ARL-TR-8294 ● FEB 2018

US Army Research Laboratory

The Effect of Visual Task Difficulty on the 

Fixation-Related Lambda Response

by Anthony J Ries, David Slayback, and Jon Touryan

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ARL-TR-8294 ● FEB 2018

US Army Research Laboratory

The Effect of Visual Task Difficulty on the 

Fixation-Related Lambda Response

by Anthony J Ries, David Slayback, Jon Touryan

Human Research and Engineering Directorate, ARL

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The Effect of Visual Task Difficulty on the Fixation-Related Lambda Response

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14. ABSTRACT

Fixation-related potentials further our understanding of overt orienting by leveraging rather than limiting eye movements in 

experimental paradigms. The lambda response, a prominent neural signature of the fixation-related potential, has been used to 

examine stimulus-driven and cognitive influences on early stages of visual processing and overt orienting behavior. Prior 

experiments have shown changes in lambda response amplitude due to top-down effects from auditory task difficulty;

however, it is still not clear to what degree this component is sensitive to changes in visual task difficulty. Here we modulated 

difficulty using 2 different visual tasks. In the first, difficulty was manipulated via the working memory load of a visual NBack task while eye movements were systematically guided across a search grid. For the second task we used a modified 

Tetris game where difficulty was manipulated via tetrad fall speed, without imposing eye movement constraints. Subjective 

reports, behavior, and other physiological measures confirmed our task manipulations increased difficulty in both paradigms. 

The results showed that lambda response amplitude was significantly attenuated at high with respect to low difficulty levels in 

the N-Back task. In contrast, the Tetris task exhibited the opposite effect showing increased lambda amplitude as a function of 

task difficulty. Critically, these effects were maintained when correcting for overlapping neural activity elicited from 

temporally adjacent stimuli and saccadic events. Together, our results suggest that task difficulty may differentially affect 

early visual processing depending on the requisite cognitive and perceptual processes. Understanding how the lambda 

response is affected by task difficulty in the visual domain may provide a more direct way to index task demands in search 

behavior without relying on a secondary task or probe stimulus.

15. SUBJECT TERMS

lambda potential, fixation-related potentials, working memory, eye tracking, FRP, task difficulty, cognitive load, video game

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Anthony J Ries

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Contents

List of Figures v

List of Tables v

Acknowledgments vi

1. Introduction 1

2. Materials and Methods 3

2.1 Stimuli and Procedure 3

2.2 Participants 5

2.3 EEG and Eye Tracking 5

2.4 Data Processing 6

3. Results 7

3.1 Behavior 8

3.1.1 Subjective Report 8

3.1.2 Accuracy and Reaction Time 9

3.2 Physiological Metrics 10

3.2.1 Saccade Magnitude 10

3.2.2 Pupil Diameter and HRV 11

3.3 FRPs: Lambda Potential 12

3.3.1 Without Overlap Correction 13

3.3.2 With Overlap Correction 15

3.4 AEPs 16

4. Discussion 16

4.1 Task Difficulty 16

4.2 Stimulus and Ocular Overlap Correction 18

4.3 Subjective and Physiological Measures of Task Difficulty 19

5. Applications and Conclusion 20
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6. References 22

List of Symbols, Abbreviations, and Acronyms 27

Distribution List 28
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v

List of Figures

Fig. 1 Task layout. The left image shows the layout of the experimental 

environment while a participant performs the Tetris task. The right 

image shows an example of 4 successive fixations in the medium 

difficulty (0-Back) condition of the visual N-Back task. Note that only 

1 Gabor stimulus appeared on the screen at any given time. The red 

arrows indicate the direction of each saccade/fixation. ........................ 3

Fig. 2 Box and whisker plots of participants’ TLX ratings of perceived effort 

and mental demand in the N-Back (white boxes) and Tetris (shaded 

boxes) tasks as a function of task difficulty (low, medium, high)........ 9

Fig. 3 The effect of task difficulty on pupil diameter and HRV in the N-Back 

(white) and Tetris (shaded) tasks. Error bars represent the standard 

error..................................................................................................... 12

Fig. 4 FRPs obtained from electrode Oz as a function of task difficulty in the 

N-Back (top row) and Tetris (bottom row) tasks. The right and left 

columns show FRPs with and without stimulus/saccade overlap 

correction, respectively. Scalp voltage (microvolts) maps highlight the 

spatial distribution of the lambda response 70–90 ms post-fixation. 

Electrode Oz is depicted as the white circle on the scalp maps. FRPs 

and scalp maps are plotted using a –300 to –100 ms pre-fixation 

baseline. .............................................................................................. 14

Fig. 5 Comparison of lambda amplitudes as a function of task, condition, and 

overlap correction. P values were obtained from planned paired 

comparisons between levels of task difficulty. Error bars represent the 

standard error of the mean. ................................................................. 15

List of Tables

Table 1 Behavioral performance for auditory targets in the N-Back and Tetris 

tasks as a function of task difficulty ................................................... 10

Table 2 Saccade magnitude, pupil diameter, and heart rate variability (HRV) in 

the N-Back and Tetris tasks as a function of task difficulty. Note: 

Numbers represent the mean with standard deviation in parentheses for 

each measure....................................................................................... 11

Table 3 Paired t-tests for significant main effects of task difficulty................ 11
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vi

Acknowledgments

The authors thank Matthew Miller for his valuable feedback on the manuscript and 

Matthew Jaswa for his help in task development and data acquisition.

This research was sponsored by the US Army Research Laboratory and was

accomplished under CAST 076910227001 and ARL-74A-HR53.
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1. Introduction

Overt visual orienting is a ubiquitous component of our everyday interactions with 

the environment and fundamental to how we perceive the world. Consequently, 

decades of research have been dedicated to investigating the constituent perceptual

and neural mechanisms of eye movements in visual search (Eckstein 2011; Torralba

et al. 2006; Wolfe 2007). An important component of this investigation is 

understanding how cognitive processes, such as working memory, influence eye 

movements and visual orienting. However, the majority of studies exploring the 

neural components of these phenomena have been conducted in highly controlled 

laboratory settings, requiring participants to constrain their eyes to a fixed location. 

