Nonlinear responses in fMRI: The balloon model, volterra kernels, and other hemodynamics

doi:10.1006/NIMG.2000.0630

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Nonlinear responses in fMRI: The balloon model, volterra kernels, and other hemodynamics

Journal Article•DOI•

Nonlinear responses in fMRI: The balloon model, volterra kernels, and other hemodynamics

Karl J. Friston¹, Andrea Mechelli¹, Robert Turner¹, Cathy J. Price¹•Institutions (1)

Queen's University¹

01 Oct 2000-NeuroImage (Neuroimage)-Vol. 12, Iss: 4, pp 466-477

TL;DR: The full hemodynamic model is presented, how its associated Volterra kernels can be derived, and the model's validity in relation to empirical nonlinear characterizations of evoked responses in fMRI and other neurophysiological constraints are addressed.

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About: This article is published in NeuroImage.The article was published on 2000-10-01. It has received 1115 citations till now. The article focuses on the topics: Volterra series & Nonlinear system identification.

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Journal Article•DOI•

Dynamic causal modelling.

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Karl J. Friston, Lee M. Harrison, William D. Penny

01 Aug 2003-NeuroImage

TL;DR: As with previous analyses of effective connectivity, the focus is on experimentally induced changes in coupling, but unlike previous approaches in neuroimaging, the causal model ascribes responses to designed deterministic inputs, as opposed to treating inputs as unknown and stochastic.

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4,182 citations

Cites background or methods from "Nonlinear responses in fMRI: The ba..."

...Four of these are of secondary importance and correspond to the state variables of the hemodynamic model presented in Friston et al. (2000)....
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...These equations have been described elsewhere (Friston et al., 2000) and constitute a hemodynamic model that embeds the Balloon–Windkessel model (Buxton et al....
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...These equations have been described elsewhere (Friston et al., 2000) and constitute a hemodynamic model that embeds the Balloon–Windkessel model (Buxton et al., 1998; Mandeville et al., 1999)....
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Journal Article•DOI•

Emerging concepts for the dynamical organization of resting-state activity in the brain

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Gustavo Deco¹, Viktor K. Jirsa², Viktor K. Jirsa³, Anthony R. McIntosh⁴•Institutions (4)

Pompeu Fabra University¹, Center for Complex Systems and Brain Sciences², Centre national de la recherche scientifique³, University of Toronto⁴

01 Jan 2011-Nature Reviews Neuroscience

TL;DR: Three large-scale neural system models of primate neocortex that emphasize the key contributions of local dynamics, signal transmission delays and noise to the emerging RSNs are reviewed.

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Abstract: A broad body of experimental work has demonstrated that apparently spontaneous brain activity is not random. At the level of large-scale neural systems, as measured with functional MRI (fMRI), this ongoing activity reflects the organization of a series of highly coherent functional networks. These so-called resting-state networks (RSNs) closely relate to the underlying anatomical connectivity but cannot be understood in those terms alone. Here we review three large-scale neural system models of primate neocortex that emphasize the key contributions of local dynamics, signal transmission delays and noise to the emerging RSNs. We propose that the formation and dissolution of resting-state patterns reflects the exploration of possible functional network configurations around a stable anatomical skeleton.

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1,544 citations

Journal Article•DOI•

Bayesian model selection for group studies.

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Klaas E. Stephan¹, William D. Penny¹, Jean Daunizeau¹, Rosalyn J. Moran, Karl J. Friston¹ - Show less +1 more•Institutions (1)

Wellcome Trust Centre for Neuroimaging¹

15 Jul 2009-NeuroImage

TL;DR: The hierarchical Bayesian approach is considerably more robust than either of the other approaches in the presence of outliers and is expected to prove useful for a wide range of group studies, not only in the context of DCM, but also for other modelling endeavours, e.g. comparing different source reconstruction methods for EEG/MEG.

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1,353 citations

Cites background from "Nonlinear responses in fMRI: The ba..."

...This is also known as the Laplace approximation, a full treatment of which can be found in Friston et al. (2007). For any approximation to the conditional density, the free-energy bound on the log-evidence can be re-written as a mixture of accuracy and complexity:...
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Journal Article•DOI•

HomER: a review of time-series analysis methods for near-infrared spectroscopy of the brain.

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Theodore J. Huppert¹, Solomon G. Diamond², Maria Angela Franceschini², David A. Boas²•Institutions (2)

University of Pittsburgh¹, Harvard University²

01 Apr 2009-Applied Optics

TL;DR: The practical implementation of various signal processing techniques for removing physiological, instrumental, and motion-artifact noise from optical data are described within the context of the MATLAB-based graphical user interface program, HomER, which is developed and distributed to facilitate the processing of optical functional brain data.

