Signal processing for functional near-infrared neuroimaging

Signal processing for functional near-infrared neuroimaging

A Thesis

Submitted to the Faculty

of

Drexel University

By

Ajit Devaraj

in partial fulfillment of the

requirements for the degree

of

Master of Science in Electrical Engineering

June 2005

© Copyright 2005

Ajit Devaraj. All Rights Reserved.

ii

Dedications

To my mother

Shylaja Devaraj

iii

ACKNOWLEDMENTS

I have only the deepest gratitude and respect for my advisors Drs. Banu Onaral

and Kambiz Pourrezaei. It is solely due to them that I had this incredible opportunity to

work on a cutting edge neuroimaging modality. I have learnt a lot from them and not just

about signal processing and research. This experience will have a lasting influence on my

life.

My special thanks to Dr. Scott C. Bunce for serving on my committee. A

discussion with Dr. Bunce never failed to leave me with an exciting new train of thought.

It has been a pleasure working with him.

Meltem and Kurtulus Izzetoglu have been an immense source of expert guidance

and support throughout my stay with the fNIR brain imaging group. Their belief in me

has buoyed me up time and again.

My parents and sister have always been a source of strength and love, particularly

during my stay in Philadelphia. I could not have done much without their support.

iv

TABLE OF CONTENTS

LIST OF TABLES................................................................................................. vi

LIST OF FIGURES .............................................................................................. vii

ABSTRACT........................................................................................................... ix

1. INTRODUCTION .............................................................................................1

1.1. Brain Imaging: An Overview .....................................................................1

1.2. Motivation...................................................................................................3

1.3. My Thesis ...................................................................................................4

2. OPTICAL BRAIN IMAGING ..........................................................................6

2.1. NIR Light Propagation in Tissue and Neuroimaging .................................6

2.2. Modified Beer Lambert Law ......................................................................8

2.3. Current Instrumentation............................................................................12

2.4. Traditional Analysis Algorithms for Neuroimaging.................................14

2.5. Experimental Paradigms for Neuroimaging .............................................16

2.6. Neurovascular Coupling: A Closer Look .................................................18

3. PRE-PROCESSING FOR SIGNAL CONDITIONING..................................24

3.1. Motion Artifact .........................................................................................24

3.1.1. Data Collection ..............................................................................25

3.1.2. Cancellation Algorithm..................................................................26

3.1.3. Results............................................................................................30

3.1.4. Discussion......................................................................................34

3.2. Vascular Artifacts .....................................................................................35

3.2.1. Data Collection ..............................................................................36

3.2.2. Extraction Algorithm .....................................................................36

v

3.2.3. Results............................................................................................38

3.2.4. Discussion......................................................................................39

3.3. Outlier Elimination ...................................................................................40

3.3.1. Data Collection ..............................................................................41

3.3.2. Method ...........................................................................................41

3.3.3. Results............................................................................................42

3.3.4. Discussion......................................................................................44

4. FEATURES EXTRACTION FOR SINGLE TRIAL ANALYSIS .................46

4.1. The Data....................................................................................................47

4.2. Method......................................................................................................47

4.3. Results.......................................................................................................48

4.4. Discussion.................................................................................................54

5. CONCLUSION AND FUTURE WORK ........................................................58

5.1. Conclusion ................................................................................................58

5.2. Future Work..............................................................................................59

LIST OF REFERENCES.......................................................................................61

APPENDIX A: SPECTRAL SIGNATURE OF EROS.........................................66

vi

LIST OF TABLES

3.1 Sample of the SNR gain and CC∆ results for Wiener and LMS filter..................30

3.2 Results of the t test for the Wiener filtering results in the stationary protocol ......30

3.3 SNR gain (dB) in the ambulatory protocol for the 3 subjects................................33

3.4 p-values (<0.01) after data analysis without outlier elimination ...........................42

3.5 p-values (<0.01) after data analysis with outlier elimination ................................43

vii

LIST OF FIGURES

1.1 The functional brain map .........................................................................................1

2.1 Shining a flash light through one’s hand .................................................................7

2.2 Absorption factors of various chromophores vs. wavelength..................................7

2.3 Light propagation through brain ..............................................................................8

2.4 cwfNIR source-detector geometry...........................................................................9

2.5 Experimental setup.................................................................................................12

2.6a Close up of the probe .............................................................................................13

2.6b Probe geometry showing the 16 voxels .................................................................14

2.7 Close up of probe placement on forehead..............................................................14

2.8 Imaged sites on the PFC ........................................................................................14

2.9 Popular experimental paradigms............................................................................17

2.10 Time evolution of tissue oxygenation in cerebral cortex. Dotted region indicates stimulus onset and duration. Solid black line represents oxygen response averaged across 72 trials and the dashed lines represent 1 SD of the mean. [J. K. Thompson et al, 2003] .............................................................................................................19

2.11 The initial dip in tissue oxygenation (light) is due to increased neural activity whereas the subsequent rise in tissue oxygenation (dark) reflects an increased blood flow. [J. Mayhew, 2003]..............................................................................20

2.12 Representative time course of oxyHb and deoxyHb following neural activation [M. Jones et al, 2001] ............................................................................................21

2.13 Spectral signature of the measured optical signal following a stimulus................23

3.1 LMS Filter structure...............................................................................................28

3.2 Wiener filtering results: From the top panel slow, medium and fast movement ...31

3.3 LMS filtering results: From the top panel slow, medium and fast movement ......32

3.4 Wiener filtering results for two random segments in the ambulatory protocol .....33

3.5 Sample results from the filtering algorithm. Top panel – time course; Bottom Panel – PSD Spectrum...........................................................................................38

viii

3.6 Sample results from the filtering algorithm. Top panel – time course; Bottom Panel – PSD Spectrum...........................................................................................39

3.7 Analysis results without outlier elimination registered on the brain .....................43

3.8 Analysis results with outlier elimination registered on the brain ..........................44

3.9 Possible 2-D Feature space ....................................................................................45

4.1 Parameter ia for 9s pre-stimulus segment (Subject A) .........................................48

4.2 Parameter ib for varying pre-stimulus segment (Subject B). From the top panel 6s and 9s .....................................................................................................................50

4.3 Parameter ib for subject C ......................................................................................52

4.4 ROC curve for voxel 9 computed across 10 subjects. Area under the curve = 0.947710.................................................................................................................55




4.8 Blood pressure in each section of the systemic and pulmonary circulations [J.Ross, 2005].........................................................................................................57

A.1 Time course of ( )tΓ ..............................................................................................66

A.2 Frequency spectrum of ( )tΓ .................................................................................67

ix

ABSTRACT Signal processing for functional near-infrared neuroimaging

Ajit Devaraj Dr. Banu Onaral and Dr. Kambiz Pourrezaei

Functional near infrared imaging (fNIRi) is an optical brain imaging modality

based on the multi-wavelength absorption spectroscopy using near infrared light with the

neuro-physiological underpinning governed by the neurovascular coupling. It is the state-

of-the-art in achieving a good balance between the spatial resolution (the two smallest

adjacent regions that can be significantly distinguished) and the temporal resolution (the

images have to be acquired in real time at a rate comparable to the time evolution of the

neural response) while minimally constraining the subject. These factors are crucial in

deciding the impact of a brain imaging modality.

Signal processing algorithms for optimally processing the recorded data are an

essential aspect in the success of any brain imaging technology. Since fNIRi is a

relatively young modality (neurovascular coupling was directly confirmed only in 2003),

most of the research has concentrated on validation, developing better engineering

solutions, improving the SNR and understanding the physics behind the process. This

work aims at laying the ground work for a signal theoretic approach for processing fNIRi

data. The focus is on developing an understanding of the spectral signature of the signal

based on underlying physiology, artifact suppression schemes for cleaning the data,

outlier elimination and extraction of features to pave the way for the powerful single trial

data analysis schemes.

The spectrum of a typical fNIR signal has 4 bands – B waves, M waves,

respiration and arterial pulsation (heart beat). The neural response is embedded in the B

x

and M waves bands. The knowledge of the physiological basis of these signals provide a

sense of the stationarity of the signal and help in the interpretation of the results; making

it vital for the development of any advanced algorithm.

fNIR signals are corrupted by three major artifacts – motion, respiration and

arterial pulsation and measurement outliers. We present a general adaptive frame work

based on the Wiener filter to suppress the motion artifact. The respiration and arterial

artifacts are handled by estimating the PSD of the signal of interest which is then used to

generate an artifact suppression filter. The Measurement outliers are identified via 2

specifically selected features. The efficacy of all these algorithms is demonstrated on

actual data.