Thus, much of this work has employed covert orienting tasks, which require 

selecting a target stimulus in a display without making directed eye movements. 

This approach has a clear benefit for electrophysiology in that it reduces the large 

and often confounding eye-movement related artifacts produced by changes in the 

corneo-retinal potential (Hickey et al. 2008; Kiss et al. 2008; Luck and Hillyard 

1994). However, this controlled presentation of stimuli, in the absence of eye 

movements, provides an incomplete representation of how we process visual 

information in real-world settings and how cognitive factors influence information 

processing. 

Therefore, to fully understand overt visual orienting in real-world scenarios,

neurophysiological experiments must leverage rather than limit eye movements. 

Specifically, researchers can evaluate multiple stages of neural processing by 

extracting electroencephalogram (EEG) during periods prior and subsequent to an 

eye movement to create saccade and fixation-related potentials (S/FRPs),

respectively (Dimigen et al. 2011; Kaunitz et al. 2014). The most prominent and 

widely studied FRP component is the lambda response, a large positive waveform 

that peaks around 100 ms post-fixation. Similar to the P1 event-related potential 

(ERP), the lambda response reflects the afferent flow of information to the visual 

cortex and is affected by stimulus properties such as luminance and spatial 

frequency (Billings 1989; Thickbroom et al. 1991; Yagi 1979). Unlike the P1 ERP, 

the lambda response is affected by saccade magnitude such that its amplitude 

increases as a function of saccade size (Dandekar et al. 2012; Dimigen et al. 2011; 

Kaunitz et al. 2014; Yagi 1979). Other critical differences between lambda and ERP 

components are seen when directly comparing their latency and amplitude under 

the same stimulus conditions. In this case, the lambda response generally peaks 

earlier and has a larger amplitude compared to the visually evoked P1 ERP (Billings 

1989; Kaunitz et al. 2014; Kazai and Yagi 2003). The increased signal to noise 

observed in the lambda response is potentially inherited from extra retinal 
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mechanisms not active during traditional tasks that impose eye fixation constraints 

(McFarland et al. 2015; Reppas et al. 2002). 

Like the P1, the lambda potential is also affected by cognitive processes, such as 

those related to working memory. In one of the first studies to evaluate these topdown effects on the lambda response, participants searched for a target stimulus 

while ignoring auditory tones or performed an auditory oddball task while moving 

their eyes but ignoring target stimuli (Yagi 1981). The results from this study 

showed a decreased lambda response during the auditory relative to the visual task; 

however, it was not clear if this was due to an active inhibition of the passive visual

task or rather a result of resource limitations in visual processing. In our previous 

study (Ries et al. 2016), we expanded on the findings by Yagi (1981) by 

incorporating a dual-task paradigm where participants responded to predefined 

targets during guided visual target detection while simultaneously performing an 

auditory N-Back task. Here, the visual demands were kept constant while auditory 

task difficulty varied by varying working memory load. Our results showed a 

significant decrease in the lambda amplitude with an increase in auditory task 

difficulty, providing further evidence for a link between cross-modal processing 

resources. Finally, Takeda et al. (2012) assessed the effect of verbal and spatial 

working memory on lambda amplitude. In this study, all participants performed a 

simulated driving task where half of the participants performed a simultaneous 

verbal working memory task (monitoring a stream of aurally presented digits), and 

the other half performed a simultaneous spatial working memory task (performing 

easy or difficult mental rotation based on directional auditory input). While it is not 

clear from this study if the working memory tasks affected driving performance, 

the electrophysiological results showed a similar decrease in the lambda response 

during the high-load spatial working memory task. 

Given our increasing understanding of this neural component, the lambda response 

may provide a natural indicator of a more general cognitive state, such as working 

memory load, in the context of tasks requiring overt visual attention. Using the 

lambda response to track changes in visual task difficulty would provide a more 

direct way to index visual task demands in natural search behavior without the need 

of a secondary auditory task. To address this, we sought to determine if the lambda 

response was modulated by visual task difficulty in 2 disparate paradigms. In the 

first, a visual N-Back task, we controlled the nature of task difficulty (i.e., via 

working memory load) while maintaining a uniformity of eye movements and 

fixated stimulus properties (i.e., via guided search) to enable an unambiguous 

determination of the source of lambda response amplitude modulation. In the 

second, a Tetris task, eye movements were unconstrained and we quantified the 

effect of task difficulty on the lambda response by manipulating tetrad fall speed
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3

(Miller et al. 2011). Importantly, we were able to control for overlapping neural 

activity from temporally adjacent events by implementing a multiple regression 

technique specifically designed for this purpose (Smith and Kutas 2015a, 2015b). 

Likewise, to establish the effect of our manipulations, we included several other 

subjective and physiological measures that are known indicators of changes in task 

difficulty. Based on the previous work described above, we expected to see a 

decrease in the amplitude of the lambda potential with increased task difficulty, 

specifically that induced by working memory load.

2. Materials and Methods

2.1 Stimuli and Procedure

Participants performed a dynamic visual N-Back and Tetris task from a distance of 

approximately 80 cm (Fig. 1) with the order of the tasks counterbalanced across the 

sample. These tasks were performed on a 21-inch, 1920 × 1080 pixel, 60-Hz

monitor and controlled using Psychtoolbox-3 (Brainard 1997; Kleiner et al. 2007). 

In the N-Back task a Gabor stimulus subtending 3° visual angle (45° tilt, 2 cycles 

per degree, 100% Michelson contrast) containing a digit (RGB: 255,255,255) in the 

center randomly appeared every 1500–2000 ms in 1 of 49 locations on an invisible 

7 × 7 grid. 

Fig. 1 Task layout. The left image shows the layout of the experimental environment while 

a participant performs the Tetris task. The right image shows an example of 4 successive 

fixations in the medium difficulty (0-Back) condition of the visual N-Back task. Note that only 

1 Gabor stimulus appeared on the screen at any given time. The red arrows indicate the 

direction of each saccade/fixation.

