Elsevier

NeuroImage

Volume 49, Issue 3, 1 February 2010, Pages 2113-2122
NeuroImage

Technical Note
Investigating hemodynamic response variability at the group level using basis functions

https://doi.org/10.1016/j.neuroimage.2009.11.014Get rights and content

Abstract

Introduced is a general framework for performing group-level analyses of fMRI data using any basis set of two functions (i.e., the canonical hemodynamic response function and its first derivative) to model the hemodynamic response to neural activity. The approach allows for flexible implementation of physiologically based restrictions on the results. Information from both basis functions is used at the group level and the limitations avoid physiologically ambiguous or implausible results. This allows for investigation of specific BOLD activity such as hemodynamic responses peaking within a specified temporal range (i.e., 4–5 s). The general nature of the presented approach allows for applications using basis sets specifically designed to investigate various physiologic phenomena, i.e., age-related variability in poststimulus undershoot, hemodynamic responses measured with cerebral blood flow imaging, or subject-specific basis sets. An example using data from a group of healthy young participants demonstrates the methods and the specific steps to study poststimulus variability are discussed. The approach is completely implemented within the general linear model and requires minimal programmatic calculations.

Introduction

Previous work has demonstrated that the hemodynamic response (HDR) to neural activity measured with blood oxygen level dependent (BOLD) fMRI varies across the brain and across individuals (Aguirre et al., 1998, Handwerker et al., 2004). This poses a problem for accurate quantification of an individual's BOLD activation when a canonical hemodynamic response function (HRF), i.e., a generalized model of the HDR is used. A simple solution to this problem has been to estimate an individual's HDR using simple visual or motor tasks (D'Esposito et al., 1999, Zarahn et al., 1997), resulting in an estimate of an individual's specific HRF model for use in their statistical analyses. Although this approach is an advance over the canonical HRF model, it has its own drawbacks: it requires additional scans, which cannot be acquired retrospectively, and fails to capture any intraindividual variance that may exist between the region used to derive the HRF and regions of interest for the main experiment. Therefore, this method still leaves potentially unaccounted for variance in the estimate of the BOLD HDR across regions of the brain.

One approach to capturing intraindividual variance in the BOLD HDR is with basis sets. Instead of a single function to model the HDR, a basis set uses multiple (typically two or three) related functions. Through weighted combinations of the functions, many HDR shapes may be modeled, allowing for investigations of hemodynamic variability in a variety of patient populations with various sensory stimuli (Ford et al., 2005, Handwerker et al., 2004, Salek-Haddadi et al., 2006, Stevens et al., 2005, Wierenga et al., 2008). The most prominent basis set currently used is derived from a series expansion of the standard ‘double-gamma’ HRF model (Friston et al., 1998, Glover, 1999). Other similar basis sets have been developed using a principal components analysis (PCA) of large sets of physiologically plausible BOLD HRFs (Friman et al., 2003, Liao et al., 2002, Woolrich et al., 2004). Of particular note is the work by Liao et al. (2002) who designed a basis set to be sensitive to large delays in the BOLD response to stimulation. This approach demonstrates the feasibility that basis sets may be developed to address specific physiological or clinical questions.

Unfortunately, one drawback of using any basis set is that many model fits result in physiologically ambiguous or implausible results (Calhoun et al., 2004, Woolrich et al., 2004). Restrictions on the potential model fits are therefore required to limit a basis set to plausible shapes. One approach to do so is to only investigate estimated HDRs that have a time to peak within a specific time window (Calhoun et al., 2004, Henson et al., 2002). While this approach may improve analyses at the individual level, translating these results to higher-level statistical analyses presents it own difficulties (Calhoun et al., 2004, Friman et al., 2003, Kiehl and Liddle, 2001, Worsley and Taylor, 2006). The main such difficulty regards the manner of excluding or including the variance accounted for by the multiple basis functions. One approach to deal with this variance is to fit a basis set and then only perform higher level analyses on the primary basis function, thus excluding the variance attributed to the secondary basis function(s) (Kiehl and Liddle, 2001). An alternative approach is to include the variance accounted for by all functions in the set at higher level analyses by using the magnitude calculated across the basis function estimates for higher level analyses (Calhoun et al., 2004).