The robustness of the analysis is directly dependent on the chosen experimental

protocol which in turn depends on the information that can be extracted from the

recorded signal. We present new features which can potentially be used in single trial

analysis – a class of powerful analysis schemes that allow innovative experimental

design. As a first step towards the validation of their utility, these features are used in the

single trial detection of visual odd ball task. To our best knowledge this is the first

attempt at single trial analysis for fNIRi.

Together these algorithms constitute a gateway for further development of

advanced signal processing schemes for fNIR imaging.

1

1. INTRODUCTION

1.1 Brain Imaging: An Overview

Generating a valid and robust human brain map is at the heart of all brain imaging

research. Human brain maps identify areas of the brain activation in response to specific

stimuli. A good brain map has far reaching effects – it can help understand the neural

circuitry responsible for deception (hence detect deception) to making early detection of

brain disease possible. Figure 1.1 gives an overview of the current human brain map. As

indicated the prefrontal cortex (PFC) is the seat of executive process in the brain [Amen

Clinics, 2005; D. T. Stuss and M. P. Alexander, 2000; E. E. Smith and J. Jonides, 1999].

Figure1.1 The functional brain map

2

An improved understanding of PFC will help investigate human problem solving, the

ability to feel and express emotions, critical thinking, short attention span and poor

judgment [Amen Clinics, 2005] and even help address issues like deception.

The intense advancement in the field of human brain mapping has been largely

fueled by the advent of functional neuroimaging modalities like fMRI, PET (indirect

imaging technologies based on hemodynamic manifestation of neural activity) and MEG,

EEG (direct imaging technologies based on electric/magnetic manifestation of neural

activity). Functional imaging is primarily used for brain mapping and exploring the

neural architecture at the macroscopic level. These objectives necessitate that ideally

neuroimaging modalities possess high spatial and temporal resolution. But most of the

fore mentioned techniques are at either end of the scale i.e. possess high temporal

resolution but lack spatial resolution (MEG, EEG) or vice versa (fMRI, PET).

Continuous wave functional near-infrared (cwfNIR) imaging is a multi-

wavelength optical spectroscopy technique introduced as a noninvasive neuroimaging

modality in the recent past [B. Chance et al, 1993; A. Villringer et al, 1993]. Ability to

capture the temporal evolution of the neural response makes it a functional neuroimaging

modality [H. Obrig et al, 1996]. The technique primarily banks on local cerebral

hemodynamics, in particular the blood oxygenation, as a true and reliable functional

correlate of neural activity. The relationship between cerebral hemodynamics and neural

activity is known as neurovascular coupling [A. Villringer et al, 1995; M. Jueptner and C.

Weiller, 1995] and forms the basis of most other indirect imaging modalities.

cwfNIR imaging is the state-of-art in providing a good practical balance between

temporal and spatial resolution – it has temporal resolution in the order of seconds and a

3

spatial resolution in the order of centimeters. The technology permits a compact even

wireless hardware implementation [A. Bozkurt, 2004; G. Yurtsever et al, 2003], making

the modality highly portable and minimally intrusive. With this cwfNIR brings together

some characteristics that are usually mutually exclusive in a neuro imaging modality – it

is non-invasive, portable, minimally-intrusive and provides good spatio-temporal

resolution i.e. it is an ideal tool for neuroscience studies in the field and clinic. It is

particularly effective in imaging the PFC and hence in studying human cognition. It has

also been used to investigate the linearity of the neurovascular coupling [P. Wobst et al,

2001], explore the cortical functional architecture [R. D. Frostig et al, 1990] and there are

strong indications that it can used to study the autorregulation mechanism of cerebral

blood flow [H. Obrig et al, 2000].

1.2 Motivation

cwfNIR is a promising technology all set to carve a niche for itself as the

modality of choice for safe non-invasive, portable and minimally-intrusive neuroimaging.

However the raw signal is corrupted by various artifacts, the functional activation

information needs to be extracted from the signal and the conclusion drawn must be

check for statistical significance. All of which call for signal processing algorithms.

Signal processing has always been a necessary element for the success of any

neuroimaging modality. Resolving functional correlates in the presence of distortion

requires advanced data processing. The need is felt again when trying to extract these

correlates from the spatio-temporal datasets. The real power of signal processing lies in

the exploratory analysis algorithms which resolve and/or extract the correlates with little

input from the experimental paradigm, like ICA, unsupervised learning and cluster

4

analysis. Over the years such algorithms have been developed for other modalities like

fMRI and EEG. They have significantly improved the reach of these modalities both in

terms of broadening the application areas and in achieving better results. However due to

inherent differences in the signal origin and information content these schemes have to be

redeveloped to suit each modality.

Since cwfNIR is an emerging technology most of the research is concentrated on

signal validation, study of the signal origin and possible application areas. This has

created a lack of signal processing algorithms tailor made for cwfNIR. The development

of such algorithms will broaden the scope of deployment and open the doors to more

involved studies.

1.3 My Thesis

This work is a first step towards developing advanced signal processing

algorithms custom made for cwfNIR imaging. It presents optimized pre-processing

algorithms – adaptive artifact suppression schemes for both motion and vascular artifacts

and an improved outlier elimination algorithm. These algorithms increase the SNR

helping improve the power and robustness of fNIR imaging. They have a direct impact

on the deployment areas of the technology.

Also presented here is a novel features and its extraction algorithm that open the

possibility of single trial analysis for cwfNIR. The ability to draw detect/estimate the

neural activation in one trial is a coveted ability in any neuroimaging modality. The

resulting flexibility in designing the experimental paradigms permits the study of various

new neural events.

5

The emphasis is on algorithm development and validation hence the implementation is

offline. Chapter 2 provides a closer look at optical brain imaging – the physical and

working principle behind cwfNIR, the current hardware and the underlying neuro-

physiological basis of imaging. It also introduces the basics of neuroimaging –

experimental paradigms, protocols and differential imaging. It establishes the spectral

signature of the signal of interest which guides all the subsequent algorithms. Chapter 3

describes the pre-processing schemes and associated results. Chapter 4 introduces the

features for single trial analysis and presents their extraction algorithm. Appendix A

illustrates the spectral analysis of the event related optical signal.

6

2. OPTICAL BRAIN IMAGING

2.1 NIR Light Propagation in Tissue and Neuroimaging

Light propagation in tissue is governed by photon scattering and absorption. The

overall effect of absorption is a reduction in the intensity of the light beam traversing the

medium. The relationship between the absorption of light in a purely absorbing medium

and the structure and pigments present in the medium is given by the Beer Lambert law.

Scattering is the basic physical process by which light interacts with matter. Changes in

internal light distribution, polarization, and reflection can be attributed to the scattering

processes. Since scattering increases the optical path length of light propagation, photons

spend more time in the tissue than with no scattering thus changing the absorption

characteristics of the medium. Light propagation in a turbid (scattering) medium can be

modeled by the modified Beer Lambert law (MBLL).

The electromagnetic spectrum has two unique characteristics in the NIR range

(700nm-900nm). First, biological tissues weakly absorb NIR light allowing it to penetrate

several centimeters through the tissue and still be detected. As shown in figure 2.1 the

reddish hue with which a white flash light exits when shined through one’s hand

demonstrates this physical property. More crucially the dominant chromophores (light

absorbing molecules) in the NIR window are oxy-haemoglobin (oxyHb) and deoxy-

haemoglobin (deoxyHb). The principle chromophores in tissue are water (typically 80%

in brain tissue), lipids, melanin and haemoglobin [H. Q. Woodard and D. R. White,

1986]. The absorption spectrum of lipids closely follows that of water and melanin

though an effective absorber contributes only a constant attenuation. The graph in figure

7

2.2 [B. L. Horecker, 1943; A. Yodh and B. Chance, 1995] clearly indicates that water is

‘transparent’ to NIR light. Thus spectroscopic interrogation of tissue relies on oxyHb and

deoxyHb as the biologically relevant markers and neurovascular coupling allows their

absorption spectra to reliably track neural activity.

Figure 2.1 Shining a flash light through one’s hand

Figure 2.2 Absorption factors of various chromophores vs. wavelength

8

Based on the type of information retrieved, currently there are three variants of

NIR imaging - time resolved (TRS), frequency domain (FD) and continuous wave (CW)

techniques. A. Villringer and B. Chance, 1997 and G. Strangman et al, 2002 give a

review of the various systems, their comparison, experimental setup and applications.

This work is solely concerned with the CW system. However all the variants are based on

the same concept – NIR light is shined onto the scalp and is detected as it exits the head

(figure 2.3). The absorption spectrum is then used to extract information regarding neural

activity.

