Elsevier

NeuroImage

Volume 18, Issue 4, April 2003, Pages 990-1000
NeuroImage

Rapid communication
Spatial dependence of the nonlinear BOLD response at short stimulus duration

https://doi.org/10.1016/S1053-8119(03)00035-1Get rights and content

Abstract

Most functional magnetic resonance imaging studies use linear models to predict the measured response by convolution of an impulse response with the stimulus profile. Using very short visual presentation times (<2 s), deviation from the linear model in the measured BOLD data from the human brain was found for the response integral, amplitude, and width. In this study, high temporal and spatial resolution were used to quantify nonlinear effects and investigate the spatial dependence. Data at 4 Tesla showed at short stimulus duration a nonlinearity, i.e., deviation from a linear model, with an index up to 400%, whereas data at 7 Tesla exhibited a nonlinearity index up to 40%. The effect was more pronounced for response amplitude than for response area. A reduced width and sharpening of responses at shorter stimulus duration was also found. A voxel-based analysis of 7 Tesla data with 1.2 × 1.2 × 2 mm3 resolution revealed a correlation between response onset and nonlinearity index. This suggests that the nonlinearity effects are a tissue-specific phenomenon and are likely to be more localized to the site of neuronal activity. The observed magnetic field dependence and the demonstrated nonlinearity in the response width support the hypothesis that the source of the nonlinearity at short stimulus duration has a considerable hemodynamic contribution. The nonlinearity was modeled as a “switch”-type initial hemodynamic response onset. Understanding these nonlinearities in the BOLD response is important for design and the analysis of rapid event-related fMRI experiments with brief stimulus presentations.

Introduction

Most fMRI studies use linear models to predict the measured BOLD response based on the convolution of an impulse response function with the stimulus profile. Experimental evidence for the presence of a linear, time-invariant relationship between the stimulus and the BOLD response has been reported (Boynton et al., 1996). On closer look, systematic deviations from the linear model—termed “nonlinearities”—were found and investigated using various approaches including deconvolution, Volterra kernels, and the Bayesian technique Savoy et al 1995, Vazquez and Noll 1998, Glover 1999, Friston et al 2000, Kershaw et al 2001. Accurate modeling of the nonlinearities in the BOLD response is especially critical for rapid event-related designs using short randomized presentation times (Hinrichs et al., 2000). Interactions between rapid brief stimuli and refractory periods have been found Huettel and McCarthy 2000, Ogawa et al 2000, but have not been specifically modeled or accounted for in most of the common fMRI analysis.

Correlation of BOLD data with measurements of neural activity via somatosensory evoked potentials (SEP) (Ogawa et al., 2000), visual evoked potentials (VEP) (Janz et al., 2001), or local field potentials (LFP) from simultaneous electrophysiological recording (Logothetis et al., 2001) provides a link between brain activity and the BOLD response. These studies reported linear relationships between BOLD data and electrical potentials measured. However, Ogawa et al., (2000) reported that the nature of the linear relationship changes with stimulus separation. Sources of nonlinear relationships were found between stimulus and neuronal response, neuronal activation and blood flow response, and blood flow and the BOLD response Ances et al 2000, Yang et al 2000, Mechelli et al 2001, Miller et al 2001. In addition, evidence of a spatial dependence of the nonlinearity has been reported Kershaw et al 2001, Birn et al 2001.

The goal of the present study was to investigate BOLD nonlinearities in the human brain for very short visual stimuli with stimulus durations (SD) at or under 2000 ms. High spatial and temporal resolution was used to investigate the tissue specificity and spatial dependence of the nonlinearities. Signal-to-noise gains at a high magnetic field of 7 Tesla made a voxel-based analysis feasible at a 1.2-mm spatial and 125-ms temporal resolution. With further studies at 4 Tesla, an influence of the magnetic field strength on the observed nonlinearities was tested to demonstrate that, at short SD, the response nonlinearity has a considerable hemodynamic contribution (in addition to its possible neural origin) and thus must be accounted for in event-related fMRI paradigms.

Preliminary results of this work have been published in abstract form Pfeuffer et al 2000a, Pfeuffer et al 2000b, Pfeuffer et al 2000c, Pfeuffer et al 2002a, Pfeuffer et al 2002.

In this paper, we defined the term “nonlinearity” as the nonconformity of the BOLD response to the linear model with zero intercept. If response parameters, for example the response amplitude, change in a linear fashion with alterations in SD, but if as SD approaches zero there a residual amplitude exists, this is considered a nonlinear behavior.

