Nonlinear Aspects of the BOLD Response in Functional MRI

doi:10.1006/nimg.1997.0316

NeuroImage

Volume 7, Issue 2, February 1998, Pages 108-118

https://doi.org/10.1006/nimg.1997.0316 Get rights and content

Abstract

Functional magnetic resonance imaging (fMRI) using blood oxygenation level-dependent (BOLD) contrast has progressed rapidly and is commonly used to study function in many regions of the human brain. This paper introduces a method for characterizing the linear or nonlinear properties of the hemodynamic response. Such characterization is essential for accurate prediction of time-course behavior. Linearity of the BOLD response was examined in the primary visual cortex for manipulations of the stimulus amplitude and duration. Stimuli of 1, 2, 4, and 8 s duration (80% contrast) and 10, 20, 40, and 80% contrast (4 s duration) were used to test the hemodynamic response. Superposition of the obtained responses was performed to determine if the BOLD response is nonlinear. The nonlinear characteristics of the BOLD response were assessed using a Laplacian linear system model cascaded with a broadening function. Discrepancies between the model and the observed response provide an indirect measure of the nonlinearity of the response. The Laplacian linear system remained constant within subjects so the broadening function can be used to absorb nonlinearities in the response. The results show that visual stimulation under 4 s in duration and less than 40% contrast yield strong nonlinear responses.

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Citation Excerpt :
While this may be viewed as a nonlinearity in that the HDR for the single stimulus cannot predict the HDR for the second stimulus of the pair, it may also be viewed as a violation of time-invariance in that the HDR for a given stimulus depends on when the stimulus is presented, and therefore this refractory effect indicates that the HDR can change with time when using short inter-stimulus intervals. The most commonly considered form of nonlinearity that is perhaps the most relevant for fast fMRI is the violation of the additivity property, which can be seen readily as a disproportionately large BOLD response to short-duration stimuli (Birn and Bandettini, 2005; de Zwart et al., 2009; Glover, 1999; Hirano et al., 2011; Janz et al., 2001; Liu and Gao, 2000; Miller et al., 2001; Nangini et al., 2005; Pfeuffer et al., 2003; Robson et al., 1998; Soltysik et al., 2004; Vazquez and Noll, 1998; Wager et al., 2005; Yeşilyurt et al., 2008), which we will refer to as amplitude effects. In addition, the temporal properties of the HDR are different for short-duration stimuli compared to long-duration stimuli: the HDR to brief stimuli is faster than predicted from the linear system (Lewis et al., 2018b, 2016; Liu and Gao, 2000; Pfeuffer et al., 2003; Soltysik et al., 2004; Vazquez and Noll, 1998; Yeşilyurt et al., 2008), which we will refer to as temporal effects.
Fast fMRI enables the detection of neural dynamics over timescales of hundreds of milliseconds, suggesting it may provide a new avenue for studying subsecond neural processes in the human brain. The magnitudes of these fast fMRI dynamics are far greater than predicted by canonical models of the hemodynamic response. Several studies have established nonlinear properties of the hemodynamic response that have significant implications for fast fMRI. We first review nonlinear properties of the hemodynamic response function that may underlie fast fMRI signals. We then illustrate the breakdown of canonical hemodynamic response models in the context of fast neural dynamics. We will then argue that the canonical hemodynamic response function is not likely to reflect the BOLD response to neuronal activity driven by sparse or naturalistic stimuli or perhaps to spontaneous neuronal fluctuations in the resting state. These properties suggest that fast fMRI is capable of tracking surprisingly fast neuronal dynamics, and we discuss the neuroscientific questions that could be addressed using this approach.
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For a reliable estimation of neuronal activation based on BOLD fMRI measurements an accurate model of the hemodynamic response is essential. Since a large part of basic neuroscience research is based on small animal data, it is necessary to characterize a hemodynamic response function (HRF) which is optimized for small animals. Therefore, we have determined and investigated the HRFs of rats obtained under a variety of experimental conditions in the primary somatosensory cortex. Measurements were performed on animals of different sex and strain, under different anesthetics, with and without ventilation and using different stimulation modalities. All modalities of stimulation used in this study induced neuronal activity in the primary somatosensory cortex or in subcortical regions. Since the HRFs of the BOLD responses in the primary somatosensory cortex showed a close concordance for the different conditions, we were able to determine a cortical rat HRF. This HRF is based on 143 BOLD measurements of 76 rats and can be used for statistical parametric mapping. It showed substantially faster progression than the human HRF, with a maximum after 2.8 ± 0.8 s, and a following undershoot after 6.1 ± 3.7 s. If the rat HRF was used statistical analysis of rat data showed a significantly improved detection performance in the somatosensory cortex in comparison to the commonly used HRF based on measurements in humans.

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^☆: B. A. Carlson

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Regular ArticleNonlinear Aspects of the BOLD Response in Functional MRI☆

Abstract

NeuroImage

Proceedings of the Second International Conference on Functional Mapping of the Human Brain

Timecourse EPI of human brain function during task activation

Magn Reson Med

Functional mapping of the human visual cortex by magnetic resonance imaging

Science

Linear systems analysis of functional magnetic resonance imaging in human V1

J. Neurosci.

A biomechanical contribution of the BOLD signal time course: The balloon model

Proceedings of the Fifth International Society of Magnetic Resonance in Medicine Conference

Relative contributions of occipital, temporal and frontal cortex to visual perception and working memory: A fMRI study

Proceedings of the Second International Conference on Functional Mapping of the Human Brain

Selective averaging of individual trials using FMRI.In

Proceedings of the Third International Conference on Functional Mapping of the Human Brain

Susceptibility contrast undershoot is not matched by inflow contrast undershoot

Proceedings of the Society Magnetic Resonance, 2nd Annual Meeting

fMRI of human visual cortex

Nature

Stimulus rate dependence of regional cerebral blood flow in human striate cortex, demonstrated by positron emission tomography

J. Neurophysiol.

Mapping of human visual cortex with positron emission tomography

Nature

Focal physiological uncoupling of cerebral blood flow and oxidative metabolism during somatosensory stimulation in human subjects

Proc. Nat. Acad. Sci. USA

Nonoxidative glucose consumption during focal physiology neural activity

Science

Regular Article
Nonlinear Aspects of the BOLD Response in Functional MRI☆