Figure 2.3 Light propagation through brain

2.2 Modified Beer Lambert Law

The geometry of the light propagation in the brain is shown in figure 2.3 and

depicted in more detail in figure 2.4. The fractions of the incident light that are remitted,

scattered and absorbed depend on the optical properties of the tissue. The amount of

absorption is directly dependent on the chromophore concentration. The optical path

9

taken by remitted photons is an characteristic “banana shape” whose dimensions,

particularly the depth of penetration L , are dictated by the source-detector separation d .

Figure 2.4 cwfNIR source-detector geometry

cwfNIR recordings are basically quantified trend measurements. It does not

attempt to predict the absolute oxygen level at any given time, but track neural activity by

recording the oxygen level changes with time. The theoretical basis of this method is the

MBLL [D. T. Delpy et al, 1988]. Applying MBLL to the source-detector geometry in

figure 2.4 we obtain,

010log IA c d DPF G

Iλ λε⎛ ⎞= ≈ ⋅ ⋅ ⋅ +⎜ ⎟⎝ ⎠

(2.1)

Where

Aλ Light intensity attenuation for wave length λ expressed in terms of optical density (OD), 1OD corresponds to a 10 fold reduction

0,I I Input and output light intensity respectively

10

λε Absorption factor/specific absorption coefficient/ extinction coefficient for wavelengthλ . It is defined as the numbers of ODs of attenuation produced by the absorber at a concentration of 1 µ M and over a physical path of 1cm, hence the dimensions ODcm-1µ M-1

c Concentration of the chromophore in terms of µ M (micro moles)

d Distance between the source and detector in terms of cm

DPF Differential pathlength factor, a dimension less constant to account for photon path lengthening effect of scattering

G Additive term for fixed scattering losses

Since only the changes in oxygen level at any given time t with respect to that at

an arbitrary time instant 0t = (called the baseline) are required, eqn. 2.1 can be modified

as

( )( )

010

0

log0

I tA c d DPF

Iλ λε⎛ ⎞

∆ = = ∆ ⋅ ⋅ ⋅⎜ ⎟⎜ ⎟⎝ ⎠

(2.2)

The two chromophores oxy and deoxy haemoglobin can then be taken into account by

( )( )

20

1010

log0 i i

i

I tA c d DPF

Iλ λε=

⎛ ⎞ ⎛ ⎞∆ = = ∆ ⋅ ⋅ ⋅⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠

∑ (2.3)

A similar measurement at another wavelength is needed to solve for the two ic∆ , turning

the eqn. 2.3 into a matrix-vector equation

1 1

1 11

2 2 2

2 2

1oxyHb deoxyHb

oxyHb

deoxyHboxyHb deoxyHb

cDPF DPFAcA d

DPF DPF

λ λ

λ λλ

λ λ λ

λ λ

ε ε

ε ε

⋅ ⋅

⋅ ⋅

⎡ ⎤⎢ ⎥ ∆∆ ⎡ ⎤⎡ ⎤ ⎢ ⎥= ⎢ ⎥⎢ ⎥ ⎢ ⎥ ∆∆⎣ ⎦ ⎣ ⎦⎢ ⎥⎢ ⎥⎣ ⎦A C

ε

(2.4)

11

Careful selection of the wavelengths will result in a nonsingular ε allowing

solution by direct matrix inversion. K. Uludag et al, 2004 discuss the possible optimal

combinations of wavelength for NIRS. The final two measures oxygenation (oxy) and

blood volume (bv) are extracted from the ic∆ as

oxyHb deoxyHboxy c c= ∆ −∆ (2.5)

oxyHb deoxyHbbv c c= ∆ + ∆ (2.6)

Dimensions of both Oxy and Bv are in µ M. As a general guideline DPF can be assumed

to be 6 [Duncan et al, 1996]. A more accurate value accounting for its dependence on

wavelength is give by [D. A. Boas et al, 2002],

( )

1 2'

1 2'

31 112 1 3

s

a s a

DPFd

λλ

λ λ λ

µµ µ µ

⎡ ⎤⎛ ⎞ ⎢ ⎥= −⎜ ⎟ ⎢ ⎥+⎝ ⎠ ⎣ ⎦ (2.7)

Where

'sλµ Reduced scattering coefficient of blood at wavelength λ

aλµ Absorption coefficient of blood at wavelength λ

An in depth discussion of the physics behind the tissue-light interaction and its

application to optical imaging can be found in V.V. Tuchin et al, 2002 and V.V. Tuchin,

2000. Information on optical characteristics of brain tissue can be found in P. van der Zee

et al, 1993; S. Wray et al, 1987 and W. Cheong et al, 1990.

The depth of light penetration (L in figure 2.4) plays a pivotal role in the

information content of the extracted signal. A good rule of thumb for maxL , based on light

transmission in homogenous tissue, is 3d . However optical neuroimaging involves light

propagation through layers of heterogeneous tissue with cerebrospinal fluid (CSF) greatly

12

influencing the depth of light penetration. E. Okada et al, 1997 and M. Firbank et al,

1997 give a detailed analysis of signal contribution from the various tissues of adult head.

2.3 Current Instrumentation

The system currently uses the wavelengths 730nm and 850nm. An overview of

the typical experimental setup is as shown in figure 2.5. The dashed line indicates an

option used in some experimental paradigms.

Figure 2.5 Experimental setup

The actual data acquisition is achieved through a 12 bit ADC at the rate of two

images per second on a National Instruments multifunction PCMCIA data acquisition

card (DAQ 1200). This card also generates the drive currents for the LED NIR sources on

the probe and switching signals for the control box. The control box consists of switching

circuits for time division multiplexing of shined wavelength and a particular source-

13

detector combination. To time synchronize fNIR recordings w.r.t. the task events a

communication link via a serial/parallel port is established between the data acquisition

computer and the task presentation computer.

The current probe is expressly designed to image the PFC. With 4 LED light

sources and 10 photo detectors and a source-detector separation of 2.5 cm, the probe can

image 16 voxels in total (figure 2.6b). It consists of two parts: a reusable, flexible circuit

board that carries the necessary infrared sources and detectors, and a disposable, single-

use cushioning material with a medical grade double sided sticky tape that serves to place

the probe on the subject’s forehead securely and easily. The flexible circuit provides a

reliable, integrated wiring solution, as well as consistent reproduction of component

spacing and alignment. Since the circuit board and cushioning materials are flexible, the

probe can adapt to the contours of the subject’s head, allowing the sensor elements to

maintain an orthogonal orientation to the skin surface, improving optical coupling

efficiency and signal strength. A close up of the probe and the probe placement are

shown in figures 2.6a and 2.7 respectively. Figure 2.8 is an accurate depiction of the sites

on the PFC imaged by the system.

Figure 2.6a Close up of the probe

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Figure 2.6b Probe geometry showing the 16 voxels

Figure 2.7 Close up of probe

placement on forehead

Figure 2.8 Imaged sites on the PFC

2.4 Traditional Analysis Algorithms for Neuroimaging

The brain as a system is in a constant state of flux, it never stops responding to

stimuli both intrinsic and extrinsic. Even when cleaned of physiological and measurement

15

artifacts the amount of spontaneous neural activity (background activity) at any given

brain location at any given time is overwhelming. However the object of interest for brain

studies is the neural activity specific to the presented stimuli. This is referred to as the

event related activation (ERA). In the context of optical imaging ERA is known as event

related optical signal (EROS). The term evoked response is also used interchangeably

with ERA/EROS. Typical SNR of the ERA (signal level of ERA w.r.t. background

activity) is ( )310O − . This has to be accounted for in the data analysis paradigms.

Data analysis is based on the assumed theory of brain function - either functional

specialization (each brain region specializes in one function only) or functional

integration (a group of brain regions work in tandem to respond to a task). Accordingly

there are two analysis paradigms – the subtraction paradigm a.k.a. differential imaging

(for the functional specialization analysis) and the covariance paradigm (for the

functional integration analysis). In practice usually both approaches are used to discover

unexpected patterns in the data.

Differential imaging [B. Horwits and O. Sporns, 1994] is an intuitive approach for

resolving the ERA and assumes that the ERA rides atop the background activity. The

ERA is extracted by contrasting the recorded activation to two stimuli. The contrast

stimulus can be a) blank or no stimulus b) complementary stimulus i.e. the stimulus is

expected to evoke little or contradictory response c) the cocktail response i.e. the sum

average of all the responses. Differential imaging significantly improves SNR but for

truly robust analysis further improvement is necessary. This is achieved by appropriate

enhancements to the experimental paradigm (the manner of sequencing the stimuli for

16

presentation to subjects). This technique has been extensively covered by L. Sirovich and

E. Kaplan, 2002.

Covariance analysis [B. Horwits and O. Sporns, 1994] bypasses the issue of SNR

by aiming to uncover the temporal covariance between different brain regions during a

particular task. Regions with significant covariance are termed functionally connected.

