microsaccades: a microcosm for research on oculomotor control
TRANSCRIPT
CHA
Martinez-Conde, Macknik, Martinez, Alonso & Tse (Eds.)
Progress in Brain Research, Vol. 154
ISSN 0079-6123
Copyright r 2006 Elsevier B.V. All rights reserved
PTER 9
Microsaccades: a microcosm for research onoculomotor control, attention, and visual perception
Ralf Engbert�
Computational Neuroscience, Department of Psychology, University of Potsdam, PO Box 601553, 14415 Potsdam,Germany
Abstract: Miniature eye movements occur involuntarily during visual fixation. The most prominent con-tribution to these fixational eye movements is generated by microsaccades, which are rapid small-amplitudesaccades with a rate of about one per second. Recent work demonstrates that microsaccades are optimizedto counteract perceptual fading during perception of a stationary scene. Furthermore, microsaccades aremodulated by visual attention and turned out to generate rich spatio-temporal dynamics. We conclude thatthe investigation of microsaccades will evolve into a new research field contributing to many facets ofoculomotor control, visual perception, and the allocation of attention.
Keywords: fixational eye movements; microsaccades; random walk; visual perception; covert attention
Introduction
Visual perception is based on motion. This fact isobvious for some nervous systems in animals: aresting fly is invisible to a frog. The situation rap-idly changes as soon as the fly starts to move. Thus,motion is an essential prerequisite for sensation infrogs (Lettvin et al., 1959). Because motion infor-mation is critical in predator–prey relationships,the detection of motion might have been a key ad-vantage for the evolution of visual systems.
The human visual system shows a rapid adap-tation to stationary objects. The adaptation causesperceptual fading when the retinal image is artifi-cially stabilized in the experimental paradigm ofretinal stabilization (Ditchburn and Ginsborg,1952; Riggs et al., 1953). This is a potential fin-gerprint of evolutionary history in the human vis-ual system. Equipped with such a visual systemoptimized for the detection of motion and change,
�Corresponding author. Tel.: +49-331-9772869;
Fax: +49-331-9772793; E-mail: [email protected]
DOI: 10.1016/S0079-6123(06)54009-9 177
we were unable to process fine details of a com-
pletely stationary scene without active refresh of
the retinal image, because retinal adaptationwould induce a bleaching of constant input. To
counteract retinal adaptation our oculomotor sys-
tem generates miniature eye movements (Ratliff
and Riggs, 1950). Thus, ironically, the term ‘‘visualfixation’’ is a misnomer, since there is rich dynam-
ical behavior during each fixation. To capture this
built-in paradox, the term fixational eye movements
is used most often.It has been well documented long before the ad-
vent of research into modern eye movement in the
1950s that our eyes are never motionless. For ex-ample, Helmholtz (1866), one of the pioneers of
eye-movement research, noticed the difficulty of
producing perfect fixation. Interestingly, Helmholtz
had already suggested the prevention of retinalfatigue as a perceptual function for fixational eye
movements. Fixational eye movements are rather
erratic (Fig. 1) — the eye’s trajectory representsa random walk. Therefore, adequate mathematical
methods for the analysis of fixational eye movements
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Fig. 1. Fixational eye movements during fixation. A human observer fixated a small stimulus for a duration of 3 s (left and right panels
refer to data from the left and right eye, respectively). The trajectory is rather irregular, but contains three microsaccades, which can be
characterized by a linear movement episode. The numbers refer to the sequences of microsaccades and indicate the endpoints of the
microsaccades.
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come from statistical physics, a discipline whichcan be traced back to Einstein’s work on Brownianmotion (Einstein, 1905).
Fixational eye movements in human observersfall into three different physiological categories:microsaccades, tremor, and drift. All three types offixational eye movements occur involuntarily and un-consciously. Microsaccades are rapid small-amplitudemovements of the eyes with an average rate of1–2 s�1. As a consequence, the eyes move morelinearly during a microsaccade than during the re-maining part of the trajectory (Fig. 1).1 The linearmovement during a microsaccade might be an effectof the eye’s inertia, i.e., microsaccades are ballistic,which is compatible with the fact that the kinematicproperties of microsaccades are very similar to thoseof voluntary saccades (Zuber et al., 1965). Drift is alow-velocity movement with a peak velocity below30min arc s�1. Tremor is an oscillatory componentof fixational eye movements within a frequencyrange from 30 to 100Hz superimposed to drift.
