Comparison of hemodynamic response nonlinearity across primary cortical areas
Introduction
Functional magnetic resonance imaging (fMRI) using blood oxygenation level-dependent (BOLD) contrast has emerged as a noninvasive method to measure vascular oxygenation changes due to brain activity Kwong et al., 1992, Ogawa et al., 1992. (For a review, see Hennig et al., 2003). The shape of the evolving hemodynamic response is a function of stimulus intensity, stimulus duration, inter-stimulus interval duration, and incompletely understood interrelationships among neural activity, cerebral metabolic rate of oxygen consumption (CMRO2), cerebral blood flow (CBF), and cerebral blood volume (CBV) (Buxton et al., 1998). If the stimulus trials are repeated identically and separated sufficiently in time, the experimenter can assume that the hemodynamic response will be the same each time in activated cortical regions Aguirre et al., 1998, Miezin et al., 2000. However, if a stimulus presentation parameter changes, the experimenter cannot make this assumption, but must know the relationship between the stimulus parameter and the hemodynamic response to accurately interpret the functional data.
Early experiments (Boynton et al., 1996) pointed to a linear relationship between stimulus parameters, such as duration, and the hemodynamic response. Others Cohen, 1997, Friston et al., 1994 have shown that a linear systems analysis can be used to model the BOLD response. However, more recent papers and abstracts (Table 1) have shown that nonlinearity does indeed exist between the stimulus parameters (duration, rate, and amplitude) and the resulting hemodynamic response for various types of stimuli.
The origin of the nonlinearity of the hemodynamic response remains a mystery. Since a cascade of physiological processes occurs after stimulus presentation, it is likely that multiple factors between the stimulus and the measured BOLD response contribute to nonlinearity. Nonlinearities in the responses of neuronal activity, oxygen extraction, blood flow, and blood volume are possible, for example. Rees et al. (1997) found a nonlinear BOLD response and a linear CBF response in the auditory cortex as a function of presentation rate, suggesting that a factor other than CBF is responsible for the nonlinearity. The authors suggested that the nonlinearity might be caused by changes in the oxygen extraction fraction (OEF). However, Miller et al. (2001) reported a strongly nonlinear response as a function of stimulus duration for both CBF and BOLD in the visual cortex. Logethetis et al. (2001) reported a linear relationship between local field potentials (LFP) of neurons and the BOLD response and stated that both LFPs and the BOLD response were nonlinear functions of visual stimulus contrast. This result suggests that any nonlinearity of the BOLD response may be due to nonlinearities in the neural response. Although one study (Birn et al., 2001) did not find any correlation between response latency and degree of nonlinearity, another study (Pfeuffer et al., 2003) did find such a correlation, suggesting that vessel size may be a contributing factor to nonlinearity. The exact origin of the nonlinear effect is still not clear. Perhaps, the nonlinearity of the BOLD response is caused by a combination of factors, such as neural adaptation, blood flow, and oxygen extraction.
Few of the studies represented in Table 1 describe the ranges of linearity or nonlinearity for the BOLD response. Robson et al. (1998) reported that the BOLD response in the primary auditory cortex is nonlinear for stimuli less than 6 s and linear above this duration. Two studies looking at the primary visual cortex reported that the BOLD response is nonlinear for stimuli less than 4 s (Vazquez and Noll, 1998) or nonlinear for stimuli less than 3 s (Liu and Gao, 2000), and linear above these durations. No one has reported such ranges for the primary motor cortex. Knowledge of these ranges for different cortices would be very helpful in designing experiments where stimulus duration is likely to change.
Two studies Birn et al., 2001, Pfeuffer et al., 2003 have looked at the variation of nonlinearity on a spatial basis. Individual voxels were assigned indices of nonlinearity based on the response profiles for several stimulus or task durations. In a motor task experiment, Birn et al. (2001) found that the measure of nonlinearity for voxels differed between the SMA and primary motor cortex. This study also found voxelwise variation of the nonlinearity index in the primary visual cortex, but no clear difference between the visual and motor cortices. Pfeuffer et al. (2003) looked at the spatial dependence of the nonlinearity only within the visual cortex. Therefore, further research is necessary to compare the nonlinearity across different cortices of the brain.