These are generally multivariate data analysis strategies free of pre-assumptions

regarding the activation functions. Some examples are ICA, PCA and unsupervised

learning.

The final aim of any neuroimaging data analysis algorithm is the generation of the

activation maps - visual representations of brain regions with statistically significant

activation. The covariance analysis schemes need no further processing as they directly

generate activation maps. For the differential imaging schemes further processing using

inferential analysis or causal analysis. Inferential analysis usually takes the form of

Statistical parametric maps (SPM). Generalized linear model (GLM) [K. J. Firston et al,

1995] including methods like ANCOVA, Pearson’s coefficient and t-test is a well

established type of SPM.

Most functional neuroimaging studies are designed using a combination of the

above concepts.

2.5 Experimental Paradigms for Neuroimaging

The neural phenomenon being investigated dictates the choice of the experimental

paradigm. The predominant paradigms are the repeated single trial paradigm and the

blocked trial paradigm.

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The blocked trial paradigm aims to maintain a higher level of evoked response

and consequently a better SNR by an extended response interval through repeated

presentation of the same stimulus. This paradigm tends to use no stimulus as the contrast

stimulus. The repeated single trial paradigm models the brain responses as a stationary

process, hence the ensemble of evoked responses to each trial would be independent and

identically distributed (iid) samples of the actual evoked response and an average across

them will result in a better estimate of the evoked response, thus improving the SNR.

More the number of trials better the SNR, but it also will result in inordinately long

experiment intervals (an important factor for human studies). As little as 16 repetitions

have been known to give satisfactory results.

Figure 2.9 Popular experimental paradigms

18

The validity of these paradigms is a subject of ongoing discussion in the

neuroscience community, particularly the repeated single trial paradigm [J. I. Aunon,

1992; W. J. Freeman, 2000]. None the less they are still standard practices in

neuroimaging.

2.6 Neurovascular Coupling: A Closer Look

The spacing of the stimuli w.r.t. each other in an experimental paradigm decides if

and by how much the evoked responses overlap (precisely spaced sequentially ordered

set of stimuli is known as an experimental protocol). The nature of the neurovascular

coupling will then determine whether the overlap (if it exists) is linear. In optical imaging

it is natural that the background neural activity manifests itself as spontaneous

oscillations in the cerebral hemodynamics. These factors are critically important to the

interpretation and design of imaging studies. A clear understanding of the EROS time

evolution, neurovascular coupling and the spectral signature of the hemodynamics is

indispensable in addressing these concerns.

One of the earliest references to neurovascular coupling was made by C. S. Roy

and C. S. Sherrington, 1890. Since then numerous studies have provided empirical

confirmation of its existence. It was only recently that J. K. Thompson et al, 2003

provided the most direct confirmation. This study characterized in unambiguous terms

the closeness and nature of the coupling, the spatial scale on which it occurs and its

evolution in time. It is necessary while discussing neurovascular coupling to distinguish

between tissue oxygenation and blood oxygenation. Tissue oxygenation refers to the

amount of oxygen stored directly in the tissue (myoglobin is the typical oxygen binding

protein in tissues) and cannot be monitored by NIRS. Blood oxygenation refers to oxygen

19

saturation of the blood (with emphasis on oxygen transport rather than storage and

hameoglobin as the oxygen binding protein) and can be monitored by NIRS. J. K.

Thompson et al, 2003 present their results in terms of tissue oxygenation. A

representative time course of tissue oxygenation as reported by them is shown in figure

2.10.

Figure 2.10 Time evolution of tissue oxygenation in cerebral cortex. Dotted region indicates stimulus onset and duration. Solid black line represents oxygen response averaged across 72 trials and the dashed lines represent 1 SD of the mean. [J. K.

Thompson et al, 2003]

Summarizing their results, high average spike rates result in a large dip and a

small delayed peak, whereas low average spike rates result in small dip and a large peak.

Correlation between the oxygen response and spike rate is significantly (P < 0.0005)

correlated between 3.25 and 14.0 s after stimulus onset. To explain the results they

suggest two competing mechanisms, competing because their time courses overlap (see

20

figure 2.11). First the oxygen consumption of activated neurons fuels an initial dip/fast

response. The oxygen depletion triggers an increase in regional blood flow (hyperemia)

causing a hyper-oxygenation phase. These mechanisms however operate on different

spatial scales; the initial dip is strictly localized to areas of neural activation while the

hyper-oxygenation phase is more spread out. This effect is sometimes referred to as

“watering the garden for the sake of one thirsty flower” [R. B. Buxton, 2001].

Figure 2.11 The initial dip in tissue oxygenation (light) is due to increased neural activity whereas the subsequent rise in tissue oxygenation (dark) reflects an increased blood flow.

[J. Mayhew, 2003]

Naturally the changes in tissue oxygenation have corresponding counterparts in

blood oxygenation. This is reflected in concentration changes of both oxyHb and

deoxyHb. U. Lindauer et al, 2001 and M. Jones et al, 2001 provide an excellent study

into the exact nature of the manifestations. Though both studies are based on similar

experimental protocols and use comparable schemes to extract concentration changes

from the remitted attenuation measurements, their conclusions about the presence of the

21

fast response/initial dip in deoxyHb time course is at odds but concur about changes in

the oxyHb time course. Explanations for these apparently conflicting results can be found

in the commentaries by I. Vanzetta and A. Grinvald, 2001 and R. B. Buxton, 2001. These

four papers have gone a long way in establishing, now widely accepted, notions

regarding the nature of the hemodynamic response following a neural activation: a) a fast

early increase in deoxyHb without a concomitant decrease in oxyHb (figure 2.12a) b)

followed by a slow increase in oxyHb with a concomitant decrease in deoxyHb (figure

2.12b) c) higher intensity of stimulation results in a bigger response

Figure 2.12 Representative time course of oxyHb and deoxyHb following neural

activation [M. Jones et al, 2001]

22

J Mayhew et al, 1999 do report a concomitant decrease in oxyHb, however they achieve

this only after trial averaging and applying a generalized linear model (GLM) scheme to

the data. The linearity and effects of stimulus presentation rate have been dealt with in

detail by F.M. Miezin et al, 2000 and P. Wobst et al, 2001

The spectral signature of the measured optical signal from a healthy adult human

cortex is generally expected to contain four frequency bands centered around 0.8Hz,

0.2Hz, 0.1Hz and 0.03Hz [J. Mayhew et al, 1996; C. E. Elwell et al, 1999; H. Obrig et al,

2000 and independently confirmed by this author]. A classic example of the power

spectral density (PSD) spectrum of the post stimulus signal segment is shown in figure

2.13. The hemodynamic response following neural activation is embedded in the 0.1Hz

and 0.03Hz bands. The 0.8Hz and 0.2Hz bands correspond to heart rate and respiration

respectively [A. Malliani et al, 1994] and as will be demonstrated in chapter 3 are

relatively easy to extract. The 0.03Hz band, a.k.a B-waves or very low frequency

oscillations (VLFO), is assumed to reflect the periodic variations generated by the

various brain stem nuclei in the vasomotor tone of cerebral arterioles [N. Lundberg,

1960]. Since the PSD estimation procedures have a tremendous effect on this band,

caution has to be exercised, particularly data de-trending should not be used [T. Muller et

al, 2003]. T. Muller et al, 2003 also give an exhaustive list of studies concerning the

spectral content of cerebral signals. The 0.1Hz band (a.k.a V-signal, low frequency

oscillations (VLO), Mayer waves or M-waves) wields by far the most influence on

EROS. Their frequency ranges overlap and the peak to peak SNR is as bad as -14db [J.

Mayhew et al, 1999]. Vasomotion, i.e. the rhythmic dilation and contraction of the pre-

capillary sphincters in the cortical capillary beds is suspected to be the origin of these

23

signals. The oscillations are not peculiar to subject species, anesthetic state or brain

structure being probed [J. Mayhew et al, 1996]. It is affected by hypercapnia and rate of

respiration [H. Obrig et al, 2000]. The most common approach to its extraction is

averaging over individual trials. This will be dealt with in detail in chapter 4.