It has been an open research problem overthe last 30 years to find a specific function for
1The data used to illustrate properties of microsaccades were
obtained from a simple fixation task. For details of the methods
see Engbert and Kliegl (2004).
microsaccades. Cornsweet (1956) originally sug-gested that microsaccades might correct the errorsproduced by the drift component of fixational eyemovements. There are, however, two main lines ofevidence against such a straightforward functionalinterpretation of microsaccades. First, microsacca-des can be suppressed voluntarily for severalseconds without perceptual bleaching (Steinmanet al., 1967). This result lends support to the hy-pothesis that the contribution of microsaccades tothe prevention of retinal adaptation can simply bereplaced by slow movements. Second, microsacca-des are naturally suppressed in laboratory analogsof high-acuity tasks like threading a needle orshooting a rifle (Winterson and Collewijn, 1976;Bridgeman and Palca, 1980). Therefore, a specificfunction for microsaccades was rejected. WhileDitchburn (1980) argued that the fact that humanscan learn to prevent microsaccades does not con-tradict a specific role of microsaccades for normalvision, Kowler and Steinman (1980) concludedthat microsaccades serve no useful purpose. Thedebate was unresolved and presumably generated adecrease in the interest in microsaccades and fix-ational eye movements during the 1980s until themid-1990s, which is evident in the number of pub-lications on or relevant to microsaccades (Fig. 2).
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Fig. 2. Number of publications on microsaccades and fixational eye movements per year based on the references cited in the review
article by Martinez-Conde et al. (2004).
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A renaissance of research on microsaccades hasbeen triggered by (i) new techniques in eye-move-ment recording, which facilitate the measurementof microsaccades in laboratory situations andthe computational analysis of large datasets and(ii) neurophysiological findings, which demonstratethe impact of microsaccades on visual informationprocessing. As an example for the latter line ofresearch, it has been discovered that microsacca-des are correlated with bursts of spikes in theprimary visual cortex (Martinez-Conde et al.,2000, 2002). Since this and related findings weresummarized and discussed in a recent reviewarticle by Martinez-Conde et al. (2004), we focuson the behavioral aspects of microsaccades here.The article is organized as follows: we discussthe problem of microsaccade detection, summarizethe main kinematic and dynamic properties, andaddress the modulation of microsaccade rate byvisual attention.
2Our algorithm is available on the internet at: http://
www.agnld.uni-potsdam.de/�ralf/micro/.
Detection of microsaccades
Microsaccades can be detected in eye-movementdata because of their higher velocity comparedto drift. We developed an algorithm based on atwo-dimensional (2D) velocity space for the eyes’
trajectories (Engbert and Kliegl, 2003a).2 First, thetime series of eye positions is transformed to ve-locities by
~vn ¼~xnþ2 þ ~xnþ1 � ~xn�1 � ~xn�2
6Dt(1)
which represents a weighted moving average overfive data samples to suppress noise (for details seeEngbert and Kliegl, 2003b). As can be seen inFig. 3, the transformation of the trajectory into 2Dvelocity space results in a scattering of data sam-ples around the origin of the coordinate system. Inthis representation, microsaccades are ‘‘outliers’’with much higher velocity than what one wouldexpect from assuming a normal distribution.
Second, we compute the standard deviation sx,yto estimate the noise level of an individual trial andtake a fixed multiple l of this value as a thresholdZx,y for the detection of a microsaccade:
sx;y ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiv2x;y
D E� vx;y� �2r
(2)
Zx;y ¼ l sx;y (3)
where �h i denotes the median estimator to suppressthe influence of the high-velocity samples arising
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Fig. 3. Detection of microsaccades. After transformation of the trajectory into 2D velocity space, microsaccades can easily be
identified by their high velocity (data samples outside ellipse, where l ¼ 5 compared to the slower drift component (inside ellipse). The
raw data correspond to the same trials as the data plotted in Fig. 1.
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from the microsaccades. Because the analysis isperformed separately for horizontal and verticalcomponents, the corresponding thresholds Zx andZy define an ellipse in the velocity space (Fig. 3).As a necessary condition for a microsaccade, werequire that all samples ~vk ¼ ðvk;x; vk;yÞ fulfill thecriterion
vk;x
Zx
� �2
þvk;y
Zy
!2
41 (4)
Third, we apply a lower cutoff of 6ms (or threedata samples) for the microsaccade durations toreduce noise.