Participants were instructed to saccade to and hold fixation on the digit in the center 

of the Gabor pattern until the next Gabor pattern appeared. In the Ignore condition 

participants fixated each stimulus disregarding the digit, while in 2 other conditions 
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they used the digits in a 0-, 1-, or 2-Back task. In the 0-Back condition participants 

made a response with their right index finger on a game pad when the number zero 

appeared. In the 1-Back condition each digit was compared to the one prior 

requiring a response when these digits were the same (i.e., target). In the 2-Back

condition each digit was compared to the one that occurred 2 trials back. For the 

purposes of analysis we separate these conditions into 3 task difficulty levels: low, 

medium, and high. Specifically, Ignore = low, 0-Back and 1-Back = medium, and 

2-Back = high. Some participants performed the 0-Back while others performed 

the 1-Back; however, based on preliminary analysis we found no difference 

between these conditions and they are henceforth combined into the medium task 

difficulty condition. Each participant performed 2 consecutive 3-minute blocks of 

each condition, with conditions counterbalanced. Target probability was 0.15. 

Participants practiced the 0- and 2-Back conditions until they reached at least 50% 

target accuracy. 

Tetrad fall speed was used to manipulate task difficulty in the modified Tetris game

(Zhang 2010). Fall speed was measured as the vertical travel of the current block 

piece per unit of time. Fall speeds 2, 3, 4, 5, and 7 steps per second were used for 

this task. As with the N-Back task, these conditions were separated into 3 task 

difficulty levels: low, medium, and high. Specifically, fall speeds 2 and 3 = low, 4 

and 5 = medium, and 7 = high. Some participants performed the 2 and 4 speed

conditions while others performed the 3 and 5 speed conditions. We found no 

difference between speeds 2 and 3 or between speeds 4 and 5; therefore, they were

combined into the low and medium task difficulty conditions respectively. All 

participants completed 2 consecutive 3-minute blocks at each fall speed with the 

order of fall speed counterbalanced. Participants were aware of the fall speed prior 

to the start of the game. The right hand was used to manipulate the rotation of the 

tetrad blocks using the up, left, and right arrows on a keyboard. The down arrow 

was not used in order to prevent participants from increasing the tetrad fall speed. 

If the tetrad block stack reached the top of the screen before the end of the block, 

all blocks were cleared and the game restarted with an empty tetrad field. Before

the experiment participants performed a 2-minute practice block with fall speed of 

5 to become familiar with the task.

Participants performed a 2-stimulus auditory oddball task simultaneously with the 

N-Back and Tetris task. The auditory oddball task required participants to make a 

speeded response by pressing a highlighted region (4 × 4 inches,  in Fig. 1) with 

their left hand on a 19-inch Elo touch-screen monitor to an infrequent (P = 0.12, 

2000 Hz) auditory stimulus presented in a series of frequent (P = 0.88, 1000 Hz) 

tones. Auditory tones were presented through Audio-Technica ATH-M50x 

headphones at a volume of 16 on Realtek HD Audio headphone device for 100 ms 
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5

with a 3–4-s inter-stimulus interval using 100 ms jitter. The touch-screen monitor 

was located close to the visual task monitor and the highlighted response region

was large enough to enable participants to make the auditory task response without 

an eye/head movement. Participants were instructed to rest their left hand on an 

adjacent mouse pad between target responses to ensure responses were initiated 

from the same distance. After each block of the N-Back or Tetris task, the auditory 

task was stopped and participants completed a modified version of the NASA Task 

Load Index (TLX) using a continuous visual analogue scale (1–100) to rate their 

perceived effort (“How hard did you have to work to accomplish your level of 

performance?”) and mental demand (“How mentally demanding was the task?”). 

2.2 Participants

Sixteen right-handed males participated in the experiment (average age 31.1 years) 

each having 20/20 vision or corrected to 20/20 vision. Due to a problem with the 

eye tracker, we were unable to obtain enough reliable samples in the eye-tracking 

data for 1 participant in the Tetris task. Consequently, all eye-based measurements 

for this task were calculated from the remaining 15 participants. The voluntary, 

fully informed consent of the persons used in this research was obtained in 

accordance with the US Army Research Laboratory’s (ARL’s) Institutional Review 

Board requirements (32 CFR 219 and AR 70-25).

2.3 EEG and Eye Tracking

EEG data were acquired from an Advanced Brain Monitoring (ABM) B-Alert X24 

Sensor Headset (sampling rate 256 Hz; linked mastoid reference) with the singletrial ERP montage using the B-Alert software package. In addition to the scalp 

electrodes, 2 external input channels placed just below the right clavicle and below 

the left rib were used to acquire the electrocardiogram (ECG). 

Ocular data were recorded from a distance of approximately 80 cm using the Tobii 

TX300 eye tracker. Data from each eye were sampled at 300 Hz and acquired using 

custom software with the Tobii SDK. Each participant performed a 9-point 

calibration before experimentation. Eye tracking data were used to identify saccade

and fixation events, as well as provide continuous estimates of pupil diameter and

gaze location. The Tobii TX300 system included continuous, online correction of 

gaze location and pupil diameter for changes in head position. 
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2.4 Data Processing

EEG and eye-tracking data synchronization was performed in MATLAB using 

custom software by aligning independently injected events into each data stream. 

EEG and subsequent FRP data were processed with EEGLAB using the ERPLAB 

and regression analysis (rERP) plugins (Burns et al. 2013; Delorme and Makeig 

2004; Lopez-Calderon and Luck 2014). EEG data were filtered using a 

second-order Butterworth filter with a 0.1–40 Hz passband. Blinks were identified 

from stereotyped gaps in the gaze position data (Holmqvist et al. 2011) while

saccades (and corresponding fixations) were detected using the velocity-based 

algorithm provided in the EYE-EEG plugin (http://www2.huberlin.de/eyetracking-eeg) for EEGLAB (Dimigen et al. 2011; Engbert and

Mergenthaler 2006). Specifically, we used a velocity factor of 6, a minimum 

saccade duration of 30 ms, and a minimum fixation duration of 200 ms keeping 

only the largest saccade and subsequent fixation if 2 or more saccades were detected 

within the minimum fixation duration window.