Figure 2.13 Spectral signature of the measured optical signal following a stimulus

24

3. PRE-PROCESSING FOR SIGNAL CONDINTIONING

Pre-processing algorithms refer to cleaning procedures like artifact filtering and

signal smoothing. They help improve the SNR of the measured signal. The following

studies on vascular artifacts, motion artifacts and outlier elimination constitute the

development of pre-processing algorithms for the fNIR signals.

Unless otherwise mentioned, all the subjects for the studies reported below were

volunteers who gave an informed consent to participate. The informed consent and all the

protocols were approved by the human subjects Institutional Review Board (IRB) at

Drexel University, except for the treadmill protocol (section 3.2.1) which was carried out

at the University of Pennsylvania, in this case the informed consent and protocol were

approved by the IRB of that institution. The subjects were healthy, right-handed

individuals in the age group of 18 to 35 with vision correctible to 20/20. They reported no

previous history of mental or neurological abnormalities, denied having a history of

tobacco use, denied having consumed alcohol for a period of 24 hours prior to the

experiments and reported no unusual stressful experiences in the week before the

experiment. They were also instructed to minimize the intake of caffeine for a period of

24 hours before the experiment.

3.1 Motion Artifact

Motion artifacts are a source of significant distortion in fNIR imaging and are

seen quite regularly. They can appear anywhere in the spectrum and have no amplitude

constraints. This makes handling them relatively more involved than other artifacts. Lack

of prior information about the artifacts necessitates the use of adaptive algorithms.

25

Their presence can be explained by a variety of factors. Some of the more likely

factors include changes in the optical coupling between the subject’s forehead and the

fNIR sensor and changes in arterial blood pressure. The photo detectors in the fNIR

probe are sensitive to the angle at which the remitted light is received and the reflectance

of the skin surface depends on the angle of incidence. Both of these can be modulated by

motion. Also motion is possible only by muscle activation i.e. increased blood flow in the

muscle vasculature around the forehead. This can easily register on the fNIR sensor,

indeed the same technology has been successfully used to monitor muscle metabolism in

athletes [Y. Lin et al, 2002]. In some cases, motion can affect the arterial blood pressure

in the neural vasculature (network of arteries and veins in the brain) which can, again, be

recorded by the fNIR sensor. It is difficult and largely unnecessary to differentiate

between the contributions of these sources. However they contribute significant amount

of error variance to studies of brain function and therefore the need to be eliminated.

For the simplicity of analysis and design in this study, motion artifact is classified

into two groups – stationary scenarios, where the subject is seated with head motion

being the only significant source of motion and ambulatory scenarios, where the subjects

can move freely. This classification greatly helps in developing a general frame work for

motion artifact cancellation.

3.1.1 Data Collection

For the stationary scenario, the experimental protocol consisted of 2 repetitions of

three 20s head movement intervals interlaced with 20s rest intervals. Prior to beginning

the protocol, the subjects (N=11) were instructed that, in the protocol, head movement

referred only to up-down movement of the head in the vertical axis and to consciously

26

keep as still as possible during the rest intervals. The speed of movement in the three

movement intervals gradually increases from slow to medium and finally fast. However,

the same speed was maintained for the duration of any movement interval. In addition to

the fNIR sensor, an accelerometer placed on the forehead was used to monitor motion.

The data was sampled at 2Hz.

The ambulatory scenario used an emotion protocol with a 3 minute rest interval in

the beginning. The stimuli were a series of images chosen to evoke different emotions.

The experiment was conducted twice consecutively, once with the subject sitting, then

with the subject walking/running on a treadmill. A random and different series of images

were used for the two sessions. The subject was free to walk/run at his own pace on the

treadmill and was not expected to maintain a constant speed. Also, the treadmill speed

was not monitored. The data was sampled at 1.5Hz, causing aliasing of the heart

pulsation signal to around 0.5Hz. This study was a feasibility study and hence had a small

subject pool (N=3).

3.1.2 Cancellation Algorithm

A stationary process ( )x t embedded in additive noise ( )n t , observed as

( ) ( ) ( )y t x t n t= + can be optimally estimated as ( )x t by a Wiener smoother if ( )x t and

( )n t are uncorrelated i.e. ( ) ( ){ }, 0E x t n t = . ( )x t will be optimal in the sense that the

mean-square error will be minimum.

( )( ){ } ( ) ( )( ){ }2 2min E e t E x t x t⎡ ⎤= −⎢ ⎥⎣ ⎦

(3.1)

The development of the Wiener smoother also assumes stationarity,

uncorrelatedness and the availability of second order statistics, i.e. correlation functions

27

of the processes ( )x t and ( )y t . In the frequency domain the correlations functions

correspond to the power spectral densities (PSD) of the processes. The Wiener smoother

in frequency domain would then be given by

( ) ( )( )

xWienerSmoother

y

PSDW

PSDω

ωω

= (3.2)

T. Kailath et al, 2000 give an in depth treatment of Wiener filtering.

The possible origins of the motion artifact as indicated in section 3.1 strongly

suggest that the artifact is additive and uncorrelated to the signal of interest. Accordingly

( )x t indicates the signal of interest, ( )y t the measured optical signal and ( )n t the

motion artifact. The terms in equation 3.2 would then be ( )xPSD ω – the PSD of signal

of interest and ( )yPSD ω – the PSD of the measured optical signal and is equal to

( ) ( )x yPSD PSDω ω+ .

For the stationary protocol, three Wiener smoothers are developed, one for each

speed of movement. The rest intervals are used to estimate ( )xPSD ω and the movement

intervals are used for ( )yPSD ω . A traditional LMS adaptive filter was also applied to

this data for comparison.

For the ambulatory protocol, ( )xPSD ω is generated from the session where the

subject is stationary and ( )yPSD ω by the session on the treadmill. The 3 minute rest

interval from both sessions is divided into 3 equal segments and the first segments are

used to generate the Wiener filter. The Welch method (Hanning window,

28

13

windowLength SegmentLength= , 12

overlap windowLength= and 512nfft = ) was

used to estimate the PSDs. All the filters were then applied in the frequency domain as

( ) { }{ }Re WinerSmootherFilteredSignal iFFT W FFT MeasuredSignalω⎡ ⎤= •⎣ ⎦ (3.3)

The stationary protocol data was also cleaned using a least mean square (LMS)

filter. A typical LMS adaptive noise canceller is given in figure 3.1 [S. Haykin, 2001].

Figure 3.1 LMS Filter structure

The primary input ( )d n is the original raw signal and the reference input ( )u n is

strongly correlated to the noise. The filter coefficients ( )w n are updated at each time

point n using ( )d n and ( )u n to estimate the noise as ( )y n [S. Haykin, 2001]. An

estimate of the signal of interest is then obtained as ( ) ( ) ( )e n d n y n= − . When applied to

motion artifact suppression for fNIR signals ( )d n is the measured optical signal, ( )u n is

the accelerometer signal and ( )y n the cleaned signal.

29

To quantify the improvement the change in signal to noise ratio ( )SNR∆ was used as a

measure of performance. For the stationary protocol SNR∆ was computed as

e iSNR SNR SNR∆ = − (3.4)

Where 2

10 210Log xe

e

SNR σσ

= (SNR of the cleaned signal), 2

10 210Log xi

n

SNR σσ

= (SNR of

measured optical signal), ( )x t is the motionless data from the rest intervals, ( )x t is the

estimated signal, ( )e t is the estimation error given by ( ) ( ) ( )e t x t x t= − , 2nσ is the

variance of the motion artifact from the accelerometer recording and 2σ is the variance

of the respective signals. An additional measure of performance defined as

e iCC CC CC∆ = − (3.5)

was also used. Here eCC is the correlation coefficient between the motionless data and

the estimated cleaned data and iCC the correlation coefficient between the motionless

data and the motion artifact. These calculations were performed on the results from both

Wiener and the LMS filter.

The SNR gain for the ambulatory protocol was computed as

1010Log rawSignalgain

filteredSignal

AvgPowerSNR

AvgPower= (3.6)

The average power for the raw and filtered signals, by Parseval’s theorem, is computed as

( )12

AvgPower PSDπ

π

ωπ −

= ∑ (3.7)

30

3.1.3 Results

The LMS filter is a traditional approach to motion artifact suppression. As shown

in figures 3.2 and 3.3 in the stationary protocol both filters suppress the motion artifact.

However the Wiener filter significantly out-performs the LMS filter as indicated by table

3.1. The consistency of these results over the subject pool can be assessed by the

student’s t test analysis. The t and p values in table 3.2 indicate that results are

statistically consistent. Also, unlike the Wiener filter, the LMS filter requires an

independent tracking signal like the accelerometer signal, and as evident from figure 3.3,

initially lags in adapting to changes.