Fourth, microsaccades are traditionally de-fined as binocular eye movements (Lord, 1951;Ditchburn and Ginsborg, 1953; Krauskopf, 1960;see also Ciuffreda and Tannen, 1995). With mod-ern video-based eye-tracking technology, binocu-lar recording is easily available. Because (i) botheye traces can be analyzed independently and(ii) microsaccades are relatively rare events(roughly less than every 100th data sample be-longs to a microsaccade), the amount of noise canbe reduced dramatically, if we require binocular-ity. So far, we detected candidate microsaccadesbased on monocular data streams according toEqs. (2)–(4). Operationally, we define binocular
microsaccade by a temporal overlap criterion. Ifwe observe a microsaccade in the right eye withonset time r1 and endpoint at r2, we look throughthe set of microsaccade candidates in the left eyewith corresponding onset time l1 and offset time l2.A temporal overlap of (at least) one data sample isequivalent to
r24l1 and r1ol2 (5)
It is straightforward to check the symmetry ofthe criterion by exchanging the roles of the left andright eyes. Figure 3 shows an example with threebinocular microsaccades (numbered as 1–3). Thetwo monocular microsaccades occurring in the lefteye (labeled M and M0) are unlikely to representoutliers or noise, given the high peak velocity.Thus, we speculate that monocular microsaccadesmight also exist (Engbert and Kliegl, 2003b).We also identified differences in average orientat-ions for monocular microsaccades (see Fig. 5).To implement a conservative detection algorithm,however, we generally use the temporal overlapcriterion (Eq. (5)). More importantly, most re-searchers record the movements of one eye only,which precludes the use of the more-conservativebinocularity criterion.
Additionally, we would like to remark that, ifa temporal overlap is verified, the binocular
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Fig. 4. Patterns of 220 microsaccades generated by a participant during 100 trials of a simple fixation task, each with duration of 3 s.
Top panels: microsaccades translated so that the starting point is the origin of the coordinate system. Bottom panels: same data as in
the top panels with microsaccades at their real locations relative to the fixation stimulus.
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microsaccade is defined to start at time t1 ¼ min(r1,l1)and to end at time t2 ¼ max(r2,l2). As a conse-quence of this definition, microsaccades 1 and 3 inFig. 3 in the right eye appear to start within theellipse, i.e., with sub-threshold velocity. In the nextsection, we perform a quantitative analysis of thekinematics of microsaccades, which were detectedby the algorithm discussed here.
Kinematic properties
Some of the kinematic properties of microsaccadescan already be seen from visual inspection, if weplot all microsaccades generated by one participant
during 100 trials, each with a duration of 3 s, ina simple fixation task (Fig. 4). The top panels inthe figure show all microsaccades generated bythe participant with the starting point translatedto the origin. The corresponding plots for theleft and right eyes clearly indicate the preferencefor horizontal and vertical microsaccades, withoblique microsaccades only in rare exceptions.
The bottom panels in Fig. 4 show the same datawith all microsaccades at their real locations. Aglance at these plots verifies that microsaccadescover almost all parts of the central 21 of the visualfield. Obviously, the majority of microsaccades ishorizontally oriented. These descriptive results al-ready demonstrate that microsaccades generate
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Fig. 5. Polar plot of angular orientations. (a) Binocular microsaccades, plotted in Fig. 4, show a clear preference for horizontal
orientations. (b) Monocular microsaccades, generated by the same participant consist of comparable contribution from horizontal and
vertical orientations.
3The astronomical term ‘‘main sequence’’ refers to the rela-
tionship between the brightness of a star and its temperature.
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rich statistical patterns, which might reflect im-portant requirements of the oculomotor and/orperceptual systems. Thus, patterns of microsacca-des may be exploited to help to understand theoculomotor system and even aspects of visual per-ception and the dynamics of allocation of visualattention.
A polar plot of microsaccade orientations (Fig. 5)shows that the majority of binocular microsaccadesis horizontally oriented. For those microsaccadesthat were detected monocularly, horizontal andvertical orientations are comparable in frequency(Fig. 5b). To understand these properties of micro-saccades from the neural foundations, it is impor-tant to note that different nuclei in the brainstem circuitry for saccade generation are responsi-ble for the control of horizontal and verticalsaccades (Sparks, 2002). While neural mechanismsfor the control of oblique movement vectors existfor voluntary saccades, we speculate that formicrosaccades, which are generated involuntarily,such mechanisms are questionable. As a conse-quence, the distribution of angular orientationsfor microsaccades is dominated by the maincontributions, i.e., purely horizontal or verticalorientations. Since binocular movements are relatedto the control of disparity, binocular microsaccadesmight contribute to changes of binocular disparity.Therefore, a preference of binocular microsaccades
for horizontal orientations seems compatible withoculomotor needs. From this perspective, theinvestigation of binocular coordination in micro-saccades (Engbert and Kliegl, 2003b) might con-tribute to the general problem of monocular vs.binocular control of eye movements (Zhou andKing, 1998).
