Recorded LFP and MUA for each of the nine stimulus amplitudes, obtained from the region-of-interest averaged response of the seven rats is shown in for conditions 3, 6 and 9, as examples. For this work, we considered either the magnitude of each peak or the area under the peak for each electrophysiology measurement summed over the 16 pulses in the stimulus train, which provided four different possible combinations of input data as constraint to guide the parameter estimation (MUApeak, MUAarea, LFPpeak and LFParea).
Figure 2 (a) Average LFP (black) and MUA (blue) responses (not normalized) for the entire 2 s stimulus train of whisker stimulation for three different stimulus amplitudes. (b) Evoked hemodynamic responses for these amplitudes; average CBF, HbO, HbR and HbT measurements (more ...)
The model was used to fit the experimental averaged response curves of cerebral blood flow and hemoglobin concentrations for all the nine conditions simultaneously. shows the model fits to the experimental data for conditions 3, 6 and 9, when the integrated MUA peaks (MUAarea) were taken as the neuronal input information to the convolution with the transfer function to be estimated. Similar matches between experimental and model prediction were found when using the other three combinations of input data.
The model parameters estimated for all four MUA and LFP cases analyzed were within the physiological ranges reported previously (Mandeville et al 1999
, Boas et al 2003
, Zheng et al 2005
, Herman et al 2006
), and close to those obtained by Huppert et al (2007)
. The structural parameters did not differ among the trials, independent of the input data we used, as expected. The Windkessel vascular reserve, for example, was estimated between 2.4 and 2.8, while the vascular transit time remained in a range of 0.72 and 0.74 s. Both parameters are in agreement with evoked responses found in previous studies (Mandeville et al 1999
, Zheng et al 2005
). In addition, we examined the 95% confidence intervals with Monte Carlo simulations, as described in section 2.3. We also analyzed the influence of the initial guess of the model parameters, and verified that the final estimates did not change significantly among trials and they always fell within the model uncertainty, independent of the starting position. summarizes all these findings for MUAarea
Table 1 All 14 model parameters used to fit the experimental data: three for each of the transfer functions; four to describe the structural variables of the system; and four parameters to describe the baseline oxygenation. Physiological ranges were used to bound (more ...)
The goodness-of-fit was examined by the correlation between the measured and predicted responses. The averaged R2
values from the nine conditions were calculated for our four sets of input data, and are provided in , as well as their comparison to those obtained by Huppert et al (2007)
. Although slightly smaller when compared to those obtained in the previous cited paper, our optimization model yielded highly statistically significant fits for all combinations of input data. Furthermore, these new model fits were obtained using the electrophysiological measurements as constraints, significantly decreasing the degrees of freedom in the system, i.e. the total number of parameters to be estimated. This is clearly seen in the F-statistics for each of these models, which penalizes for the additional degrees-of-freedom of the Huppert et al
model. According to the F-statistics, our neural transfer model is significantly better, being able to provide similar modeling of the data with 70% fewer degrees-of-freedom.
Table 2 Goodness-of-fit for the model fits of the four combinations of electrophysiological parameters. Uncertainty of the values was calculated from standard deviation of the fits to the nine stimulus conditions. The total R2 values indicate the fraction of (more ...)
The transfer functions estimated from either MUA or LFP to the arterial dilation and CMRO2 changes are presented in . Irregardless of the type of the input data (integrated sum or peak magnitude), the transfer function obtained for each electrophysiology observation was similar, although the amplitude of the LFP transfer functions was smaller. The transfer function for the vascular response was more delayed in its onset and had a wider temporal response, while the transfer function for the metabolic response was more instantaneous and narrower in time. The temporal width of the transfer functions suggests that the vascular response (arterial dilation) is slower than the metabolic response, which is reasonable given the biomechanical nature of the vascular response.
Figure 3 Estimated transfer function for the (a) neuro-metabolic and (b) neuro-vascular systems, which represents their respective response to a single stimulus pulse. Solid (dotted) lines correspond to estimation when using integrated area over MUA (LFP) recordings. (more ...)
The physiological response of each system, represented by the change in CMRO2
and arterial dilation, can be calculated from the direct convolution of the input data with the corresponding transfer function estimated. shows the changes in these states for conditions 3, 6 and 9 when using LFParea
to guide the optimization process. The maximum flow—oxygen consumption ratio, a common rate calculated from functional responses, was found at 3.27, which is consistent with reported values (Kastrup et al 2002
, Hoge et al 2005
Electrophysiological recordings evidence different processes of the neuronal system. MUA is directly related to spiking activity, while LFP measures a weighted sum of transmembrane currents due to synaptic and dendritic activities (Devor et al 2003
). Because these measurements clarify different neuronal-related mechanisms, one might analyze the influence of one or another when used as neuronal information for studying the neuro-metabolic-vascular coupling of the cerebral evoked response. Indeed MUA statistics are slightly higher than LFPs in our results, as shown in , but this difference was not statistically significant (P
< 0.05; T
-test). Perhaps these differences would become more apparent with different stimulation paradigms that evoked characteristically different behavior in MUA and LFP. Of particular interest is the surround vaso-constriction behavior observed during fore-paw stimulation (Devor et al 2007
) that appears to arise from relatively greater hyper-polarization and supports the intriguing hypothesis that depolarization drives dilation and hyperpolarization drives constriction. Our analysis framework enables a model test of this hypothesis by separating the MUA and LFP responses into depolarization and hyperpolarization components that individually drive dilation and/
or constriction. We tested this idea with the present whisker barrel data and found no significant support for or against this hypothesis.