Table 3.1 Sample of the SNR gain and CC∆ results for Wiener and LMS filter Head

movement

speed

SNR (dB)

(LMS Filter)

SNR (dB)

(Wiener Filter)

Correlation coefficient

(LMS Filter)

Correlation coefficient

(Wiener Filter)

Slow 3.3560 5.2526 0.1519 0.2929

Medium 4.1722 9.0539 0.0024 0.2977

Fast 2.7906 5.7574 0.1431 0.4407

Table 3.2 Results of the t test for the Wiener filtering results in the stationary protocol Head Movement Speed t and p values for SNR∆ t and p values for CC∆

Slow t = 4.95; p < 0.001 t = 6.11; p < 0.000

Medium t = 3.73; p < 0.004 t = 3.59; p < 0.005

Fast t = 4.3; p < 0.002 t = 3.10; p < 0.011

31

Figure 3.2 Wiener filtering results: From the top panel slow, medium and fast movement

32

Figure 3.3 LMS filtering results: From the top panel slow, medium and fast movement

33

Figure 3.4 Wiener filtering results for two random segments in the ambulatory protocol

Table 3.3 SNR gain (dB) in the ambulatory protocol for the 3 subjects Subject 1 Subject 2 Subject 3

Segment 1 2.257 4.467 2.732

Segment 2 5.012 9.574 1.931

Segment 3 0.7789 7.356 1.348

34

An independent tracking signal for the LMS filter in the ambulatory protocol

implies a 3D tracking signal. Acquiring a 3D tracking signal is not trivial and involves a

very elaborate system setup. In contrast, the Wiener filter approach can be easily

manipulated to extract the artifact. Figure 3.4 and table 3.3 demonstrate that the filter

performs efficiently in this scenario. The small subject pool doesn’t permit a meaningful

statistical analysis reported for the stationary protocol. The ability to extract the artifact

with out a separate tracking signal and the improved performance by far out weigh the

disadvantage of having to include rest intervals needed to update the Wiener filter in the

experimental protocol.

3.1.4 Discussion

These results have been reported in M. Izzetoglu et al, 2005 and A. Devaraj et al,

2004. Together the stationary and ambulatory scenarios model most real life situation

where fNIR systems can be deployed. The described Wiener approach can be used as a

general framework to develop motion artifact filters for real world applications. For

example, fNIR recordings from an autistic subject pool will see an increased level of

motion artifacts, and, owing to the special condition of the subjects, it is impossible to

curtail subject motion. A possible solution is to record fNIR signal for a brief interval

with the subject anesthetized before/after the actual experimental protocol and use this

recording to estimate ( )xPSD ω while developing the Wiener filter.

Part of the success of the Wiener filter approach is because it takes full advantage

of the physiological factors of neurovascular coupling brought out in section 2.6. The

vascular response component of the measured optical signal in the frequency spectrum is

constrained to below 0.13Hz. The signal level between EROS and the M waves differ by

35

14dB. M waves are invariant to changes in the physiological state of the subject including

his anesthetic state. This permits estimation of ( )xPSD ω by an independent prior/post

fNIR recording. As these results indicate, this estimate is quite accurate and consistent.

3.2 Vascular Artifacts

The spectral signature of the measured optical signal (figure 2.13) clearly

indicates two other artifact sources - the respiration and arterial/heart pulsation signals

centered around 0.2Hz and 0.8Hz respectively. Due to their origin these are referred to as

the vascular artifacts.

The dynamics of blood flow in the capillary beds by itself is not sufficient to

account for these signals as blood pressure in the capillaries is fairly constant and local

micro-regulation of blood flow is expected to compensate for changes due to respiration.

A more plausible explanation would be the presence of neural vasculature in the voxel

being imaged. During optical imaging the imaged volumes invariably cut across a sulcus

(the outer most portions of the human cerebral hemispheres are continuous highly folded

sheets of cortex which itself is a sheet-like array of neurons. The folds form a system of

ridges known as gyri and valleys labeled sulci on the brain surface. The physical

structures of the sulci direct the vasculature in the brain. Respiration and arterial/heart

pulsation are strongly reflected in any vasculature. Thus sulci and the associated neural

vascular in the imaged voxel can account for the presence of these artifacts in the

measured optical signal. Aside from the error variance contributed to the signal of

interest, these vascular signals do contain important information regarding the subject’s

physiological state, adding more incentive to extract and quantify these signals.

36


The experimental protocol was target categorization - a cognitive odd-ball task.

The subjects (N=10) were presented with a series of Os interspersed with Xs such that Os

would be more common (context) than Xs (targets). They were asked to press a different

button on the response pad for the Os and Xs, using their non-dominant hand i.e. left

hand. Each stimulus presentation lasted for 500ms with an inter-stimulus interval of

1500ms. Any two target stimuli were separated by 12 context stimuli, and to prevent

subjects from predicting future stimuli, 4 targets were randomly presented in close

succession. A total of 516 stimuli were presented of which 36 (including the 4 non-

targets) were targets. The data was sampled at 1.5Hz causing aliasing of the heart

pulsation signal to around 0.5Hz.

3.2.2 Extraction Algorithm

Figure 2.13 clearly indicates the additive nature of the vascular artifacts. The filter

specifications can be either fixed, as when dictated by prior information about the

spectral signature of the signal or it can be generated adaptively. A Wiener smoother

developed for each trial incorporates the best of both of these approaches.

Designing a Wiener smoother entails determining the correlation matrix i.e.

power spectral density (PSD) of either the signal of interest or the artifact. With prior

knowledge about the signal spectrum from section 2.6 can be used to estimate the PSD

spectrum of the signal of interest ( ( )SignalOfIntersetPSD ω ). A sum of two Gaussian curves

is fitted to the PSD spectrum of the measured signal ( ( )MeasuredSignalPSD ω ) in the

frequency interval 0.0-0.13Hz. The fitted curve is then allowed to roll off to -30dB and

37

this extended curve serves as an estimate of ( )SignalOfIntersetPSD ω . The Wiener smoother,

in PSD domain, would then be [T. Kailath et al, 2000]

( ) ( )( )

SignalOfIntersetWienerSmoother

MeasuredSignal

PSDW

PSDω

ωω

= (3.7)

This is repeated for every trial allowing the filter to adapt to changes in the spectrum.

A robust non-linear least squares implemented by the trust region algorithm in

Matlab was used for the curve fit. More information on the fitting procedure can be found

in the documentation for Matlab’s Curve Fitting tool box. The model used for the fit

2

2

1

i

i

x bc

ii

y a e

⎡ ⎤⎛ ⎞−⎢ ⎥−⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

=

=∑ (3.8)

The fit was weakly constrained by forcing ib i.e. the mean of the Gaussians to lie in the

band of the B and M waves.

Determining the PSD of the measured signal requires some care. To avoid making

assumptions about the signal model, the non-parametric PSD estimation methods were

preferred. The short signal interval (just 15s giving just 24 data points) is detrimental to

the spectrum resolution. To achieve the maximum possible resolution the boxcar function

was used for windowing and the short signal interval also meant the window length

would be the same as the signal length. These constraints essentially implied the use of

the periodogram method of PSD estimation. A 512 point FFT was used. Since the filter

was designed in the frequency domain it was implemented in the frequency domain as

( ) { }{ }512 512Re Pt WienerSmoother PtFilteredSignal iFFT W FFT MeasuredSignalω⎡ ⎤= •⎣ ⎦ (3.9)

38

3.2.3 Results

Figures 3.5 and 3.6 show the results for two subjects in both time and frequency

domain. The SNR gain, as given by equation 3.4, for the depicted samples are 3.271dB

and 1.390dB respectively. The results of this study were also presented at the 2004

annual BMES fall meeting [A. Devaraj et al, 2004].