A key property of microsaccades is that theyshare the fixed relation between peak velocity andmovement amplitude with voluntary saccades(Zuber et al., 1965). This finding is a consequenceof the ballistic nature of microsaccades. To un-derline the importance of the result, the fixed re-lation of peak velocity and amplitude is oftenreferred to as the ‘‘main sequence’’ (Bahill et al.,1975).3 Given the validity of the main sequence,one useful application of this property of micro-saccades is to check detection algorithms. Devia-tions from the main sequence might reflect noise inthe detection algorithm.
In a larger study of fixational eye movements, 37participants were required to fixate a small stim-ulus (black square on a white background, 3�3pixels on a computer display with a spatial exten-sion of 0.121). Each participant performed 100 tri-als with duration of 3 s. Eye movements were
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recorded using an EyeLink-II system (SR Re-search, Osgoode, Ont., Canada) with a samplingrate of 500Hz and an instrument whose spatialresolution was better than 0.011 (for details see themethods section in Engbert and Kliegl, 2004).Figure 6a shows the main sequence for about20.000 microsaccades generated by all participantsin the simple fixation task. Corresponding distri-butions of amplitude and peak velocity are shownin Figs. 6b and 6c, respectively. The analysis of thelarge number of microsaccades indicates that ourdetection algorithm reproduces the main sequencewell. The smallest microsaccade detected in the setof about 20.000 microsaccades had an amplitudeof 0.03611 or about 2min arc. We conclude that
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Fig. 6. Kinematic properties of microsaccades. The figure contains
during a simple fixation task (100 trials, 3 s fixation duration). (a) T
(c) amplitude, and (d) duration.
video-based recording techniques can be applied todetect even small-amplitude microsaccades. Thedistribution of microsaccade durations (Fig. 6d) isless smooth with a lower cutoff at 6ms (or threesamples) owing to the detection criteria.
A straightforward hypothesis on their functionis that microsaccades help to scan fine details of anobject during fixation. This hypothesis would im-ply that fixational eye movements represent asearch process. According to this analogy, the sta-tistics of microsaccades can be compared to othertypes of random searches. An important class ofrandom-search processes are Levy flights, whichhave been found in foraging animals (Viswanathanet al., 1996). Moreover, it has been shown that this
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he main sequence (see text). Histograms for: (b) peak velocity,
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class of random searches is optimal, if target sitesare sparsely distributed (Viswanathan et al., 1999).With respect to research on eye movements,Brockmann and Geisel (2000) suggested that in-spection of saccades during free picture viewingrepresent an example of a Levy flight. Given theseresults, we check whether the amplitude distribu-tion of microsaccades follows a similar law.
Levy flights are characterized by a certain dis-tribution function of flight lengths lj. The flightlengths correspond to microsaccade amplitudes infixational eye movements. For a Levy flight, thedistribution function of flight lengths has the func-tional form
PðljÞ / l�mj (6)
where the exponent m is limited to the range1omr3. If the distribution decays with mZ3, weobtain a normal distribution for the search proc-ess, owing to the central limit theorem (Metzlerand Klafter, 2000).
To investigate the distribution of microsaccadeamplitude in our dataset of 20.000 microsaccades,we plot the tail of the distribution in Fig. 7 on adouble-logarithmic scale. This plot clearly indicatesa power-law decay of the tail of the distribution for
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Fig. 7. Power-law distribution for amplitudes. The tail of the
amplitude distribution obeys a power-law with an exponent
given by the slope in the log–log plot.
amplitudes ranging from 0.31 to 11 of visual angle.The exponent, however, has a value of m ¼ 4:41;which rejects the hypothesis of a Levy flight. Thus,we conclude that even if the statistics of micro-saccades during free viewing of a stationary scenemight represent a Levy flight (Brockmann andGeisel, 2000), this law does not transfer to thesmall scale in fixational eye movements.