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Abstract: Near-infrared spectroscopy (NIRS) is a noninvasive neuroimaging tool for studying evoked hemodynamic changes within the brain. By this technique, changes in the optical absorption of light are recorded over time and are used to estimate the functionally evoked changes in cerebral oxyhemoglobin and deoxyhemoglobin concentrations that result from local cerebral vascular and oxygen metabolic effects during brain activity. Over the past three decades this technology has continued to grow, and today NIRS studies have found many niche applications in the fields of psychology, physiology, and cerebral pathology. The growing popularity of this technique is in part associated with a lower cost and increased portability of NIRS equipment when compared with other imaging modalities, such as functional magnetic resonance imaging and positron emission tomography. With this increasing number of applications, new techniques for the processing, analysis, and interpretation of NIRS data are continually being developed. We review some of the time-series and functional analysis techniques that are currently used in NIRS studies, we describe the practical implementation of various signal processing techniques for removing physiological, instrumental, and motion-artifact noise from optical data, and we discuss the unique aspects of NIRS analysis in comparison with other brain imaging modalities. These methods are described within the context of the MATLAB-based graphical user interface program, HomER, which we have developed and distributed to facilitate the processing of optical functional brain data.

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1,174 citations

Journal Article•DOI•

Modeling the hemodynamic response to brain activation.

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Richard B. Buxton¹, Kâmil Uludağ¹, David J. Dubowitz¹, Thomas T. Liu¹•Institutions (1)

University of California, San Diego¹

01 Jan 2004-NeuroImage

TL;DR: Quantitative modeling of the hemodynamic response, when combined with experimental data measuring both the BOLD and CBF responses, makes possible a more specific and quantitative assessment of brain physiology than is possible with standard BOLD imaging alone.

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1,161 citations

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References

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Open Access

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Journal Article•DOI•

Linear Systems Analysis of Functional Magnetic Resonance Imaging in Human V1

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Geoffrey M. Boynton¹, Stephen A. Engel¹, Gary H. Glover¹, David J. Heeger¹•Institutions (1)

Stanford University¹

01 Jul 1996-The Journal of Neuroscience

TL;DR: Results from three empirical tests support the hypothesis that fMRI responses in human primary visual cortex (V1) depend separably on stimulus timing and stimulus contrast, and the noise in the fMRI data is independent of stimulus contrast and temporal period.

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Abstract: The linear transform model of functional magnetic resonance imaging (fMRI) hypothesizes that fMRI responses are proportional to local average neural activity averaged over a period of time. This work reports results from three empirical tests that support this hypothesis. First, fMRI responses in human primary visual cortex (V1) depend separably on stimulus timing and stimulus contrast. Second, responses to long-duration stimuli can be predicted from responses to shorter duration stimuli. Third, the noise in the fMRI data is independent of stimulus contrast and temporal period. Although these tests can not prove the correctness of the linear transform model, they might have been used to reject the model. Because the linear transform model is consistent with our data, we proceeded to estimate the temporal fMRI impulse-response function and the underlying (presumably neural) contrast-response function of human V1.

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2,339 citations

Journal Article•DOI•

Analysis of fMRI time-series revisited--again.

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Keith J. Worsley¹, Karl J. Friston¹•Institutions (1)

Hammersmith Hospital¹

01 Sep 1995-NeuroImage

TL;DR: Correct results are presented that replace those of the previous paper and solve the same problem without recourse to heuristic arguments and a proper and unbiased estimator for the error terms are introduced.

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2,154 citations

"Nonlinear responses in fMRI: The ba..." refers methods in this paper

...Volterra kerels were estimated by expanding the kernels in terms f temporal basis functions and estimating the kernel oefficients up to second order using a generalised linar model (Worsley and Friston, 1995)....
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Journal Article•DOI•

Analysis of functional MRI time‐series

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Karl J. Friston¹, Peter Jezzard², Robert Turner²•Institutions (2)

The Neurosciences Institute¹, National Institutes of Health²

01 Jan 1994-Human Brain Mapping

TL;DR: A method for detecting significant and regionally specific correlations between sensory input and the brain's physiological response, as measured with functional magnetic resonance imaging (MRI), is presented in this paper.

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Abstract: A method for detecting significant and regionally specific correlations between sensory input and the brain's physiological response, as measured with functional magnetic resonance imaging (MRI), is presented in this paper. The method involves testing for correlations between sensory input and the hemodynamic response after convolving the sensory input with an estimate of the hernodynamic response function. This estimate is obtained without reference to any assumed input. To lend the approach statistical validity, it is brought into the framework of statistical parametric mapping by using a measure of cross-correlations between sensory input and hemodynamic response that is valid in the presence of intrinsic autocorrelations. These autocorrelations are necessarily present, due to the hemodynamic response function or temporal point spread function.