A linear system is defined by the principle of superposition (Oppenheim et al., 1999). If the responses of a system to inputs x1 and x2 are T(x1) and T(x2), then a linear system requires T(x1 + x2) is equal to T(x1) + T(x2). This is the property of additivity. In addition, if the response of a system to input a·x, where a is a scalar constant, is T(ax) then a linear system requires T(ax) is equal to aT(x). This is the property of scaling. It is important to note that increasing the duration of the stimulus will not cause a scaled increase in the resultant hemodynamic response in a linear system as it would for a change in stimulus intensity. The effect of changing duration can be predicted with a test of additivity, that is, summing the responses to shorter stimuli, the durations of which add up to the duration of the longer stimulus. For the purposes of this experiment, only the parameter of duration was tested in examining the linearity of the BOLD response.
Another way to test the linearity of a system is by trying to estimate the impulse response function of the response due to several different inputs (Liu and Gao, 2000). The impulse response function in a discrete time system can be defined as the response of a system to an input stimulus of unit time, or 1 s in the case of typical fMRI data. The response to a stimulus of greater duration can be found by convolving the stimulus function, x(t), with the impulse response function, i(t),In a linear system, the impulse response function would be the same for any stimulus duration. In a nonlinear system, the impulse response function would not be the same for different stimulus durations. Knowing how the shape of the impulse response function changes with changes in stimulus duration can help to visualize the point at which the system changes from linear to nonlinear.
The main purpose of this study was to examine the ranges of linearity and nonlinearity for the relationship between stimulus duration and hemodynamic response for three primary cortices (auditory, motor, and visual). A single group of subjects was used to examine any differences that might exist in the nonlinearity between cortices. The results of this analysis will be useful for designing fMRI experiments where the stimulus or task duration is not constant. In addition, the results of two different methods for examining the nonlinearity of the BOLD response with respect to duration were compared. Finally, the nonlinearity of the hemodynamic response was modeled using a neural adaptation function.
Section snippets
Subjects
Five right-handed male volunteers (19.9 ± 1.9 years old) were scanned. The subjects gave informed consent according to local IRB protocol. For a fixed-effect analysis, the use of five subjects allowed an inference of 55% of the population with α = 0.05 and β = 0.05 (Friston et al., 1999). The subjects were age- and gender-matched to avoid variations in the BOLD response due to differences caused by age (D'Esposito et al., 1999) and gender (Levin et al., 1998). Each subject reported having no
Averaged HRFs
Results for the hemodynamic responses in the primary auditory, motor, and visual cortices activated for the five different duration periods in one subject are shown in Fig. 1. The amplitudes for the auditory and motor responses reach a plateau after roughly 4 s of stimulus or task presentation. The amplitude for the visual response appears to reach a plateau at a point between 8 and 16 s of stimulus presentation. The response amplitudes appear to match across all three cortices for the shorter
Discussion
This study examined the nonlinearity of the BOLD response with respect to duration in three primary cortices. Ranges of linearity and nonlinearity were assessed for each cortex. A single group of subjects was used allowing the comparison of these ranges across primary cortices. In addition, a neural adaptation model was used to explain the observed nonlinearity.
The two separate methods of testing the linearity of the hemodynamic response produced somewhat different results (Table 5). In the
Conclusion
The research on the nonlinearity of the hemodynamic response presented in this study has yielded ranges of stimuli or task duration for which the BOLD response is nonlinear or linear with respect to duration. The ranges of nonlinearity have been found to vary between cortices. This variation may be caused by regional differences in neuronal output or cerebral vasculature.
Researchers desiring to stimulate cortical areas of the brain for varying amounts of time may want to take into account the
Acknowledgements
This research was supported in part by NIH grant P50-DC03888, the Center of Excellence Grant #F2182C, and the VA RR&D Brain Rehabilitation Center, Gainesville, FL.
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- 1
Current address: Department of Medical Physics, Memorial Sloan-Kettering Cancer Center, New York, NY 10021.
- 2
Current address: Department of Radiology, Division of Neuroradiology, University of Texas Southwestern Medical Center at Dallas, Dallas, TX 75390.