Figure 3.5 Sample results from the filtering algorithm. Top panel – time course; Bottom

Panel – PSD Spectrum

39

Figure 3.6 Sample results from the filtering algorithm. Top panel – time course; Bottom

Panel – PSD Spectrum

3.2.4 Discussion

As shown in appendix A the spectrum of EROS can be expected to be uniformly

flat in the frequency range 0.0 - 0.1Hz. This places several constraints on any filter that is

applied to the measured signal. First, the filter has to be zero-phase or, at least, linear-

phase, else it would introduce significant phase distortion. Second the transition width

40

has to be quite narrow. Both of these conditions ensure that the filter order is quite high

and the traditional FIR filter design methods to satisfy them are quite involved. A filter

designed and implemented in the frequency domain as described above is relatively

easier and effectively addresses all of these issues. This is possible by exploiting the fact

that data acquisition has been completed before further processing. The estimated PSDs

are, by definition, real thus generating zero-phase Weiner smoother with the appropriate

cut off. Since the filter is derived for each trial it can adapt to changes due to the quasi-

stationary nature of the signals and to individual variation in subjects. Any fixed FIR

filter design would have to be based on the spectral signature shown in figure 2.13, but

this signature is derived from studies on healthy adult volunteers in reasonably normal

environments. As fNIR imaging is increasingly used in broader application areas this

assumption will not hold, underlining the need for adaptive algorithms. The ability of the

proposed technique to adapt the cut-off frequency to changes in the spectrum is an

advantage that cannot be matched by traditional FIR filter design. Also, as an added

advantage, one can simultaneously extract important information regarding the B and M

waves. This information as will be shown in chapter 4 is quite useful.

3.3 Outlier Elimination

Outliers, as the name suggests are random anomalies in the measured signal. They

are noticeable as segments of inconsistent recordings. The measured values in such

segments can be either greater or lesser than the majority of the recordings. Since the

usual mode of data analysis for repeated trial paradigms is to average across trials, they

can generate a strong bias in the results and hence the need for their elimination. The

origins of these inconsistencies are unclear. Hardware transients, optode pops (a change

41

in the optical coupling between the fNIR probe and the subject’s forehead) and a real but

non-consistent brain response are some of the possible causes.


The algorithm was originally developed for use with the data from guilty

knowledge task (GKT). The protocol is based on the repeated trial paradigm and consists

of 16 repetitions of 4 types of stimuli. Two of the stimuli complementary, and the other

two are control stimuli. The two complementary stimuli are designed to elicit a truth and

lie response from the subject. Differences in the neural activation to the two

complementary stimuli when contrasted against each other are expected to reveal neural

activation as a response to deception. The control stimuli are necessary to check for

activation due to the manner of stimuli presentation rather than deception. A detailed

discussion of the GKT protocol can be found in D. T. Lykken, 1959, 1960.

The data was collected at 2Hz and the subject pool consisted of 21 volunteers.

3.3.2 Method

Two features – the range (the difference between the maximum and minimum

values) and mean (the average of all the values) are extracted from the post stimulus

segment of each trial. The length of the post stimulus segment is not significant to the

algorithm but usually depends on the protocol design, in this case it was 11s. The mean

and the standard deviation (SD) of the features are then computed. Any trial with either

of the features at distance greater than 2.5SD± from the respective feature mean is

considered as an outlier and discarded.

42

3.3.3 Results

The effects of this elimination are most visible in the results of the final analysis

for the data set. To study how the response evolves in time, a 11s post stimulus epoch

was extracted from each trial. These were first averaged across trials and then across

subjects. They were then segmented and averaged across segments 1.5s long. The p-

values indicate the statistical significance of the differentiation between the neural

responses to telling the truth vs. telling a lie. The p-values with and without elimination

are shown in table 3.4 and table 3.5. Figures 3.7 and 3.8 depict the same graphically.

Voxel 4 does not show differentiation before outlier elimination demonstrating the

efficacy of the elimination algorithm.

Table 3.4 p-values (<0.01) after data analysis without outlier elimination 0.0s-1.5s 1.5s-3.0s 3.0s-4.5s 4.5s-6.0s 6.0s-7.5s 7.5s-9.0s 9.0s-10.5s 10.5s-11.0s

Voxel 1 - - 0.008 0.002 0.001 0.001 0.002 0.001 Voxel 2 - - - - 0.002 0.001 0.007 - Voxel 3 - - - 0.006 0.005 0.002 0.002 - Voxel 4 - - - - - - - - Voxel 5 - - - - - - - - Voxel 6 - - - - - - - - Voxel 7 - - - - - - - - Voxel 8 - - - - - - - - Voxel 9 - - - - - - - -

Voxel 10 - - - - - - - - Voxel 11 - - - - - - - - Voxel 12 - - - - - - - - Voxel 13 - 0.001 0.002 0.009 - - - - Voxel 14 - - - - - - - - Voxel 15 - - 0.002 0.002 0.001 0 - - Voxel 16 - 0.001 0 0 0 0 0.001 -

43

Table 3.5 p-values (<0.01) after data analysis with outlier elimination 0.0s-1.5s 1.5s-3.0s 3.0s-4.5s 4.5s-6.0s 6.0s-7.5s 7.5s-9.0s 9.0s-10.5s 10.5s-11.0s

Voxel 1 - - 0.007 0.002 0.002 0.004 0.007 0.006 Voxel 2 - - - - 0.001 0.003 - - Voxel 3 - - - 0.009 0.008 0.005 - - Voxel 4 - - 0.008 0.008 0.006 0.004 - - Voxel 5 - - - - - - - - Voxel 6 - - - - - - - - Voxel 7 - - - - - - - - Voxel 8 - - - - - - - - Voxel 9 - - - - - - - -

Voxel 10 - - - - - - - - Voxel 11 - - - - - - - - Voxel 12 - - - - - - - - Voxel 13 - 0.002 0.009 - - - - - Voxel 14 - - - - - - - - Voxel 15 - - 0.009 - - - - - Voxel 16 - 0.005 0.001 0.001 0 0 0.005 -

Figure 3.7 Analysis results without outlier elimination registered on the brain

44

Figure 3.8 Analysis results with outlier elimination registered on the brain

3.3.4 Discussion

Previously, only the mean of the post stimulus segments was used for outlier

elimination. This has the disadvantage of smoothing the fluctuations in the data sequence

allowing some outliers to escape the detection process. This has been remedied with the

inclusion of another feature - the range.

Use of two features suggests development of the algorithm in the 2-D feature

space with data points represented as shown in figure 3.9. But just 16 data points are

grossly insufficient to capture the relationship between the two features making

algorithms based on this very ineffective. This has been overcome by considering both of

the features separately and any trial with either of the feature values outside the set range

45

of mean feature value 2.5SD± is discarded. Further 16 trials is an acute under-sampling

of the underlying probability distributions. This makes generating global parameters,

needed by most non-parametric stochastic methods like clustering, very difficult. In the

light of these issues the presented method is a practical, easily implemented and as

indicated by the results quite sufficient.

Figure 3.9 Possible 2-D Feature space

46

4. FEATURE EXTRACTION FOR SINGLE TRIAL ANALYSIS

Certain neuroimaging studies require analysis of events that cannot be performed

in blocks. In some studies the task is inherently brief, for example the process of

swallowing. Other tasks depend on the presentation of unpredictable stimuli like the

study of inhibitory control. Such tasks are studied through event related (ER) functional

paradigms. This paradigm also allows responses to stimuli to be sorted and analyzed

based on subject’s performance. Analysis of ER studies is generally more complicated

when compared to blocked design studies which can be analyzed by a simple statistical

test such as the t-test. Traditionally a constant inter stimulus interval (ISI) ER design with

repeated trials have been used to analyze the ER studies. The ISI is usually set around

15s-20s to permit the evolution of the entire hemodynamic response to each stimulus.

The drawback of this design is that the stimuli are presented rather infrequently leading to

long acquisition times and difficulty in keeping the subject adequately engaged in the

task. These concerns are even more acute in neuropsychological studies.

Single trial analysis addresses all of the above concerns without compromising

the advantages of the ER paradigm. There are two forms of single trial analysis –

estimation and detection. The estimation problem is to extract the time course of the

response while the detection deals with detection of the event-related signal changes.

Single trial analysis is generally hard to develop because of inherently low SNR values in

neuroimaging.

The aim of the present study was to identify features for single trial detection and,

as validation, present results on data from a visual odd-ball task. An attempt to explain

47

the possible neuro-physiological basis has also been made. To the author’s best

knowledge single trial analysis for fNIR imaging has not been attempted before.

4.1 The Data

The proposed method was checked for validity on a target categorization (the

visual odd-ball task) data set. The protocol and data collection has been described in

section 3.2.1.

4.2 Method

The feature extraction algorithm consists of two parts. The first step is to compute

the PSDs. Two segments are extracted from each of the 32 target trials – a post-stimulus

segment (15s in duration) and a pre-stimulus segment (6s in duration). The PSDs of both

these segments were then computed. Estimating the PSDs was according to the concerns

outlined in section 3.2.2 (Periodogram with a 512 point FFT).

The peak frequencies in the B and M wave bands, along with the amplitude of the

respective peaks, can serve as features for the single trial analysis. The features are

extracted by using a parametric curve fit to the spectrum in the range 0.0Hz – 0.13Hz.

