Long Duration Stimuli and Nonlinearities in the Neural–Haemodynamic Coupling

Abstract

Recent studies have shown that the haemodynamic responses to brief (o2 secs) stimuli can be well characterised as a linear convolution of neural activity with a suitable haemodynamic impulse response. In this paper, we show that the linear convolution model cannot predict measurements of blood flow responses to stimuli of longer duration (42 secs), regardless of the impulse response function chosen. Modifying the linear convolution scheme to a nonlinear convolution scheme was found to provide a good prediction of the observed data. Whereas several studies have found a nonlinear coupling between stimulus input and blood flow responses, the current modelling scheme uses neural activity as an input, and thus implies nonlinearity in the coupling between neural activity and blood flow responses. Neural activity was assessed by current source density analysis of depthresolved evoked field potentials, while blood flow responses were measured using laser Doppler flowmetry. All measurements were made in rat whisker barrel cortex after electrical stimulation of the whisker pad for 1 to 16 secs at 5 Hz and 1.2 mA (individual pulse width 0.3 ms).

Coupling between somatosensory evoked potentials and hemodynamic response in the rat

“…Disagreement between rat and human studies-Human fMRI studies have found nonlinearity of the hemodynamic response to short stimuli durations (<2 s) (Birn et al, 2001;Liu and Gao, 2000;Nangini et al, 2006), while animal studies have found non-linearity of the hemodynamic response for long stimuli duration (>8 s) (Ances et al, 2000;Martindale et al, 2005;Ureshi et al, 2004). Martindale et al (Martindale et al, 2005) suggest that this discrepancy is attributable to different analysis methods.…”

“…Martindale et al (Martindale et al, 2005) suggest that this discrepancy is attributable to different analysis methods. Essentially, the smaller SNR and lower temporal resolution of BOLD fMRI makes problematic the measure at short durations.…”

“…Despite technical difficulties, progress has been made in combining microelectrode recordings of MUA and LFP, or evoked potentials measured on the scalp, with BOLD fMRI (Logothetis et al, 2001). These studies have arrived at differing conclusions with respect to the coupling between neuronal activity and the hemodynamic response, with some finding the coupling to be linear (Logothetis et al, 2001;Matsuura and Kanno, 2001) and others finding it to be non-linear (Devor et al, 2003;Hoffmeyer et al, 2007;Jones et al, 2004;Martindale et al, 2005;Norup Nielsen and Lauritzen, 2001;Sheth et al, 2004). Since, depending on the experimental protocol, the non-linear effects can be small and the signal-to-noise ratio (SNR) of the measurements limited, in many cases both linear and non-linear models fit the data adequately, with no statistically significant differences.…”

A novel method for integrating MEG and BOLD fMRI signals with the linear convolution model in human primary somatosensory cortex

“…These studies have found that brief stimuli (<4 s) elicit hemodynamic signals that cannot be well-characterized using the simplest version of the convolution model based on using the stimulus envelope as an input waveform [e.g., Boynton et al, 1996;Pfeuffer et al, 2003;Vazquez and Noll, 1998]. However, animal studies that incorporate electrophysiological measurements of neural activity have found that responses to brief stimuli (<4 s) do not deviate from linearity [e.g., Ances et al, 2000;Martindale et al, 2003Martindale et al, , 2005. Several authors have suggested that nonlinearities in the signaling process between stimulus input to neural response may account for this discrepancy, such as adaptation of the neural signal [Boynton et al, 1996;Miller et al, 2001;Nangini et al, 2005;Pfeuffer et al, 2003;Soltysik et al, 2004].…”

“…Because BOLD fMRI signal linearity studies in humans have not been conducted with a complementary neural measurement, it is unknown whether the failure of the convolution model is based on poor representation of the neural activity input to the convolution model [Martindale et al, 2005], or deviation from the convolution model itself. The natural next step is to investigate whether replacing the stimulus boxcar waveform with an appropriate waveform derived directly from MEG measurements can provide better characterization of BOLD signal behavior under the convolution model for different duration stimuli.…”