Temporal correlations
While kinematic properties of microsaccades havelong been investigated from the beginnings of eye-movement research (e.g., Zuber et al., 1965), thequestion of temporal correlations did not receive asimilar amount of attention. The main reason isobviously that a typical fixation duration in freeviewing or reading is roughly between 200 and500ms. Therefore, the probability of observingmore than one microsaccade in a single fixationwill be rather small. Temporal correlations in theseries of microsaccades, however, might also beindicative of specific functions and/or neural mech-anisms underlying microsaccades. In the simplestcase, the probability that a microsaccade is gener-ated is time-independent. More precisely, the prob-ability of observing a microsaccade in an arbitrarytime interval ðt; tþ DtÞ is rDt, where r is the rateconstant and Dt a small time interval, i.e., Dt-0,so that only one event can happen in the time in-terval of length Dt. This assumption constitutes aPoisson process. It is important to note that thenumber of events found in time interval ðttþ DtÞ iscompletely independent of the number of occur-rences in (0,t). Experimentally, a simple observableparameter is the waiting time between two eventsof the process. For the Poisson process, the cor-responding probability density of waiting time t isan exponential function (Cox and Miller, 1965),
pðtÞ ¼ r e�rt (7)
as in the general case of Markov processes. Thewaiting-time distribution is normalized in the sensethat with certainty an event will occur, if we waitinfinitely long, i.e.,
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pðtÞ dt ¼ 1:To check whether the temporal patterns of
microsaccades represent a Poisson process, we
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Fig. 8. Statistics of inter-microsaccadic intervals (IMSIs). (a) Histogram of 16.931 IMSIs. (b) A semi-logarithmic plot verifies an
exponential distribution, compatible with the assumption of a Poisson process.
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computed inter-microsaccade intervals (IMSI) forthe microsaccade data shown in Fig. 8. This proce-dure is only possible if at least two microsaccadesoccur during a single trial. Obviously, this methodis only an approximation to the problem ofestimating the probability density, Eq. (7), whichwould ideally require recordings for several min-utes to extract many IMSIs from a single timeseries. The rate constant r can be read off from theslope of the plot and has a numerical value of1.86 s�1, which is equivalent to a mean IMSIinterval of 538ms. Thus, we conclude that thetemporal pattern of microsaccades represents aPoisson process, i.e., there are no temporal corre-lations of the numbers of microsaccades duringtwo different time intervals. In a non-stationarysituation with changing visual input and/or attent-ional shifts, however, the microsaccade rate willno longer be constant (see the section on modu-lation of microsaccades below). In this situationthe temporal pattern of microsaccades can be de-scribed by an inhomogeneous Poisson process.
Dynamic properties: time-scale separation
A typical trajectory generated by the eyes dur-ing fixational movements shows the clear fea-tures of a random walk (Fig. 1). Different classesof random walks can be distinguished by their
statistical correlations between subsequent incre-ments (Metzler and Klafter, 2000). Such correla-tions can be investigated, if we plot the meansquare displacement Dx2
� �of the process as a
function of the travel time Dt. A key findingrelated to Brownian motion is that the meansquare displacement Dx2
� �increases linearly with
the time interval Dt (Einstein, 1905). This result isequivalent to the property of Brownian randomwalks in which the increments of the process areuncorrelated.
A generalization of classical Brownian motionwas introduced by Mandelbrot and Van Ness(1968) to account for processes showing a power-law of the functional form
Dx2� �
/ DtH (8)
where the scaling exponent H can be any realnumber between 0 and 2. In classical Brownianmotion, we find H ¼ 1, which is a direct conse-quence of the fact that the increments of the randomwalk are uncorrelated. When H41, increments arepositively correlated, i.e., the random walk showsthe tendency to continue to move in the currentdirection. This behavior is called persistence. In thecase Ho1, the random walk generates negativelycorrelated increments and is anti-persistent.
Motivated by the study of Collins and De Luca(1993) on human postural data, we applied a ran-dom-walk analysis to fixational eye movements
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(Engbert and Kliegl, 2004). To characterize thebehavior in the eye’s random walk during fixation,we introduce a displacement estimator (Collinsand De Luca, 1993),
D2ðmÞ ¼1
N �m
XN�m
i¼1
~xiþm � ~xi�� ��2 (9)
which is based on the two-dimensional time seriesf~x1; ~x2; ~x3; . . . ; ~xNg of eye positions. The scalingexponent H can be obtained by calculating theslope in a log–log plot of D2 vs. lag Dt ¼ m � T0;where T0 ¼ 2ms is the sampling time interval.The analysis of 100 trials generated by one sub-ject indicates two different power-laws by linearregions in the log–log plot (Fig. 9). On a shorttime scale (2–20ms), the random walk is persist-ent with H ¼ 1:28; whereas on a long time scale(100–800ms), we find anti-persistent behavior.Thus, we observe a time-scale separation withtwo qualitatively different types of motion.
The fact that microsaccades are embedded in thedrift and tremor components of fixational eyemovements poses a difficult problem for the in-vestigation of potential behavioral functions of
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Fig. 9. Random-walk analysis of fixational eye movements.