FRPs were created separately for each participant in each task (N-Back, Tetris) and 

condition (low, medium, high) from epochs (–1000 to 2000 ms) time-locked to 

fixation with and without overlap correction. Without Overlap Correction:

Fixation-locked epochs were not included if peak-to-peak activity surpassed a 

120-V threshold (–500 to 700 ms with respect to fixation onset) from all channels 

(excluding F1, F3, Fz, F2, and F4) using a 100-ms window size and a window step 

of 50 ms. Likewise, epochs were not included if they were immediately preceded 

or followed by an auditory target trial, blink, or boundary event. All other 

fixation-locked epochs were included in the final average, and are henceforth

referred to as valid trials. With Overlap Correction: All fixation-locked epochs 

were included in the rERP, with a separate FRP estimated for each condition (Burns 

et al. 2013; Smith and Kutas 2015a). Importantly, stimulus onset (Gabor or tetrad) 

ERPs were simultaneously estimated to remove the overlapping effect on the 

subsequent FRP. In the rERP framework, an event E1 (either stimulus or fixation) 

produces an ERP response β1 spanning a range of latencies from zero (event onset) 

to τ. The observed signal at each electrode is then considered a linear transform of 

β1 plus an independent Gaussian noise tem, ε ~ N(0, σI). In this way, the EEG 

signal at each electrode (e.g. Oz) can be represented as

β1 = [β10 β11 β12 ⋯ β1τ]

T

(1)

Oz = Α1β1 + ε (2)
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7

over the M observations (data samples). Here, A1 is an M × τ matrix of event 

occurrences at each latency τ of the ERP. This formulation can be extended to 

incorporate multiple events, including potentially overlapping ERPs and FRPs. 

Now each event type (1...n) and corresponding ERP/FRP can be represented as 

A = [A1 A2 A3 ⋯ An] (3)

β = [(β1)

T

(β2)

T

(β3)

T ⋯ (βn)T

]

T

(4)

In this way, the EEG signal at Oz now becomes

Oz = Αβ + ε (5)

The event ERPs can then be estimated through least-squares regression, with 

solution 

βreg = (A

TA)−1ATOz ≅ β (6)

Since this parameter space is large, a regularization method is applied to the 

pseudoinverse (in the case of L2 nom penalized regression). More information 

about the rERP method and toolbox can be found at 

https://sccn.ucsd.edu/wiki/RERP.

Auditory evoked potentials (AEPs) were created separately for each subject by 

averaging epochs (–200 to 1000 ms) time-locked to auditory stimulus onset in each 

task and condition. Epochs were rejected if peak-to-peak activity surpassed a 

120-V threshold (–200 to 800 ms with respect to stimulus onset) from all channels 

(excluding F1, F3, Fz, F2, and F4) using a 100-ms window size and a window step 

of 50 ms or if a blink occurred –200 to 800 ms relative to stimulus onset.

3. Results

In the following sections (Behavior and Physiological Metrics) we report 

subjective, behavioral, and physiological results to establish the efficacy of our 

primary manipulation, increase in task difficulty, for both the N-Back and Tetris 

task. Greenhouse–Geisser statistics are reported for all ANOVA analyses 

(Greenhouse and Geisser 1959).
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3.1 Behavior

3.1.1 Subjective Report

Subjective reports of task difficulty were analyzed using the “effort” and “mental 

demand” factors from the modified TLX to compare perceived difficulty both 

within and between tasks (N-Back/Tetris). Due to the ordinal scale of the data we 

used the non-parametric Wilcoxon Signed Rank Test to compare participants’ 

median subjective ratings between tasks, which showed significantly higher ratings

in Tetris relative to N-Back in both effort (Tetris = 53.08 [IQR = 42-60.79], N-Back

= 43.25 [IQR = 28.04-49.63], Z = 3.16, p = .002) and mental demand factors (Tetris 

= 50.25 [IQR = 42.38-62.04], N-Back = 39.75 [IQR = 26.29-49.29] , Z = 2.9, p = 

.004). A Friedman test was used to evaluate the effect of task difficulty (low, 

medium, high) in each task for the effort and mental demand factors. The effect of 

task difficulty was significant in the N-Back condition for both effort (χ2 = 21.13, 

p < .001) and mental demand (χ2 = 27.65, p < .001) factors. Task difficulty was also 

significant in the Tetris condition for effort (χ2 = 24.6, p < .001) and mental demand 

(χ2 = 24.5, p < .001) factors (Fig. 2). Together the subjective reports indicate that 

participants perceived the Tetris task as more effortful and mentally demanding

than the N-Back, and within each task perceived increases in effort and mental 

demand were associated with increased task difficulty. 
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9

Fig. 2 Box and whisker plots of participants’ TLX ratings of perceived effort and mental 

demand in the N-Back (white boxes) and Tetris (shaded boxes) tasks as a function of task 

difficulty (low, medium, high)

3.1.2 Accuracy and Reaction Time

Target-detection accuracy and reaction time were analyzed in the visual N-Back

task. However, the low-difficulty condition did not require responses from the 

participant (see Stimuli and Procedure); therefore, only the medium and high 

conditions are reported. Here the effect of task difficulty was significant, F(1,15) = 

11.6, p = .004, 2 = .44, with higher accuracy in the medium (98.4%, stdv 3.8%) 

relative to high (85.5 %, stdv 15.3%) condition. Reaction time also showed a 

significant effect of task difficulty, F(1,15) = 83.08, p < .001, 2 = .85, with 

medium (744.4 ms, stdv 84.1 ms) having faster RTs than high (933.9 ms, stdv 104.1 

ms). Similarly, Tetris scores showed a significant relationship with task difficulty

F(1.38,20.74) = 209.52, p < .001, 2 = .93 with the most points obtained in the 

high (292.81, stdv 32.87), followed by medium (241.59, stdv 33.46) and low (104, 

stdv 23.01) conditions. Points were awarded based on the number of lines cleared 

in the game and since more tetrads were presented with increased difficulty it is not 

surprising that more points were given in the high-difficulty condition. An 

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


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additional performance metric for the Tetris task was the frequency at which the 

game board was cleared and game restarted due to the tetrad stack reaching the top 

of the game board. This metric also showed a significant effect of task difficulty, 

F(1.57,23.59) = 30.33, p < .001, 2 = .67, with low (0.0, stdv 0), medium (1.0, stdv 

0.97), and high (2.38, stdv 1.5) conditions all different from each other, p < .05. In 

sum, our manipulation of task difficulty induced changes in both perceived mental 

effort and behavioral performance.

