see ).
Table 4 Recovered baseline properties and measured hypercapnic changes. Values for the estimated model parameters were used to calculate the values for baseline total hemoglobin (THC), volume (CBV), flow (CBF), cerebral oxygen delivery (DO2), oxygen extraction (more ...)
We found no significant difference in the magnitude of the absolute flow changes under normal and hypercapnic conditions , while there was a significant difference in the magnitude of the relative flow changes (). This is consistent with the results and discussions presented in Ref. 17
. To further probe this, we examined the neurometabolic and neurovascular coupling relationship by correlating the values of the evoked CMRO2
and blood flow signals predicted by our model with the magnitudes of the stimulus and experimentally measured neural signals. For this, we examined both the evoked relative and absolute changes in CMRO2
and blood flow changes (see Sec. 4.2). Similar to the hemodynamic measurements, we found that both flow and CMRO2
changes were approximately linear with the stimulus deflection amplitude. We noted that the goodness of fit for the linear model was R2
=0.91* (normal) and 0.70* (hypercapnia) for the CMRO2
, and R2
=0.96* (normal) and 0.97* (hypercapnia) for the flow changes ( * indicates p < 0.05).
We further examined the ratio of the evoked flow and consumption changes. We found that both the relative and absolute valued flow-consumption relationships could be fit using a linear model, which implies that the flow-consumption ratio did not significantly vary over the nine stimulus conditions within each gas state (normal or hypercapnia). The goodness-of-fit statistics for these linear fits were R2=0.72* (normal) and 0.56* (hypercapnia) for the ratio of relative changes, and R2=0.88* (normal) and 0.77* (hypercania) for the ratio of absolute changes ( * indicates p < 0.05). However, because the evoked relative blood flow response was statistically lower under hypercapnia but the oxygen consumption change was not, the ratio of relative flow-to-consumption changes was also lower for the hypercapnic relationship (p = 0.03). The statistical significance of this difference was tested through a two-way ANOVA analysis using the quotient of flow and consumption changes as the dependent variable, and CO2 level and stimulus condition as the two independent variables. The flow-to-consumption ratio was not significantly different across stimulus conditions (p > 0.3), which is consistent with the previous statement of linearity. This result implies that although flow and consumption changes were correlated across the stimulus conditions, there was an intrinsically different gain between normal and hypercapnic conditions. The ratio of the relative flow change to relative consumption change was 2.5:1 and 2.0:1 for the normal and hypercapnia responses, respectively. In comparison to the relative flow-to-consumption ratio, the ratio of absolute flow and absolute consumption was not statistically different between the normal and hypercapnic conditions (p > 0.4, two-way ANOVA as previously described). These ratios were estimated to be 27:1 and 31:1 mL/ 100 g/ min per mL O2 / 100 g / min for the normal and hypercapnic conditions. This ratio was also not significantly different across the multiple stimulus conditions (p > 0.15). This finding suggests that the ratio of absolute flow and absolute oxygen consumption is more robust to changes induced by hypercapnia. Note that this ratio of absolute changes is equivalent to normalization of both the normal and hypercapnic evoked responses to a common baseline state, whereas the report of relative flow and consumption changes is equivalent to independent normalization to the respective normal and hypercapnia level of baseline values. Unfortunately, the latter renormalization is a more realistic expectation for most experimental human neuroimaging studies, since we generally do not know the level of base-line physiology and therefore cannot correct for baseline changes across longitudinal sessions.
4.2 Baseline Physiology
Using our model-based approach to examine the relative temporal properties of multimodal measurements, the estimated model parameters, in particular the baseline concentration of total hemoglobin, mean vascular transit time, and oxygen saturation levels can be related to estimates of baseline vascular and metabolic physiology as detailed in Refs. 21
. Baseline total hemoglobin, which estimated the calibration factor between the normalized (fractional) changes estimated from the model on the basis of relative changes in blood flow and the relative magnitudes of the oxy- and deoxyhemoglobin changes, can be related to the value of baseline cerebral blood volume for a given value of the hemoglobin content of the blood (see Sec. 2). These baseline values were also used to renormalize the relative evoked signals to provide estimates of the absolute units of CMRO2
and flow changes. The value of normal and hypercapnic levels of blood flow and volume allows the calculation of the changes evoked during the hypercapnic swing. Because these estimates are obtained from the dynamics of the evoked responses at each gas level, and makes no use of the data measured during the swing period, these estimates allow the model to be cross-validated by comparing these estimated values to the direct measurement of these changes.
In , we present the model estimated and experimentally measured changes in blood flow, volume, and CMRO2
between normal and hypercapnia states. We found that cerebral blood volume increased from 2.5 to 2.6 ml/100 g, representing a 4.5 ± 3.2% increase (95% confidence bounds), which was comparable with the 3.2% experimentally measured increase in total hemoglobin content during the hypercapnia transition. The model-estimated blood flow increase during the hypercapnic transition was 17%. This was almost four-fold larger than the volume change. These flow and volume changes follow the previously proposed steady-state flow-volume relationship [r
] with an exponent of 1 / (α + β )= 0.27. The measured blood flow change (9.0 ± 1.8%) was lower than the model estimated value, but within the range of the error bounds of the estimates. Using the measured values of flow and volume changes during the transition as given in , 1 / (α + β )= 0.36 ± 0.1.