Section snippets

Modeling

For comparison of the experimental results with theoretical predictions, a linear model was used to simulate the hemodynamic responses to brief stimuli. Although other models have been proposed to predict nonlinear relations between stimulus and response Friston et al 2000, Miller et al 2001, they do not include the nonlinear threshold-like behavior of the very brief stimuli used in this study. Stimuli were chosen with duration ranging from 0.25 to 10 s and convolved with the impulse response

Results

Typical BOLD responses to short visual stimuli at 7 Tesla are shown in Fig. 3a. The amplitude and area of the response decrease with SD. Anatomical FLASH and EPI images in the sagittal slice of the visual cortex are shown in Fig. 3b and c. The cross-correlation and onset maps in Fig. 3d and e were calculated from an experiment with 2000-ms stimulation. The activation pattern is aligned along the gray/white matter border and follows the gray matter of the cortex. Highest cc values (yellow) were

Discussion

Nonlinearities of the BOLD response to short visual stimuli were found in the response area and amplitude as well as in the response width being consistent with a sharper BOLD response at shorter SD. The nonlinearity in area and amplitude was much less pronounced at 7 Tesla than at 4 Tesla. The nonlinearity in the response width was in contrast much larger at higher magnetic field, which might be a partial volume effect due to the necessary larger voxel sizes used at 4 Tesla due to

Acknowledgements

The authors thank Prof. Nikos K. Logothetis, Tübingen and Prof. Gary H. Glover, Stanford for stimulating discussions and helpful comments, and also for providing the 1.5 Tesla data, and C. Julia Vance for revision of the typoscript. This work was supported by National Institutes of Health grants RR08079 and RO1MH55346, the W. M. Keck Foundation, the MIND institute, and the Max-Planck Society (J.P.).

References (29)

  • G Adriany et al.
  • B.M Ances et al.

    Coupling of neural activation to blood flow in the somatosensory cortex of rats is time-intensity separable, but not linear

    J. Cereb. Blood Flow Metab.

    (2000)
  • G.M Boynton et al.

    Linear systems analysis of functional magnetic resonance imaging in human V1

    J. Neurosci.

    (1996)
  • R Gruetter et al.

    Field mapping without reference scan using asymmetric echo-planar techniques

    Magn. Reson. Med.

    (2000)
  • Cited by (64)

    • Imaging faster neural dynamics with fast fMRI: A need for updated models of the hemodynamic response

      2021, Progress in Neurobiology
      Citation Excerpt :

      The effect in voxels adjacent to these large pial vessels is dramatic because large vessels on the pial surface are quite sparse in the human cerebral cortex (Bollmann et al., 2020; Duvernoy et al., 1981). Just as the HDR exhibits spatial heterogeneity, the severity of the observed nonlinearity in the BOLD response varies across cortical gray matter voxels (Birn et al., 2001; Huettel and McCarthy, 2001; Pfeuffer et al., 2003), across cortical areas (Glover, 1999; Miller et al., 2001; Soltysik et al., 2004), across cortical and subcortical responses (Lau et al., 2011; van Raaij et al., 2012) and even across individuals (Handwerker et al., 2004). Recent evidence also points to an increased linearity of the BOLD response within the cerebral cortical parenchyma (Gomez et al., 2020; Lewis et al., 2018b; Zhang et al., 2009), where the response is less influenced by large draining vessels on the surface, suggesting that BOLD responses from the microvasculature may exhibit more linearity and perhaps a stronger CBF-BOLD coupling compared to BOLD responses dominated by the microvasculature (Tak et al., 2015, 2014).

    • A cortical rat hemodynamic response function for improved detection of BOLD activation under common experimental conditions

      2020, NeuroImage
      Citation Excerpt :

      Therefore, it has to be assumed that the BOLD response is also dependent on the pulse length. The observed deviations from linearity of the BOLD response are consistent with several human studies (Huettel and McCarthy, 2000; Miller et al., 2001; Pfeuffer et al., 2003; Vazquez and Noll, 1998; Wager et al., 2005; Yeşilyurt et al., 2008), in which such deviations have partly been attributed to neuronal adaptation. However, several rodent studies showed that the BOLD response changed approximately linearly with neuronal activation (Brinker et al., 1999; Herman et al., 2009; Logothetis et al., 2001; Ogawa et al., 2000), suggesting a nonlinearity between stimulation and neuronal activity.

    View all citing articles on Scopus
    View full text