Accuracy and reaction time were also calculated for the targets presented in the 

auditory oddball task as a function of (visual) task difficulty in each condition. 

Interestingly, task difficulty did not significantly affect auditory target accuracy 

F(1.25,18.84) = 1.49, p = .244, 2 = .09, or reaction time F(1.87,28.06) = 1.65, p 

= .211, 

2 = .099 in the N-Back task. In the Tetris task there was a main effect of 

task difficulty, though just short of statistical significance, on auditory target 

accuracy F(1.97,27.54) = 3.35, p = .051, 2 = .193 with highest accuracy in the 

low load condition (Table 1). Likewise, reaction time was not significantly 

modulated by task difficulty F(1.36,18.99) = 1.89, p = .185, 2 = .119. These results 

suggest that increased visual task difficulty generally had a negligible effect on the 

auditory oddball detection performance.

Table 1 Behavioral performance for auditory targets in the N-Back and Tetris tasks as a 

function of task difficulty

3.2 Physiological Metrics

3.2.1 Saccade Magnitude

A number of studies have shown that saccade magnitude affects the amplitude of 

the lambda response. Specifically, lambda amplitude has been shown to increase 

with saccade magnitude (Dandekar et al. 2012; Dimigen et al. 2011; Kaunitz et al. 

2014; Yagi 1979). Therefore, we compared saccade magnitude in each condition

(high, medium, low) in both tasks (N-Back and Tetris) to determine if changes in

lambda amplitude could be attributed to this feature. As expected, we found no 

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Task Difficulty % Correct Reaction Time (ms)

Low 98.5 (3.1) 970.9(141.0)

N-Back Med 99.5(2.1) 950.8(109.5)

High 96.3(8.0) 1001.1(85.5)

Low 99.2(2.4) 966.1(142.8)

 Tetris Med 95.5(8.6) 1018.0(169.2)

High 93.4(9.3) 1066.7(309.0)
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significant effect of condition on saccade magnitude in the N-Back task, 

F(1.82,27.29) = 2.04, p = .15; however, there was a significant effect of condition

on saccade magnitude in the Tetris task, F(1.71, 23.88) = 6.11, p = .01, 2 = .30, 

with increased task difficulty associated with decreased saccade magnitude (Tables

2 and 3). This suggests that the lambda amplitude should be smaller in the high 

with respect to low load condition if saccade magnitude is the primary influence on 

this response.

Table 2 Saccade magnitude, pupil diameter, and heart rate variability (HRV) in the 

N-Back and Tetris tasks as a function of task difficulty. Note: Numbers represent the mean 

with standard deviation in parentheses for each measure.

Table 3 Paired t-tests for significant main effects of task difficulty

3.2.2 Pupil Diameter and HRV

The main effect of task difficulty on pupil diameter was analyzed for both the 

N-Back and Tetris tasks using a repeated measures ANOVA. This effect was highly 

significant in both the N-Back [F(1.82, 27.28) = 45.1, p < .001, 2 = .75] and Tetris

[F(1.99, 27.82) = 55.95, p < .001, 2 = .8] tasks showing increased pupil diameter 

as a function of task difficulty (Fig. 3). A similar analysis was performed on 



N-Back Measure Low Medium High

Sac Mag (deg) 11.97(2.08) 12.63(1.76) 12.06(1.61)

Pupil Dia (%change) -2.18(1.66) -1.34(2.05) 4.88(2.1)

HRV (ms) 79.58(41.18) 67.78(37.28) 59.5(29.68)

Tetris Measure Low Medium High

Sac Mag (deg) 13.6(2.2) 13.27(2.2) 12.4(2.3)

Pupil Dia (%change) -4.09(2.5) 0.36(1.33) 4.08(1.95)

HRV (ms) 68.88(37.3) 58.98(30.7) 58.03(27.8)

Low/Med Low/High Med/High

N-Back Measure t(df) p t(df) p t(df) p 

Sac Mag (deg) NA NA NA NA NA NA

Pupil Dia (%change) -1.24(15) 0.233 -8.16(15) <.001 -7.05(15) <.001

HRV (ms) 3.82(15) 0.002 4.78(15) <.001 2.06(15) 0.058

Low/Med Low/High Med/High

Tetris Measure t(df) p t(df) p t(df) p 

Sac Mag (deg) 1.12(14) 0.281 2.87(14) 0.012 2.55(14) 0.023

Pupil Dia (%change) -5.57(14) <.001 -8.73(14) <.001 -4.88(14) <.001

HRV (ms) 3.78(14) 0.002 2.68(14) 0.018 0.32(14) 0.751



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measures of HRV, calculated by taking the standard deviation of the beat-to-beat

interval. Here, we found decreased HRV as a function of task difficulty in both the 

N-Back [F(1.79, 26.83) = 14.07, p < .001, 2 = .48] and Tetris [F(1.53, 21.45) = 

6.8, p = .009, 

2 = .33] tasks (Fig. 3).

Fig. 3 The effect of task difficulty on pupil diameter and HRV in the N-Back (white) and 

Tetris (shaded) tasks. Error bars represent the standard error.

