On the distinguishability of HRF models in fMRI.

Paulo N Rosa,Carlos J Silvestre,Patricia Figueiredo

doi:10.3389/fncom.2015.00054

Abstract

Modeling the Hemodynamic Response Function (HRF) is a critical step in fMRI studies of brain activity, and it is often desirable to estimate HRF parameters with physiological interpretability. A biophysically informed model of the HRF can be described by a non-linear time-invariant dynamic system. However, the identification of this dynamic system may leave much uncertainty on the exact values of the parameters. Moreover, the high noise levels in the data may hinder the model estimation task. In this context, the estimation of the HRF may be seen as a problem of model falsification or invalidation, where we are interested in distinguishing among a set of eligible models of dynamic systems. Here, we propose a systematic tool to determine the distinguishability among a set of physiologically plausible HRF models. The concept of absolutely input-distinguishable systems is introduced and applied to a biophysically informed HRF model, by exploiting the structure of the underlying non-linear dynamic system. A strategy to model uncertainty in the input time-delay and magnitude is developed and its impact on the distinguishability of two physiologically plausible HRF models is assessed, in terms of the maximum noise amplitude above which it is not possible to guarantee the falsification of one model in relation to another. Finally, a methodology is proposed for the choice of the input sequence, or experimental paradigm, that maximizes the distinguishability of the HRF models under investigation. The proposed approach may be used to evaluate the performance of HRF model estimation techniques from fMRI data.

Highlights

The hemodynamic response function (HRF) describes the local changes in cerebral blood flow, volume, and oxygenation associated with neuronal activity, and it is extensively used to model Blood Oxygen Level Dependent (BOLD) signals measured using functional Magnetic Resonance Imaging (Logothetis and Wandell, 2004)
We extend the results in Silvestre et al (2010b), by first introducing the concept of absolutely inputdistinguishable systems and showing that, for systems with forced responses, the distinguishability between two models can be significantly affected by the shape and magnitude of the external input signals
We have addressed the problem of the distinguishability of Hemodynamic Response Function (HRF) models in the analysis of functional Magnetic Resonance Imaging (fMRI) data of brain activation, based on the biophysically informed description of the HRF as a nonlinear time-invariant input-state-output dynamic system

Summary

Introduction

The hemodynamic response function (HRF) describes the local changes in cerebral blood flow, volume, and oxygenation associated with neuronal activity, and it is extensively used to model Blood Oxygen Level Dependent (BOLD) signals measured using functional Magnetic Resonance Imaging (fMRI) (Logothetis and Wandell, 2004). Mapping of stimulus/task-related BOLD changes is most frequently achieved by fitting a general linear model (GLM) to the data, consisting on the stimulus/task time course convolved with a pre-specified HRF model (Friston et al, 1994), assuming a linear time invariant system (Boynton et al, 1996). Extensive HRF variability has been reported across brain regions (Handwerker et al, 2004), scanning sessions (Aguirre et al, 1998), tasks (Cohen and Ugurbil, 2002), physiological modulations (Liu et al, 2004), subjects (Handwerker et al, 2004), and populations (D’Esposito et al, 2003), which may hinder or confound the measurement of BOLD changes associated with brain activity, limiting the interpretability of fMRI studies

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Methods

Conclusion