The specific implementation of Calhoun et al. (2004) addresses some of the concerns of using a basis set for group-level analyses. This approach, however, is not general enough for use with other basis sets and requires specific normalization of the regressors in the model. The result is that the specific ratio described in their work is only meaningful with the basis set they used and would have a different meaning if directly applied to other basis sets, i.e., FLOBS as implemented with the FSL package. In addition, the canonical HRF, and its first derivative basis set, is specifically sensitive to temporal shifts, making it unsuitable for study of other physiological variations such as poststimulus undershoot variations. For instance, systematic differences in the size of the poststimulus undershoot between young and elder healthy participants were found in one study (Wierenga et al., 2008), while another study found no significant differences in the BOLD HDR shape between age groups (D'Esposito et al., 2003). In addition, growing application of BOLD fMRI to study disease states (Matthews et al., 2006) may introduce important variations in BOLD HDR shapes which need to be addressed. Specifically, studies of the hemodynamic responses to epileptiform discharges have shown large variability in the BOLD response as a function of proximity to the discharge site (Lemieux et al., 2008, Salek-Haddadi et al., 2006).

Importantly, the current advance of cerebral blood flow imaging (CBF fMRI) also requires that many of the original questions regarding the shape and variability of hemodynamic responses be revisited with this hemodynamic marker. For instance, in a recent study using BOLD and CBF fMRI, age-related differences were found, within subject, in the poststimulus undershoot using CBF but not in BOLD (Ances et al., 2009). This suggests that the underlying hemodynamic response of CBF and BOLD fMRI differ and the same HRF model may not be optimal. Therefore, with CBF fMRI, new hemodynamic response models, and therefore basis sets, will need to be developed to be specifically sensitive to this new imaging modality (Woolrich et al., 2006, Yang et al., 2000). This is a clear instance in which there is a need for a general approach to group-level analyses with basis functions.

This technical note presents an approach using the general linear modeling framework (i.e., using the SPM or FSL packages) to address the two main limitations of using a basis set: the need for model fitting restrictions and the need for a means of translating individual-level improvements in model fitting to higher-level analyses. The approach is straightforward and applicable to any basis set, allowing for flexible designations of physiological limitations, thereby correcting many of the difficulties presented when using basis sets. The specific normalizations of the design matrix required for this approach are calculated so that they may be performed after model estimation; therefore, no modifications are required to the design matrix as created by SPM or FSL. Furthermore, with such a general framework, it is possible to investigate more subtle questions regarding hemodynamic responses to neural activity. One potential application of this method will be to investigate the physiological origins of variations in the poststimulus undershoot measured with BOLD and CBF fMRI. An approach to addressing such a question is used as a specific example and laid out in detail later in the paper. Other applications will include the study of the spatial dynamics of BOLD responses to epileptic seizures (Lemieux et al., 2008) or investigation of the spatial variability of the temporal delay of BOLD responses. Data from a group of young participants engaged in a simple visual experiment are used to demonstrate the methods and software to implement the key calculations (for SPM or FSL) are posted at: http://cumc.columbia.edu/dept/sergievsky/cnd/steffener.html.

Section snippets

Participants

Ten young healthy volunteers (50% females; mean age = 23.9 years ± 5.4; education = 15.4 ± 2.4 years) participated in the fMRI study. The study was approved by the New York State Psychiatric Institute IRB and all subjects provided informed consent.

fMRI parameters

Scanning used a Philips Medical Systems Intera 1.5 T machine with echo planar imaging (EPI) capabilities (TR/TE = 3000/50 ms, flip = 90°, slice thickness = 5 mm (no gap), 32 slices, orientation angle of 30° to the AC–PC line, FOV = 20 × 20 cm, and a 64 × 64 matrix).

Results

The HDR estimates for the two visual cortex regions of interest demonstrate the variability that the derivative term captures (Fig. 4). For most participants, the mean time to peak was earlier than the primary basis function's time to peak (Table 2). Therefore, the additional regressor in the model mainly accounted for early occurring HDRs. The variability in the time to peak estimates was not significantly correlated with age, education, nor did it differ by gender in any of the regions.

The

Discussion

The method described here is a simple and straightforward general framework for taking advantage of the added flexibility of basis sets at the group level while avoiding problematic implausible results. Our method incorporates the potential increased response magnitude from using any basis set and allows for a flexible means of limiting results to predefined physiologically plausible ones.

This study showed that estimated hemodynamic responses in the visual cortex to the visual stimuli tended to

Acknowledgments

The authors are grateful to Martin Lindquist for helpful discussion and expertise. This research was supported by the National Institute of Aging, grant number 1K01AG21548 to M.H. Tabert.

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