Abstract

Functional near-infrared spectroscopy (fNIRS) is a noninvasive neuroimaging technique that uses low levels of light to measure changes in cerebral blood oxygenation levels. In the majority of NIRS functional brain studies, analysis of this data is based on a statistical comparison of hemodynamic levels between a baseline and task or between multiple task conditions by means of a linear regression model: the so-called general linear model. Although these methods are similar to their implementation in other fields, particularly for functional magnetic resonance imaging, the specific application of these methods in fNIRS research differs in several key ways related to the sources of noise and artifacts unique to fNIRS. In this brief communication, we discuss the application of linear regression models in fNIRS and the modifications needed to generalize these models in order to deal with structured (colored) noise due to systemic physiology and noise heteroscedasticity due to motion artifacts. The objective of this work is to present an overview of these noise properties in the context of the linear model as it applies to fNIRS data. This work is aimed at explaining these mathematical issues to the general fNIRS experimental researcher but is not intended to be a complete mathematical treatment of these concepts.

Highlights

  • Functional near-infrared spectroscopy is a noninvasive brain imaging technique that uses low levels of red to near-infrared light to measure changes in oxy- and deoxy-hemoglobin in the brain.[1]

  • This paper offered a review of the noise structures that are often observed in Functional near-infrared spectroscopy (fNIRS) data and the impact that this noise has on common statistical tests

  • We discussed the assumptions that the statistical regression models often make and how these assumptions can be violated by the properties of fNIRS such as serially correlated noise due to physiology or outliers to the normal noise distribution due to motion artifacts

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Summary

Introduction

Functional near-infrared spectroscopy (fNIRS) is a noninvasive brain imaging technique that uses low levels of red to near-infrared light to measure changes in oxy- and deoxy-hemoglobin in the brain.[1] Biological tissue in the range of around 650 to 900 nm (termed the “near-infrared window”) has low intrinsic absorption and allows light to remain detectable after passing through up to centimeters of tissue. In this wavelength range, tissue is highly turbid (scattering), which results in a stochastic and diffuse path as the photons migrate through the tissue. The number of fNIRS studies has been steadily growing over the last decade (see Ferrari and Quaresima[8] and Boas et al.[9] for reviews)

The Linear Model
Solving the Linear Model
Noise in Functional Near-Infrared Spectroscopy Is Nonspherical
The Noise in Functional Near-Infrared Spectroscopy Is Correlated
Functional Near-Infrared Spectroscopy Data Exhibits Heteroscedasticity
Noise Prewhitening
Noise Precoloring
Correcting Heteroscedastic Noise in Functional Near-Infrared Spectroscopy
Comparison of Methods
The Design Matrix for Functional Near-Infrared Spectroscopy Studies
The Deconvolution Finite-Impulse Response Model
The Canonical Model
Relationship of Finite-Impulse Response and Canonical Models
Findings
Conclusion

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