Nonparametric Estimation of Hemodynamic Response Function: A Frequency Domain Approach

Bai, Ping; Truong, Young K.; Huang, Xuemei

doi:10.1214/09-lnms5712

Cited by 11 publications

(13 citation statements)

References 39 publications

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“…3. It will be interesting to compare our procedure when it is adapted to the spatio-temporal regularization method [17], the nonparametric method based on orthonormal causal Laguerre polynomials [14], the wavelet approach [12], the spline method [19], and the coherence based method [1]. 4.…”

Section: Discussionmentioning

confidence: 99%

“…There is spatio-temporal regularization method [17], nonparametric methods such as those based on orthonormal causal Laguerre polynomials [14], wavelet approach [12], spline methods [5; 19; 18], and the frequency domain coherence based method [1]. There are also data-driven and model-driven methods [9; 13].…”

Section: Figure 2 a Block Design Stimulus S(·) (Left) A Model Of Thmentioning

confidence: 99%

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Adaptive statistical parametric mapping for fMRI

Bai

Huang

Shen

et al. 2010

Statistics and Its Interface

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Brain activity is accompanied by changes in cerebral blood flow (CBF) and the differential blood oxygenation that are detectable using functional magnetic resonance imaging (fMRI). The process of identifying brain activation regions can be facilitated by estimating the hemodynamic response function (HRF). There have been some remarkable new developments in statistics to handle this problem. In this paper, we introduce a novel procedure which is capable of adapting itself to any of the existing methods by improving its performance through the application of a penalized smoothing technique. Using a computer experiment and a real fMRI data set, the proposed procedure is assessed by comparing its performance very favorably to the popular SPM based method.

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Section: Discussionmentioning

confidence: 99%

Section: Figure 2 a Block Design Stimulus S(·) (Left) A Model Of Thmentioning

confidence: 99%

Adaptive statistical parametric mapping for fMRI

Bai

Huang

Shen

et al. 2010

Statistics and Its Interface

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“…Model (1) without the term of the 2nd-order Volterra kernel is the GLM (Friston et al, 1995). There is a vast literature on the estimation of the HRF h i,k ( t ), including parametric methods (e.g., Worsley and Friston, 1995; Friston et al, 1998a; Glover, 1999; Henson et al, 2002; Riera et al, 2004; Lindquist and Wager, 2007; Lindquist et al, 2009) and nonparametric methods (e.g., Aguirre et al, 1998; Dale, 1999; Lange et al, 1999; Woolrich et al, 2004; Zarahn, 2002; Vakorin et al, 2007; Bai et al, 2009; Wang et al, 2011). Estimation of V i , k 1 k 2 ( t 1 , t 2 ) is more challenging than that of the HRF, because the Volterra kernel function, defined on the two-dimensional space, involves many more parameters, while the number of observations, T , for each subject is usually limited.…”

Section: Methodsmentioning

confidence: 99%

A semi-parametric nonlinear model for event-related fMRI

Zhang

Gonzalez

et al. 2014

NeuroImage

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Nonlinearity in evoked hemodynamic responses often presents in event-related fMRI studies. Volterra series, a higher-order extension of linear convolution, has been used in the literature to construct a nonlinear characterization of hemodynamic responses. Estimation of the Volterra kernel coefficients in these models is usually challenging due to the large number of parameters. We propose a new semi-parametric model based on Volterra series for the hemodynamic responses that greatly reduces the number of parameters and enables “information borrowing” among subjects. This model assumes that in the same brain region and under the same stimulus, the hemodynamic responses across subjects share a common but unknown functional shape that can differ in magnitude, latency and degree of interaction. We develop a computationally-efficient strategy based on splines to estimate the model parameters, and a hypothesis test on nonlinearity. The proposed method is compared with several existing methods via extensive simulations, and is applied to a real event-related fMRI study.

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“…Specifically, in the frequency domain, MASM assumes that

ϕ_{Y} (f, d) = < ϕ_{boldH} (f, d), ϕ_{boldX} (f) > + ϕ_{ε} (f, d),

where ϕ H ( f, d ) = (ϕ H 1 ( f, d ),…, ϕ H m ( f, d )) T , ϕ X ( f ) = (ϕ X 1 ( f ),…, ϕ X m ( f )) T . An advantage of MASM in (2) is that the temporal correlation structure can be reduced since the Fourier coefficients are approximately asymptotically uncorrelated across frequencies under some regularity conditions [8,1]. Moreover, ϕ ε ( f, d ) is assumed to be a complex process with the zero mean function and a finite spatial covariance structure.…”

Section: Model Formulationmentioning

confidence: 99%

Adaptively and Spatially Estimating the Hemodynamic Response Functions in fMRI

Wang

Zhu

Fan

et al. 2011

Lecture Notes in Computer Science

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Abstract.In an event-related functional MRI data analysis, an accurate and robust extraction of the hemodynamic response function (HRF) and its associated statistics (e.g., magnitude, width, and time to peak) is critical to infer quantitative information about the relative timing of the neuronal events in different brain regions. The aim of this paper is to develop a multiscale adaptive smoothing model (MASM) to accurately estimate HRFs pertaining to each stimulus sequence across all voxels. MASM explicitly accounts for both spatial and temporal smoothness information, while incorporating such information to adaptively estimate HRFs in the frequency domain. One simulation study and a real data set are used to demonstrate the methodology and examine its finite sample performance in HRF estimation, which confirms that MASM significantly outperforms the existing methods including the smooth finite impulse response model, the inverse logit model and the canonical HRF.

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Nonparametric Estimation of Hemodynamic Response Function: A Frequency Domain Approach

Cited by 11 publications

References 39 publications

Adaptive statistical parametric mapping for fMRI

Adaptive statistical parametric mapping for fMRI

A semi-parametric nonlinear model for event-related fMRI

Adaptively and Spatially Estimating the Hemodynamic Response Functions in fMRI

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