3.3 FRPs: Lambda Potential

The lambda potential was measured at electrode Oz both with and without 

correcting for overlapping neural activity due to temporally adjacent stimuli and 

short inter-saccadic intervals. Lambda peak latency and amplitude was evaluated 

separately for each task (N-Back and Tetris) with task difficulty (low, medium, 

high) as the main factor. Amplitude was measured as the mean voltage over 20 ms 

(± 10 ms) around the peak latency value for each participant and condition. FRP 

calculations were performed separately for data with and without overlap correction

for temporally adjacent stimuli. For data not corrected for temporally adjacent 

overlap, we focused only on valid nontarget trials that met the criteria for inclusion 

(see Data Processing), while all nontarget trials were analyzed in the overlap 

corrected data. The nontarget trials were chosen due to their relative frequency 

(compared with target trials) and hence better signal-to-noise ratio. FRP

measurements were all relative to a –300 to –100 ms pre-fixation baseline. For data 

without overlap correction, the average number of trials, with standard deviation,




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for each participant in the N-Back task was 90.8(31.4) for low, 94.3(29.9) for 

medium, and 106.6(33.6) for high conditions. Likewise, for the Tetris tasks the 

average number of trials, with standard deviation, was 219.1(73.8) for low, 

262.5(70.1) for medium, and 275.8(80.5) for high conditions. For data with overlap

correction, the average number of trials, with standard deviation, for each 

participant in the N-Back task was 131.4(30.7) for low, 138.8(31.4) for medium, 

and 141.9(27.1) for high conditions, and 294(76.2) for low, 331.8(80.4) for 

medium, and 339.1(88.8) for high conditions in the Tetris task.

3.3.1 Without Overlap Correction

The main effect of task difficulty on the peak latency of the lambda component was 

not significant in either the N-Back [F(1.23,18.37) = 0.07, p = 0.845] or Tetris 

[F(1.96,27.42) = 0.58, p = 0.563] tasks. However, as predicted there was a 

significant effect of difficulty on lambda amplitude in the N-Back [F(1.71,25.64) = 

4.28, p = 0.03, 

2 = .22] task and approached significance in the Tetris 

[F(1.99,27.85) = 2.98, p = 0.07, 

2 = .18] task (Fig. 4). Interestingly, the direction 

of this effect was different between tasks as lambda amplitude decreased as a 

function of difficulty in the N-Back task but increased with task difficulty in the 

Tetris task (Fig. 5).




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Fig. 4 FRPs obtained from electrode Oz as a function of task difficulty in the N-Back (top 

row) and Tetris (bottom row) tasks. The right and left columns show FRPs with and without 

stimulus/saccade overlap correction, respectively. Scalp voltage (microvolts) maps highlight 

the spatial distribution of the lambda response 70–90 ms post-fixation. Electrode Oz is depicted 

as the white circle on the scalp maps. FRPs and scalp maps are plotted using a –300 to –100

ms pre-fixation baseline.
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Fig. 5 Comparison of lambda amplitudes as a function of task, condition, and overlap 

correction. P values were obtained from planned paired comparisons between levels of task 

difficulty. Error bars represent the standard error of the mean. 

3.3.2 With Overlap Correction

To rule out the possibility that our effects were caused by overlapping neural 

activity from temporally adjacent events, we employed a multiple regression 

technique recently developed for this purpose (Smith and Kutas 2015a, 2015b). 

Briefly, this technique uses a general linear modeling framework to simultaneously 

estimate the response of each event of interest, in this case stimulus and fixation 

onset. By calculating a simultaneous estimate of each process, this approach can 

robustly attribute overlapping activity to the eliciting event as well as minimize the 

contribution of independent signals (e.g., artifacts). After application of this 

technique, the effect of difficulty on the lambda latency remained nonsignificant 

for both the N-Back [F(1.47,22) = 0.484, p = 0.565] and Tetris [F(1.99,27.96) = 

0.343, p = 0.712] tasks. Lambda amplitude, however, was significantly affected by 

difficulty in both the N-Back [F(1.69,25.40) = 3.8, p = 0.04, 

2 = .202] and Tetris 

[F(1.9,26.73) = 5.58, p = 0.01, 

2 = .285] tasks. Figure 4 indicates that 

Gabor-evoked activity significantly overlapped the lambda response in the N-Back 

task as the overall lambda amplitude decreased after this activity was removed. 

While the overall amplitude changed, the main effect of task difficulty on the 

lambda response did not. In contrast, there was little effect of stimulus and saccade 

overlap on the lambda response in the Tetris task. However, in contrast to the 




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N-Back task the lambda amplitude significantly increased with difficulty in the 

Tetris task. 

3.4 AEPs

Only nontarget AEPs were analyzed due to their relative frequency and therefore 

better signal-to-noise ratio. Here, we focused on the N1 (140–160 ms) and P2 (220–

280 ms) components of the AEP from electrode Cz. AEP measurements were

relative to a –200 to 0 ms pre-stimulus baseline. We found no significant effect of 

difficulty in the N-Back task for the N1 [F(1.98,29.63) = 0.84, p = .442] or P2 

[F(1.49,22.28) = 2.41, p = .125]. Likewise, we found no significant effect of 

difficulty for the N1 [F(1.74,26.09) = 0.302, p = .712] and P2 [F(1.52,22.73) = 1.24, 

p = .298] components in the Tetris task. Importantly, this result corresponds to the 

behavioral findings and together these suggest that the auditory oddball task 

required too little effort (accuracy near ceiling) to be significantly affected by 

increased visual task demands, or participants allocated the same amount of 

cognitive resources to the oddball task irrespective of the modulations in task 

difficulty. 

4. Discussion

4.1 Task Difficulty

In this study we investigated the effect of visual task difficulty on the amplitude of 

the fixation-related lambda potential in 2 disparate tasks, an N-Back task that 

controlled for stimulus and saccade properties and a Tetris task that used a dynamic, 

unconstrained paradigm while still preserving parametric control of difficulty 

(Lindstedt and Gray 2015). Perceived subjective ratings of effort and mental 

demand, behavioral performance, HRV, and pupil diameter were all significantly 

affected by changes in difficulty for both tasks. Critically, it was shown that the 

amplitude of the lambda response was significantly reduced under high with respect 

to low visual task difficulty when controlling for saccadic magnitude and stimulus 

properties in the N-Back task. This extends upon prior research that showed high

compared to low auditory task difficulty, manipulated through working memory 

load, significantly attenuated the amplitude of the lambda response (Ries et al.