The optical measurements of oxy- and deoxyhemoglobin changes during the hypercapnic transition can also be used to estimate change in the relative oxygen extraction fraction and relative CMRO2 in combination with the blood flow measurements. From both the direct measurements and the model-based analysis, we estimated that the oxygen extraction fraction decreased in the transition from normal to hypercapnia (see ). In both of the model analysis and direct experimental measurements, this decrease was less than the fractional flow increase, which implies that CMRO2 increased over this period. In both the model and direct measurement assessments, the elevation of CMRO2 was observed but was not statistically significant. In addition, the measured root-mean-squared fluctuations (spectral power) of the MUA signal increased by approximately 1.1% under hypercapnia, but this was also not significant.
4.3 Neuro-Metabolic-Vascular Coupling
In comparison to the majority of previous studies that have been restricted to relative changes, the model-based assessment of both relative and absolute changes in oxygen metabolism, flow, and hemodynamic variables allows us to further investigate the relationships between evoked neuronal and hemodynamic changes. First, we note that in the case of the measured oxy- and deoxyhemoglobin responses, the normal and hypercapnic responses were significantly different from one another, although in both cases the response magnitudes were approximately linear with respect to the stimulus condition. In contrast, both MUA and LFP responses were fairly nonlinear with respect to the stimulus condition. More notably, however, there were no significant differences between the responses under normal and hypercapnic states for either evoked or baseline MUA. Thus, although a similar linear relationship was observed between oxy- and deoxyhemoglobin and the electrophysiological signals, the coupling constant was different for the normal compared to the hypercapnic responses (). The normal and hypercapnic relationship between the peak LPF response and oxy- and deoxyhemoglobin was significantly different using a two-way ANOVA test (p < 0.01 and p < 0.02 for HbO2 and HbR, respectively; see ). Furthermore, the linear coupling between the hemoglobin changes and the peak MUA responses were also significantly different between the normal and hypercapnic conditions (p < 0.001 and p < 0.002 for HbO2 and HbR, respectively).
Fig. 5 Neuro-metabolic-vascular coupling. In this figure, we show the relationships between flow and metabolism changes and the electrophysiological measurements. In each panel, the relative change (flow or CMRO2) is given on the left-side axis (red line). Absolute (more ...)
Table 5 ANOVA analysis of neurovascular coupling. This table shows the probability and result (as significant, yes or no) of the null hypothesis for a three-way ANOVA test for the differences between the normal and hypercapnic neurovascular coupling (plots shown (more ...)
In contrast to the measured hemoglobin responses, which were significantly different between normal and hypercapnic conditions, the absolute flow change was unaltered by the hypercapnia (). In comparison, the relative blood flow responses (with the hypercapnic response renormalized to the elevated baseline) were significantly lower in the hypercapnia condition (). This suggests an additive model of the flow response to neuronal changes. We examined the coupling between these flow responses and the electrophysiological measurements and found significant differences in the coupling of relative versus absolute flow (). Although we observed that the relationships were qualitatively similar in all four combinations, we found that the coupling between relative flow and the integrated LFP responses was shifted between the normal and hypercapnic responses (). In comparison, the integrated LFP response and absolute flow coupling were not significantly altered under hypercapnia (p > 0.2, two-way ANOVA). Similarly, we found that coupling between relative flow changes and integrated MUA to be different under normal versus hypercapnia (p < 0.007). The MUA to absolute flow relationship was similar between these two conditions (p < 0.5). We found that the coupling between LFP or MUA and flow was well approximated with a linear model (R2=0.83 and 0.86 for LFP and MUA coupling under normal conditions, and R2=0.94 and 0.94 respectively under hypercapnic conditions). The previously introduced nonlinear model (a·x/ (b·x)c) provided a slightly better fit than the linear model, but these differences were nonsignificant after adjusting for the additional degree of freedom (paired T-test on the Z-transformed R values).Finally, we examined the coupling between neuronal activity and oxygen metabolism (CMRO2). There were no significant differences between the normal and hypercapnic metabolic responses (). Thus, the coupling between the LFP (or MUA) measurements and relative CMRO2 and absolute CMRO2 were similar and not significantly different. We found a significant linear relationship between LFP or MUA and relative CMRO2 changes (R2=0.93 and 0.84 for LFP and MUA coupling under normal conditions, and R2=0.94 and 0.90 respectively under hypercapnic conditions). The coupling between the LFP and MUA responses and CMRO2 were slightly better approximated with the nonlinear relationship than a simple linear relationship, but this improvement was not significant given the additional degree of freedom in the nonlinear model.
Finally, we compared the linear models of neurovascular and neurometabolic coupling to examine whether the intercepts of these relationships were significantly nonzero. We found that the flow-MUA and flow-LFP linear relationship had a significantly nonzero intercept, which would indicate that at small changes in neural activity, flow changes were not evoked, and indicates a minimum activation energy for the flow response. We note, however, that we cannot differentiate between a linear model with a nonzero intercept (piecewise linear model) and our nonlinear model that contains the zero-zero crossing. However, both of these models are significantly better than the slope-only (simple linear) model based on the fit to the data and degrees of freedom of the model (T-test of Z-transformed model fit metric; adjusted R-squared). In contrast to the neurovascular coupling, the intercept of the CMRO2 and MUA or LFP responses was not significantly different from zero, which indicates that there was no significant minimum electrical threshold required to evoke a CMRO2 change.