Linear regions in this log–log plot of the mean square displace-
ment as a function of time indicate a power-law. On a short
time scale, the random walk is persistent with a slope H41,
while on a long time scale, we observe anti-persistence, i.e.,
slope Ho1.
microsaccades, because microsaccades will proba-bly interact with these two other sources of ran-domness. To this aim, we cleaned the raw timeseries from microsaccades and applied the ran-dom-walk analysis (Engbert and Kliegl, 2004).First, we found that microsaccades contribute topersistence on the short time scale. Even aftercleaning from microsaccades the drift still pro-duced persistence. This tendency is increased bythe presence of microsaccades. Second, on the longtime scale, the anti-persistent behavior is specifi-cally created by microsaccades. Since the persistentbehavior on the short time scale helps to preventperceptual fading and the anti-persistent behavioron the long time scale is error correcting and pre-vents loss of fixation, we can conclude that micro-saccades are optimal motor acts to contribute tovisual perception.
The random-walk analysis discussed here wasmotivated by the successful application of theframework to data from human postural control,where the center-of-pressure trajectory is statisti-cally very similar to fixational eye movements, thedynamics unfold on a longer timescale. In a land-mark study, Collins and De Luca (1993) observedthe time-scale separation with the transition fromanti-persistence to persistence. This discovery gen-erated numerous publications since then. Com-bined with the observation that input noise canenhance sensory and motor functions (e.g., Collinset al., 1996; Douglass et al., 1993; Wiesenfeld andMoss, 1995), this research even inspired a technicalapplication with the construction of vibrating in-soles to reduce postural sway in elderly people(Priplata et al., 2002, 2003).
Modulation of microsaccade statistics by visual
attention
The dynamic properties discussed in the last sec-tion support the view that microsaccades enhancevisual perception and, therefore, represent a fun-damental motor process with a specific purpose forvisual fixation. Recent work demonstrated, how-ever, that microsaccades are strongly modulatedby display changes and visual attention in spatialcuing paradigms (Engbert and Kliegl, 2003a; see
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(b)
(c)
Fig. 10. Modulation of microsaccade rate by a display change. (a) Series of microsaccades generated during 100 trials by one
participant. All microsaccades are plotted relative to cue onset at t ¼ 0ms. (b) Microsaccade rate computed from the series of events
shown in (a). The rate was estimated by a causal window (see text). (c) Average modulation (bold line) induced in all 30 participants
(thin lines). An early microsaccade inhibition is followed by a later enhancement.
4The baseline of the microsaccade rate is generally about 1
microsaccade per second, but will depend on the specifics of the
paradigm used.5Figure 10 represents raw data and re-analyses of Experiment
1 by Engbert and Kliegl (2003a).
187
also Hafed and Clark, 2002). Effects were relatedto microsaccade rate (rate effect) and to the an-gular orientation of microsaccades (orientationeffect). Thus, while microsaccades might be essen-tial for visual perception, they are — nevertheless— highly dynamic and underlie top-down modu-lation by high-level attentional influences.
In a variant of a classical spatial cuing paradigm(Posner, 1980), we instructed participants to pre-pare a saccade or manual reaction in response to acue, but to wait for a target stimulus before thereaction was executed (Engbert and Kliegl, 2003a,b). As the rate effect related to cue onset, we re-ported a rapid decrease of the rate of microsaccades
from a baseline level4 to a very low level, followedby an enhancement or supra-baseline level, until therate resettled at baseline level.
The generation of microsaccades is a pointprocess, i.e., discrete events are generated in con-tinuous time (Fig. 10a).5 Therefore, the problem ofcomputing a continuously changing rate over timefrom many discrete events is equivalent to the
188
estimation of neuronal discharge rates from aseries of action potentials in single-cell research.Following Dayan and Abbott (2001), we canformally describe the series of i ¼ 1; 2; 3; . . . ; Nmicrosaccadic ‘‘spikes’’ at times ti by
rðtÞ ¼XNi¼1
dðt� tiÞ (10)
where d(t) denotes Dirac’s d function. For thecomputation of a continuous microsaccade raterðtÞ; a window function w(t) must be chosen, sinceany rate estimate must be based on temporal av-eraging, i.e.,
rðtÞ ¼
Z 1
�1
dt wðtÞrðt� tÞ (11)
Because the approximate firing rate at time t
should depend only on spikes fired before t, acausal window of the form
wðtÞ ¼ a2t expð�atÞ (12)
which is defined for tZ0 only and vanishes forto0. Figure 10b shows the estimated microsac-cade rate computed from the raw data in Fig. 10ausing Eqs. (10)–(12). The corresponding rate esti-mates from 30 participants are plotted in Fig. 10c(thin lines), which were averaged to obtain a stableestimate of the microsaccade rate (bold line). Thereliability of the estimate can be seen from therelatively constant baseline over the pre-cue inter-val (�300–0ms). Microsaccadic inhibition starts100ms after cue onset and lasts about 150ms. Mi-crosaccadic enhancement starts roughly 250ms af-ter cue onset, until the rate resettles at baselinelevel approximately 450ms after cue onset.