2016; Takeda et al. 2012). Together these findings suggest the lambda response is 

directly affected by capacity-limited processing resources involved in working 

memory.

Contrary to our prediction, the lambda response in the Tetris task was significantly 

larger in high with respect to low task difficulty. This finding could not be attributed 
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17

to differences in saccade magnitude as saccades in the high task difficulty condition 

were significantly smaller than those in the low difficulty condition. If saccade 

magnitude was the primary contributor to lambda response amplitude, this 

observation would have led to smaller lambda amplitudes in the high with respect 

to low conditions. Similarly, the change in lambda amplitude between conditions 

could be due to luminance differences at each fixation location. It is well-known 

that lambda amplitude increases as a function of luminance (Gaarder et al. 1964). 

The high task difficulty condition could have resulted in more high-luminance 

fixations since, on average, more tetrads were present on the game board relative 

to the other conditions. However, it is unlikely that luminance was the main 

contributor to the lambda amplitude in the Tetris task as pupil size increased with

task difficulty (e.g., Beatty 1982). Since luminance likely increased as a function 

of difficulty, we would have expected a smaller, not larger, pupil diameter in the 

high difficulty condition. 

A tenable hypothesis concerning the differential effect of task difficulty on the 

lambda response in our 2 tasks is that the N-Back and Tetris tasks relied on different 

processing mechanisms. The N-Back task primarily recruited cognitive processes 

related to working memory while those in the Tetris task required more perceptual 

and motor processes. Indeed it has been shown that cognitive and perceptual load 

produce differential effects on behavior such that when perceptual load is high, 

peripheral distractors are less likely to be processed; however, when cognitive 

demands are high due to working memory load, irrelevant peripheral distractors are 

more likely to be processed (Lavie et al. 2004). This supports the possibility that 

processing resources may have been allocated differently in our experiment based 

on the load requirements of the task consistent with predictions from perceptual 

load theory (Lavie 1995, 2005). Participants required more cognitive processing 

resources for internal maintenance of information in the N-Back task as difficulty 

increased; therefore, fewer cognitive resources were available for visual stimulus 

processing at fixation. This is consistent with smaller lambda amplitudes in the high 

compared to low difficulty condition. In the Tetris task fewer perceptual processing 

resources were needed to successfully perform the task in the low compared to high 

load as the slow fall speed allowed ample time to align the tetrad. Once aligned, 

participants could disengage from the task and wait for the tetrad to fall into place

since they could not control its downward trajectory. Alternatively, in the high 

difficulty condition, tetrads were moving quickly and there was little time to 

disengage from the task, thus demanding more perceptual processing resources to 

complete the task. This is consistent with larger lambda amplitudes in the high 

compared to the low difficulty condition. Future research must control for stimulus 

features between levels of cognitive and perceptual load to adequately address the 
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possibility that the lambda amplitude, like behavior, is differentially influenced by 

these constructs. Together the results demonstrate that the lambda response is 

affected by capacity-limited processing resources related to task difficulty, 

specifically those involved in working memory. 

4.2 Stimulus and Ocular Overlap Correction

An additional goal of our FRP analysis was to evaluate the potential confounding 

influence of both preceding stimuli (which were subsequently fixated) and 

temporally adjacent saccades on the lambda potential. It is not clear from prior 

research whether the effects of task difficulty on the lambda response could be 

attributed to differential overlapping neural activity between conditions. It is 

possible that inter-saccadic intervals were different between difficulty levels, which 

would result in different degrees of overlap. For example, neural activity from one 

FRP overlaps with the subsequent FRP at short inter-fixation intervals (less than 

500 ms), such that the response elicited from one fixation will extend into 

subsequent fixation intervals (Nikolaev et al. 2016). Furthermore, when 

participants must saccade/fixate an abruptly appearing visual stimulus in the 

periphery, the stimulus-evoked neural activity will overlap with the fixation-evoked 

response. The separation or deconvolution of overlapping stimulus-evoked or 

saccade-related potentials on the lambda response is an open methodological 

inquiry. In this study, we applied a regression-based technique that has been shown 

to accurately separate temporally overlapping ERPs (Burns et al. 2013; Smith and

Kutas 2015a, 2015b). This overlap correction procedure demonstrated that 

stimulus-evoked activity produced in the N-Back task had a substantial impact on 

the subsequent lambda response, as the amplitude of the response was significantly 

smaller after correction (see Fig. 5). Importantly, while the stimulus-evoked 

activity did have an impact on the fixation-locked neural response, it did not change 

the overall pattern of results, with the exception of the medium difficulty condition.

As there were significantly more trials included in the overlap correction analysis, 

this difference could have been the result of additional noise contained within these 

trials. Using a heuristic approach to excluding trials, as is common in ERP analysis, 

can result in reduced noise in the ERP. However, this can come at the cost of a large 

number of trials and is potentially susceptible to subjective criteria for exclusions. 

By using both a standard exclusion and overlap correction approach we provide a 

more confident assertion that the observed modulation in the lambda amplitude was 

not a conflation of the stimulus response nor a consequence of artifact 

contamination. 

Interestingly, temporal overlap from eye movements had a minimal effect in the 

Tetris task where eye movements were unconstrained. Upon further inspection, this 
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19

result was not surprising given the average inter-saccadic interval in this tasks (i.e.,

fixation duration) was 667 ms. Given this interval, the fixation-locked neural 

response was returning to baseline well before the next saccade occurred. Although 

inter-saccadic overlap was not a factor in this study, due to the relatively long 

fixation durations, other tasks such as free-view visual search tend to produce even

shorter fixation durations and thus may have a more confounding impact on the 

lambda response. While this study was focused on the lambda response, which has 

a relatively short onset latency, later components such as the P300 are more likely 

to be impacted by temporal overlap (e.g., Devillez et al. 2015), which will benefit 

from the removal from adjacent neural responses. 