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1,748 citations

"Nonlinear responses in fMRI: The ba..." refers methods in this paper

...We have presented previously a model-free characterization of these effects using generic techniques from nonlinear system identification, namely a Volterra series formulation....
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...In Friston et al. (1994) we presented a linear model of hemodynamic responses in fMRI time-series, wherein underlying neuronal activity (inferred on the basis of changing stimulus or task conditions) is convolved, or smoothed with a hemodynamic response function....
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Journal Article•DOI•

Dynamics of blood flow and oxygenation changes during brain activation: the balloon model.

[...]

Richard B. Buxton¹, Eric C. Wong¹, Lawrence R. Frank¹•Institutions (1)

University of California, San Diego¹

01 Jun 1998-Magnetic Resonance in Medicine

TL;DR: Calculations based on the model show pronounced transients in the deoxyhemoglobin content and the blood oxygenation level dependent (BOLD) signal measured with functional MRI, including initial dips and overshoots and a prolonged post‐stimulus undershoot of the BOLD signal.

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Abstract: A biomechanical model is presented for the dynamic changes in deoxyhemoglobin content during brain activation. The model incorporates the conflicting effects of dynamic changes in both blood oxygenation and blood volume. Calculations based on the model show pronounced transients in the deoxyhemoglobin content and the blood oxygenation level dependent (BOLD) signal measured with functional MRI, including initial dips and overshoots and a prolonged poststimulus undershoot of the BOLD signal. Furthermore, these transient effects can occur in the presence of tight coupling of cerebral blood flow and oxygen metabolism throughout the activation period. An initial test of the model against experimental measurements of flow and BOLD changes during a finger-tapping task showed good agreement.

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1,693 citations

"Nonlinear responses in fMRI: The ba..." refers background or methods in this paper

...At the same time Buxton and colleagues developed a mechanistically compelling model of how evoked changes in blood flow were transformed into a blood oxygenation level dependent (BOLD) signal (Buxton et al., 1998)....
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...The Balloon model (Buxton and Frank, 1997; Buxton et al., 1998) is an input-state-output model with twostate variables volume (v) and deoxyhemoglobin content (q)....
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...It aims to: (i) show that the Balloon/Windkessel model (Buxton and Frank, 1997; Buxton et al., 1998; Mandeville et al., 1999) is sufficient to account for nonlinearities in event-related responses that are seen empirically and (ii) describe a nonlinear dynamical model that couples changes in…...
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...In this section we describe the data used to estimate the Volterra kernels....
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...In this paper we combine these system identification and model-based approaches and ask whether the Balloon model is sufficient to account for the nonlinear behaviors observed in real time series....
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Journal Article•DOI•

The Effects of Changes in PaCO2 Cerebral Blood Volume, Blood Flow, and Vascular Mean Transit Time

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Robert L. Grubb, Marcus E. Raichle, John O. Eichling¹, Michel M. Ter-Pogossian¹•Institutions (1)

Washington University in St. Louis¹

01 Sep 1974-Stroke

TL;DR: The relationships between cerebral blood volume (CBV), cerebral blood flow (CBF), and the cerebral vascular mean transit time (t®v) during acute changes in the PaCO2 over a range of 15 to 76 torr were investigated in vivo in rhesus monkeys by serially determining themean transit time of a vascular tracer, 15O-labeled carboxyhemoglobin, and the mean transitTime of a diffusible tracer

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Abstract: The relationships between cerebral blood volume (CBV), cerebral blood flow (CBF), and the cerebral vascular mean transit time (t v ) during acute changes in the PaCO 2 over a range of 15 to 76 torr were investigated in vivo in rhesus monkeys by serially determining the mean transit time of a vascular tracer, 15 O-labeled carboxyhemoglobin, and the mean transit time of a diffusible tracer, 15 O-labeled water. Over this range of PaCO 2 , a significant linear relationship of CBV = 0.041 PaCO 2 + 2.0 was found. For each one torr change in PaCO 2 , there is a change in CBV of 0.041 ml/100 gm of perfused tissue. At a normocarbic value of PaCO 2 (37 torr), an average value of 3.5 ml/100 gm was found. A nonlinear relationship of CBV and CBF was found. This relationship is expressed in the equation, CBV = 0.80 CBF 0.38 . A significant linear relationship was found between CBF and PaCO 2 . This was described by the equation, CBF = 1.8 PaCO 2 - 16.75. For each one torr change in the PaCO 2 , there is a 1.8 ml/100 gm per minute change in the CBF. At a normocarbic value of PaCO 2 (37 torr), an average value of CBF of 50 ml/100 gm per minute was found. The relationship of CBV and t v was nonlinear and was expressed in the equation, t C15O = 41 CBF -0.62 .

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1,021 citations

"Nonlinear responses in fMRI: The ba..." refers background in this paper

...The critical questions this section addresses are (i) “can the hemodynamic model account for the form of empirical kernels up to second order?” and (ii) “are the model parameters required to do this physiologically plausible?”...
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...At steady state empirical results from PET suggest a ' 0.38 (Grubb et al., 1974)....
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