Table 1. Rate and orientation effects for microsaccades
Reference Cue type Rate effec
Inhibition E
Engbert and Kliegl (2003a) Endogenous, arrows 150
Endogenous, color 150
Display change 150
Laubrock et al. (2005a) Exogenous, flash 180–200
Endogenous, color 200 40
Rolfs et al. (2005) Exogenous, visual 150–225 35
Auditory 150 30
aA significant effect was observed only for cues to the left.
As the orientation effect, Engbert and Kliegl(2003a) found a bias of microsaccade orientationstoward the cue direction. While in Experiment 1 oftheir study, arrows used as endogenous (central)cues induced the orientation effect during the en-hancement interval, the data from Experiment 2with color cues showed a later (and weaker) orien-tation effect. Thus, the results of Engbert and Kliegl(2003a) already indicated that the rate and orien-tation effects are not mandatorily coupled. Finally,in Experiment 3, it was shown that a relativelysmall display change, i.e., the same stimuli appliedin a simple fixation task without instructions forattentional cuing, was sufficient to replicate the rateeffect without producing an orientation effect.Therefore, the rate effect alone could also be inter-preted as a response to a display change.
In a series of experiments, the relation betweenrate modulation, covert attention, and microsac-cade orientation was further investigated (Laubrocket al., 2005; Rolfs et al., 2005). Depending on thedetails of the task, these studies replicated the rateeffect with both inhibition of microsaccades about150ms after the first display change related to theappearance of the cue (Table 1) and an enhance-ment of microsaccade rate, which was found around400ms after cue onset. More importantly, the rateeffect was reproduced in a simple display changecondition (Engbert and Kliegl, 2003a) and in purelyauditory cuing, i.e., without any visual displaychange (Rolfs et al., 2005). Therefore, the rate effectmight be interpreted as a stereotyped response to asudden change in — possibly multisensory input.The patterns of results on the orientation effect,however, turned out to be more complex. The list of
t (ms) Orientation effect (ms)
nhancement Cue-congruent Cue-incongruent
350 300–400 —
350 350–600 —
350 — —
450 Early: 50–200, late: 600–800 250–550
0–600 — 500–700
0–500 — 250–500
0–350 150–300a —
189
effects for the orientation effect in Table 1 showsthat there are combinations of early and late effectswith both cue-congruent and cue-incongruent mod-ulations of microsaccade orientations.
Can we explain the rate and orientation effectsfrom our knowledge on the neural circuitry con-trolling saccadic eye movements? Numerous publi-cations have contributed to the current view thatmultiple voluntary and reflexive pathways exist togenerate saccades (Fig. 11). Most of these pathwaysare convergent to the superior colliculus (SC), astructure controlling brain stem saccade generationequipped with several sensory and motor maps(Robinson, 1972; Schiller and Stryker, 1972; see alsoBergeron et al., 2003). Deeper layers of the SC aremultisensory, which can explain the auditory effectsreported by Rolfs et al. (2005). In the rostral poleof the SC, fixation neurons are activated to keepour gaze stable. According to Krauzlis et al. (2000),fixation neurons are better conceived of as rostral,i.e., small-amplitude, build-up neurons. Thus, theamount of activation of the fixation neurons in theSC will determine the rate of microsaccades.
A key dynamical feature of the spatio-temporalevolution of activation in the SC has inspiredmodels of local excitation and global inhibition
cochlear
retina
LGN
visualcortex
parietalcortex (LIP)
SC
brainsteRF
visualinput
auditoryinput
reflexive pathway
direct pathway
Fig. 11. Neural circuitry underlying saccade generation (modified aft
distinguished (BG ¼ basal ganglia, DLPC ¼ dorso-lateral prefrontal
cleus, SC ¼ superior colliculus, and RF ¼ reticular formation). The
reflexive pathway is related to computation of spatial orientation. The
influences.
(e.g., Findlay and Walker, 1999; Trappenberget al., 2001). As a consequence of the latter prop-erty, a global change in sensory input will induce ahigher mean-field activation, which will lead to anincreased inhibition of the fixation neurons in therostral pole of the SC. Consequently, we can ex-pect a decrease of the microsaccade rate after adisplay change (or a sudden auditory stimulus).Given the time course with the fast inhibitory partof the rate effect, we further suggest that the‘‘direct’’ or retinotectal connection from sensoryinput to the SC is responsible for the inhibitioneffect. In addition to the inhibition, the subsequentenhancement of microsaccade rate could also begenerated by the intrinsic dynamics of global in-hibition and local excitation, since after the globalinhibition of fixation neurons the global increaseof activation will fade out with the consequencethat the remaining activation of fixation neuronswill locally rise. The enhancement, however, ismore difficult to interpret, because a latency of350–400ms is sufficient for multiple pathways tocontribute to this effect.