4.3 Subjective and Physiological Measures of Task Difficulty

To establish the effect of our manipulations, we included several other subjective 

and physiological measures that are known indicators of changes in task difficulty. 

Specifically, we compared the modulation of the lambda response with another 

ERP component, the AEP, which has been shown to index visual task difficulty 

(Allison and Polich 2008; Miller et al. 2011). As such, participants performed an 

auditory oddball task in conjunction with both visual tasks (N-Back and Tetris). 

Other reliable measures of task difficulty were also included: the TLX subjective 

rating scale (Hart and Staveland 1988), HRV (Backs et al. 1994; Prinzel et al. 

2003), main sequence (Di Stasi et al. 2011), and tonic pupil dilation (Beatty 1982; 

Kahneman and Beatty 1966; Van Orden et al. 2000). Subjective ratings of 

perceived mental demand and effort significantly increased with task difficulty. 

Additionally, HRV significantly decreased while pupil diameter significantly 

increased as a function of task difficulty.

Based on previous studies (Allison and Polich 2008; Miller et al. 2011), we 

expected to find a significant influence of visual task difficulty on both behavior 

and AEP amplitude. While there was a small reduction in accuracy for auditory 

targets in the high difficulty condition for Tetris, overall the effect of visual task

difficulty on auditory oddball detection was negligible. One potential explanation 

for this concerns the way in which participants responded to the auditory targets. 

Participants were instructed to keep their hand in a fixed position some distance 

from the touch screen throughout the experiment; however, it is likely resting hand 

position varied somewhat throughout the experiment thus introducing large 

fluctuations in measured reaction time. While we did not see an effect of visual task 

difficulty on the AEP components, a critical difference between the current and past 

studies is that Allison and Polich (2008) and Miller et al. (2011) incorporated

primarily passive, task-irrelevant auditory probes. Using irrelevant auditory stimuli 

allowed participants to allocate their attentional resources contingent on visual task 
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20

difficulty only. Participants in the current study had to allocate resources to the 

auditory task to identify and respond to oddball targets. Additionally, the oddball 

targets used in the current study were simple pure tones and easy to discriminate 

from the standard tones. Recent research has shown that auditory evoked responses 

are more sensitive to modulations in visual task difficulty when more complex 

auditory probes are used (Dyke et al. 2015). The implementation of the oddball task 

in the current experiment also varied slightly from those used in prior studies. For 

example, in Miller et al. (2011) a single auditory tone was presented every 6–30 s; 

however, in the current study 1 of 2 auditory tones was presented more frequently 

(approximately 3.5 s). This required participants to attend to the auditory stream to 

make frequent target/non-target discrimination decisions. As such, participants may 

have favored the auditory over the visual task by allocating the necessary 

processing resources to auditory processing to ensure optimal performance. 

Moreover, the increased frequency of auditory tones may have led to habituation 

of the auditory evoked response (e.g., Pan et al. 2000). A design limitation of this 

task was not having a true baseline auditory response. It would have been beneficial 

to have measured the auditory evoked response either before any visual task was 

presented or included a passive viewing condition in the Tetris task. Nevertheless, 

there is convincing corroborating evidence from multiple measures (e.g., subjective 

ratings, pupil diameter, HRV, and behavior) that our task difficulty manipulations 

were effective despite the lack of modulation in the auditory data. 

5. Applications and Conclusion

Lambda amplitude has been used in a variety of applied contexts. For example, 

Yagi et al. (1998) found a positive correlation between lambda amplitude and 

mental concentration under various lighting conditions. Other research has found 

increased lambda amplitude over time during enjoyable tasks while lambda 

amplitude decreased when tasks were perceived as boring or fatiguing (Daimoto et 

al. 1998; Takeda et al. 2001). Daimoto et al. (2007) assessed the effect of 

perceptual, motor, and cognitive workload on the lambda response by crossing a 

high/low difficulty manual tracking task with a high/low difficulty numerical 

problem. While the results of this study showed that the lambda amplitude was 

smaller under the high difficulty condition relative to the others, the potentially 

confounding effects of changes in the distribution of eye movements and stimulus 

properties were not reported. It is possible that the observed dynamics of the lambda 

response were due to differences in saccade magnitude or luminance contrast of the 

fixated locations, both of which have direct effects on the amplitude of the lambda 

response (Kazai and Yagi 2005; Yagi 1979). Moreover, it was not clear if 

overlapping activity from temporally adjacent saccades impacted the results. It is 
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21

well known that both stimulus and ocular events occurring in rapid succession 

produce overlapping neural activity (Devillez et al. 2015; Woldorff 1993).

The current study demonstrates that the lambda response of the fixation-related 

potential is affected by changes in task difficulty, specifically those that affect 

working memory when controlling for saccade size, stimulus properties, and 

temporal overlap from adjacent neural responses. The lambda response amplitude 

may therefore be a useful metric to obtain task demand information. Acquiring task 

demand information in this way would allow individuals to interact with their 

environment and augment current measures of cognitive state. Traditional 

subjective measures of task difficulty often break task flow by interrupting the user 

at various times throughout the task, leading to disruptions in mental concentration. 

Additionally, subjective self-assessments are not sensitive to fluctuations of 

cognitive state within a task; instead they provide an average estimate over an 

interval of time, often on the order of several minutes, which can introduce 

unintended effects due to memory lapses (Moroney et al. 1995). Likewise, 

introducing a secondary task or probe stimuli may disrupt performance in the 

primary task of interest. However, caution must be used when leveraging FRPs in 

general, and the lambda potential in particular, as an indicator of task difficulty

since FRP component amplitudes are affected by stimulus characteristics and 

saccade distance. 
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List of Symbols, Abbreviations, and Acronyms

ABM Advanced Brain Monitoring

AEP auditory evoked potential

ARL US Army Research Laboratory

ECG electrocardiogram

EEG electroencephalogram

ERP event-related potential

FRP fixation-related potential

HRV heart rate variability

NASA National Aeronautics and Space Administration

rERP regression analysis

S/FRPs saccade and fixation-related potentials

TLX Task Load Index
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