The curve fit aspects are exactly similar to those explained in section 3.2.2. For

convenience, the fit model is repeated here

2

2

1

i

i

x bc

ii

y a e

⎡ ⎤⎛ ⎞−⎢ ⎥−⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

=

=∑ (4.1)

48

The fit was weakly constrained by forcing ib , i.e. the mean of the Gaussians, to

lie in the band of the B and M waves. The fit parameters - ia (the amplitude), ib (the

mean) and ic (the variance) were the extracted features.

4.3 Results

The utility of the features depends on their ability to significantly differentiate

between pre and stimulus intervals. Figure 4.1 illustrates all the parameters for one

subject. A cursory visualize inspection is sufficient to realize that the best features are ia

and ib . Also to check for systematic errors the features from different pre-stimulus

segments were also extracted and figure 4.2 displays the results for one subject. Finally,

figure 4.5 shows the extracted values of ib from three different subjects.

Figure 4.1 Parameter ia for 9s pre-stimulus segment (Subject A)

49

Figure 4.1 (Continued) Parameters ib (top panel) and ic (bottom panel) for 9s pre-

stimulus segment (Subject A).

50

Figure 4.2 Parameter ib for varying pre-stimulus segment (Subject B). From the top panel

6s and 9s

51

Figure 4.2 (Continued) Parameter ib for varying pre-stimulus segment (Subject B). From

top panel 12s and 15s

52

Figure 4.2 (Continued) Parameter ib for 18s pre-stimulus segment (Subject B).

Figure 4.3 Parameter ib for subjects C

53

Figure 4.3 (Continued) Parameter ib for different subjects. From top panel subjects D and

E

54

4.4 Discussion

Figures 4.1 -4.3 show the plots in the 2_D feature space for the three parameters.

Among the parameters the best differentiation is obtained for ia and ib . But the

differentiation boundaries for ia varies widely across subjects, hence ib (for which the

differentiation boundaries remain fairly consistent across subjects) is preferred for single

trial detection. To ensure that there are no systematic errors, the analysis was repeated

with varying pre-stimulus segment lengths. The results for 6, 9, 12 and 15s pre-stimulus

segments for one subject are shown in figure 4.4. The poor differentiation in 12, 15 and

18s can be explained as result of small time interval (18s) between two targets stimuli.

The longer the pre-stimulus interval the more it extends into the post stimulus interval of

the previous target. However longer segments are needed for better frequency resolution.

Since the feature values in the 9s segment follow those in the 6s segment, in spite of

being a relatively short segment, 6s is the optimal choice.

Based on these two features, a simple linear classifier can be developed to classify

between pre-stimulus and post-stimulus segments. The ROC curves from such a classifier

for voxels 9, 10, 11 and 12 are shown in figures 4.4 - 4.7. The area under the curve is

respectively 0.947710, 0.954331, 0.925996 and 0.933431.

The ib represent the peaks in the frequency spectrum between 0.0Hz and 0.13Hz.

As stated in section 2.5 the two peaks in this range correspond to B and M-waves. These

signals are known to be effects of local auto regulation of cerebral micro circulation. The

M-waves in particular are associated with vasomotion. Considering that fNIR monitors

neural activity through cerebral hemodynamics these factors strongly support that results

in figure 4.3 represent valid single trial features.

55

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

False Alarm Rate

Sen

sitiv

ity

Figure 4.4 ROC curve for voxel 9 computed across 10 subjects.

Area under the curve = 0.947710

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

False Alarm Rate

Sen

sitiv

ity



56

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

False Alarm Rate

Sen

sitiv

ity



0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

False Alarm Rate

Sen

sitiv

ity



The neural activity induced by stimulation is traditionally assumed to be

superimposed on the background activity. This assumption forms the basis for data

analysis algorithms like averaging across repeated trials. The proposed approach opens

57

the possibility that the induced neural activity can be seen as a frequency modulation of

the Vasomotion signals. The features from the pre-stimulus segments have a clear linear

relation to each other while post-stimulus this relationship is lost, hinting that the increase

oxygen demands are met by changes in frequency of Vasomotion. Other researchers [A.

Villringer and B. Chance et al, 1997] have stated that the fNIR signal is more probably

due to blood flow than changes in blood volume and blood flow changes by variation in

velocity is improbable since blood pressure in capillary beds is maintained consistently

[J. Ross, 2005] and as show in figure 4.8. This further corroborates that the neural

response in the fNIR signals maybe embedded as frequency modulation in Vasomotion.

Figure 4.8 Blood pressure in each section of the systemic and pulmonary circulations

[J.Ross, 2005]

58

5. CONCLUSION AND FUTURE WORK

5.1 Conclusion

cwfNIR is an emerging neuroimaging technology that has gained popularity on

account of being safe, non-invasive, portable and minimally intrusive. However a more

extensive deployment of this technology, both in the clinic and the field, necessitates the

development of specific signal processing algorithms. The purpose of this research was to

lay the ground work for advanced signal processing as applied to fNIR signals. The

efficacy of any algorithm grossly depends on how well it takes into consideration the

characteristics of the signal and its origins. To this end, we have investigated the neuro-

physiological basis of the signal and established its spectral signature. Subsequently, all

the algorithms have been developed based on these findings. We not only present the

basic preprocessing steps, i.e., artifact suppression and outlier elimination, but also make

a foray into more exploratory analysis namely the single trial analysis.

Artifact cancellation, or extracting the signal of interest, is an important stage in

any biological signal processing. For fNIR signals, the two major classes of artifacts are

the motion and vascular artifacts. A general frame work for offline motion artifact

cancellation has been developed in this thesis. We used Wiener filtering for artifact

cancellation and showed that the proposed algorithm is efficient in artifact cancellation in

two different situations – both stationary and ambulatory scenarios. A comparison

between Wiener filtering and the more traditional adaptive LMS filter shows that the

proposed algorithm outperforms the LMS filter. We characterized the vascular artifacts in

the frequency domain and identified the requirement for the optimal filter. These

59

requirements are then met by a novel approach that also has an ability to adapt. Tests on

the target categorization dataset indicate its utility. We also demonstrated an improved

method for outlier elimination. We have identified two features that show great potential

for use in single trial analysis, particularly in single trial detection schemes. Their

efficacy has been successfully demonstrated on the target categorization dataset.

5.2 Future Work

The Wiener approach to motion artifact cancellation is essentially an offline

algorithm; an online/real-time algorithm could potentially be developed using Kalman

filters. Kalman filters are recursive and hence are well-suited for real time applications.

The filters must also be tested on protocols with cognitive tasks.

The proposed features for single trial detection have been applied on a well

known protocol, i.e., target categorization. To establish it as a robust methodology it must

be tested on other protocols. This will make it necessary to develop more powerful

classifiers like a neural network to distinguish between responses to different types of

stimuli. A comprehensive investigation of the relationship between the M-waves,

hemodynamic response and respiration will help improve the confidence in these

features. Two protocols would be needed for this. First, a protocol with a constant ISI of

at least 25s is needed to check for the effects of longer segment lengths. Second, a

protocol with intervals of controlled respiration at different rates would be necessary to

evaluate the effects of respiration.

Alternative non-parametric approaches to single trial analysis worth investigating

include blind source separation techniques, like the ICA, and transient frequency analysis

methods, like wavelets and time-frequency distributions.

60

Protocol design plays an important role in data analysis and ISI is crucial factor in

protocol design. Optimal ISI and appropriate analysis schemes must also be explored.

61

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APPENDIX A SPECTRAL SIGNATURE OF EROS

Figure A.1 Time course of ( )tΓ

The hemodynamic response to neural activation has been modeled as a gamma

function ( )tΓ by many researchers [P. Wobst et al, 2001; F. M. Miezin et al, 2000, G.

M. Boynton et al, 1996].

( ) tt At eα β−Γ = (A.1)

Here A is the amplitude, α controls the time to peak and β the roll off rate after the

peak. An idea of the spectral contents of this function will be helpful in visualizing EROS

in the frequency spectrum. The time course of ( )tΓ with 1A = , 3.75α = , 1.1β = and

sampled at 20Hz is as shown figure A.1. The frequency spectrum of the signal as

computed by the Welch method (boxcar window, 128windowLength = , 64overlap =

and 512nfft = ) is shown in figure A.2.

67

Figure A.2 Frequency spectrum of ( )tΓ

Figure A.2 strongly suggests that EROS will be a wide band signal with

frequencies in the range 0Hz - 0.13Hz.

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Signal processing for functional near-infrared neuroimaging