For the interpretation of the orientation effect, aprimary difference between experiments is whetherendogenous or exogenous cues were used (Table 1).
FEF
DLPC
BG
thalamus
m
(micro)saccade
voluntarypathway
er Munoz and Everling, 2004). Three separate pathways can be
cortex, FEF ¼ frontal eye fields, LGN ¼ lateral geniculate nu-
direct pathway generates very fast, stereotyped responses. The
voluntary pathway can mediate excitatory as well as inhibitory
190
We start with a discussion of cue-congruent effects.For endogenous cues, microsaccade orientationswere biased toward the cue direction as early as300ms after cue onset (Engbert and Kliegl, 2003a).Such an orientation effect is likely to be controlledby the ‘‘reflexive pathway’’ with contributions fromoccipital/visual and parietal cortex (Fig. 11). Rolfset al. (2005) found a similar cue-congruent effectinduced by auditory cues with a somewhat shorterlatency. For exogenous flash cues, Laubrock et al.(2005) reported an early cue-congruent effectstarting o100ms after cue onset. From thetimescale alone, we can conclude that the directpathway must generate this effect.
Cue-incongruent effects might represent inhibi-tory influences from cortex. From the neural cir-cuitry in Fig. 11, we see that inhibitory control ismediated via frontal eye fields (FEF), dorso-lateralprefrontal cortex (DLPC), and basal ganglia (BG).As a consequence of this long-loop control circuit,we expect longer latencies for effects mediated viathe ‘‘voluntary’’ pathway. Experimentally, we ob-served results highly compatible with this picture:Cue-incongruent effects have latencies roughlyaround 300ms for exogenous cues (Laubrocket al., 2005; Rolfs et al., 2005) and 600ms for en-dogenous color cues (Laubrock et al., 2005). There-fore, a detailed analysis of spatio-temporal responsepatterns of microsaccades in human behavioral test-ing seems a promising approach to investigate prin-ciples of the neural circuitry of saccade generation.
Summary: microsaccades as a new toolbox?
Visual fixation is a platform for almost all visualperception. As a consequence, we can expect newinsights into the organization of perception, whenwe carefully investigate the dynamics of fixationaleye movements, in particular, the dynamics of mi-crosaccades. Converging evidence from researchon basic oculomotor control (Engbert and Kliegl,2004; Engbert and Mergenthaler, 2006), attentio-nal cuing (Engbert and Kliegl, 2003a; Rolfs et al.,2004, 2005; Laubrock et al., 2005), and neuro-physiology (Martinez-Conde et al., 2000, 2002)suggests that microsaccades represent highlyoptimized motor behavior essential to visual
perception. Furthermore, a recent study (Rolfset al., 2006) demonstrates that microsaccades in-teract with ongoing saccade programming, whichcan produce both increased or decreased latenciesfor upcoming saccades.
On the one hand, research on microsaccades willbenefit from our understanding of the visual sys-tem, on the other, new findings on the propertiesand on the functional role of microsaccades willclearly prove our current knowledge of many sys-tems from oculomotor control to the allocation ofvisual attention. An important application of theorientation effect is straightforward: microsacca-des can be exploited to map the time course ofthe allocation of visual attention. For example,Deaner and Platt (2003) observed reflexive effectsof attention in monkeys and humans, which werealso present in fixational eye movements. Rolfset al. (2004) used microsaccade orientations to rep-licate the effect of attentional enhancement oppo-site to a peripheral cue (Tse et al., 2003). Galfanoet al. (2004) reproduced the effect of inhibition ofreturn from analyses of microsaccades (see Klein,2000, for a recent overview). These results dem-onstrate that microsaccades might be used as anindependent indicator of covert attention.
In summary, we can expect that the investiga-tion of microsaccades will become a productivefield of research with contributions to many as-pects of perception, oculomotor control, and thecontrol of visual attention.
Acknowledgments
The author wishes to thank Reinhold Kliegl,Jochen Laubrock, Konstantin Mergenthaler,Hannes Noack, Antje Nuthmann, ClaudiaPaladini, and Martin Rolfs for many discussionsand comments on the manuscript. This work wassupported by Deutsche Forschungsgemeinschaft(Grant no. KL 955/3).
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